0 .B School of Chemistry, Monash University, Victoria, Australia UNIVERSITY PRESS UNIVERSITY PRESS Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Bangkok Buenos Ares Cape Town Chennai Dares Salaam Delhi HongKong Istanbul Karachi Kolkata KualaLumpur Madrid Melbourne Mexico City Mumbai Nairobi S2o Paulo Shanghai Taipei Tokyo Toronto Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York O Alan Bond, 2002 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2002 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer A catalogue record for this title is available from the British Library Library of Congress Cataloging in Publication Data (Data available) ISBN 0 19 850477 2 (Pbk) ISBN 0 19 850478 0 (Hbk) 1 0 9 8 7 6 5 4 3 2 1 Typeset by Newgen Imaging Systems (P) Ltd, Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., Guildford & King's Lynn Dedication To Tunde, Stephen, and Andrew 1998 I was privileged to be present at the University of Oxford as the inshelwood Lecturer in the Physical and Theoretical Chemistry Laboratory and as a Christensen Fellow at St. Catherine's College. Financial support for the lectureship was kindly provided by ICI. The Hinshelwood lecture series, named after Cyril Norman Hinshelwood (1897-1967), 1956 Nobel Laureate in Chemistry (with N.N. Semenov), was entitled 'Broadening Electrochemical Horizons'. The presentation provided an opportunity to develop an integrated series of lectures aimed at illustrating the principles and applications of voltammetric methodology to a variety of problems of a fundamental and applied significance. In view of the fact that the audience for the lectures had a wide range of levels of expertise in electrochemistry, the standard chosen for the presentation was equivalent to that appropriate for a senior level undergraduate or postgraduate course rather than for specialists in the field of electrochemistry. The highly active Oxford University electrochemical environment was invaluable to the lecture presentation because examples of studies undertaken in the author's research progamme at Monash University in Australia could be supplemented by extensive reference to material kindly made available by ofessors Richard Compton, Allen Hill and Fraser Armstrong and colleagues their Oxford University research groups. At the completion of the lecture series, it was suggested that a written version of the material could be developed as a guide for researchers and educationalists who wish to learn how the principles of voltammetry can be systematically ited to solve problems relevant to a wide area of scientific disciplines. The version of the Hinshelwood lectures, written in the years 1999-2001, is fore expressly aimed at achieving this goal. I hope that the readers of this will find the account of studies presented of assistance in providing them a systematic approach to unravelling the mysteries that frequently accomstudies of processes that take place at or near to an electrode surface during urse of voltammetric experiments. It is, of course, just these 'curiosities' that have fascinated this author throughout his scientific career. nash University A. M. B. I would like to specifically acknowledge the contributions of the following people and organizations: The Physical and Theoretical Chemistry Laboratory, St. Catherine's College, and ICI for their generosity in hosting the 1998 Hinshelwood Lectureship. The School of Chemistry at Monash University for generously allowing me leave at the University of Oxford in 1998 in order to present the Hinshelwood Lectures. Professor Richard Compton for extensive editorial advice during both the Hinshelwood Lectures and the preparation of this book. Professors Richard Compton, Allen Hill, Fraser Armstrong, and members of their research groups at Oxford University and my colleagues at Monash University for their friendship and for generous provision of material referred to in this book. At the time the Hinshelwood Lectures were presented, material provided by colleagues often was unpublished. However, during the time the book version was developed, much of this work has now appeared in the open literature under the authorship of the relevant colleagues so that due recognition can now be given via citation of these recently published articles. Glenda Oliver who typed the text without ever complaining, despite being confronted with numerous drafts and then amendments to what she had been advised was the final version. My wife, Tunde, and children, Stephen and Andrew, who displayed significant patience and understanding while the book was written. I have dedicated this book to them as an expression of my appreciation of their tolerance in allowing me to spend countless hours hidden away in my study during evenings and at weekends during times which otherwise would have been devoted to fimily activities. The fundamentals of electrochemistry 1 Introductory remarks Redox reactions, electrochemical cells, and standard potentials 2 3 Thermodynamics versus kinetics Calculation of reaction volumes and entropies from the 4 dependence of the reversible potential on temperature and pressure 5 Voltammetry and kinetics Application of the principles of electrochemistry to fuel cells, 6 photovoltaic cells, and the lead-acid battery 6.1 Fuel cells 6.2 Dye-sensitized photovoltaic cells 6.3 Lead-acid battery References rinciples of voltammetry, electrolysis, spectroelectrochemistry, and other techniques employed in studies involving solution ase and surface-based electrode processes An overview The electrochemical cell used for voltammetric experiments The electrodes used in voltammetric experiments 3.1 Working electrodes 3.2 Reference electrodes 3.3 Counter /auxiliary electrodes The two major classes of voltammetry 4.1 Transient voltammetry 4.2 Steady-state voltammetry Evaluation of electrode reaction mechanisms Factors contributing to the nature of the current-potential curve obtained in voltammetric experiments 6.1 Faradaic and non-Faradaic currents Understanding the basic features of an electrode process when the redox active species are soluble in the solution phase 7.1 Mass transport 7.2 Electron transfer 7.3 Homogeneous chemical kinetics 7.4 Electrochemical and chemical reversibility Cyclic voltammetry under transient conditions when the redox active species are soluble in the solution phase 8.1 Theory of cyclic voltammetry xii Contents 9 10 11 12 13 14 15 36 17 18 Hydrodynamic voltammetry 9.1 Rotating-disc electrode voltammetry 9.2 Channel electrodes 9.3 Wall-jet electrodes 9.4 A survey of the use of the theory of hydrodynamic voltammetly Voltammetric studies at microelectrodes when the redox active species are soluble in the solution phase 10.1 Principles of the theory of microelectrode voltammetry Semi-integration and semi-differentiation (convolution voltammetry) 11.1 Some valuable properties of the semi-integral 11.2 Measurement of uncompensated resistance by semi-integration 11.3 Semi-differentiation General features associated with the modelling of voltammetric experiments 12.1 Information required to solve voltanimetric theory 12.2 Methods used for solving voltammetric theory A sunimary of the theoretical principles of voltammetry 13.1 Application of Faraday's law 13.2 A general approach to understanding a voltamnletric problem Comparison of voltammetric techniques when the redox active species are soluble in the solution phase 14.1 A quantitative comparison of the kinetic discrimination of homogeneous reactions at common electrode geometries under voltammetric steady-state conditions 14.2 A comparison of the homogeneous kinetic discrimination of steady-state and transient experiments Bulk electrolysis 15.1 Theory of bulk electrolysis 15.2 Cells for bulk electrolysis Spectroelectrochemistry 16.1 ESR spectroelectrochen~istry 16.2 IR spectroelectrochemistry 16.3 UV-visible spectroelectrochemistry 16.4 NMR spectroelectrochemistry 16.5 Combining mass spectrometry and electrochemistry Voltammetry at variable pressure and temperature Voltammetric studies on solids attached to electrode surfaces in the form of thin films 18.1 General aspects 18.2 Electron transfer in ideal redox active thin films attached to electrode surfaces 68 69 71 74 75 78 79 83 84 85 87 88 88 90 91 91 92 95 96 98 100 102 104 107 108 113 116 117 117 123 128 128 131 Contents ... xi11 18.3 Chemical reactions coupled to ideal thin-film electron-transfer process 18.4 Nuances associated with adsorption 19 Techniques for obtaining molecular level information on reactions associated with the voltammetry of surface-attached species 19.1 The use of scanning probe microscopies in electrochemistry 19.2 The electrochemical quartz crystal microbalance References llustrating the basics of voltammetry for solution-soluble redox active species involving reversible electron transfer and reversible coupled chemical reactions: the reduction of electrochemically rich polyoxometalate compounds Introduction Structural features of polyoxometalates Coupled electron- and proton-transfer reactions associated with ~ ~ ] ~ the reduction of a- [ P ~ w ~ ~ oand comparison of simulated and experimental cyclic voltammograms obtained in aqueous media as a function of pH 3.1 Reduction of ~ - [ P ~ w ~ ~ o ~ ~ ] ~ 3.2 Reduction o f a - [ ~ ~ ~ ~ ~ 0 ~ ~ ] ~ 3.3 Discussion of results obtained from the simulation of the reduction of a - [ ~ 2 ~ 1 ~ 0and ~ ~ a ]- ~[ - ~ 2 ~ ~ ~ 0 ~ ~ ] ~ Studies of the electrochemical reduction of ~ - [ s ~ M o ~ ~ino ~ ~ ] ~ aprotic and protic media3 ~ ~ ] ~acetonitrile 4.1 Voltammetry of C X - [ S ~ M O ~ ~inOaprotic media 4.2 Spectroelectrochemistry in acetonitrile 4.3 Electrochemical synthesis of one- and two-electron reduced forms of [ s ~ M ~ ~ ~ o ~ ~ ] ~ 4.4 A systematic approach to chemical synthesis of a two-electron reduced form of [s2Mo180 6 ~ 1 ~ 4.5 Voltammetry of in acidic (95/5) acetonitrile/water media using O a~ ~ ] ~ 4.6 Photoelectrochernical studies of [ s ~ M O ~ ~ hydrodynamic channel electrode Use of voltammetric techniques to identifjr the products formed when [ ~ ~ ~ o reacts ~ with ~ 0 Ph3P ~ and ~ ]Bu3P ~ in- (95/5) CH3CN/H20 5.1 Reaction of [ s ~ M ~ ~ ~with o ~Ph3P ~ ]in~(95/5) CH3CN/H20 5.2 Reaction of [ S ~ M O $30621 4- with Ph3P under irradiative conditions xiv Contents with o "Bu3P ~ ~ ] in~ (95/5) 5.3 Reaction of [ s ~ M ~ ~ ~ CH3CN/H2 0 : an explanation of differences relative to reaction with PPh3 6 An overview of results obtained by application of voltammetric, simulation, and spectroelectrochemical techniques to polyoxometalate reduction studies 6.1 Cyclic voltammetry 6.2 Rotated-disc electrode voltammetry 6.3 Channel-electrode voltammetry 6.4 Microdisc-electrode voltammetry 6.5 Spectroelectrochemistry 6.6 Bulk electrolysis 6.7 Combinations of techniques References 4 Electrode processes that illustrate the influence of irreversible homogeneous reactions and the competition between reactions that occur in the solution phase and on the electrode surface: fundamental studies, photovoltaic dye-sensitizers, stripping voltammetry and glucose biosensors 1 Introduction 2 Elucidation of the homogeneous reaction pathways that accompany the electrochemical oxidation of cis, m e r - ~ n( ~ ($ 0 -dpm) ) ~ (q2-dpm) Br(dpm = Ph2PCH2PPh2)in dichloromethane 2.1 Voltammetric studies in dichloromethane 2.2 Bulk electrolysis and spectroelectrochemical experiments 2.3 Simulation of the voltammetry 2.4 Conclusions derived from electrochemical studies on cis, m e u - M n ( ~ 0(ql-dpm) )~ (q2-dpm)~r 3 Electrochemical studies on the [v(co)~]-'~ process in aqueous media 3.1 Voltammetric oxidation of [V(CO)6]- in acetone solutions containing water 3.2 Voltammetric, EQCM, and chronocoulometric studies on the oxidation of p ( C 0 ) 6 ] - in water 3.3 Conclusions derived from voltammetric studies on [V(C0)6]- in aqueous media 4 Voltammetric studies on the oxidation of the highly surface-active polypyridyl ruthenium photovoltaic sensitizer cis-R~(II)(dcbpy)~ (NCS)2(dcbpy = 2, 2'-bipyridine-4, 4'-dicarboxylic acid 4.1 Reference studies on model mass-transport-controlled processes 4.2 Electrochemical studies on cis-R~(dcbpy)~(NCS)~ in acetone in tetrahydrofuran, 4.3 Voltammetry of cis-R~(dcbpy)~(NCS)~ acetonitrile, and dimethylformamide 248 248 b 250 251 253 260 261 262 262 264 268 269 272 280 Contents 4.4 Conclusions related to the voltammetry of surface-active cis-R~(dcbpy)~(NCS)~ Stripping voltammetry 5.1 Anodic stripping voltammetry with thin-film mercury electrodes 5.2 Theoly for a reversible process 5.3 Comparison of experimental results and theory 5.4 Mechanism associated with the adsorptive stripping voltammetry of cobalt (and nickel) dimethylglyoxime complexes at mercury electrodes Glucose biosensors 6.1 The ferrocene-based glucose sensor 6.2 Optimization of the performance of a solution-phase electrochemical glucose biosensor 6.3 Fabrication of a glucose bioelectrochemical sensor employing glucose oxidase immobilized onto an electrode surface 6.4 Glucose analysis of whole blood with a commercially available glucose bioelectrochemical sensor References llustration of the principles of voltammetry at solid-electrode-solvent (electrolyte) inteflaces when redox active microparticles are adhered to an electrode sudace Introduction Strategies to detect factors that may be important in the voltammetry of redox active microparticles adhered to an electrode surface Mechanistic aspects of the electron and ion-transport processes across the electrode-solid-solvent (electrolyte)interface when arrays of non-conducting microparticles are attached to an electrode 3.1 The oxidation of decamethylferrocene 3.2 Electrochemistry of microparticles of trans-Cr(CO)2(dpe)2, trans-[Cr (CO), (dpe)2][XI salts, and ~ i s - C r ( C 0(dpe)2, )~ (dpe = bidentate Ph2PCH2CH2PPh2,X - = anion) attached to an electrode surface 3.3 Overview of factors that influence the voltammetry of decarnethylferrocene and trans-Cr (CO)2(dpe)2 attached to an electrode surface 3.4 Problems with a theoretical description of the voltammetry of non-conducting microcrystals Voltammetry of T C N Q adhered to an electrode surface: detection of solid-state transformation, redistribution, and dissolution processes by application of X-ray diffraction, electron scanning microscopy, atomic force microscopy and electron spin resonance techniques xvi Contents 4.1 Solution-phase voltammetry of T C N Q 4.2 Voltammetric studies on microcrystals of T C N Q adhered to , ~ b ' , and CS+ electrode surfaces in contact with ~ a +K+, containing electrolytes 4.3 Electrochemically driven transformation of microcrystalline T C N Q to tetraalkylammonium [TCNQ-] salts 4.4 Dissolution of solid T C N Q and [TCNQ-] salts from electrode surfaces 4.5 Comparison of electrochemical data with microcrystals and other forms of surface-confined T C N Q 4.6 Conclusions related to the electrochemistry of T C N Q adhered to electrode surfaces Voltammetric studies on systems where coupled electron and 5 ion transport within an adhered microparticle are rate determining 6 Voltammetric studies on adhered microparticles where 'thin-film' behaviour is exhibited 7 An overview of the techniques used in electrochemical studies of microparticles adhered to electrode surfaces References 6 Use o f metalloprotein voltammetry to illustrate the nuances o f electrochemistry related to blocked electrodes, chemically modified electrodes, electrode functionality, and microscopic aspects o f electrode behaviour 1 Introduction 2 Structural features of metalloproteins that may give rise to features that are different to those encountered in the voltammetry of small molecules 3 Studies on protein-surface attachment to a gold electrode by in situ scanning probe microscopy The influence of surface attachment of 4 metalloproteins on voltammetric studies 4.1 General features of voltammetry of metalloproteins at bare (unmodified) gold electrodes 4.2 The transient nature of the voltammetry of cytochrome c at 'bare' gold electrodes: an explanation based on a self-blocking mechanism Voltammetry of metalloproteins at chemically modified 5 gold electrodes Voltammetry of metalloproteins at naturally and deliberately 6 functionalized carbon electrodes 6.1 Cytochrome c 6.2 Plasto cyanin 6.3 Ferredoxin Contents 6.4 General conclusions concerning the voltammetry of metalloproteins at carbon electrodes Quantitative use of a microscopic model to explain the unusual features of metalloprotein voltarnmetry at carbon electrodes 7.1 Cytochrome c voltammetry at carbon macrodisc electrodes 7.2 Cytochrome c voltammetry at carbon microdisc electrodes 7.3 Conclusions derived from modelling the voltarnmetry of cytochrome c at carbon electrodes Evidence that chemical modification of the electrode surface can alter the reversible potential 8.1 The thermodynamic effects of chemical modification of graphite electrodes on rubredoxin electrochemistry 8.2 Thermodynamic effects of chemical modification of graphite electrodes on ferredoxin electrochemistry 8.3 Conclusions concerning the dependence of the reversible potential on the presence of a surface modifier Long-range electron-transfer effects encountered in cytochrome c voltammetry at long-chain alkane thiolate modified electrodes Voltammetry of metalloproteins in surfactant environments Conclusions related to the voltammetry of metalloproteins References d ndex mistry is regarded as a mature scientific discipline, having a ed two-hundred-year-old history (Table 1.1). Electrochemistry iants such as Faraday and Nernst are well known to all students of chemistry. urthermore, important applied devices based on electrochemical technology ave been in widespread use by the general public throughout the twentieth century. An obvious example of an electrochemical 'product' that has been well known for generations is the lead-acid battery used in motor vehicles (Section 6.3). Examples of other 'products' frequently encountered in everyday life and derived from electrochemical technology include: fuel cells (Section 6.1) and photovoltaic cells (Section 6.2 and Chapter 5); objects made from metals such as aluminium, copper (Section 5) or zinc which are produced by electrorefining techniques; a hand-held sensor for monitoring glucose in diabetes atients (Chapter 4); pacemakers and bionic ears. Corrosion also represents an important example of an electrochemical process that has a significant impact on modern society. Given the industrial significance of electrochemical technology for the last two centuries and the widespread teaching of the basics of electrochemistry in undergraduate university and senior school science courses, it could be logically assumed that most chemists have an excellent understanding of the theoretical and experimental aspects of the subject. However, informal surveys of student attitudes by this author and other colleagues who teach the subject, indicate that electrochemistry is regarded as a subject which is very difficult to master from a theoretical point of view, and that experimentally it is seen to be a 'fiddly' technique. With respect to the theory, it seems that the sign conventions associated with electrode potentials have caused misery for generations of students and, from the experimental point of view, cries of 'my electrode is blocked/broken', frequently reverberate around school and university student laboratories. During the course of presenting the Hinshelwood Lectures at The University of Oxford in 1998, the author had the opportunity of assessing the status of electrochemistry at that institution. The exchange of views between an examiner and a science candidate during the course of a natural science viva Table 1.1 A chronology of some important events in the history of electrochemistry over the period 1791-1960" L. Galvani (1737-98) published his results on electrical experiments with frogs (De Bononiensi Scientiarum et Artium Institute atque Academia Commentarii VII (1791) 363). A. Volta (1745-1827) communicated the construction of his electrochemical pile (voltaic battery) in a letter to Sir Joseph Banks, published in Philos. Trans. 90 (1800) 403. W. Nicholson (1753-1815) and A. Carlisle (1768-1840) used Volta's pile to demonstrate electrolytic conduction (electrolysis) (Nicholson's Journal 4 (1800) 179). W. Cruikshanks (1745-1800) published the first qualitative analysis (copper) performed with the aid of electrolysis (Nicholson's Journal 4 (1800) 187). H. Davy (1778-1829) published his theory of electrolysis (Philos. Trans. 97 (1807) 1). J.J. Berzelius (1779-1848) published his electrochemical theory and developed the concept of the electrochemical series (Journalfur Chemie und Physik 6 (1812) 119, Essai sur la Thkorie des Proportions Chimiques et sur l'ln$uence Chimique de ~'~lectn'citk, Paris, 1819). G.S. Ohm (1787-1854) published his law (Schwei~er'sJournal 46 (1826) 137). M. Faraday (179 1-1 867) published numerous observations based on data obtained from electrochemical experiments, including the famous law, and introduced modern electrochemical nomenclature (e.g. ion, anion, cation, electrolyte, electrode) (Philos. Trans. 1832-34). W.R. Grove (1811-96) described the first practical fuel cell (Philos. Mag. 14 (1839) 127). E. Becquerel (1820-90) reported the photovoltaic effect (Compt. Rend. Acad. Sci. (Paris) 9 (1839) 561). R.L.G. Plant6 (1834-89) demonstrated the operation of the lead-acid battery (Compt. Rend. Acad. Sci. (Pavis) 50 (1860) 640). W. Gibbs (1822-1 908) published the first electrogravimetric analysis (Fresenius' 2.Anal. Chem. 3 (1864) 334). W. Nernst (1864-1941) published his fundamental equation which relates the potential to ion activities in his dissertation (Die elektromotorische Wirksamkeit der Jonen, Leipxig, 1889). F.G. Cottrell (1877-1948) published the equation which is now known as the Cottrell Equation (Z. phys. Chem. 42 (1903) 385). B. Ku?era (1874-1 92 1) introduced the dropping mercury electrode for electrocapillary studies (Ann. Phys. 11 (1903) 529). J. Heyrovsk9 (1890-1967) published his first results with the dropping mercury electrode method using a technique which he soon calls polarography (Chem. Listy 16 (1922) 256, Philos. Mag. J. Sci. 45 (1923) 303). D. Ilkovic (1907-80) published the equation which is now known as the Ilkovi? Equation (Coll. Czech. Chem. Commun. 6 (1934) 498). J.E.B. Randles (1912-98) (Trans. Faraday Soc. 44 (1948) 327) and A. Sevzik (Coll. Czech. Chem. Comm. 13 (1948) 349) independently described the technique of cyclic voltammetry. G.C. Barker (1915-2000) and I.L. Jenkins introduced square-wave techniques (Analyst 77 (1952) 685). G.C. ~ a r k e and r A.W. Gardner introduced pulse techniques (Fresenius' Z. Anal. Chem. 173 (1960) 79). "Adapted from information provided by courtesy of F. Scholz, C. Russell, and The Royal Society of Chemistry. Introductory remarks (oral examination) late in the nineteenth cent1~ r is y reproduced below: Natural Science viva, c. 1890 Examiner: Candidate: What is Electricity? Oh, Sir, I'm sure I have learnt what it is-I'm sure I did know-but I've forgotten. Examiner: How very unfortunate. Only two persons have ever known what Electricity is, the Author of Nature and yourself. Now one of the two has forgotten. Source: Falconer Madan, Oxfovd Outside the Guide-Books, 1923. Quoted in: The Oxford Book of Oxfovd, Jan Morns, OUP, 1978. Undoubtedly, many equivalent exchanges have occurred during the course of oral examinations of electrochemistry-based theses at the University of Oxford throughout the course of the twentieth century. In 1991, Professor P.W. Atkins of Lincoln College, University of Oxford, one of the most distinguished chemical educators of our times, summarized his views on the subject by stating [I], I think we ought to expand our view of what electrochemistry is about. It is not just about electrode potentials and electrolysis, it is half of modern inorganic chemistry. 'k and also, Electrochemistry-in the broadest sense-will be one of the great achievements in chemistry in the next millennium, and one should prepare our people for it. Thus, whilst electrochemistry may be seen as a 'tricky' discipline to master, nevertheless according to Atkins, it will be of considerable significance in this twenty-first century. Concurring with Atkins' thesis that education in electrochemistry will be even more important in the future than in the past, the author titled the 1998 Hinshelwood Lectures, Broadening Electrochemical Horizons. The aim of the Hinshelwood Lectures, and this book, which was generated from the lecture series, is to demonstrate via presentation of a systematic account of the subject, that the present commonly accepted limitations and correspondingly conservative image of the subject, are unwarranted. As in many technologydriven subjects, there have been, in fact, numerous innovations achieved in recent times which now make it possible to apply electrochemical methodology to solving problems in almost all branches of science. Developments in electrochemistry in the twenty-first century may well be restricted more by limited imagination, than by fundamental scientific impediments. Intrinsic to many of the themes associated with the 'broadening of electrochemical horizons' concept, are recent innovations that have become possible via advances in materials science. Electrode sizes used, now range from the nanometre (molecular dimensions) to the metre (electrorefining)size scales. The materials from which electrodes are now constructed, and the electrode configurations and media in which they can be used, are now very wide-ranging. Up 4 Thefundamentals of electrochemistry until the middle of the twentieth century, electrodes used in both fundamental studies and in applied devices were usually made from highly conducting metals such as platinum, lead, silver, gold or mercury, or graphitic forms of carbon. Now electrodes may be manufactured also from semiconducting and even poorly conducting materials, many forms of carbon, including glassy carbon (GC) (a high-temperature form used widely in analytical applications of voltammetry) and doped forms of diamond, and from an infinite range of composite materials. Furthermore, the electrodes may be modified extensively to achieve characteristics associated with molecular recognition by addition, for example, of conducting polymer coatings or enzymes, to the electrode suriace. Advances in membrane technology also now enable a wide range of chemical separation and speciation features to be coupled with the well-established operational aspects of an electrode or electrochemical cell. Thus, the generation ofthe 'smart' electrode system is now emerging in the area of sensor technology. Naturally, advances in instrumentation (especially computer technology) are also having a significant impact in almost all aspects of electrochemical experiments, although in the last decade, the rapid expansion of new electrode materials and innovations in electrochemical cell design, arguably have had an even greater impact on the subject than instrumentation advances aided by computer technology. However, in reality, it is of course the combination of advances in materials science, electronics, computing, mathematics, physics, chemistry, and the biological sciences, that has enabled the marvellous electrochemical packages to be constructed. These now allow electrochemical techniques to be applied routinely in liquid, solid, and gas phases, under conditions where restrictions associated with high resistance, capacitance, size, or the need to achieve charge neutralization were thought to be major impediments to progress. At the start of this millennium, it needs to be recognized that the situation has been reached, where almost any problem involving reduction or oxidation of a chemical moiety may be addressed, or even exploited, by an appropriate electrochemical technique. Of course, as is presently the case, there may be superior spectroscopic or other techniques to solve a given problem, and electrodes will still foul up under many circumstances, so that an electrochemical solution to a problem will always be employed only if the right sets of circumstances apply. However, via both the Hinshelwood Lecture Series and publication of this book, the author wishes to convey the message that recently the electrochemical horizons have been broadened so significantly, that one may predict confidently that techniques of electrochemistry will continue to be highly significant in both the fundamental and applied senses in the twenty-first century. Atkins, in the quotations cited earlier, may have exaggerated slightly the level of brightness of the electrochemical future, but the general thrust of his highly positive remarks, in all probability, will be realized. In presenting the Hinshelwood Broadening Electrochemical Horizons Lecture Series on a broad-based subject with a very long history, the need to focus the content on only one or two aspects of the subject was essential. At the same time, the more general theme of Broadening Electrochemical Horizons needed to emerge Introductory remavkr 5 as a general conclusion. T o achieve both these objectives, this Hinshelwood lecturer chose to use the widely used electrochemical technique of voltammetry to illustrate the theme of the chosen topic, using in the main, examples taken from recent research undertaken in the author's or colleague's laboratories. In general terms, voltammetric techniques are associated with the measurement and interpretation of current-potential-time (I-E-t) relationships. In the sense that current flows in the course of an experiment of this kind, voltammetry must be defined as a dynamic rather than an equilibrium technique of electrochemistry. Simple consideration ofthe operational principles and outputs of batteries, photovoltaic cells, and the glucose monitor mentioned previously, reveals that current must flow through the devices when they are being used for their intended purposes. Consequently, a detailed understanding of voltammetric techniques and methodology enables the behaviour of the devices to be understood at both the applied and fundamental levels. In contrast, the wellknown pH and ion-selective electrode electrochemical sensors operate under equilibrium conditions (zero current flow). Usually, the principles of these so-called potentiometric devices may be understood by using the well-known ernst and related equilibrium or thermodynamic equations [2]. Of course, a dynamic voltammetric technique may operate under conditions where the response is almost equivalent to the equilibrium response given by the ernst or other thermodynamic equations. An equilibrium-type response can occur in the special case where zero current flow conditions prevail or where all electron-transfer and coupled chemical reactions are so fast, within the timescale of the measurement, that the voltammetric response is indistinguishable from that calculated for the reversible or equilibrium situation. However, irrespective of whether or not a voltammetric device is operating under apparently equilibrium conditions, a fundamental understanding of the theory and practice of voltammetry requires a detailed knowledge of both the heterogeneous kinetics, which define the electron-transfer step taking place at the electrodesolution, electrode-redox active solid, or relevant multi-phase interface, and the homogeneous or heterogeneous reactions that may be coupled to the electrontransfer step. Naturally, the interfacial region where these dynamic reactions occur may contain both resistance and capacitance terms, which are also likely to exert a profound influence on the I-E-t behaviour of the voltammetric response. That is, the theoretical description of voltammetry represents a solution to an inherently complex problem, because a wide range of kinetically controlled heterogeneous and homogeneous reactions need to be described in an interfacial region of space where resistance and capacitance are likely to be present. T o conclude these introductory remarks, it may be noted that, as is always the case with any branch of science, there are both 'good news' and 'bad news' aspects of the subject that need to be given when presenting an overview of a subject. The 'good and bad news' features of electrochemistry are summarized in Table 1.2. 6 Thefundamentals of electvochemistry Table 1.2 Dynamic electrochemistry The good news Integral to many problems of fundamental and applied significance: e batteries e photovoltaic cells e biologically important electron-transfer reactions e glucose sensors electrochemical synthesis of metals (Zn, Cu, Al) The bad news Without great care, years of research, and 'good luck' they break, become Electrodes: fouled, commonly stop working Resistance is always present and has a deleterious effect on an Ohm's law: electrochemical process when current flows Capacitance: Associated with undesirable background currents or time constants when time-dependent phenomena are operative Theory: Often considered complex because: e historically, different sign conventions have been used in different countries and at different times in the reporting of standard electrode potentials and oxidation and reduction currentsa e second-order differential equations need to be solvedb e knowledge of surfaces and interfaces required e knowledge of homogeneous and heterogeneous kinetics required, and e knowledge of thermodynamics required. 'Use of International Union of Pure and Applied Chemistry rules is strongly recommended to avoid this difficulty (e.g. (i) standard electrode potentials being reported as reduction reactions (see Table 1.3);(ii) designation of oxidation currents as positive and reduction currents as negative) when reporting voltarnrnetric data. b~nalytical solutions are rare, but numerical methods are now readily used (Chapter 2) to solve the relevant equations. Despite the fact that a kinetic theoretical description is required to explain electrochemical devices or experiments involving current flow, the majority of textbooks that focus on dynamic aspects of the subject still commence with a description of thermodynamic relationships that exist when species are oxidized and reduced in an electrochemical cell (Fig. 1.1) containing two electrodes referred to as either the negative or positive electrodes, or the anode (where oxidation occurs) and the cathode (where reduction occurs).' The reason for ' ~ o t ethat when a cell is in an equilibrium state, it is inappropriate to apply the names 'anode' or 'cathode' to either electrode because no net chemistry is occurring. That is, the cell is neither galvanic nor electrolytic and it is an equilibrium cell. Additionally, the definition of which electrode is the anode and which is the cathode changes, for example, when a lead-acid battery is charging or discharging. T o minimize these kinds of R e d o x reactions, electvochemical cells Galvanic cell (b) 7 Electrolytic cell Fig. 1.1 Schematic diagrams of typical (a) galvanic and (b) electrolytic cells. introducing the subject of electrochemistry in this manner is that the fundamental thermodynamic relationships, relating chemical and electrochemical energy (but not of course the mechanistic details), readily emerge from a relatively simple equilibrium treatment of the subject. Furthermore, and importantly from a didactic viewpoint, electrochemical equilibrium relationships associated with electrochemical cells can be readily understood, since only the potential difference between two half-cell reactions need to be considered under a range of conditions, to illustrate the Nernst-type relationships associated with potential difference, the nature of the redox couples in each half-cell, and the influence of concentration (activity) of species present in the half-cell reactions. However, most importantly, since these equilibrium-type principles must also represent a limiting case of the dynamic response associated with generally non-equilibrium voltammetric techniques, which are of paramount interest in this book, a brief review of relationships between classical chemical redox reactions and reactions that take place in a conventional electrochemical cell (Fig. 1.1) is also presented in this introductory chapter. Extensive details of these classical accounts of equilibrium electrochemistry are available in references [3-51, while the, inherently, far more complex kinetic description required to explain the details of voltammetry is introduced in Chapter 2. In order to qualitatively understand the nature of a process involving the transfer of electrons, it is useful to consider the visually obvious features associated with a redox reaction such as the so-called 'copper nail' experiment in which a nail, made of iron, is placed in a blue aqueous solution of copper(I1) sulphate. In this experiment, details of the course of the reaction may be monitored conveniently by periodically removing the nail from the copper(I1) sulphate solution and noting changes that have occurred, in both the nail and the solution, as a function of time. An obvious visual conclusion reached with respect to the initially pure iron nail is, that it has become progressively coated with metallic copper, while close inspection of the solution phase would reveal ambiguities, the terms 'anode' and 'cathode' are avoided wherever possible in this book. Fortunately, the terms 'working' and 'reference' (or 'counter') electrodes can be introduced in Chapter 2 onwards to avoid any confusion related to the function of the electrodes used in a voltammetric experiment. 8 Thefundamentals of electuochemisty, a concomitant decrease in intensity of the blue colour, associated with a lowering in the concentration of the blue copper(I1) ions in solution. Quantitative analysis of the composition of the solution phase by atomic absorption spectrometry, would confirm that the copper concentration in the solution phase has indeed decreased and, in fact, has been replaced by iron now dissolved in the solution phase. Quantitative analysis of the chemical composition of the nail would reveal that the percentage of metallic iron decreases as the percentage of copper increases. That is, the overall reaction that occurs is2 Of specific interest to an electrochemist is the fact that the overall reaction written in eqn (1. l ) may be treated as the summation of two reactions, each involving an electron-transfer process because Fe(meta1) has been converted or oxidized to Fe2+(solution),and c u 2 +(solution)converted or reduced to Cu(meta1). Based on this kind of formalism, eqns (1.2a) and (1.2b) can be used to represent the two half-reactions that on summation give eqn ( 1 . 2 ~which )~ (as required) is identical to eqn (1.I): f ~e(so1id)--+ i Fe2+(solution)+ e- $ ~u~+(solution) + e- ---t i solid) (oxidation) (1.2a) (reduction) (1.2b) f Fe(so1id)+ f cu2+(solution)--+ $ Fe2+(solution) + i solid) (overall redox reaction) (1.2~) It should be noted that representing electrode reactions as one-electron processes as above, with respect to eqns (1.2a-c), simplifies calculations of thermodynamic parameters that may be derived from data obtained from electrochemical experiments. This practice is adopted therefore at all times in this book. In an analogous manner, the chemically spontaneous reaction + 2~e~+(solution) + Iz(solution)+ 2ce3+(solution) 21- (solution) (1-3) 21n the early stages of this Introductory Chapter, half-cell and overall reactions are written (e.g. eqns (1.1)-(1.9)and Fig. 1.l) as irreversible processes (+) in order to highlight the dominant direction of the reaction. In principle, thermodynamic treatments require that all processes in a reaction scheme need to be considered as being reversible ( ) rather than irreversible (+). The concept of treating processes as being inherently reversible will be adopted whenever quantitative calculations of electrochemicalreactions are undertaken. R e d o x reactions, electrochemical cells 9 may be written in the formally equivalent electrochemical format shown in eqns (1.4a) and (1.4b) to give the overall redox reaction (eqn 1 . 4 ~ ) : I- (solution) --+- 1 Iz(solution) + e- + ~e~+(s01ution)e- +ce3+(solution) I- (solution) (oxidation) (1.4a) (reduction) (1.4b) + ~e~+(solution) +f (solution) + ce3+(solution) (overall redox 12 reaction) ( 1 . 4 ~ ) - (solution) + 2ce4+(solution)+I2(solution) + 2ce3+(solution) (1.4d) At this stage it should be noted that a spontaneous reaction is one which occurs without any input of energy, in contrast to the reverse reaction, which has to e driven by input of energy, which may, of course, be electrochemical energy redox reactions as two half-reactions enables the relationship nt electrochemical half-cell reactions to be readily identified. mica1 cell, the reduction reaction occurs at one electrode (the electrode that accepts electrons) and the oxidation reaction at the other electrode (the electrode that donates electrons), and an electrochemical cell may be seen to consist of two half-cell reactions, each of which, effectively, may be said to have its own potential or energy. Conventional schematic forms of representation of electrochemical cells, with examples of half-cell reactions, are shown in Fig. 1.1. Figure 1.1(a) represents a galvanic cell and Fig. 1. l (b) an electrolytic cell. In the galvanic cell shown in Fig. 1.1(a), the two half-cells are separated by a salt bridge or membrane to prevent c u 2 + ions present in one half-cell coming into contact with the metallic zinc which would lead to the occurrence of a spontaneous chemical redox reaction. Thus, prior to connecting the two half-cells, a chemical form of energy is stored, but may be made available for conversion into electrical ergy. When the electrochemical cell is connected as in Fig. 1.1(a), current w is associated with the occurrence of the two half-cell reactions + ~n(so1id)+ f zn2+(solution) e;cu2+ (solution) + e- -+ fcu(so1id) (1.5a) (1.5b) continues until the equilibrium position for the reaction Zn(so1id) + c u 2 +(solution) z n 2 +(solution) + Cu(so1id) (1.6) is reached. The magnitude of the current flowing in a galvanic cell at any given time will be determined by the rates of numerous processes, which include the eterogeneous and homogeneous reactions that occur in each half-cell, as well 10 Thefundamentals of electrochemistry as the rate at which species present in the solution phase can be transported to and from the electrodes by diffusion, migration or convection. Normally, at the start of the experiment when the circuit is connected, the current will be at its maximum value, since the forward reactions in eqns (1.5a) and (1.5b) will be at their maximum values and the backward reaction rates will be negligible. In contrast, at equilibrium, no net reaction occurs, since the forward and reverse reaction rates are equal by definition, so that no net current flows. Clearly, a relationship must exist between the magnitude of the current as a function of time and rates of heterogeneous reactions at the electrode-solution interface, and mass transport of species towards or away from electrodes. Voltammetry, the subject ofmajor interest in this book, is all about these kinetic factors, because in this technique it is the application of a suitable potential which drives a specific half-cell reaction at a finite rate and, in turn, it is the occurrence of the reaction that gives rise to a kinetically controlled current flow which is a function of the net rate of the numerous processes that occur in a half-cell. The other half-cell in a voltammetric experiment is a reference electrode system, which is assumed to operate under equilibrium conditions and hence independently of any current that may flow through this part of the circuit (Chapter 2). Figure 1.l(b) is an electrolytic cell in which energy from a battery or a current source must be supplied to drive the overall reaction + + 2Cu(solid) 2 ~ ~ ~ + ( s o l u t i o n2H20(liquid) ) + O2(gas) + 4H+(solution) (I.7) since the reverse direction of this reaction is the spontaneously favoured one. It should be noted that a salt bridge to separate the two half-cells is not required in this particular cell configuration because the product at the copper electrode (metallic copper) adheres to the electrode and the product at the platinum electrode (oxygen) bubbles out of the solution, so that direct contact of the products which would give rise to a spontaneous reaction (eqn 1.8) does not occur. The overall reaction given in eqn (1.7 or 1.9c,d) may be written as the two half-cell reactions shown in eqns (1.9a) and (1.9b). f c u 2 +(solution) + e- + fcu(solid) Cu Pt 1H20(1iquid) -+ 2 + 0 2 (gas) + H+(solution)+ e- 2~u~+(solution)2H20(liquid)+ 2Cu(solid) (1.9a) (1.9b) + O 2(gas) + 4~+(solution) (1.9d) R e d o x reactions, electrochemical cells 11 While current flows, an electrochemical cell, by definition, is a kinetically controlled device. In the chemical sense, the equilibrium position of the overall reaction may be calculated from the difference in Gibbs free energy of products and reactants, which is given the symbol A GO, when the reaction is carried out under standard conditions [2-51. In the electrochemical sense, the equilibrium osition (no net current flow) of the overall reaction may be calculated from the difference in potentials of the two half-cell reactions. Therefore, under standard conditions of X ° C , and with unit activity of all species involved in the reaction, it follows that [2-51: where K is the equilibrium constant for the overall reaction, R is the universal gas constant, F is the Faraday constant, T is the temperature (in Kelvin), AE0 is the difference in the standard potentials of the two half-cell reactions and the number of electrons associated with each charge-transfer step is unity.3 Table 1.3 gives a list of standard potentials (E0 values) for selected half-cell reactions which, for both convenience and ease of calculation of the thermodynamics, are all written as reversible one-electron processes. By convention, the value of the standard hydrogen electrode (SHE) process solution) e2(gas))is given a value of exactly zero. It is of historical interest to note the relationship of these quantitative data to e qualitative development of the Electrochemical Series (Table 1.4) developed by Berzelius [6] (Table 1.1) almost 200 years ago. This form of the series was based on qualitative observations made during the course of electrolysis experiments on numerous metal salts and compounds. Generally speaking, standard tentials of half-cell reactions involving elements towards the top of Berzelius7 ctrochemical Series have large positive values (e.g. oxygen, 1.23 V), while those towards the bottom have large negative values (e.g. potassium, -2.93 V). The historical background to the development of Berzelius7 Electrochemical eries is intriguingly related, in a recent publication by Russell [6], to the work of the pioneers of electrochemistry (see Table 1.1). At the beginning of the nineteenth century, the results of two enormously significant discoveries were published. The possibility of a continuous electric current was demonstrated by the Italian physicist Volta, who took alternating discs of copper and zinc and sandwiched them between damp cardboard to create the first wet battery. Within months, Nicholson and ~arllsle,in London, found that decomposition of water occurred, when in contact with both poles of what, in those days, was termed a pile [7]. They had discovered what Michael araday later called 'electrolysis'. Shortly afterwards, Humphrey Davy used this technique to decompose a number of solutions and fused materials, and by 1807 he had isolated sodium and potassium for the first time [6]. + + + 3~alf-cellreactions and equations derived from them are written from now on as reversible ) to signifj. that they have thermodynamic significance even when the processes ( reaction for either the forward or backward direction may be heavily favoured. Also see footnote 2 in this chapter. + 12 Thefundamentals of electrochemistry R e d o x reactions, elect~ochemicalcells 13 Table 1.4 Berzelius' Electrochemical Seriesa O ~gen Y Sulfur Nitrogen Muriatic radical Fluoric radical Phosphorus Selenium Arsenic Molybdenum Chromium Tungsten Boron Carbon Antimony Tellurium Tantalum Titanium Silicon Osmium Hydrogen Gold Iridium Rhodium Platinum Palladium ( + 1.23V) (0.00 V) ( + I S 2 V) (+1.19V) Mercury Silver Copper Nickel Cobalt Bismuth Tin Zirconium Lead Cerium Uranium Iron Cadmium Zinc Manganese Aluminium Yttrium Beryllium Magnesium Calcium Strontium Barium Sodium Potassium 'Adapted from reference [6]; order is from oxygen at top to potassium at bottom of series. Potentials in parenthesis are standard potentials for half-cell reactions selected from the present day Electrochemical Series (Table 1.2 and reference [2]). With the exception of oxygen and hydrogen, the half-cell reactions selected involve reduction of the metal-ion (highest oxidation states commonly found) to the metal. erzelius, after learning of Davy's results, undertook new and enlightening experiments with Volta's pile. In 1808 he discovered the use of liquid mercury as an electrode material. Davy, in turn, promptly isolated magnesium, calcium, strontium, and barium by using mercury as an electrode and distilling off the from the resultant amalgams [6]. ver valuable these discoveries of elements may have been, they were n importance by the theoretical concepts that subsequently emerged. avy deduced that electrolysis involved the reversal of chemical combination. It dawned on him that what kept elements combined in salts and other electrolytes was electrical attraction, and that electrolysis neutralized the positive charge on the metal and the negative charge on the other part of the electrolyte. He called this an electrochemical theory [6]. 14 Thefundamentals of electvochemistvy Berzelius pursued the concepts of Davy much further and, in so doing, generated a philosophy of chemistry. For Berzelius, every compound was polar and held together by electrostatic attraction. He then proceeded to develop the concept that what determined an element's polarity was its position in a vast electrochemical series (Table 1.4) ranging from the most electronegative of elements (oxygen) to the most electropositive (potassium). Thus, a very positive metal would possess a larger polarity ('charge') than one further up the series. There was much more to his theory than this, but essentially he was proposing that inorganic compounds were held together by electrochemical forces and could be pulled apart by electrolysis. The great strength of his electrochemical theory became apparent when he combined his concepts with those of Dalton's atomism in his essay on 'The Theory of Chemical Proportions and the Chemical Influence of ~lectricity',which was published in several languages over the period 1814-19 [6]. Detailed treatment of electrochemical half-cells, and the relevant thermodynamics that apply to equilibrium reactions derived by combining two half-ceh, are available in very readable form in the book by Compton and Sanders [2]. Obviously most textbooks on physical chemistry also treat this subject in considerable detail. In essence, electrochemical half-cell reactions are expressed by convention as reversible reduction processes, the simplest being Ox + e- 6 Red (1.11) where Ox is the oxidized form of a species, Red is the reduced form and the number of electrons transferred in the charge-transfer step is assumed to be unity again. Solely for reasons of convenience, the charges on Ox and Red in eqn (1.11) have been omitted, although of course it must always be remembered that charge balance is an important prerequisite in electrochemistry. The equation relating the equilibrium potential to the species involved in an electron-transfer reaction was first derived by Nernst for a metal cationmetal electrode reaction of the kind given in eqns (1.5a) and (1.5b). The more general form of the equation is now known as the Nernst equation, which for the reaction given in eqn (1.1I), is: where E is the potential of the electrode, EO is the standard electrode potential (measured relative to the SHE), R (8.31451J K-' mol-') is the universal gas constant, T is the temperature (in Kelvin), F (96484.6 C mol-') is the Faraday constant, and ai is the activity of species i. The activity for species dissolved in solution is commonly related to concentration by the expression where yi is the activity coefficient of species i and [i] is the concentration of species i, whilst for a metal or other pure solid substance it is unity. R e d o x reactions, electrochemical cells 15 The tendency for the reaction to occur relative to the SHE is given by hen concentrations are used instead of activities, as is normally the case, the ernst equation becomes ere EO f is the formal potential4 (measured relative to the SHE) whose value now depends on the activity coefficient and hence on the medium. Calculations based on standard potentials, such as those in Table 1.3, and s (1.10)-(1.15), are heavily emphasized in physical chemistry text books. wever, such calculations enable only a very limited range of practical electrochemical problems to be addressed because most reactions do not occur under standard conditions and they are kinetically rather than thermodynamically controlled. However, several features of some of the reactions considered in eqns (1.1)-(1.9) may be understood via equilibrium-type calculations. Knowledge of the standard electrode potentials of the half-cell reactions ows the thermodynamically favoured direction of the cell reaction to be estab~ ~all~ cells when written in lished. By convention, the standard potential, E : for standard notation (see Figs 1.1 and 1.2) is calculated as: Therefore, from eqn (1.10) it follows that Thus, if A E0 is greater than zero, K will be greater than one, which means that the forward direction of the overall reaction, when written as the summation of the cell reaction at the right-hand electrode (a reduction process) and the cell reaction at the left-hand electrode (an oxidation process) is the spontaneous ection of the cell reaction. In contrast, if AE' is negative, then K will be less an unity for the cell reaction, so that the reverse reaction will be the spontaneous one, or energy will be required to drive the reaction in the forward irection of the cell reaction. Thus, the standard electrode potentials of the metal/metal-ion half-cells considered in eqns (1.5) ( c u 2 + / c u and z n 2 + / z n ) 'Also known as the conditional potential. 16 The fundamentals of electrochemistry (a) 7 7 1 EXTERNAL CIRCUIT 1 I Electron Q flow ( current Z n 1 z n 2 +(aq) (aZ,z+) 11 c u 2 + (aq) (aC,2+) 1 C U @ flow 7 7 1 EXTERNAL CIRCUIT (b) Current I Cu 1 Cu2+(aq) (ac,,z+) 11 zn2+ (aq) (azn2+)1 Z n I Electron @ Q Fig. 1.2 Standard form of representation of an electrochemical cell. Irrespective of whether the cell is written as in form (a) or (b), via convention E:,,~ = E,'& The value (sign) of AGO = - F E : ~ ~=~ -RT In K calculated using this convention is used to determine the direction -Eft. of the spontaneous reaction and hence the direction of current flow in a galvanic cell. See text for further details. may be treated as follows: The EO data provided for the Mn+/M couples in Table 1.3 gives the thermodynamics of the cell reaction Pt (solid) I Hz(gas)(P = 1 atm) ( solution) (a = 1)(1 solution) (a = 1) I M(so1id) (1.18) under standard conditions. Therefore the reversible chemical reaction for this cell is Thus, in the case of copper, the standard electrode potential is 0.34V for the reversible reaction Scu2' (solution) +- H~(gas) + S solid) + H+(solution) and the standard free energy is (1.20) Redox reactions, electrochernical cells 17 (Table 1.3) gives an EL^^ value of -0.76 V for the reaction + iH2( p s ) i~n(so1id)+ H+(solution) 1zn2+(solution) 2 (1.22) so that A Go = 0.76 FJ mol-' or AGO = -0.76 F J mol-' for the reverse reaction, which means that the of metallic Zn with aqueous acid (H', a = 1) is strongly favoured in the thermodynamic sense. The data obtained in eqns (1.21) and (1.23) enable attention to be given to the galvanic cell presented in Fig. 1.1. The overall reaction $ ~n(so1id)+ 2 c u 2 +(solution) & zn2+(solution) + K' solid) (1.24) is obtained by subtraction of eqn (1.22) from eqn (1.20). Thus, for the reaction in eqn (1.24) which implies that this reaction is, as expected, strongly favoured in the forward irection in the thermodynamic sense. In fact the equilibrium constant K' for the cell reaction given in eqn (1.24), after noting that the activities of Cu(so1id) and Zn(so1id) are unity by convention, may be calculated as follows: K' = (aZn2+) 'I2 = exp 1.1OFIRT = x (acu") lI2 4 x 1018 (at 25°C) This means that for the reaction written in the more usual form as the equilibrium constant is given by quivalent use of relevant data in Table 1.3 enables confirmation to be made that reactions given in eqns ( 1 . 2 ~ (1.4c), )~ and ( 1 . 9 ~ are ) spontaneous in the thermodynamic sense, and their equilibrium constants can be calculated. In principle, C~+(solution)could be included in the cell reaction given in rather than ~e~+(solution) could have been the prodig. 1.1 and ~e~+(solution) uct of the 'copper nail' experiment. Why then have the reactions given not included these metal-ion species in these different oxidation states? It is common chemical knowledge that both monovalent Cu(1) and divalent Cu(I1) ions, 18 Thefundamentals of electvochemistry solution) and cu2+(solution)respectively, may exist under some conditions in aqueous solution. The disproportionation reaction may be considered in terms of the two half-cell reactions and solution) + e 6 ~u+(solution) (1.29) which, according to Table 1.3, have EO values of 0.52 and 0.16V respectively. Thus, for the reaction CU' (solution) + $ H2(gas) Tf Cu(so1id)+ H+(solution) AGO (1.30) = -0.52F J mol-' and for the reaction + 1 Hz(gas) + cu2+(solution) AGO CU+ (solution) + H+(solution) (1-31) = -0.16FJ mol-' The two reactions (eqns 1.30 and 1.31) may be subtracted to give the disproportionation reaction in eqn (1.28), for which The equilibrium constant for this disproportionation reaction is calculated as K=- acu2+ = exp 0.36FIRT = 1.2 x lo6 at 25°C (~cU+)~ (1.33) Thus, thermodynamically the disproportionation reaction is highly favoured at 25°C. Indeed, the kinetics of the reaction are also very fast, so that uncomplexed copper(1) ions, rapidly formed when a copper(1) salt is dissolved in water, disproportionate to give metallic copper and copper(I1) ions. In fact, it is only when Cu(1) ions are stabilized by strong complexation, for example by chloride, that the copper(1) oxidation state is thermodynamically stable in water. Thermodynamics versus kinetics 19 general, it may be shown [2] for the disproportionation reaction (a + b)MX+(solution)+ a~(~+~)+(solution) + bM("-')+ (solution) (1.34) EL~+/M(~+~)+ (1.35) that - which leads to the conclusion that A G O will be negative, and therefore the disproportionation reaction favourable, if In the case of Cu+(solution), thus disproportionation of CU' (solution) is favourable. In contrast so the reaction is not favoured. Thus, the addition of metallic iron to a solution of ~e~+(solution) to the formation of Fe2+(solution).These two pieces of information explain in the 'copper nail' experiment, the iron-containing product formed reaction of metallic iron nails is Fe2+(solution)and not Fe3+(solution), and, why no Cu+(solution)species are included in the reaction, as written in . in Table 1.3 also may be used to confirm that the spontaneous eqn ( 1 . 2 ~ )Data reaction direction written in eqn ( 1 . 4 ~is) correct. The direction of eqn 1.8 as + 1 spontaneous reaction under standard conditions, which include a ~ = -- 0), may also be confirmed via calculations based on data contained in e 1.3. However, at other pH values, different reaction pathways to that in (1.8) may be favoured [2], as the value of A G, and hence the equilibrium ion for the range of possible reaction pathways, is strongly dependent on a ~ (pH). + The dependence of the equilibrium position of a reaction on pH, at least one of the half-cell reactions contains a term for a ~ +is, discussed ail in reference [2]. odynamics versus kinetics n Section 2, the use of electrode potentials to predict the position of chemical equilibria of redox reactions that may be written in terms of half-cell reactions 20 Thefundamentals of electrochemistry has been illustrated. However, the predictions are subject to kinetic limitations [2]. That is, even if a reaction is thermodynamically feasible, the question still arises as to whether the reaction proceeds at a reasonable rate. Consider the hypothetical reaction ~ OH+ (complexation or precipitation). which neglects interaction of M ~ with Data in Table 1.3 advise that which implies that for the reaction :Nlg2+(solution) + H2(gas) iMg(solid) + H+(solution) the standard free energy change at 25°C is Likewise, since (Table 1.3) for the reaction H 2 0(liquid) 4 OH- (solution) + H+(solution) (1.45) Thus, for the reaction of interest, when magnesium is in contact with water (eqn 1.40) This large negative A GO value implies, from a thermodynamic perspective, that when magnesium metal is dipped in water, evolution of hydrogen gas is expected to occur. However, in practice, little or no reaction is observed, since a thin film of magnesium oxide, present on the metal surface, prevents the reaction taking place at a significant rate. That is, the oxide layer passivates the metal. Similar reasoning explains the well-known, and of course industrially and commercially important, lack of reaction of 'thermodynamically reactive9 aluminium metal with water. Reaction volumes and entropy calculations 21 ulation of reaction volumes and entropies from bviously, most chemical redox and electrochemical cell reactions do not occur under standard conditions of temperature (25°C) and pressure (1atm). Thus, in most practical situations, the reversible potential dependence of AE,O on these parameters needs to be established, and in fact may be used to calculate the reaction volume (A V) and entropy (AS) of an electrochemical cell under equilibrium conditions. The use of the fundamental thermodynamic equations [8,9] enables the required equilibrium relationships to be derived, which in turn enable A V and A S to be calculated. Thermodynamics deals with the most probable microstate of a system. At equilibrium, the system must have a uniform temperature and ressure, a constant number of phases and a constant chemical potential of these hases. For a single-phase half-cell of a redox system in which the number of moles is constant, the free energy (G) is given by the equation n eqn (1.48), H is the enthalpy, U is the internal energy, T is the temperature, S is the entropy, P is the pressure and V is the volume for a system with only a single phase, as may be encountered in a half-cell reaction of an electrochemical cell involving only solution-soluble species. Thus, the change in free energy (a G) for a closed system is given by the equation For more complex systems involving two or more phases, where chemical species move across boundaries, as is the case in solid-state electrochemical piAni and yA (in a differentiated form) need to be reactions, the terms added to the above relationships, where pi and ni are the chemical potential and number of moles of species i respectively, y is the surface tension and A the surface area. Reactions involving deviations from equilibrium are also more complex. Equation (1.49) provides access to two very important relationships that may be exploited via electrochemical measurement of the reversible potential in order to define completely many solution phase redox systems in a thermodynamic sense. These additional relationships involve the change in free energy 22 Thefundamentals of electrochemistry with respect to temperature or pressure as given in eqns (1S O ) and (1.51) which, respectively, define the entropy and the volume for a half-cell reaction. It has been established previously that A GO = -FA EO at standard conditions or A G = -FAE; when other conditions prevail. Since the reaction volume (the difference in molar volumes of reactants and products in a chemical process) or A V is related to the pressure dependence of the Gibb's free energy (A G) through eqn (1.5I), it follows that this parameter may be determined from the dependence of the formal potential of the electrochemical cell reaction (equivalent to the chemical redox reaction) on pressure, and use of the relationship Analogously, the reaction entropy (the difference in entropy of reactants and products in a chemical redox process) may be determined from temperature dependence of the formal potential and use of the relationship It follows from the above discussion that the temperature and pressure dependence of the reversible potential of the reference electrode (second half-cell reaction) normally needs to be known in order to calculate A V and AS for a cell reaction. The thermodynamic treatment of multi-phase redox systems, as noted above, is more complex, and requires the introduction of additional relationships associated with the interface, some ofwhich are considered in Chapter 4. However, in this introductory chapter, it is necessary to emphasize that measurements of the reversible potential of electrochemical cells lead to more information than measurements of A GO (or A G) and equilibrium constants of chemical reactions, which are the thermodynamic parameters emphasized in the majority of textbooks on Physical Chemistry. It was emphasized in Section 1 that the thermodynamic treatment of chemical and electrochemical cell reactions, strictly applies only to equilibrium conditions when zero net current is flowing. Thus, none of the equations presented to date, Voltammetry and kinetics 23 contain terms that can account for the (time-dependent) current which flows under dynamic conditions, when reactions are occurring spontaneously, as in a galvanic cell, or else when chemical reactions are being electrochemically driven by superimposition of an externally applied voltage or current onto the electrochemical cell. Consequently, in order to understand the fundamentals of the voltammetric techniques where an electron-transfer reaction is driven by application of potential and, indeed, how the devices based on electrochemical technology such as batteries, photovoltaic cells or glucose monitors operate, a knowledge of the time dependence of the processes which contribute to the experimentally measurable I-E-t relationship is required. The importance of the dynamics of the various reactions coupled to the electron-transfer step, is revealed by considering the large-scale production of metals such as Al, Cu, and Zn by electrorefining technology. The half-cell reactions of direct importance that occur at the cathode in these economically important metal deposition processes may be written simply as: . 1.3 Electrodeposition of copper at large-sized electrodes (cathodes) used for electrorefining of copper. Photograph provided by courtesy of Copper Refineries, Townsville, Queensland, Australia. 24 Thefundamentals of electvochemistvy with, of course, another half-cell reaction occurring at the anode. In essence, these metal deposition reduction processes obey Faraday's law where, for a 100 per cent efficient electrolysis reaction, the product of I and t (current x time), assuming constant current for the duration of the electrolysis, represents the number of coulombs, Q, required to generate Q / n F moles of metal which is plated onto the cathode. However, to obtain a metal deposit of very high purity in the form of a smooth copper sheet attached to a giant-sized electrode (see Fig. 1.3), via a reaction approaching 100 per cent efficiency, has required decades of intensive research. The purity and nature of the metal deposit formed on the electrode suriace, and the efficiency of the process, are determined by the composition and design of both the cathode and anode, the composition and purity of the electrolyte, the magnitude of voltage and/or current applied to the cell, the distribution of potential and current, the absolute value and constancy of temperature of the electrolyte, the hydrodynamics of the entire electrolytic plant, the elimination of undesirable side reactions and, dare one say it, possibly even 'the phase of the moon'. An intriguing insight into the difference between the macroscopic and microscopic worlds of electrochemistry, is gained by comparison of the results of the deposition of copper onto a giant electrode of the kind shown in Fig. 1.3, and onto arrays of very small carbon microdisc-electrodes (Fig. 1.4). The microdisc array electrode contains 7-pm diameter carbon fibres randomly distributed Fig. 1.4 Electrodeposition of copper at a random assembly of carbon-fibre microdisc electrodes M RAM^^ electrode). Photograph provided by courtesy of Stephen Fletcher, CSIRO, Division of Minerals, Clayton, Victoria, Australia. Application ofprinciples ofelectvochemistry 25 within an epoxy resin. At this electrode, mass transport (see Chapter 2) is much enhanced at the edges of each carbon-fibre microdisc electrode. Furthermore, copper is only deposited after a nucleation and growth phase of the reaction occurs, so that the copper deposited onto each very small electrode is now subject to the random statistics associated with stochastic processes, to give the range of fascinating crystalline forms of metallic copper observed at different carbon-fibre electrodes, as shown in Fig. 1.4. The absence of a copper deposit on a particular carbon fibre in Fig. 1.4 could be a statistically expected result or simply indicate that this fibre is not electrically connected or has 'failed7 during the course of the experiment. Clearly, in the electrorefined form of copper (Fig. 1.3), the remarkably smooth deposit represents the result of the careful averaging of many events. This commercially important 'averaged' result represents the triumph of the combined skills of materials scientists, physicists, chemical engineers, chemists, and electrochemists, who have, over many years, learned how to control the dynamics of the numerous events that occur during the course of electrodeposition of a metal onto an electrode surface. The example of copper deposition into electrode surfaces therefore gives another opportunity to highlight the fact that the standard thermodynamic treatment of a metal deposition reaction given in most physical chemistry textbooks, reveals no more than the average amount of energy required to deposit copper onto an electrode surface at 25°C. In reality, even this most basic of electrochemical metal deposition processes represents the result of a series of complex dynamic reactions that occur at a finite rate over a finite period of time, and which encompass a wide range of homogeneous and heterogeneous processes. Consequently, usually a kinetic rather than thermodynamic description of all the events taking place, is required to achieve any significant level of understanding of a metal deposition, or indeed any dynamic electrochemical process, as always will be encountered in voltammetry. n the very first paragraph of this book, it was noted how frequently 'products7 erived from electrochemical technology are used in modern society. T o conclude this introductory chapter, it is now appropriate to highlight very briefly how the general principles of electrochemistry presented above, apply to the operation of fuel cells, photovoltaic cells and the lead-acid battery. These, and all other electrochemical devices, are characterized by the performances of the electrodes and the electrolyte. Since thermodynamics have to be favourable by definition, it is the kinetics that usually determines the commercial viability. Thus, most research in the area of electrochemical technology is aimed at speeding up desirable processes that occur in the electrochemical cell and slowing down the rates of unwanted side reactions. Importantly, voltammetric techniques considered in the remainder of this book play a powerful role Thefundamentals ofelectrochemistry 26 in quantifying the rates of the individual half-cell reactions, and hence the performance of the overall cell reaction. 6.1 Fuel cells Almost immediately following Volta7sdiscovery of the battery, Nicholson and Carlisle used this new device to 'split' water into oxygen and hydrogen gases (Table 1.1). That is, oxygen gas was produced at the anode of the battery and hydrogen at the cathode. In today's terminology the following two half-cell reactions can be written to describe the oxidation and reduction processes: 12 ~0 2 (liquid) solution) -+ 0 2 (gas) + H+(solution) + e- (oxidation) + e- -+ i ~ ~ ( ~ a s ) 12 ~ 2 0 ( l i q u i d + ) Hz(gas) (reduction) + o2(gas) or 2H20(liquid)-+ 2H2(gas) + 02(gas) 9 (1.57a) (1.57b) (1.57~) (overall redox reaction) (1.57d) Data in Table 1.3 reveal that under standard conditions of 1 atm of H2(gas)and 1 atm of Oa(gas)at 25OC AGO = 1 . 2 3~~m o l - ' (1.58) which implies that a large amount of energy is required to drive this reaction. However, for the reverse reaction as) + 0 2 (gas) ---t H20(liquid) (1.59) A GO = -1 . 2 3J~mol-' (1.60) which advises that a great deal of energy will be released when this reaction takes place. That is, large amounts of electricity should be available by reacting these common gases in an electrochemical cell format. However, in the absence of a catalyst, the reaction in eqn (1.59) is extremely slow, again highlighting the need to understand the kinetics as well as the thermodynamics of reactions when considering the practical usefulness of an electrochemical cell. Fuel cells require the aid of 'catalytic7electrodes to exploit thermodynamically favourable reactions such as that in eqn (1.59) and, like batteries, they transform chemical energy into electricity. However, unlike batteries, fuel cells do not store electrical energy. Rather, they convert energy from chemical reactions directly into electrical energy. The history and key features of the fuel cell have been reviewed recently by Holper [I 01, Fuller [111 and Mobius [12]. William Grove produced the first fuel cell over a hundred and fifty years ago (Table 1.1). He knew, on the basis Application ofprinciples of electrochemistry 27 ofthe work of Nicholson and Carlisle, that sending an electric current through water splits the water into its component parts ofhydrogen and oxygen. Thus, in essence Grove demonstrated how to reverse the reaction and combine hydrogen and oxygen to produce electricity and water in the first practical fuel cell. Grove's and other simple fuel cells, as well as most electrochemically based devices, consist of two electrodes separated by an ionic conductor (a salt or acid solution) which acts as the electrolyte. In the hydrogen-oxygen fuel cell, hydrogen is pumped to the anode, and oxygen to the cathode; a wire carries the electrical current out of the fuel cell and ions carry the electrical current through the electrolyte [lo]. This cycle continues, as long as the hydrogen and oxygen fuel is supplied, with hydrogen and oxygen being turned into water while generating electricity (Fig. 1.5). Each hydrogen-oxygen fuel cell generates up to 1.23V under standard conitions (see eqn 1.58). However, most fuel cells operate at temperatures higher than 25'C and pressures higher than 1atm so that the cell thermodynamics usually must be derived on the basis of the equations and discussion presented in Section 4. Individual cells can be wired together to produce greater voltages or higher currents. The American space shuttle has 96 individual cells arranged in three stacks. When hydrogen and oxygen are pumped into the shuttle's fuel cells, they generate a 28-V power source or electricity supply as well as heat and water. The heat is put to good use, vaporizing the liquid fuels before they reach the fuel cells. Water flows into storage containers for drinking and other cells are based on simple principles. However, the chemical reactions d usually occur very slowly and unless special materials are used to construct the cells, very little current is produced. Consequently, much of the research associated with commercial fuel cells is focused on the development of suitable electrode materials and electrolytes to ensure that the rates of all rocesses are sufficiently rapid so that power is available 'instantly'. . 1.5 Diagrammatic representation of the hydrogen-oxygen fuel cell. Adapted from: Chem. in Aust. October 1998, 21. 28 Thefundamentals of electvochemistry Photovoltaic effects were first observed more than a hundred and fifty years ago when Becquerel (Table 1.1) detected a photovoltage when sunlight was allowed to shine on one of two electrodes he had placed in an electrolyte solution. Figure 1.6 contains schematic representations of photovoltaic cells based on the use of thin-film dye-sensitized cells introduced by Tsubomura et al. [13] and then developed extensively by Gratzel to give efficiencies in excess of 10 per cent [14]. In this regenerative Gratzel-type photoelectrochemical cell, a dye, usually based on compounds of the type Ru(bpy),(NCS), (bpy = bipyridine; NCS- = N-bonded thiocyanate) absorbs light. As shown in Fig. 1.6, the dye coats a nanostructured wide-band-gap semiconductor, such as T ~ o ~which , permits efficient charge transfer. Again, -as for the fuel cell and all other electrochemically based devices, two electrodes and an electrolyte are present. In the ~ r a t z e l - t y ~photovoltaic e cell (Fig. 1.6 and Scheme 1. i ) , the ruthenium dye, after excitation by light, takes on a standard potential that is considerably different from the ground state or dark potential. The interaction with light requires the use of a semi-conductor electrode rather than the simple metal or carbon-based electrodes previously considered. Furthermore, the electrolyte used in a dye-sensitized photovoltaic cell commonly contains the non-photoactive components that constitute a 'dark' half-cell reaction. excitation: - e injection: dye regeneration: RU" hv (dcbpy,) ( N C S ) ~ F=+ T2 [RU"' (dcbpy,) (NCS)~]' + e(dcbpy2)(NCS), + El (dcbpyo-) (dcbpy)(NCS)~]' [Ru"'(dcbpy2) (NCS)~]+ El- + RU"' electrolyte regeneration: El + e- + [RU"' (dcbpyo-) (dcbpy)(NCS)~]' Pt A RU" El- Scheme 1.1 Schematic representation of reactions that occur in a dye-sensitized photoelectrochemical cell which demonstrates that both the ground and excited state redox potentials of the c i s - [ ~ u ( d c b ~ ~ , ) ( ~couple ~ ~ ) ~are ] +important. /~ El and E l are the oxidized and reduced forms of the electrolyte (e.g. commonly ;1 and I- respectively). Adapted from reference [I 51. A common sensitizer used in these ruthenium-titania Gratzel-type photovoltaic systems is cis-Ru(dcbpy),(NCS), (dcbpy = 2,2'-bipyridine-4,4'dicarboxylic acid). This sensitizer provides excellent absorption in the visible spectrum, a high electron injection rate, high turnover rates and high stability in photoelectrochemical cells. Scheme 1.1 summarizes the relevant reactions associated with a photovoltaic cell based on the use of the cis-Ru(dcbpy),(NCS), dye, titania, and platinum electrodes, and acetonitrile containing I- and I, which act as both the electrolyte and constitute the chemical components in the f13(solution) + e'dark9 half-cell reaction. $1- (solution) (1.61) Application ofprinciples of electvochemistvy 29 Ru(I1) Dye-sensitized solar cells Porous T i 0 2 / RU@PY)~(NCS)~ \ Clear / ' conducting oxide ' Electrolyte containing I-/I< (b) Light 111 -Clear conducting oxide with electrocatalyst I Glass -Nanostructured T i 0 2 film -Clear conducting 1 oxide 7 , Light . 1.6 Schematic diagrams of dye-sensitized photoelectrochemical cells. (a) Provided by courtesy of Leone Spiccia, Monash University, Victoria, Australia (bpy = bipyridine); (b) adapted from: Electrochem. Soc. Inte?fdce6(3) (1997) 34 (I = ruthenium dye in ground (dark) state, I* = ruthenium dye in photoexcited state). As for fuel cells, extensive research is still taking place to improve the electrodes and electrolyte performance. Photon to electric current yields now being achieved are as high as 33 per cent [16]. The field of high-efficiency solar cells has been reviewed recently by Licht [17], who advises that progress in this area of electrochemical technology over the last decade has been quite remarkable, as indeed has been the case with fuel cells. .3 Lead-acid battevy The lead-acid battery was developed from the pioneering work of Planti in 1860 (Table 1.1). Figure 1.7(a) illustrates the main features of a three-cell 6-V lead-acid car battery. Again, as in other electrochemical devices, negative and 30 Thefundamentals of electrochemistry (a) Positive electrode Cell with electrolyte -, - E' 1-0.356 V SHE I r Cell connector I r p b EO =+1.685 I V SHE I Fig. 1.7 (a) A 6-V lead-acid storage battery is composed of three cells connected in series. Each cell produces about 2 V; (b) reaction scheme for a lead-acid battery shown for the discharge mode as a galvanic cell. Adapted from: J.E. Brady and J.R. Holum, Fundamentals of Chemistry, 3rd edn, John Wiley, New York, 1988, p. 726. positive electrodes and electrolyte are readily identified. The active component of the positive electrode is lead dioxide, P b 0 2 , that of the negative electrode is elemental lead and that of the electrolyte is aqueous sulphuric acid. The half-cell (charge-discharge) reactions of the lead-acid battery for each cell are given below. At the positive electrode, EO = 1.685 V for the reaction discharge f P ~ (solid) O ~+ 1H ~ S (aqueous) O~ + H' (aqueous) + e- F=+i p b ~ 0 (solid) 4 + HzO(liquid) charge (l.62a) At the negative electrode, EO = -0.356 V for the reaction: discharge Pb(so1id) + ; ~ ~ ~ ~ ~ ( a q u+ e o u s~) P ~ (solid) S O+~H+(aqueous) + echarge (l.62b) verall, Ecell= 2.041 V for the reaction: Lpbo2 (solid) 2 + H 2 S 0 4(aqueous) + Pb discharge + PbS04(solid) H20(liquid) charge (1.62~) + 2H2S04(aqueous)+ Pb +2PbS04(solid)+ 2H2O(liquid) discharge b 0 2(solid) charge (l.62d) Thus, the three cells in the 6-V battery in Fig. 1.7(a) each contribute about 2 V. Obviously, in the common 12-V lead-acid battery used in automobiles there are six 2-V cells. Under discharge conditions, the lead-acid battery acts as a galvanic cell as shown in Fig. 1.7(b). In the charge mode, energy is required to drive the reverse reaction, so the cell operates in a manner equivalent to an electrolytic cell. Note that this implies that the assignment of the anode and cathode can change depending on whether a lead-acid battery is being charged or discharged, so as noted previously representation of the electrodes as positive or negative is preferable terminology. Further details on the lead-acid battery are available in references [3,4]. [I] P.W. Atkins, Chem. Aust., April 1991, 128. [2] R.G. Compton and G.H.W. Sanders, Oxford Chemistry Primers, Electrode Potentials, Oxford University Press, Oxford, 1996. D.B. Hibbert, Introduction to Electrochemistry, Macmillan, London, 1993. [3] [4] K.B . Oldham and J. C. Myland, Fundamentals of Electrochemical Science, Academic Press, San Diego, 1994. [5] P.H. Rieger, Electrochemistry, 2nd edn, Chapman and Hall, New York, 1994. 161 C.A. Russell, Chem. Br., September 1998, 36. [7] S. Trasatti, J. Electroanal. Chem. 460 (1999) 1. [8] See for example, Chemical Thermodynamics with Special Reference to Inorganic Chemistry, Macdonald, London 1971, pp. 1-21 1. [9] R. Van Eldik, T. Asano, and WJ. Le Noble, Chem. Rev. 89 (1989) 549. 32 [lo] [111 [12] 1131 [14] 1151 [16] [17] Thefundamentals of electrochemistry P. Holper, Chem. Aust., October 1998, 21. T.F. Fuller, Electrochem. Soc. Integace 6(3) (1997) 26. H-H. Mobius, J. Solid State Electrochern. 1 (1997) 2. H. Tsubomura, M. Matsumura, Y. Nomura, and T. Amamiya, Nature (London) 261 (1976) 402. M.K. Nazeeruddin, A. Kay, I. Rodicio, R. Humphry-Baker, E. Miiller, P. Liska, et al., J. A m . Chem. Soc. 115 (1993) 6382. R. Argazzi, C.A. Bignozzi, T.A. Heimer, F.N. Castellano, and G.J. Meyer, Inoz. Chem. 33 (1994) 5741. U. Bach, D. Lupo, P. Comte, J.E. Moser, F. Weissortel, J. Salbeck, et al., Nature (London) 395 (1998) 583. S. Licht, Electrochern. Soc. Interface 6(3) (1997) 34. is, ince Faraday's pioneering studies (Table 1.I), it has been known that the transfer of electrons between a redox active species, dissolved in a solution phase, and solid metal, or carbon, or liquid mercury electrodes, results in interesting reaction pathways. However, voltammetric techniques, which involve the measurement and interpretation of I-E-t curves have only become popular since the 1940s, when instrumentation required to conveniently conduct such experiments became readily available. The early studies invariably used a constant or linear sweep of the direct current (DC) potential and measurement of D C current at the potential of interest. In the last 50 years a wide range of techniques have emerged (Table 1.I). Thus, Randles and Sevtik reported the first cyclic voltammetric studies in 1948 [l ,2], while the 1950s and 1960s saw the widespread use of hydrodynamic techniques such as rotating-disc electrode (RDE) voltammetry [3] and alternating current (AC) pulse and square-wave voltammetry [4-61. The 1970s and early 1980s then witnessed the wide-spread use of microelectrodes [6,7], initially under slow scan rate near steady-state conditions and subsequently, when advances in instrumentation occurred, under extremely fast scan rate, transient D C voltammetric techniques [7,8]. Recent voltammetric studies in which the redox active components are soluble in the solution phase have reported the use of a wide range of waveforms (time domains) and also combinations of macroelectrodes, microelectrodes, and different forms of mass transport [9]. At the same time studies with solids attached to electrode surfaces [lo] have emerged as a very important area of both pure and applied research and are now almost as common as solution phase studies. Thus, by the beginning of this millennium, an extensive range of voltammetric techniques have been made available and can be applied to redox active species in solution, solid and gas phases using conventional conducting electrodes, semiconducting electrodes and chemically modified electrodes. In this chapter only 'parts of Sections 2.1 to 2.13 of this Chapter have been adapted with permission from Adv. Phys. Oy. Chem. 32 (1999) 1. 34 Principles of voltammetry the relatively simple theoretical principles and techniques applicable to conventional studies will be considered, in which the redox active compound of interest is soluble in the solution phase or else attached to an electrode surface as an ideal thin film. Chapters 3 and 4 will provide a detailed discussion of the application of the concepts contained in Chapter 2, while Chapter 5 will deal with complexities associated with oxidation or reduction of solids adhered to electrode surfaces in thick film or microcrystalline formats. The concluding chapter describes the use of an integrated approach to problem solving under specialized conditions encountered with metalloprotein voltammetry. cell used for ol Figure 2.1 shows a typical experimental arrangement used for standard voltammetric experiments. This electrochemical cell has the following features: (1) Three electrodes (working, reference and auxiliary) are present in close proximity, with the working electrode being centrally placed. It is crucial that the tip of the reference electrode is near to the surface of the working electrode in order to minimize contributions of the IR, drop (I = current, Ru = uncompensated resistance) to the applied potential. This situation may be efficiently achieved using a Luggin capillary (Fig. 2.1). (2) The cell contains an inlet and outlet for an inert gas which displaces electroactive oxygen from the solution. Typical inert gases include high purity nitrogen and argon. Nitrogen is commonly used due to its low cost and Connections to potentiostat 1- Water in from thermostatic bath Working electrode Fig. 2.1 Schematic diagram of a typical format for an electrochemical cell used in voltammetric Chem. 32 (1999) 1. Copyright, Academic Press. studies. Reproduced by courtesy: Adv. Phys. 0%. Electvochemical cellfor voltammetvic experiments 35 ready availability in a highly pure form. However, for very air-sensitive systems, argon is preferred, as it is heavier than air. (3) The solution volume is typically in the range of 5-20 mL. However, specially designed cells in the pL range can be built, as can very large volume cells containing manv litres of solution. (4) The concentration of the electroactive species of interest when employing DC voltammetric techniques is typically in the range 0.1-5 rnM. The upper concentration limit is chosen to minimize IR, drop and possibly to minimize the contribution of migration current from the electroactive species (see later). At concentrations below 0.1 rnM, background current terms may start becoming significantly relative to the Faradaic current of interest. In analytical studies, trace concentrations down to M, or even lower, may be determined via use of AC, pulse or square-wave methods that enhance the Faradaic-to-background current ratio [4,11]. (5) A high concentration of supporting electrolyte (>0.1 M) is usually added to the solution to minimize the solution resistance, reduce transport of electroactive ions by migration and to establish a well defined double layer. Thus the supporting electrolyte has to be of high purity, should dissociate substantially in the solvent of interest, consist of anions and cations that are hard to oxidize and reduce (in order to provide as wide a potential window as possible), and introduce no undesirable reactivity problems.2 (6) In the absence of constant temperature conditions within the laboratory, the electrochemical cell may need to be thermostatted as voltammetric responses can show significant temperature dependence. U J The electrochemical cell in Fig. 2.1 is coupled to a three-electrode potentiostatted form of instrumentation [5,6]. If a two-electrode (working and reference) system were to be used, the current would have to flow through reference electrode, thus provoking instability in the reference potential. thermore, in a two-electrode system, the IR, drop could be substantial. In contrast, in the three-electrode potentiostatted system, essentially all the current is forced to flow through the counter electrode, thereby minimizing problems with the reference electrode. Additionally, much of the IR, potential loss is ated by the potentiostatted circuitry [5,6,12], which drives the potential the working and counter electrode to a value which compensates the of the IR, drop. However, the use of a potentiostat does not remove all of the IR, drop, since uncompensated resistance remains due to solution resistance between the tip of the reference and working electrodes, and from sistance inherently present in the working electrode and electronic circuitry. bviously conditions where a very low value of I may occur, such as with a low concentration of redox active species or when very small microelectrodes are used [6,7], would represent the situations where a two-electrode voltammetric 2 ~ o m special e features encountered in voltammetric studies undertaken in the presence of dilute supporting electrolyte or even the absence of added supporting electrolyte are elucidated in reference 7. 36 Principles of voltammetry electrochemical cell could be used, provided of course that the resistance, or more importantly the IR, drop, is not excessive. 3 3.1 The electro Working electrodes This is the electrode at which the reaction of interest takes place, e.g. the simple one-electron oxidation/reduction processes given in eqns (2.1) and (2.2) when species X and X+ or Y and Y- are soluble in the solution (electrolyte) phase: + solution) + eY(so1ution) + e- + Y - (solution) X(so1ution) (oxidation) (2.1) (reduction) (2.2) However, it should be noted that the electrode processes are frequently designated in this book via use of the formalism or Red Ox + e- (2.4) where the charges and phases associated with the chemical species have been omitted for convenience of presentation of mathematical relationships. In eqn (2.4), the symbols Red and Ox (see Chapter 1) represent the reduced and oxidized forms of the half-cell redox reaction respectively. In Chapter 1, reversible half-cell reactions were written as reduction processes when defining the thermodynamics and relationships associated with the electrochemical series. However, in voltammetry, by convention, oxidation currents are positive and reduction currents negative, so the half-cell reactions, frequently, will be written in this chapter as the oxidation reactions in eqn (2.3) or (2.4) rather than as a reduction reaction, for the purpose of a more convenient form of presentation of the I-E-t curves derived from theory. A more detailed account of the conventions is available in reference [13]. Working electrodes are fabricated from electrically conducting materials. Common examples include liquid mercury, solid platinum or gold and some forms of carbon (e.g. glassy carbon (GC) or graphite). Mercury electrodes [4] are used in the form of dropping electrodes in which the surface is continuously renewed, as a stationary hanging mercury drop electrode or as a thin film plated onto a carbon or metal substrate. Historically, mercury electrodes have been widely used for studying reduction processes (the positive potential range being limited by the ease of oxidation of mercury). However, environmental concerns related to the toxicity of mercury and its compounds are beginning to limit the use of mercury electrodes. Consequently, carbon, gold, and solid platinum electrodes are now most commonly used as working electrodes, although there is an almost infinite number of new generation electrodes being introduced as advances in materials science occur. Typically, the solid electrode materials Electrodes in voltammetric experiments Side view 37 Top view Wire connection to potentiostat Electrode material typically smooth on p m scale - Diameter typically mm+pm Solder connection of wire to back of electrode material Conducting material Electrode (i) flush to insulating surface (ii) well sealed in insulating mantle (iii) polished . 2.2 Schematic diagram of a typical disc working electrode employed in voltammetric studies. Reproduced by courtesy: Adv.Phys. Org. Chem. 32 (1999) 1. Copyright, Academic Press. are sealed into a non-conducting support (e.g. glass or Teflon) to form a disc electrode (Fig. 2.2). Macrodisc electrodes have radii in the mm range, whereas microdisc electrodes have radii in the nm to pm range (Section 10). The quality of the voltammogram obtained depends on a number offactors: (1) the integrity of the surface as measured by its cleanliness, smoothness, and reproducibility of preparation. Failure to ensure that these ideal conditions are operative may result in high, non-reproducible background currents as well as distorted (with respect to theoretical expectations) Faradaic currents. Usually electrodes are polished via systematic methods to achieve a high quality surface using alumina or diamond paste as the polishing material [I41; (2) the integrity of the seal between the electrode material and the inert, nonconducting, supporting mantle and the ability to ensure that electrode and mantle surfaces remain flush at all times (see Fig. 2.2). A poor seal or a recessed/protruding electrode may result in noisy, non-reproducible voltammograms; (3) the employment of a vibration-free environment and choice of conditions where natural convection is minimized. This ensures that mass transport (Section 7.1) is well defined; (4) the ability to minimize problems associated with resistance. As noted above, an important IRu drop term is associated with the uncompensated resistance arising from the solution between the working electrode surface and the reference electrode. Thus, in order to minimize the undesirable I R u potential drop term, small working to reference electrode separations and adequately conducting solutions are generally employed. For microampere 38 Principles ofvoltammetvy cell currents, the IR, term is in the mV range for typical organic solvent electrolyte combinations e.g. CH3CN (0.1 M Bu4NPF6).T o achieve this desired outcome, high resistance working, reference and auxiliary electrodes and highly resistive salt bridges and very low porosity, and hence highly resistive, reference electrode frits, should be avoided. Any region of high resistance in an electrochemical cell is likely to be 'bad news' with result to IR, drop, noise, or R, C time constant ( C = capacitance). 3.2 Reference electrodes The reference electrode ideally provides a fixed reference potential against which the potential of the working electrode is measured. The most commonly used reference electrode in voltammetric studies, undertaken in aqueous media, is the silver/silver chloride (Ag/AgCl) electrode depicted in Fig. 2.3. The half-cell reactions utilized in this electrode are given in eqn (2.5) Prior to environmental concerns being raised over mercury and mercury compounds, the Calomel reference electrode (eqn 2.6) 2 Hg2C12(solid) + e- - Hg(1iquid)+ Cl- (solution) A (2.6) was also very commonly used. The potentials of reversible reference electrodes at 25°C and other standard conditions of activity etc. are defined thermodynamically via their Standard Electvode Potentials in conjunction with the T o potentiostat Ag wire of (21- salt riate solver Salt bridge AgCl coating on wire Low porosity plug Solution containing the same solvent/supporting electrolyte combination as in main cell Fig. 2.3 Schematic diagram of a typical Ag/AgCl reference electrode and salt bridge. Reproduced by courtesy: Adv.Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. Electrodes in voltammetric experiments 39 ernst equation (see references [13,15,16], Chapter 1 and Table 1.3). The source of aqueous solution-phase chloride ions for both the Ag/AgCl and calomel electrodes is usually NaCl or KC1, in concentrations typically ranging from 1.0 M to saturated (in the case of the Calomel reference electrode, en a saturated solution of KC1 is used, the special term of Saturated Calomel ctrode (SCE) is used). Thus, reference electrodes are usually used under conditions of non-unity activity. However, for both these reference electrode types, the potentials are frequently accurately known [5,15,16] relative to the SHE. The SHE (eqn 2.7) is based upon the use of a high surface area 'platinum black' in contact with hydrogen gas (1 atm) and hydrogen ions (unit activity) and, as noted in Chapter 1 (Table 1.3), is defined at 25°C to have a potential of 0.000 V any other forms of reference electrode are also used: (1) Ag/Ag+(silver salt) electrodes [e.g. ~ ~ / A g + ( 0 . 0M 0 1AgNO,)] are commonly used for experiments involving conditions where AgCl is soluble. For example, when acetonitrile is used as the solvent, AgCl is soluble and a non-aqueous Ag/Ag+ (0.001 M AgNO,, CH3CN) reference electrode is ideal provided care is taken to avoid photoreduction of the Ag+ ion. (2) Ag or Pt wire quasi-reference electrodes3are frequently used for experiments where the addition of deliberately added supporting electrolyte needs to be avoided, or in solvents where no established reference electrode couple exists. (3) In voltammetric studies in organic solvents, it is now common practice to ~ H ~ ) ~ , measure the reversible potential for the oxidation of F ~ ( ~ ~ - cusually called ferrocene (Fc), to the ferricinium cation (Fc'), versus the reference electrode, or quasi-reference electrode3 actually used, and to subsequently correct potentials to the FC/FC+ scale [l7,18]. In suitable cases, Fc may be added to the solution being studied to enable an in situ form of calibration to be achieved. This can be done when the potential of the FC/FC+ process does not overlap with the process being studied and also where Fc and Fc+ are both chemically inert with respect to the oxidized and reduced forms of compounds associated with the process of interest. More commonly, ex situ reference electrode calibration is made by measurement of the reversible potential versus the reference electrode used, and employing calculations obtained from a voltammogram for the oxidation of a 5 x 1op4to 1 x 1on3M ferrocene solution in the solvent (electrolyte) of interest. The reference electrode calibration procedure is analogous to the in situ or ex situ use of Me4Si as a standard to calibrate 'H or 13cchemical shifts in N M R experiments. he half-cell reaction giving rise to the potentials of these quasi-reference electrodes may be unknown, but under the conditions of the experiment an acceptably reproducible reference potential may still be achieved. 40 Pn'nciples of voltammetry In order to minimize the risk of contamination from the salt present (e.g. KC1 or NaCl), the reference electrode may be separated from the electrolytic solution and working electrode by a salt bridge (Fig. 2.3). Care must be taken to avoid precipitation of insoluble salts at salt bridge interfaces, for example, K+ and C10,. Physical separation of the salt-bridge solution from that in the reference electrode and that in the electrochemical cell is achieved by a low porosity device such as a glass sinter, porous vycor (thirsty glass) or a membrane (see Fig. 2.3). Any junction (e.g. those associated with a salt bridge) may give rise to a liquid junction potential (El,,). Such potentials, in combination with the ohmic potential drop term (IR,) may alter the potential applied between the working and reference electrode (Eapp),SO that the effective cell potential (Ecen)is given [5] by Careful choice of electrolyte in the salt bridge can be used to minimize Ehp. For example, the liquid junction potentials at the reference/salt bridge and salt bridge/working solution interfaces will have similar magnitudes but opposite polarities and will, therefore, cancel each other out if a high concentration of a salt whose constituent ions have similar ionic mobilities is present in the salt bridge [5]. The liquid junction potential term is complicated if an aqueous reference electrode is used in conjunction with an organic solvent test solution, as a knowledge of the free energies of transfer of the ions between the aqueous and organic solvents is required if corrections are to be made to compensate for this term. Use of the Fc/Fc+ reference scale is a significant help in minimizing problems with liquid junction potentials for measurements in organic ~ o l v e n t s . ~ 3.3 Counter/auxiliavy electrodes The terms counter or auxiliary electrode are used to describe the third electrode present in a typical potentiostatted voltammetric experiment (Fig. 2.1). The counter electrode usually consists of a piece of platinum (wire or gauze) or carbon (disc or rod) of large surface area placed directly in the test solution. Since current flows through the counter electrode, it must have a sufficiently large surface area relative to the working electrode to prevent limitation of the current flowing in the total circuit. The current measured in a voltammetric experiment flows between the working and counter electrode. Thus, if a reduction reaction is being studied at the working electrode a balancing oxidation process (frequently electrolysis of the solvent medium) must occur at the counter electrode or vice versa if an oxidation process is being considered. In order to prevent extensive contamination of the test solution with products formed at the counter electrode or reaction of these products with the electroactive solution of interest, a salt bridge should be used in conjunction 4~otentials reported versus F C / F ~ +should be reproducible in any laboratory, irrespective of the reference or quasi-reference electrode employed in the actual experiment. Major classes of voltammetry 41 with the counter electrode in large-scale, long-time domain, bulk electrolysis (Section 15) and equivalent classes of experiments. asses of volta .1 Tvansient voltammetry In transient voltammetric experiments, a potential perturbation is applied to the working electrode and the resulting current response associated with the reduction of oxidation reaction of interest is measured as a function of potential (time). ransient techniques include D C linear sweep, D C cyclic, square-wave, pulsed, and AC voltammetries (also see Section 8, and references [4-6,l2,l9,2O]). In the first two cases, which are the voltammetric techniques considered most extensively in this book, the D C potential of the working electrode is scanned in a linear (or computer-generated staircase) fashion (Fig. 2.4) and the current is monitored as a function of potential (time). The important temporal aspect arises from the rate at which the potential E is ramped, dE/dt, known as the scan rate, V . When the D C potential is swept in only one direction (Fig. 2.4(a)), the technique is known as linear sweep (analogue instrument) or staircase (digital instrument) voltammetry. If the potential is swept in one direction and then reversed, and then this sequence is repeated, using a repetitive triangular potential excitation (Fig. 2.4), this technique is known as cyclic voltammetry. In most alternating, square-wave, and pulse methods, a periodic waveform is superimposed onto the relevant D C waveform and the important temporal component is usually the frequency of the superimposed signal. Figure 2.5 gives examples of the waveforms used in square-wave and differential pulse voltammetry. -1 CYCLE 1 F, CYCLE 2 -1 0.2 0 5 10 15 20 Time (s) . 2.4 Example of a typical waveform used in a D C cyclic voltammetric experiment. (a) Positive potential scan from 0.25 to 0.75 V versus SCE (this is the waveform used in D C linear sweep voltammetry). (b) Direction of scan reversed at the switching potential of 0.75 V versus SCE. (c) Negative potential scan from 0.75 V to 0.25 V versus SCE. (d) Termination of the first cycle. Reproduced by courtesy: Laboratory Techniques in Electroanalytical Chemistry, Marcel Dekker, New York, 1984, p. 87. 42 Principles of voltammetry (b) // Sample width \\ E A I I I I I I I I I I / / / II 1P Pulse period Pulse width - I I I f I I II _ - _ - _ I I II II II II A , / // / ! t t Fig. 2.5 An example of a waveform used in (a) square-wave voltammetry in which a symmetrical wave train (total amplitude 2Es,) is added to a staircase (step height AE) ramped voltage with a period o f t . The current response is sampled at the end of both the forward and reverse half cycles (at 1 and 2). When a dropping mercury electrode is used a delay time Td is employed to allow the drop to grow to a predetermined size. Reproduced by courtesy: Laboratory Techniques in Electroanalytical Chemistry, Marcel Dekker, New York, 1984, p. 157; (b) Differential pulse voltammetry in which a pulse is superimposed onto a staircase voltage and the difference in current before and after the pulse is sampled. 4.2 Steady-state voltammetry In the steady-state form of voltammetry, the concentration distributions of each species in the electrode reaction mechanism are assumed to be temporally invariant at each applied potential. Theoretically it takes an infinite time to reach steady-state after the potential is changed. Thus, in a practical sense, steady-state voltammetric experiments are conducted under conditions that approach sufficiently close to the true steady-state that the experimental uncertainty of the steady-state value of the parameter being probed (e.g. current) is greater than that associated with not fully reaching steady-state. The effective time-scale of a near steady-state process is determined by the rate at which material reaches the electrode surface. This time-scale may be varied in a number of ways: (1) Altering the convective rate of transport, for example, by changing the rotation frequency of a RDE (Section 9.1). Experiments in which the Nature of the current-potential curve 43 convective rate of transport can be altered are known as hydrodynamic techniques (see Section 9). (2) Decreasing the size of the electrode so that the ratio of radial to linear diffusion of material to the electrode surface is enhanced. Voltammetric studies at microelectrodes frequently exploit this method of altering the nature of the diffusion characteristics to obtain a steady-state response (see Section 10). ation of electrode reaction mechanisms he kinetics of voltammetrically relevant reactions may be examined by varying the critical time parameter of the experiment and monitoring its effect on some voltammetric feature associated with the process being investigated. The general cedure for obtaining quantitative kinetic data related to an electrode reaction hanism using a voltammetric technique is schematically shown in Fig. 2.6. he basic concept is that the experimental voltammetric data are collected echanism for the electrode reaction mechanism is postulated. The promechanism may be theoretically simulated by solving the appropriate matical problem. Satisfactory agreement between experiment and theory is used to provide a quantitative description for a particular mechanism, but with most kinetic studies, the identity of proposed reaction intermediates, eally, should be confirmed by an independent technique, for example, an ex situ spectroscopic or in situ spectroelectrochemical technique (Section 15). It is inherently dangerous to assume the structure or even the identity of a reaction roduct or intermediate solely on the basis of a voltammetric response. Voltammograms are usually displayed as graphical representations of the current endence (of the electrode reaction of interest) as a function of the potential ifference applied between the working and reference electrodes. Three main types of voltammetric wave shape are encountered, viz. sigmoidal or peakshaped; the latter may be symmetrical or asymmetrical. Figure 2.7(a) shows the asymmetric peak-shaped response obtained under transient conditions of C cyclic voltammetry when eqn (2.9) applies at a macrodisc electrode under stationary solution conditions. This class of transient response is characterized by oxidation and/or reduction eak potentials (EpO"and/or E:~) and peak currents (1; and/or y d ) . Figure 2.7(b) shows the sigmoidal-shaped response encountered in steadystate hydrodynamic and microelectrode voltammetry for the same class of 44 Principles of voltammetry Electrode potential defined manner between electrode Fig. 2.6 Schematic diagram illustrating the process of determining the mechanism of an electrode process using voltammetric and spectroelectrochemical techniques. Reproduced by courtesy: Adv. Phys. 0%. Chem. 32 (1999) 1. Copyright, Academic Press. electrode process. Steady-state voltammograms are usually characterized by a and a half-wave potential Figure 2.8 illustrates a limiting current (Ilim) combination of symmetrical and asymmetrical peak-shaped curves obtained in square-wave voltammetry using the waveform depicted in Fig. 2.5(a) and the mechanism in eqn (2.9). The current magnitudes in both transient and steadystate voltammetric techniques are usually proportional to the concentration of the electroactive species and the electrode geometry as well as to the kinetics of the heterogeneous and homogeneous reactions associated with the mechanism relevant to the electrode process being considered. Voltammetric studies Nature of the cuvvent-potential curve 45 Oxidative current Oxidation Reduction Current Current Reductive current - Applied potential (vs reference) - Applied potential (vs referent-e) . 2.7 Commonly encountered voltammetric wave shapes: (a) asymmetric peak-shaped response (e.g. cyclic voltammetry) and (b) sigmoidal-shaped response (e.g. steady-state hydrodynamic voltammetry). Reproduced by courtesy: Adv. Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. 15 . 2.8 Square-wave voltammograms obtained in dimensionless current (q)form of presentation when the waveform depicted in Fig. 2.5(a) is employed. (a) forward half-cycle; (b) reverse half-cycle; (c) square-wave voltammogram obtained from the net current. Adapted from: Laboratory Techniques in Electr~anal~tical Chemistry, Marcel Dekker, New York, 1984, p. 158. Also see Anal. Chem. 53 (1981) 695 for further details. on redox active solids (see Section 17 and also Chapter 5) give a vast range of shapes because the mechanisms are inherently more complex and variable than is the case when the electroactive species are soluble in the solution phase. Principles of voltammetry 46 Cb) f Without unconipensated resistance Current Current Without uncompensated resistance With uncompensated resistance - With uncompensated resistance , 'L' Potential Potential v _____) Fig. 2.9 Effect of uncompensated resistance on (a) cyclic, and (b) steady-state voltammograms. Reproduced by courtesy: Adv. Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. Current With double-layer capacitance / Fig. 2.10 Effect of double-layer capacitance on a cyclic voltammetric response. Reproduced by courtesy: Adv. Phys. Oy. Chem. 32 (1999) 1. Copyright, Academic Press. The D C voltammograms displayed in Fig. 2.7 represent an ideal reversible one-electron transfer process (eqn 2.9) in the absence of IRu drop or background current, although in real experiments the presence of contributions from both these terms are unavoidable. Figure 2.9 shows the effect of uncompensated resistance for both transient and steady-state voltammograms, whilst Fig. 2.10 shows the influence of double-layer capacitance which, usually, is the origin of the background current present in a cyclic voltammetric curve. However, it should be noted that with steady-state (time-independent) voltammetric techniques only a very low (ideally zero) capacitive background current is expected. Both IRu drop and background current terms introduce distortions which must be taken into account when comparisons are made with theory. Unfortunately, many theoretical treatments of voltammetry only encompass the Faradaic current and neglect IR, drop and background current contributions. Cyclic voltammograms can be presented in an alternative format to that shown in Fig. 2.7(a) by using a time, rather than potential, axis (see Fig. 2.1 1). The equivalent parameters to scan rate (time) in steady-state voltammetric Nature of the current-potential cuwe 47 2.11 Current-potential (a), and current-time (b) formats for presentation of a cyclic voltam~nogram.Reproduced by courtesy: Adv. Phys. 0%.Chern. 32 (1999) 1. Copyright, Academic Press. techniques are related to a hydrodynamic parameter (e.g. flow rate, rotation speed) or a geometric parameter (e.g. electrode radius in microdisc electrode voltammetry). Faradaic and non- Faradaic currents t is implied in the above discussion that the measured current contains a contribution from both Faradaic and non-Faradaic (background) terms. 6.1.1 The Faradaic current e Faradaic component is associated with the transfer of electrons resulting from oxidation/reduction ofthe electroactive species ofinterest. The magnitude of the Faradaic current is a function of many parameters and depends on the exact nature of the voltammetric experiment and the mechanism associated with e electrode process (see Section 8 for example). 6.1.2 The capacitive background cuwent As a result of the layer of oppositely charged supporting electrolyte ions being adjacent to the electrode surface [4-61, there is in effect a capacitive arrangement in an electrochemical cell, which charges and discharges whenever the electrode otential is changed. As a result, under conditions of cyclic or linear-sweep oltammetry, a capacitive charging current, Ic, is generated which is directly roportional to the scan rate, since where C' is the capacitance of the double layer per unit area (A) and is usually in the tens of pF ~ m range, - ~ Q is the charge, E the potential, t the time and w the scan rate. C' is assumed to be independent of electrode potential in the above expression, which represents a considerable simplification. Under steadystate or more strictly, the near steady-state conditions which apply in practice at 0 so capacitive currents are very small with this form slow scan rate, dE/dt of voltammetry. 48 Principles of voltalnmetry It will emerge from consideration of the theory for the Faradaic current (IF)that IF oc v1I2 for a reversible process (eqn 2.9) under transient conditions at a macrodisc electrode with mass transport governed by linear diffusion (Section 8.1) while from eqn (2.lo), Ic oc u . The different dependencies of IF and Ic on scan rate means that transient voltammetric experiments will be limited by the scan rate which can be used because ultimately at a sufficiently high scan rate, information associated with the Faradaic current will be swamped by the presence of an unacceptably large capacitive background current. Some of the problems associated with the capacitive current may be minimized by using electrodes of smaller area (and hence lower overall capacitances), but still 0) near retaining transient conditions, or by employing slow scan rate (dE/dt steady-state conditions. 6.1.3 Other background currents Background currents may also, of course, be Faradaic in nature and arise from reduction of traces of oxygen in the solution or the presence of adventitious redox active impurities on the electrode surface or in solution (e.g. oxygen containing functional group on a graphite electrode or water in a non-aqueous solvent). Since these Faradaic background currents are not capacitive in nature they, of course, are not described by eqn (2.10). Even a simple electrode process, in which the electroactive species are only present in the solution phase (eqn 2.9), is quite complex because the overall reaction consists of a considerable number of steps. e e e Mass transport of material to and from the electrode sudace. Heterogeneous electron transfer between solid or liquid (mercury) electrodes and the solution soluble electroactive species. Homogeneous chemical reactions coupled to the electron-transfer process. 7.1 Mass transport In a voltammetric experiment in which the redox active species is soluble in the solution phase, knowledge of the amount of electroactive material reaching the working electrode, and the ability to alter the rate at which material reaches 5~raditionally, the unit oflength used in electrochemistryhas been the centimetre. Accordingly, units for electrode area, the diffusion coefficient, and concentration, for example, will be: cm2, cm2 s l , and mol cm-3 respectively. Use of the metre as a unit of length is becoming more common in electrochemistry inwhich case the units for these parameters would be m2, m2 s-l, and mol m-3 respectively. Basic features of a n electrode process Diffusion due to concentration gradients Convection due to forced movement of solution 49 Migration due to electrical fields Movement of species A . 2.12 Different modes of mass transport of electroactive material to the electrode surface. Chem. 32 (1999) 1. Copyright, Academic Press. Reproduced by courtesy: Adv.Phys. 0%. electrode are crucial for the determination of the reaction mechanism. There three major pathways or modes of mass transport by which electroactive material in solution may reach an electrode (Fig. 2.12). Thus, the total current may be considered to consist of a linear contribution from three sources where Id is the current associated with the diffusion process, I, is the current associated with the migration process and Ic is the current associated with the convection process. iffusion involves the movement of species in solution due to a concentration ent and is governed by Fick's two laws. r one-dimensional diffusion of species A [5,6,9] where Jd is the diffusional flux,6 DA is the diffusion coefficient of species A, [A] is the concentration of A, and x is the distance from the electrode surface. "umber of moles of material diffusing through a unit of area in one second. 50 Principles of voltammetry For diffusion in more than one dimension, the general expression [9] may be used, where V is the Laplace operator and the flux density at the electrode surface, JS, is related to the current, I, by the expression: It follows from Fick's laws that the magnitude of the voltammetric current is dependent upon the value of D, when the electroactive species is soluble in the solution phase. The value of D, in turn, is a function of the solvent, the molecular weight, and molecular dimensions of the electroactive species, the temperature, and the electrolyte and at 25°C is usually in the range cm2s-' cm2 s-* for compounds of molecular weight below 2000 Da [21]. to 5 x At macroelectrodes, under transient voltammetric conditions, semi-infinite linear or one-dimensional diffusion is appropriate. For microelectrode geometries and steady-state conditions, the nature of diffusion is more complex, as significant diffusion may occur in more than one dimension. 7.1.2 Migration Migration results from motion of charged species, which occurs in the presence of a potential gradient. Thus, charged electroactive species and the electrolyte ions may migrate and contribute to the migration current. The total migrative flux Vm)is related to the sum of the migration fluxes for each charged species. For all the charged species (i) present, the migration flux due to a potential gradient (aElax) is given by the Nernst-Einstein relationship (see reference [5], for example): -xiF aE Jm= oi[i]all species i RT ax or more generally for multi-dimensional migrational transport: Jm= -xiF oi[i](BE) RT all species i - where z is the charge on the electroactive species, i. Obviously, migration may be neglected for a neutral species. For charged species, the magnitude and sign of the migration current is determined by the charge on the ion, xi. Thus, if an anion is being reduced it will diffuse towards the (negatively charged) working electrode but migrate to the (positively charged) counter electrode in a potentiostatted three-electrode cell or the reference electrode in a twoelectrode cell. This migration of an anion, away from the working electrode, effectively decreases the magnitude of the measured current (i.e. the current'in the absence of electrolyte will be smaller than in the presence of electrolyte). Via Basicfeaturesofanelectrodeprocess 51 With excess supporting electrolyte T C --------- Current With no electrolyte f - g I I I I I Potential 0 . 2.13 Steady-state voltammograms obtained in the presence and absence of electrolyte for oxidation of A2+ to A3+. Reproduced by courtesy: Adv. Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. See J. Electroanal. Clzem. 337 (1992) 91 for details. analogous logic it follows that when a cation is oxidized it will diffuse towards, but migrate away, from the working electrode (positively charged), so again in this situation the current measured will decrease from the diffusion-only value. Conversely, if an anion is oxidized or a cation reduced, the current will increase relative to the diffusion-only value. Figure 2.13 shows an idealized example of a voltammogram obtained under microelectrode steady-state conditions, with without added supporting electrolyte for the one-electron oxidation of species A2+ (which has a counter anion X-) to A3+ [22]. Clearly, under these circumstances, the measured current is expected to be suppressed by the presence of migration of the positively charged species A2+ away from the working electrode (assumed to be positively charged). However, in most voltammetric experiments a large excess of supporting electrolyte is utilized. Under these conditions almost all of the migrational transport is associated with the supporting electrolyte and there will be a negligible contribution of migration of the electroactive species to the overall appearance of the voltammogram 1131. 7 1.3 Convection Convection current results from the movement of solution as a whole caused by mechanical forces. The flux due to convection (7,) with a solution velocity, v,, in one direction is given by: or more generally, for a velocity vector, v: Working electrodes which have material reaching them via a form of forced convection are known as hydrodynamic electrodes. There are a wide range of hydrodynamic electrodes, the common ones being rotating disc electrodes or ' Es [23], in which the electrode rotates at a fixed frequency and 'sucks up' 52 Principler of voltammetry material to its sudace, and channel electrodes [24], over which the electroactive species flows at a fixed volume flow rate (Section 9). Each of the three mass transport terms defined above can be combined to give a general mass transport equation describing the temporal variation of each species in the electrode reaction mechanism. Thus, for species, A: Note that opposite signs apply for the convection and diffusion terms in eqn (2.19) because the concentration gradients resulting from each of these processes are in opposite directions. Since migration of the electroactive species of interest can be suppressed deliberately by the use of an excess of inert supporting electrolyte, generally, only diffusion and convection have been of interest to the mechanistic electrochemist in the past. However, the addition of supporting electrolyte is sometimes problematical and endeavours to undertake experiments without added electrolyte have recently become much more common (see reference [7]). Diffusion of material to the electrode may be controlled by altering the concentration of the electroactive species in solution and by changing the electrode size from macro-dimensions where, in effect, diffusion is one-dimensional to micro-dimensions, which may support two- or three-dimensional diffusion (Section 10). However, while many electrochemical experiments are conducted under diffusion-only conditions, when the redox active species is soluble in solution, the rate of mass transport may be most easily changed by adjusting the convective transport element. 7.2 Electron tranrfer The voltammogram for a simple oxidative electron-transfer process when the reduced (A) and oxidized (B) forms of the electroactive species are soluble in the solution phase, ~/O,kO,cx A +B + ne- (2.20) can be described (charges on species A and B are omitted for simplicity) in terms of the three parameters: (1) EfO,the reversible formal potential ( V versus reference electrode); the use of Eo, the standard electrode potential, is avoided because most voltammetric experiments are not conducted under conditions of unit activity and standard temperature and pressure (see Chapter 1). (2) ko, the heterogeneous charge-transfer rate constant (cm s-l) measured at EfO;the value of ko determines how far the peak potential (Ep)or half-wave potential (Ell2)is removed from E~O.For fast reactions (e.g. ko 2 1.0 cm s-l) Ell2 E~O.Table 2.1 contains examples of ko values for different systems. le 2.1 Typical values of ko for one-electron oxidation or reduction processes Charge-transfer process Solvent/electrolyte/electrode Temp. (K) Reference k0 (cm s-l) ---- Oxidation of ferrocene Reduction of anthracene Reduction of benzoquinone Reduction of co(H20)2' Reduction of CO(NH~);+ Reduction of RU(NH~);+ Reduction of cyclo-octatetraene Reduction of E U ~ + Acetonitrile/O. 1 M Bu4NC104/ platinum electrode Acetonitrile/O.6 M Et4NC104/ gold electrode Acetonitrile/O.6 M Et4NC104/ platinum electrode 5.6 M HC104 (aq.)/ platinum electrode 0.1 M NaC104 (aq.)/ mercury electrode 0.5 M K2S04 (aq.)/ GC electrode Dimethyl formamide/O. 1 M Pt4NC104/mercury electrode 0.3 M NaC104 (aq.)/ GC electrode "K.M. Kadish, J.Q. Ding, and T. Malinski, Anal. Chem. 56 (1984) 1741. b ~ Bond, . ~ .T.L.E. Henderson, D.R. Mann, T.F. Mann, W. Thormann, and C.G. Zoski, Anal. Chem. 60 (1988) 1878. 7.0. Howell and R.M. Wightman, Anal. Chem. 56 (1984) 524. 'J.M. Hale, Reactions ofMolecules at Electrodes (ed. N.S. Hush), John Wiley, Bath, 1971. Chapter 4. 'F. Marken, J.C. Eklund, and R.G. Compton, J. Electroanal. Chem. 395 (1995) 335. f N.S. Hush, Electrochim. Acta 13 (1968) 1005. 54 Pn'nciples of voltarnrnetvy Reaction coordinate for oxidation reaction Fig. 2.14 Reaction coordinate diagrams for simple heterogeneous electron-transfer processes at an electrode held at a potential of E: for a range of values of a . Reproduced by courtesy: Adv. Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. (3) a, the charge-transfer coefficient; it is a dimensionless parameter and it can be thought of in terms of the reaction coordinate diagram shown in Fig. 2.14. a predominantly affects the shape and not the position of the voltammetric response and, typically, it has a value of 0.5. The relationship between these parameters and the current may be represented by the Butler-Volmer equation: and [B],,o represent the electrode where A is the electrode area and [A],' surface concentrations of A and B. The full theoretical description of a voltammogram therefore is obtained by combining eqn (2.21) with the appropriate mass transport equation (i.e. the appropriate version of eqn (2.19) which leads In the case of fast electronto the required knowledge of [A],,o and [B],,'. transfer kinetics, the theoretical expression derived in this manner, as expected, becomes equivalent to that obtained by combining the Nernst equation with the mass transport equation. An alternative theory to the Butler-Volmer theory for electron transfer results from considerations associated with the Marcus-Hush theory [25,26]. However, in most cases over the potential region of interest in voltammetric studies when species are soluble in the solution phase, use of the simpler Butler-Volmer equation is usually adequate. In contrast, when species are confined to the surface and a slow rate of electron transfer occurs, use of more sophisticated relationships may usually be required (Section 17). 7.3 Homogeneous chemical kinetics It is common for homogeneous chemical reactions to accompany the electrontransfer step. Thus, an electrochemical reaction mechanism may consist of a combination of heterogeneous electron transfer and homogeneous chemical reaction steps, each with their own individual rate constants. If the product, B, Basic features of an electrode process 55 of eqn (2.20) undergoes a first-order, solution-phase chemical reaction with a pate constant, kl, ~ k ' c (2.22) then a complete description of the electrode process when the initial chargetransfer step is reversible is given by the reaction scheme: This frequently observed reaction scheme is commonly designated as an E C or Ere,Cirrevmechanism7 [27,28]. Thus, homogeneous kinetic terms may be combined with the expressions for diffusion and convection (i.e. an appropriately modified version of eqn (2.19)) to give the temporal variation of the concentration of a species in an electrode reaction mechanism. In order to model the voltammetric response associated with an ErevCirrev mechanism, a knowledge of, E:, a , ko and kl is required, or else they may be deduced from a theoretical-experimental comparison, and the set of concentration-time equations for species A, B and C must be solved, subject to the constraints of the utler-Volrner equation and the experimental design. Another example of a common electrode reaction mechanism encountered in voltammetric studies is the ECE (e.g. ErevCirrevErev) mechanism: ) ~ kl , the voltammogram epending on the relative values of (E:)~, . ( ~ f oand sociated with this ECE mechanism consists of two resolved one-electron transfer processes (Fig. 2.15 (a)) or a single overall two-electron transfer process 2.15(b)) or intermediate situations. Obviously, it is possible to construct trode reaction mechanisms with an infinite number of combinations of E C steps [5,6,9,27,28], with different levels of reversibility being associated with both the E and C components. Electrochemical and chemical reversibility A term that should be clearly defined and one that is often used haphazardly in voltammetry is Reversibility. One must make a clear distinction between Electrochemical Reversibility and Chemical Reversibility. 7~ubscripts 'rev' and 'irrev' stand for reversible and irreversible respectively, see Section 7.4. 56 Principles ofvoltammetry f One electron .'. '. \ f ECE response Current One electron response Potential Potential ) - Current T F /\ ECE response / One electron response ,//* _--___-_-____ one ,,tl , I -- I Fig. 2.15 Peak-shaped (cyclic voltammetry) and sigmoidal-shaped (steady-state) voltammograms < ( E ~ O ) ~ and (b) > ( E : ) ~Reproduced . by associated with an oxidative ECE process (a) (E~O)~ Chem., 32 (1999). Copyright, Academic Press. courtesy: Adv. Phys. 0%. (E~O)~ 7.4.1 Electrochemical reversibility The extent of electrochemical reversibility of a process is related to the heterogeneous kinetics of electron transfer at the electrode surface. For a facile electron-transfer reaction, equilibrium is achieved rapidly and the system is defined as being electrochemically reversible. Effectively, this means that both the forward and reverse electron-transfer reaction steps are rapid. Under conditions of electrochemical reversibility, the Nernst equation applies for the process described by eqn (2.20). This Nernst relationship arises as a direct consequence of the fact that the electron-transfer kinetics for the forward and reverse processes are so facile that equilibrium is attained at each potential applied on the time-scale of the particular experiment. Thus, an electron-transfer reaction under conditions of cyclic voltammetry may be termed electrochemically reversible at a scan rate of 50 rnV s-' , but irreversible at 1000 V s-'. The term is therefore a practical, rather than absolute, one and is dependent upon the time-scale of the electrochemical measurement, which means that a process may be reversible under conditions of cyclic voltammetry (e.g. slow scan rate), but irreversible under some conditions of hydrodynamic voltammetry (e.g. fast rotation rate), etc. Cyclic voltammetry under transient conditions 57 7.4.2 Chemical reversibility The level of chemical reversibility is associated with the stability of the species involved in the electron-transfer step. Therefore, if species B irreversibly reacts, as it is formed from the one-electron transfer process, to form species C, as in eqn (2.23), then the overall process (A +- C) would be described as eing chemically irreversible. However, if the chemical step associated with the chemical reaction step of B was sufficiently fast, in both the forward and backward directions, so that equilibrium is effectively maintained on the timescale of the voltammetric experiment, then the whole process would be termed chemically reversible. Thus, concepts related to electrochemical and chemical ersibility can be demonstrated by considering the E C mechanism described eqns (2.26a) and (2.26b), and a range of scenarios. (1) At extremely fast scan rates the electron-transfer step (E) is electrochemically irreversible (Eirrev) and the C step (Cirrev) is outrun. Under these conditions, the process would be described as an electrochemically irreversible process. (2) At moderate scan rates, the C step (Cine,) is outrun, but the E step (Ere,) is now reversible. This would be described as an electrochemically reversible process. (3) At slow scan rates, the E step (Ere,) remains reversible and the C step (Cirrev) is irreversible. This would be termed as an electrochemically reversible and chemically irreversible process. (4) At very slow scan rates the E (Ere,) and C steps (C,,,) are now reversible. This would be described as an electrochemically and chemically reversible process. Chapter 3 will contain detailed discussion of electrode processes where both e heterogeneous charge transfer and homogeneous chemical steps are reversible, while Chapter 4 will focus attention on what occurs when irreversibility or other nuances arise in the description of the electrode processes. Cyclic voltammetry is undoubtedly the voltammetric technique most widely used by non-specialists in the subject of electrochemistry who are interested in understanding the qualitative aspects of the mechanism of a Faradaic electrode rocess. The experimental design usually consists of an electrochemical cell containing the three electrodes described in Section 2 with both the working electrode and solution being stationary. In cyclic voltammetric experiments, 58 Principles of voltarnrnetry Fig. 2.16 Potential-time profile used in a typical cyclic voltammetric experiment. Reproduced by courtesy: Adv. Phys. 0%. Chem. 32 (1999) 1. Copyright, Academic Press. the potential at the working electrode is usually swept at a constant scan rate (v) from an initial potential value of El to a second potential E2 (Fig. 2.16(a), also see Fig. 2.4). O n reaching E2, the direction of the sweep is reversed and, when the potential returns to El, the scan may be halted and again reversed or allowed to continue to a third potential E3 (not shown). Additionally, it is common to cycle through the potential window of interest a number of times to examine the stability of products formed via heterogeneous electron-transfer reactions as well as to detect any new electroactive products formed as a result of their decomposition. Figure 2.4 contains an example where two cycles of the potential are employed. A typical potential-time profile for a single cycle experiment is illustrated in Fig. 2.16. The scan rate is represented by the magnitude of the slope of the potential-time plot so that by this convention v is always said to be positive. The expressions given in eqns (2.27) and (2.28) describe the potential (E(t)), applied at the working electrode, as a function of time: + vt Reverse Sweep: E(t) = -El + 2E2 - vt Forward Sweep: E(t) = El (2.27) (2.28) These equations assume that the initial scan direction is positive, as normally will be the case when studying an oxidation process. In eqns (2.27) and (2.28) it is assumed also that the scan rate is the same in both the initial and reverse sweep directions which need not always be the case (the scan rate may be increased in the reverse scan in order to outrun homogeneous chemical steps associated with species formed by heterogeneous electron transfer in the forward scan). The scan rate may range from a few millivolts per second [5,6] to a million volts per second [29-321. The lower scan rate limit is restricted in value by the effects of natural convection which arises from the build-up of density gradients in the solution resulting from such factors as inadequate thermostatting or mechanical vibration. Natural convection adds to the rate of mass transport of material to the electrode surface and thereby causes the experiment to deviate from the diffusion-only regime. The upper scan rate limit is restricted by capacitive charging (Section 6.1.2) since at very fast scan rates the capacitive current will mask the current associated with the Faradaic process. In cyclic voltammetric experiments and in the presence of excess electrolyte, ideally, the sole form of mass transport to the electrode surface is diffusion, and Cyclic voltammetry under transient conditions 59 . 2.17 Reaction coordinate system in a cyclic voltammetric experiment at a macrodisc electrode for the process A + B e- and mass transport by linear diffusion. Reproduced by courtesy: Adv. Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. + in the case of large macrodisc (millirnetre dimensions) electrodes, the diffusion of material to the electrode occurs in the single dimension perpendicular to the electrode surface. Figure 2.17 shows the reaction coordinate system that applies to the process A + B -I- e under these macrodisc electrode conditions. As will be discussed in Section 10 the situation is more complex for electrodes of smaller (e.g. microdisc) dimensions. Theory of cyclic voltarnrnetry 8.1.1 A reversible process onsider a simple reversible one-electron oxidation process such as the oxidation of ferrocene (species A) to the ferricenium cation (species B) in acetonitrile (0.1 M Bu4NC104 [33,34]). Initially only A is present in solution, the reaction coordinate system in Fig. 2.17 applies and transient conditions are assumed. At the usual macrodisc electrode (radius in mm range), material reaches the electrode by linear diffusion which is perpendicular to its surface (x-direction), and the concentrations of A and B may be obtained as a function of time by solving ick's second law of diffusion as applied to species A and B: Additionally, the problem is subject to a number ofboundary conditions which are defined in Table 2.2, and which are crucial to finding a solution to these differential equations. It should also be noted that the time variation of the electrode potential is given by eqns (2.27) and (2.28). Details of the solution of eqns (2.29) and (2.30) are available in references [5,6]. The theoretical cyclic voltammogram shown in Fig. 2.18 for a reversible oneelectron oxidation process is obtained by scanning from an initial potential (El) 60 Principles of voltammetry Table 2.2 Boundary conditions for the reversible one-electron oxidation process A B e under conditions of cyclic voltammetry + Time coordinate Spatial coordinate Species A Species B Reason for boundary condition t=O t>O x>O [A] = [Ale [A] = [Ale [B] = O [B] = O t>O x=O D A ( ~ [ A ] / ~ ~= )X=O (electrode --(a [B]/a t)x=o surface) x=O In([Blx=o/[A]x=o) = nF/RT(E - E~O) Initially, only A is in solution. At large distances from the electrode, the concentrations of A and B tend to their original values. The rate at which A diffuses to the electrode must equal the rate at which B diffuses away. The Nernst equation for an electrochemically reversible system applies at the site of electron transfer, i.e. the electrode surface. t>O X+OO E~O which is considerably less positive than to a value E2 which considerably more positive than EfO, and then scanning back to El. The forward and reverse peaks constitute a voltammetric wave and the entire current-potential curve represents what is termed a cyclic voltammogram. The shape of the reversible cyclic voltammogram shown in Fig. 2.18 arises for the following reasons. O n scanning the potential from El to more positive values, the concentration of A at the electrode surface ([A],,o) decreases progressively as A is converted into B; this results in an increased concentration gradient of A at the surface of the electrode, and thus the diffusional flux of A to the electrode increases. The flux of material A to the electrode surface is directly related to the current by the expression: As the potential approaches E;, [A],,o decreases even further. Thus, the flux of A to the electrode continues to increase, causing the current to rise. However, eventually [A],=o reaches zero and the flux of A cannot change any further. Under the conditions of this cyclic voltammetric experiment, once [A],=o = 0 the Nernst diffusion layer (the distance from the electrode at which concentration changes in A are associated solely with the electrolysis mechanism and the resulting diffusion is the only form of mass transport) begins to relax further into the solution as the diffusion process tries to equalize the concentrations of A and B throughout the solution. Consequently, at very positive potentials, the Cyclic voltammetry under transient conditions 61 oxidative current reduction oxidation reductive current I I/ ' E ; ~ EpOX E(vs arb. reference electrode) Typical cyclic voltammogram obtained for a reversible one-electron oxidation process at 25°C. Reproduced by courtesy: Adv.Phys. 0%. Chem. 32 (1999)l. Copyright, Academic Press. ux of A drops, and thus the current is seen to decrease at potentials more posin the peak oxidative potential (EpO")to give the characteristic asymmetric ssociated with a cyclic voltammogram. O n reversing the scan, initially a high concentration of B at the electrode surface which decreases as B ed back to A. However, at potentials sufficiently negative compared to =o will return to zero and the same asymmetric peak-shaped response is observed on the reverse sweep as for the forward sweep. Consideration of the above discussion and examination of Fig. 2.18 shows at there are a number of important parameters in cyclic voltammetry. ) The peak potentials, EpOX and E F ~ ,for the oxidation and reduction component of the experiment respectively; for a reversible process at 25"C, the peaks will be separated by 56/nmV (where n is the number of electrons transferred; in the example given in eqn (2.19), n = 1) and E; and will be independent of scan rate. The peak-to-peak separation is usually termed the AEp value for the process. (2) The midpoint, Em, or half-wave potential, Ell2, is related to the peak potentials by the expression ~r~ 62 Principles of voltammetry If A and B have equal diffusion coefficients, Ell2 is identical to the formal reversible potential (EfO).Otherwise, Ellz is related to E: by the expression: E~O For most redox couples, Ell2 only differs from by a few millivolts. respectively (note the base lines from which (3) The peak currents, IpOxand they are measured in Fig. 2.18); for a reversible process at 25'C, the value of the peak current, in ampere is given by the Randles-SevCik expression rd where [Ale or [A],=, is the concentration of A in the bulk solution (other symbols have already been defined) so that the magnitude of the ~ unity. l Equation 4.107 in Chapter 4 provides the general ratio 1 l ~ / $ e is expression for the peak current. The increase in current with scan rate may be explained by the fact that as the scan rate increases, less time is available for the Nernst diffusion layer to relax into the bulk solution phase by diffusion. Consequently, as the scan rate increases, the rate of change of concentration of A at the electrode surface increases resulting in a greater flux of A to the electrode surface which in turn gives rise to a larger observed current. 8.1.2 A n irreversible process When the electron-transfer kinetics are slow (rate-determining) relative to mass transport, the electrode process is no longer in equilibrium and therefore does not obey the Nernst equation. As a result of the departure from equilibrium, the kinetics associated with the rate of electron transfer at the electrode-solution interface (rate constant k;' for the forward direction of the electron-transfer process and kit for the backward reaction) have to be considered when discussing the voltammetry of non-irreversible systems. For the fully irreversible process, kEt can be neglected so that the solution of the equation for the fully irreversible process is achieved by replacement of the Nernst thermodynamic boundary condition (Table 2.2) by a kinetic boundary condition which gives for an irreversible oxidation process: Thus, for a completely irreversible electron-transfer process, the rate limiting step over a wide range of potentials is the electron-transfer step rather than diffusion. k;' is related to the electrode potential and the standard rate constant, kO, Cyclic voltammetry under transient conditions El E (vs arb. reference electrode) 63 E2 . 2.19 Typical cyclic voltammogram obtained for an electrochemically irreversible one-electron oxidation process. Reproduced by courtesy: Adu. Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. utler-Volmer theory (eqn 2.36). kFt = k" exp (1 - a ) ( E - E;)~F/RT (2.36) Use of the Butler-Volmer equation (only the first term in eqn (2.21) for a completely irreversible process) and Fick's laws of diffusion enables the voltammetric response of an electrochemically irreversible process to be calculated. A typical voltammogram associated with an electrochemically irreversible one-electron oxidation charge-transfer process is shown in Fig. 2.19. A number of differences, when compared to the electrochemicallyreversible case, may be noted. (1) There is no reverse peak in an irreversible cyclic voltammogram because the reverse electron-transfer process does not occur at a measurable rate. (2) The peak current, in amperes, at 25°C for an irreversible oxidation process is given by the expression [4-61 I,"" = (2.99 x Note that in eqn (2.37), n, refers to the number of electrons transferred in the E steps before the rate-limiting electron-transfer step whereas n represents the total number of electrons transferred. Comparison of eqns (2.34) and (2.37) under equivalent conditions reveals that the peak current for an irreversible process is lower than the equivalent value for a reversible one. This feature emerges because the kinetics of the electron transfer are relatively slow in the irreversible case, so that during the course of the potential scan, diffusion has more time to relax the concentration gradient of A at the electrode surface. Consequently, when [A],o = 0, the flux of A to Principles of voltammetry the electrode surface for an irreversible process is lower than for the equivalent reversible case, resulting in the occurrence of a decrease in the value of the peak current. The sluggish electron-transfer kinetics also broadens the voltammogram which results in the peak potential for the oxidation process being shifted to a significantly more positive potential compared to the formal potential (E:) for the electron-transfer process. The peak potential is a function of scan rate, unlike the case for a reversible process when the peak potentials are independent of scan rate. As the scan rate increases, oxidation peak potential shift to more positive potentials. 8.1.3 A quasi-reversible process Obviously, if both reversible and irreversible categories of process may exist, then there must be an intermediate case in which the kinetics of both the forward and reverse electron-transfer processes need to be considered. That is, both kFt and kEt (forward and backward electron-transfer rate constants) must be considered in solving the theory, which implies that both terms in the ButlerVolmer equation (eqn 2.21) are required. Such systems are described as being quasi-reversible and, as would be expected for this category of electrode process, the scan rate can have a considerable effect on the nature of the observed cyclic voltammogram. At sufficiently slow scan rates, quasi-reversible processes appear to be fully reversible. However, as the scan rate is increased, the kinetics of the electron transfer are not fast enough to maintain (Nernstian) equilibrium. In the scan rate region, when the process is quasi-reversible, the following observations can be made. The separation of the forward and reverse peaks (AEp)is larger than the value of 56/n mV associated with a reversible process at 25°C. Importantly, AEp increases with increasing scan rate and the value of the standard rate constant for the electron-transfer process, ko, may be calculated from the separation of the peaks in a quasi-reversible process [5,6], provided voltammograms are corrected for solution resistance and background current effects. The peaks become broader as the scan rate increases, and the peak current is below the value expected for a reversible electron-transfer process. The magnitude of ratio of the peak currents 1 1 ~ / 1 ~ ~ 1 is equal to unity for a quasi-reversible system when a = 0.5. It can be seen that the relative rates of electron transfer and the potential scan rate may crucially determine whether voltammograms are observed to be reversible, irreversible or quasi-reversible. Matsuda and Ayabe [35] proposed the following (ko,V) regimes in order to define whether an electron-transfer process will be observed to be reversible, quasi-reversible or irreversible: k" 2 0.3 v ' I 2cm s-' Quasi-reversible: 0.3 v'I2 > k" > (2 x v'I2 cm s-' Irreversible: k" 5 (2 x 1o - ~ )v 'I2 crn s-' Reversible: (2.38) (2.39) (2.40) Cyclic voltammetry under transient conditions 65 It cannot be emphasized too strongly, that considerable care should always be taken when interpreting the results of cyclic voltammetric experiments to ensure that the effects of the double-layer capacitance and uncompensated solution resistance are considered. Peak currents should be corrected for the baseline capacitive charging current (for example by recording a background voltarnrnogram obtained in the absence of the electroactive species and subtracting this response from voltammograrns containing the redox active component). ince the charging current is proportional to scan rate, such background subtractions of this current are particularly crucial at fast scan rates. Uncompensated solution resistance (R,) causes the peak-to-peak separation (AEp)to increase and the peaks to broaden in a cyclic voltammogram which may make a reversible system appear quasi-reversible. In the presence of uncompensated resistance, the value of the applied potential will differ from the actual value by IR,. Modern tentiostats are capable of compensating for the majority of the effects of this tion resistance, by feeding back an additional potential, equal to IR,, to the ied potential. The alternative and perhaps preferred approach when experimental data are to be compared to theory is to measure R, and include this term in the theoretical simulation of the experiment. .I .4 Chemical reactions coupled to the electron-transferprocess ach process observed in a cyclic voltammogram is indicative of an electrode reaction associated with material initially present in the bulk solution or generated at the electrode surface. Consequently, by varying the scan rate of the cyclic voltammetric experiment, new waves may appear as a result of oxidation or reduction of products formed at the relevant scan rate (time-scale). Therere, as well as providing an indication of the reversibility of an electron-transfer ocess as described above, the presence of homogeneous chemical reactions associated with the electron-transfer process may be detected by varying the scan . The example below shows the power of cyclic voltammetry to interrogate mechanisms of electrode reactions, even when they consist of a combination of heterogeneous (electron-transfer) and homogeneous (solution-phase) chemical steps. Examination of the cyclic voltammograms (Fig. 2.20) obtained [36] for the oxidation o f f a c - M n ( ~ 0 (q2-dpm) )~ ~1 VacO),where dpm is the bidentate phoshine ligand Ph2PCH2PPh2species, in acetonitrile (0.1 M Bu4NC104)at slow scan rates ( i 5 0 0 mV s-l) reveals the presence of a partially reversible oneelectron oxidation process having an oxidative peak potential of about 1.48 V (versus Ag/AgCl) and reductive peak potential off 1.41 V. However, the peak currents for the oxidation and reduction processes are not equal. The voltammogram is not fully reversible in the chemical sense because on the time-scale of this experiment (scan rate = 500 mV s-') some of t h e f a c - M n ( ~ ~ ) , ( q ~ - d p m ) ~ l cation Vat+) has isomerized to the mer cationic form (mer+) by the time the potential is swept through the reversible potential for thefacO/faci couple. Confirmation of this conclusion is found by continuing the reverse (reductive) part of the potential sweep through the facO/fac+ couple and noting that a new + 66 Principles of voltammetry Fig. 2.20 Cyclic voltammogram obtained at a platinum macrodisc electrode at a scan rate of -+ f- 500 mV s-I for the ECE mechanism (eqns 2.41a-c) which applies to the oxidation of 1 rnM f ~ c - M n ( C 0 )(r72-dprn)~1 ~ in acetonitrile (0.1 M Bu4NC104)at 20°C. Adapted from: Inorg. Chem. 16 (1977) 155. reduction feature is observed at a potential of fO.95 V, which can be shown to correspond to the reduction of the mer- [Mn(CO), (q2-dpm)~ 1 1 ' (me?+) cation to the m e r - ~ n ( ~ ~ ) , ( q ~ - (meuo) d ~ m uncharged )~l species [36]. If the second cycle of the potential is examined (Fig. 2.20), a new oxidative feature is observed at a potential of +1 .O1 V corresponding to the oxidation of the mero to the meu+ cationic form. Thus, the first part of the mechanism at scan rates <SO0 mV s-' -+ is described by the following EC scheme: However, since the mer+ species may participate in a reversible one-electron = +0.95V) on this voltammetreduction process (E,O" = +1.01 V, ric time-scale, a third reaction needs to be added to the mechanism to give ~r~ -+ t an ECE reaction sequence8 (eqns 2.4 1a-c) . +- -+ he ECE notation is introduced to indicate that the two charge-transfer steps are oxidation and reduction processes respectively (or vice versa). This distinguishes the reaction scheme from an ECE process where both charge-transfer steps are oxidation (or both reduction). Cyclic voltammetry under transient conditions 67 ~t very high scan rates, the facO/fac+ couple appears to be reversible, P concomitantly, the mer+/merO couple disappears. Thus, with I,oX = -Ped; at very short time domains, the fac+ -+ mer+ isornerization step is outrun and the oxidation process becomes a single one-electron charge-transfer process. The kinetics of thefac' + mer+ isomerization and the rates of the electrontransfer steps can, in principle, all be determined quantitatively from the scan rate dependence of the cyclic voltammetry and comparison with a voltammogram simulated according to the proposed mechanism. The isomerization rate constants for this system have been determined by alternative voltammetric methods [37].However, a quantitative cyclic voltammetric approach (Fig. 2.21) has been presented recently for a related isomerization mechanism (see reaction sequence in eqns (2.42a-c)) that occurs during the course of voltammetric oxidation of Theory -0.4 -0.6 0.0 -0.2 0.4 0.2 Potential (V vs FC/FC') . , -0.6 . , . , . , . , -0.4 -0.2 0.0 0.2 Potential (V vs Fc/Fcf) . , . 0.4 + + 2.21 Comparison of experiment and simulation (according to the E C E mechanism in 0 -dpm) ) ~ ( ~ ~ - d p min) dichloromethane ~r at 20°C eqns (2.42a-c)) for oxidation of cis, m e r - ~ n ( ~(yl using a 1-mm diameter platinum disc electrode (a) scan rate, 100 mV s-' (kl = 2.9 s-l), (b) scan-rate, 1000 m~ s-' (kl = 3.4 s-l). Reproduced by courtesy: Inoug. Ckem. 38 (1999) 2005. Copyright, American Chemical Society. 68 Principles of voltammetry cis, mer-M~(co), (11'-dpm) ( q 2 - d p m ) ~in r dichloromethane [38]. -+ E (Efo)l d [cis, mer] , - [cis, mu]+ + e- + [translo (2.42a) (E32 t E + e- [trans]' (2.42~) At 20°C, the voltammetric response was simulated using (E;), = 0.16 V versus Fc/Fc+; (E:), = -0.40 V versus FC/FC+ and kl = 3.1 f 0.3 s-'. (Also see Section 2, Chapter 4). As discussed in Section 7.1, solution-soluble material may reach the electrode surface by diffusion, migration or convection. In cyclic voltammetry at a stationary electrode, and assuming that migration can be neglected in the presence of excess supporting electrolyte, diffusion is the sole form of mass transport. However, additional material may be transported to the electrode by convection. Techniques where convection is a dominant form of mass transport, are described under the heading 'Hydrodynamic Voltammetry'. Hydrodynamic voltammetric methods have major advantages associated with being steady-state techniques (Section 4.2). As a consequence, it is easy to measure these classes of voltammograms as a function of the relevant convective parameter (flow rate, electrode angular velocity, etc.) in the absence of significant problems arising from background capacitive charging current (Section 6.1.2). The potential profile associated with hydrodynamic techniques usually takes the form of a linear or staircase sweep over the potential range in which the oxidation or reduction processes of interest occur. As for cyclic voltammetry, the gradient of the ramp represents the scan rate. However, the scan rate used must be sufficiently slow to ensure that steady-state (within experimental error) is attained at every potential during the course of the voltammetric scan. The upper value of the scan rate that may be used under the steady-state regime is therefore restricted by the rate of convective mass transport of material to the electrode surface. Clearly, the faster the rate of convective mass transport, the faster the scan rate that may be used to generate data that are consistent with the existence of steady-state conditions. With hydrodynamic voltammetry, it is the time parameter associated with the rate of convection that is critical in the examination of the heterogeneous and homogeneous kinetics associated with electrode reaction mechanisms. This term plays a role analogous to that of the scan rate in cyclic voltammetric experi m e n t ~The . ~ importance of this time parameter can be seen by examining the ' ~ i m eis implicit in hydrodynamic techniques whereas it is explicit in transient cyclic voltammetry. Hydrodynamic voltammetry Slow convective transport Fast convective transport f A k B---+ 69 f Intermediates drawn C to electrode \ Electrode 2.22 Schematic representation of an ECE reaction mechanism at a hydrodynamic electrode. ~ e ~ r o d u c by e d courtesy: Adv.Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. articular ECE mechanistic sequence given in eqns (2.24a-c). This mechanism probed in hydrodynamic voltammetry by examining the effective number of electrons transferred, NeE, as a function of mass transport of material to the ode. NeE, which will vary between one and two for this form of ECE anism, gives an indication of the competition between the loss of the intermediates into the bulk solution and the second heterogeneous electrontransfer step. For rapid rates of convective mass transport, NeKtends to a value of one, because the intermediates B and C are swept away from the electrode into bulk solution before the second E step can occur (see Figs 2.15 and 2.22). n contrast, at very low rates of mass transport, NeAtends to two, as B and C remain in the vicinity of the electrode for sufficient time to allow C to undergo an electron-transfer process at the electrode sudace (Fig. 2.22). Thus, in an EGE process, the homogeneous kinetic process competes with mass transport aterial to and from the electrode. order to fully probe the kinetics of the C step in an ECE process of the kind escribed above, the voltammetric response must be measured over a sufficiently e range of mass transport rates so that NeEvaries between one and two. For icularly rapid processes, this requirement implies that very fast rates of mass transport are required in order to avoid Neg being equal to two at all transport rates. Conversely for slow reactions, low rates of mass transport will be required achieve significant deviations from Neff equalling one. Consequently, it can appreciated that it is a study of the competition between the rates of mass transport and chemical kinetics that leads to the quantitative determination of electrode reaction mechanisms in hydrodynamic voltammetry. Importantly, for each hydrodynamic technique, there is one assessable convective transport arameter that directly relates to the kinetic time-scale. .1 Rotating-disc electrode voltammetry he rotating-disc or RDE consists of a disc electrode, made from a suitable working electrode material [23,39,40], surrounded by a non-conducting sheath. The complete electrode assembly is constructed so that the sheath and electrode 70 Principles of voltammetry I PTFE sheath Fig. 2.23 Schematic representation of a rotating-disc electrode. Reproduced by courtesy: Adv. Phys. 0%. Chem. 32 (1999) 1. Copyright, Academic Press. Flow profile from below r=O Flow profile from side Fig. 2.24 Convective flow profile associated with a rotating-disc electrode. Reproduced by courtesy: Adv. Phys. Org. Chem. 32 (1999) 1. Copyright, Academic Press. are flush (Fig. 2.23). Typically, the disc electrode faces downwards into solution and is rotated around an axis perpendicular to and through the centre of the disc. Under these conditions, a well-defined flow pattern distribution is established, as illustrated in Fig. 2.24; in effect, solution is sucked towards the electrode and then flung outwards. The following experimental conditions must be met in order to ensure compliance with the well-established theory for this technique under steady-state conditions: (1) The electrode rotates in a single plane perpendicular to the axis of rotation. (2) The frequency of rotation is stable with respect to the time required to conduct a voltammetric scan. (3) The electrode rotation frequency is sufficiently low to prevent localized turbulent flow. This typically means that the rotation rate is in the range of 4-50 HZ. Hydrodynamic voltammetry 71 The crucial parameter which controls the time-scale over which electrode reactions are examined at a RDE is the electrode angular velocity, o(rad s-I), \which is related to the rotation frequency, f (Hz), by o = 2nf. The related rotating ring disc electrode is discussed in Section 4.4.1 of Chapter 5. Channel electrodes Figure 2.25 shows a schematic diagram of a channel electrode, which consists of an electrode embedded in the wall of a rectangular duct through which solution is made to flow under well-defined laminar steady-state conditions [4O,4l]. In channel electrode voltammetry, the flow is treated as being twoimensional in the x-y plane. O n entering the channel, the solution velocity profile is essentially plug flow. However, the effect of friction at the walls causes retardation of the solution flow in the x-direction (Fig. 2.26). After a distance 1, (the entry length) from the entrance, the hydrodynamic layers from each wall merge, and the flow regime established is laminar in form [42,43] in which separate layers (laminae) of solution have characteristic velocities reaching a maximum (Vo)at the centre of the channel. The parabolic ape of the ultimate velocity profile is therefore given by the following velocity . 2.25 Schematic representation of a channel electrode. Reproduced by courtesy: Adv. Phys. 0%. Chem. 32 (1999) 1. Copyright, Academic Press. Growing boundary layers Inviscid flow A Entry length (1,) Boundary layers merge / Fully developed laminar flow over electrode surface 2.26 Convective flow profile associated with a channel electrode. Reproduced by courtesy: Adv.Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. 72 Principles of voltamrnetry components where V,, Vy, and V, are the velocities in the x,y, and r directions respectively, Vo is the velocity of the solution in the centre of the channel, h is half the cell height and d is the width of the cell. The velocity of the. solution in the centre of the channel is related to the solution flow rate, Vf, by the expression: It is this flow rate, Vf, or centre line velocity, Vo, parameter that is critical in determining the time-domain over which chemical processes can be monitored. Generally in order to develop laminar flow over the electrode, 1, should be sufficiently long so that ideally where Re is the Reynolds number which in terms of the kinematic viscosity v k is defined as: Laminar flow is generally achieved for Re < 2000. Laminar flow is obtained either by a gravity-fed flow system [24] as shown in Fig. 2.27 or by a pressurized flow system. In the gravity-fed flow system, the inlet reservoir is at a greater height than the outlet and the solution may flow through a variety of capillaries of differing diameter. Thus, the flow rate is determined by the difference in the height of the solution in the inlet reservoir and the level of the outlet tip as well as the diameter of the capillary through which the solution flows. For typical (Fig. 2.25) cell heights (2h) of 0.04 cm and cell widths (d) of 0.6 cm, flow-rates in the range IO-"-IO-' cm3 s-' are readily attainable using this apparatus. A pressurized flow system [44,45] has been recently developed which is designed to force solution through a flow cell so as to induce much higher velocity gradients at the electrode surface. Flow is achieved by applying a large pressure at the inlet reservoir end of the system, while maintaining the outlet at atmospheric pressure, otherwise the design is similar to the gravity-fed system. Values of Vo as large as 75 m s-I can be obtained using this apparatus (h = 0.01 cm, d = 0.2 cm), allowing the determination of first-order homogeneous kinetic parameters as high as lo5 s-' from steady-state measurements [44]. A major advantage of the channel electrode technique, in addition to enabling very fast reactions to be studied, is its ability to be utilized in conjunction with other techniques (e.g. photochemical or spectroscopic). This advantage has Hydrodynamic voltammetry 73 Counter electrode Flow I Channel unit Capillaries Reference II 7 Schematic representation of a gravity-fed channel electrode flow system. Reproduced by courtesy: Adv. Phys. Og. Chem. 32 (1999) 1. Copyright, Academic Press. been utilized effectively in the investigation of the photoelectrochemistry of (co),(q2-dpm)~1 in acetonitrile [46]. As discussed in Section 8.1-4, in ence of irradiation, this complex undergoes a one-electron oxidation process forming the fac- [Mn(C0)3(q2-dpm)Cl]+ cation which then isomerizes l ] + Upon irradiation of the channel to the u n e v - [ ~ n ( ~ O ) , ( q ~ - d p m ) ~cation. ectrode surface by 385-nm light, a new oxidative feature is seen at a less positive potential than obtained for the parent oxidation wave (Fig. 2.28). The half-wave potential for this new photoproduct corresponds to that expected for ation of m e r - ~ n ( ~ O ) , ( q ~ - d ~ mConsequently, )Cl. it is logically postulated the electrode reaction mechanism in the presence of light is CE in nature, the C step involving the photo-isomerization of the fac species light C fac +mer E mer ; i mer+ (2.47a) + e- (2.47b) A value of 0.07 s-' (light intensity = 40 mW cmF2)was obtained for the firstorder rate constant associated with the C step by examining the flow rate ependence of the limiting current associated with the mer oxidation wave [46]. 74 Principles of voltammetry E/ V (vs SCE) Fig. 2 -28 Channel electrode voltammogram for oxidation of 1.42 r n f a~c - ~ n(co)? ( ~ ~ - d c~1 m ) in acetonitrile (0.1M Bu4NC104)while being irradiated with light at 390 nm. Solution flow rate is 1o - ~cm3 s-' . Adapted from: J. Phyi. Chem. 97 (1993) 1601. (4 Reference electrode Elytrode , Electrode \ Solution in Fig. 2.29 (a) Schematic representation of a wall jet electrode, and (b) convective flow profile Chem. 32 (1999) 1. associated with a wall jet electrode. Reproduced by courtesy: Adv. Phys. 0%. Copyright, Academic Press. 9.3 Wall-jet electrodes In the wall-jet electrode configuration, a high, fixed-velocity jet of fluid is fired through a nozzle of diameter, a, directly towards the middle of a disc electrode (radius = rl), whose centre coincides with that of the nozzle as shown in Fig. 2.29. The solution thus impinges upon the electrode surface and is circulated outwards towards the extremities of the electrode surface, but the recirculated solution can never reach the electrode a second time. Hydrodynamic voltammetry 75 El 12 E (vs arb. reference electrode) Voltammogram obtained for a simple reversible one-electron transfer process at a hydrodynamic electrode. Reproduced by courtesy: Adv. Phys. Og. Chem. 32 (1999) 1. Copyright, Academic Press. A survey of the use of the theory of hydrodynamic voltammetvy n all forms of hydrodynamic voltammetry, electroactive material reaches the electrode via diffusion and conve~tion.'~ In the cases of the RDE and channel electrode configurations under steady-state conditions, solutions to the mass transport equations are combined with the Nernst equation to obtain the reversible response shown in Fig. 2.30. A sigmoidal-shaped voltammogram is obtained in contrast to the peak-shaped voltammetric response obtained in cyclic voltammetry. An overview of the theory for hydrodynamic voltammetry is available in nce [9] where it is shown that there are two critical parameters that are itatively important in this and other forms of steady-state voltammetry: (1) The limiting or mass-transport-limited current, Jim At sufficiently positive potentials where the mass-transport process associated with an oxidation process is rate-determining, the current for a process of the kind A -+ B n e reaches a fixed limiting current value (hi,) that is determined solely by the mass transport of material to the electrode surface. Thus, the level of reversibility of the chargetransfer process is not relevant to the value of I&. Under these conditions, material is continuously replenished at the electrode surface by convection, in contrast to the situation in a cyclic voltammetric experiment where depletion occurs and a peak-shaped response is observed. Table 2.3 gives the analytically rived expressions for the limiting currents obtained for a process of the kind -+ B ne- at the three electrode types discussed in this section. (2) The halfwave potential, Elp For a reversible redox couple in which the oxidized and reduced species have very similar diffusion coefficients, the + + l0Nligration is assumed to be negligible if the usual excess supporting electrolyte is present. Principles of voltarnrnetr), Table 2.3 Expressions for the limiting current obtained for the process A -+B ne- at a range of hydrodynamic electrodes + Electrode Convective flow parameter Expression for limiting current, hi, RDE ChE Angular rotational velocity, w Volume flow rate, Vf 0 . 6 2 n ~ ~ v,D 'l6 ~ [I ~ ~ WJE Volume flow rate, Vf 1 . 5 9 n ~ ~ ~ / ~ v ; ~ ~ ~ [ ~ L] ~~ a: -~ ~ ~/ ~ 1 1 3 / ~ ] ~ w ~ F = Faraday constant; A = electrode area; D = diffusion coefficient; w angular rotational velocity; [Ale = bulk concentration of A; vk = kinematic viscosity; Vf = volume flow rate; w =width of channel electrode (ChE); x, =length of electrode in the direction of flow; h = channel flow-cell half-height; d = channel flow width; a = nozzle diameter of wall jet electrode; rl = radius of wall jet electrode. n - slope: ~Kv intercept: E l I 2 1 -40 Potential (mV) ~ ~ 0.925n~~~/~[A]~w(~~x~/h~d)'/~ 8 -20 1 I 0 I 20 I , 40 Potential (mV) Fig. 2.31 'Log plot7form of analysis of a steady-state voltammogram for a reversible process at 25OC. half-wave potential approximates to the formal electrode potential E ~ O . For a reversible electron-transfer process, Ellz will not vary with the rate of convective mass transport to the electrode surface. Additionally, for a reversible ( ~I )~/ ,I ] ,the so-called 'log electron-transfer process a plot of E versus 1 0 g ~ ~ [ plot', will have a slope of 2.303RTlnF or 59/nmV at 25°C. Figure 2.31 contains an example of a 'log plot9analysis of a reversible steady-state voltammogram at 25°C. It follows, from analysis of the equation for a reversible process (see Fig. 2.31), that the difference in the quartile potentials (E314- Ell4)is given by the very simple expression 2.303RTlnF log 9 or 56/n mV at 25°C. Measurement of E3I4therefore provides an alternative form of (two points) data analysis to the 'log plot9 (many data points) analysis for the determination of the reversibility or otherwise of a hydrodynamic voltammogram. As for all voltammetric techniques, sluggish electron-transfer kinetics require the application of an additional potential (overpotential) to drive the electrontransfer process at the same rate as for the equivalent reversible process. Thus, the observed voltammogram is broadened relative to that found for a reversible Hydrodynamic voltammety, 77 E (vs arb. reference electrode) Comparison of voltammograms obtained for a reversible and irreversible one-electron oxidation process at a hydrodynamic electrode having equal half-wave potentials. Reproduced by courtesy: Adv.Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. process (see Fig. 2.32 where an irreversible and a reversible process with idenave potentials are shown for comparison). However, note that, as , the limiting current is identical to that observed for the reversible ed a potential sufficiently positive (oxidation) or negative (reducspect to the half-wave potential is applied. It should be noted that, as in the case of homogeneous kinetics, competition exists between heteroectron transfer and transport of material to and from the electrode nce, as the rate of convective mass transport increases, an initially ectron-transfer process may become quasi-reversible and, finally, at very high rates of mass transport, irreversible. Thus, a knowledge of the theoretical and experimental dependence of Ellz and/or hi, on the convective time-scale enables a quantitative account of an electrode process to be given. is is entirely analogous to the dependence of the cyclic voltammetric response on scan rate (Section 7.4.1). A number of studies have been conducted using fast rates of convective mass transport in order to probe the kinetics of heterogeneous processes [45,47,48]. or example [45] the heterogeneous kinetics for the reduction of benzoquinone at platinum electrodes in acetonitrile solutions was probed by examining the variation of the mass transport in a channel electrode as a function of the flow rate (over the range 10-~-3.5 cm3 s-l) of solution over the electrode surface. A value of 0.30 cm s-' was obtained for the standard heterogeneous rate constant, which is in good agreement with the value obtained using the transient cyclic voltammetric technique [B]. As discussed in Section 6, solution resistance and capacitive current can lay a significant role in voltammetry. Due to the typically low scan rates and steady-state conditions employed, capacitive charging presents a relatively small problem in hydrodynamic techniques. However, solution resistance affects the appearance of the voltammogram in much the same way as a decrease in the rate of heterogeneous electron transfer, as is the case in the transient 78 Principles of voltammetvy cyclic voltammetric technique. That is, uncompensated resistance broadens the voltammetric response because the additional IR, potential term is still present in hydrodynamic voltammetry. Thus, great care has to be taken to ensure that resistance artefacts are accounted for when assessing the kinetics of heterogeneous processes using hydrodynamic and, indeed, all other voltammetric techniques. However, note that the limiting current value measured in steady-state techniques, unlike the peak current in transient techniques, is unaffected by the solution resistance or slow electron-transfer kinetics. As noted earlier, varying the rate of convective mass transport of material to the electrode surface allows the elucidation of reaction mechanisms via monitoring of the dependence of mass transport on a particular experimental parameter (e.g. N& for an ECE mechanism). As usual, comparison of the experimental result with theory derived for a particular reaction mechanism, provides quantitative detail concerning the kinetics. Microelectrodes (also referred to as ultramicroelectrodes) are, as the name implies, tiny electrodes which possess at least one dimension that is sufficiently small so that the mass transport regime is a function of its size under steady-state conditions [49]. In practice, the upper limit of this small dimension is approximately 20 pm because with larger sizes, natural convection is likely to occur under very slow scan rate conditions required to achieve a steady-state voltammogram (Section 8). This effect is likely to interfere with the interpretation of results, which are assumed to be made under diffusion-only conditions. The lower limit is in the nm range, which approaches that associated with molecular dimensions. Attractive features of microelectrodes operating under steady-state conditions, relative to conventionally sized macrodisc electrodes and transient conditions, include increased current density, reduced charging currents, and reduced ohmic drop [7,49]. The latter feature permits experiments to be conducted in highly resistive media, particularly, for example, in non-polar solvents [7] or solutions containing an absence or near absence of added supporting electrolyte [7]. Further aspects of the exploitation of these advantages of microelectrode voltammetry under near steady-state conditions is contained in reference 7. Microelectrodes exist in a variety of geometries, the most important of which is the microdisc electrode. Microbands, cylinders and rings are other possibilities while the microsphere or hemisphere is often used to aid theoretical development since the rate of mass transport is invariant over the electrode surface. Some of the different possibilities'for microelectrode designs are illustrated in Fig. 2.33. Voltammetric studies at microelectrodes 79 Schematic diagram showing microdisc (a), band (b), hemi-cylinder (c) and ring (d) electrodes. Reproduced by courtesy: Adv. Phys. Org. Chem. 32 (1999) 1. Copyright, Academic Press. A schematic diagram of a rnicroband electrode. The arrows represent the directions of Fi diffusion to the electrode. Reproduced by courtesy: Adv.Phys. 0%.Chem. 32 (1999) 1. Copyright, Academic Press. 1 rinciples of the theory ofrnicroelectrode voltarnrnetry ionally, macrodisc electrodes operating under transient, linear, n-only conditions are characterized by one-dimensional mass transport h diffusion takes place normal to the electrode surface (Section 8.1). In contrast, with microelectrodes, such mass transport is found only at short times after electrolysis is initiated when the diffusion layer is small compared to the shortest dimension of the microelectrode. At longer times, the rate of mass transport varies locally over the electrode surface with the edges of microdisc and line electrodes, for example, receiving a greater current density owing to ossibility of convergent or radial diffusion, as illustrated in Fig. 2.34 for the ular case of a microband electrode. It is this additional mass transport by radial diffusion which leads to the significantly enhanced mass transport under steady-state conditions. or the case of a microdisc electrode of radius re, radial (convergent) diffusion to a steady-state limiting current given [7,49] by eqn (2.48) is equation shows that the limiting current scales with the electrode radius, rather than area, thereby reflecting the non-uniformity of the current density. Princiyles of voltammetry The transition between linear (shorter times) and radial (longer times) diffusion is revealed if the equation relating to the current following a potential step at a microhemisphere electrode is considered: where A is the electrode area (A = 2 n r 3 , and t is the time. At short times, the second term dominates and the mass transport is Cottrellian [5,6] so it depends on t-'l2 as expected from linear diffusion, while at longer times, when radial diffusion is dominant, the current tends to the steady-state (timeindependent) value predicted by the first term. However, note that microsphere and microhemisphere electrodes are atypical microelectrodes in that their very high symmetry dictates that the current density is uniform over the entire electrode surface. This is not the case for the microdisc, microband or microring electrodes shown in Fig. 2.33 as edge mass transport dominates. Implicit in the above discussion is the concept that current-voltage curves measured at microelectrodes at sufficiently slow scan rates of potential are characterized by a mass-transport-limited current plateau rather than a peak current as in linear sweep voltammetry at a planar macrodisc electrode. Figure 2.35(a) shows a typical microelectrode voltammogram for an electrochemically reversible system under near steady-state conditions. Of course as the scan rate is increased, the voltammetric behaviour at a microelectrode converges to that expected for linear diffusion (Fig. 2.35 (b)), until at sufficiently fast scan rates a characteristic transient-type cyclic voltammetric response is obtained when the mass transport is predominantly governed by linear diffusion. The increased rate of mass transport associated with the shrinking of the electrode size means that electrode processes which appear electrochemically reversible at slow scan rates with large electrodes may show quasi-reversible or irreversible electrode kinetics when examined under steady-state conditions at a microelectrode. However, the use of very fast scan rates may also enable departures from reversibility to be detected with transient mode microelectrode methods, provided adequate correction for charging current and resistance effects can be made under the latter conditions. The use of microelectrodes, therefore, represents an opportunity to apply two very powerful approaches to the determination of fast heterogeneous electrode kinetics, and rate constants in excess of 1 cm s-' have been reported via use of both the slow scan rate (radial diffusion) steady-state and very fast scan rate (linear diffusion) microelectrode voltammetric approaches [49]. The above discussion implies that chemical information may be extracted from microelectrode experiments either via steady-state measurements obtained under slow scan rate conditions, or via transient, often cyclic, voltammetric approaches utilizing fast scan rate techniques. In the former approach, measurements of the mass-transport-limited current are made as a function of the electrode size, which is the electrode radius for the case of a microdisc electrode. This aspect of quantitative evaluation of steady-state microelectrode data may be illustrated by reference to the ECE mechanism (eqn sequence 2.24a-c) Voltammetric studies at microelectrodes 81 Potential .35 Diagrams showing current-voltage curves measured at a microdisc electrode at scan rates corresponding to the limits of (a) radial diffusion and (b) linear diffusion. Reproduced by courtesy: Adv. Phys. Org. Chem. 32 (1999) 1. Copyright, Academic Press. k is the first order rate constant for the C step. Kinetic and mechanistic ation for this mechanism may be gleaned in an analogous manner to the , channel, or wall-jet electrode steady-state techniques, through examination of the effective number of electrons transferred, N g , but in the case of steady-state microelectrode voltammetry by studying NeKas a function of microdisc radius. Figure 2.36 shows that Nen varies between 1 and 2 as the value of the electrode radius increases. The former limit, NeE= 1, corresponds to the case of fast mass transport (small radius) where B is lost to bulk solution before it can be transformed into C while the latter, NeE= 2, case is reached for slow mass transport (large radius) where B is nearly completely transformed into C near the electrode surface. The parallel of steady-state microelectrode voltarnrnetry to hydrodynamic voltamrnetry, where rotation rate, rather than electrode radius, is the time-dependent variable (Section 9) is obvious. The dimensionless parameter ictates [49] whether the kinetics of the homogeneous first-order chemical reaction in the ECE mechanism are 'fast' or 'slow'. The term r : / ~gives an approximate measure of the time taken to move out ofthe diffusion layer of the 82 Principles of voltarnrnetry Fig. 2.36 A working curve showing the relationship between Neffand the dimensionless parameter ( k r : / ~ )for an ECE mechanism. Reproduced by courtesy: Adv. Phys. 0%.Chern. 32 (1999) 1. Copyright, Academic Press. microdisc, while the term ( k - l ) corresponds to the time taken for appreciable amounts of B to transform into C. Examination of the theoretically generated working curves for an E C type mechanism, analogous to the curves given in Fig. 2.36 for the E C E mechanism, suggest that for microdiscs of radii 1-10 pm, lifetimes of B in the range 0.1-100 ms should be amenable to quantitative study under steady-state conditions. A detailed summary of steady-state microelectrode voltammetry, and its application to studies on homogeneous chemistry, is given in the review by Montenegro [49]. As noted above, the dynamic range of microelectrode voltammetric experiments may be extended by the use of very fast scan rate techniques to give transient conditions where the mass transport approximates that seen for conventional cyclic voltammetry. However, caution in interpretation of the results is advisable under the theoretically 'tricky', intermediate conditions, where significant contributions from both linear and radial diffusion apply. For very fast scan rate experiments, the major advantage in using a microelectrode resides in its intrinsically small area which leads to a correspondingly reduced capacitance of the electrode-solution interface associated with its double layer. As noted in Section 6.1.2, it is the current associated with the capacitance which gives an upper limit to the scan rates accessible, if a Faradaic signal (arising from electron transfer between the electrode and solution-phase species) is not to be masked. The capacitance scales directly with the electrode area (eqn 2.10) so that there is a clear advantage in employing smaller-sized microelectrodes for both transient and steady-state measurements. Clearly, it also follows that the R,Cr cell time constant is lowered by the use of micro rather than macrodisc electrodes, which also leads to improved voltammetric performance, as does the decreased IR, (Ohmic) potential drop obtained with the smaller electrode size. Semi-integration and semi-d%ferentiation 83 u 0 -1 E/ V (vs SCE) -37 Voltammograms (with background correction) for the reduction of 10rnM 2,6-diphenylpyrylium perchlorate in acetonitrile at a 5-pm radius platinum disc electrode using scan rates of: (a) 250 (b) 150 and (c) 75 kV s-'. Adapted from J. Electroanal. Chenz. 324 (1992) 33. n practice, useful measurements can be made with fast scan rate cyclic voltammetry under transient conditions at microdisc electrodes to probe lifetimes of unstable species which approach the nanosecond regime. This requires the use of potential scan rates in the kV s-' or greater range. An elegant example of a very fast scan rate study concerns the electro-reduction of the 2,6-diphenylpyrylium cation in acetonitrile solution [50] using a 5-pm radius platinum microdisc electrode. Electrochemically, the cation is reversibly converted into the radical via a one-electron reductive charge-transfer process. The resulting radical can subsequently dimerize in an irreversible second order homogeneous reaction to form a species which displays no electroactivity within the potential range examined. Figure 2.37 displays cyclic voltammograms measured at scan rates between 75 and 250 kV s-'. At the fastest scan rate (250 kV s-') examined, re-oxidation of the radical is observed on the return scan. This chemical reversibility is progressively lost as the sweep time becomes comparable with the time taken for the radical to dimerize. Interpretation of eak current data in terms of an EC2 mechanism, where C2 is ;he notation for a second-order reaction, permitted the dimerization rate constant to be evaluated as 2.5 x lo9M-' s-' which corresponds to a half-life of 20-50 ns for the cation radical under the conditions studied. It was shown in Section 10 that microdisc electrode voltammetry enables steadystate, time-independent I-E curves to be obtained at slow scan rates, while transient voltammograms can be observed at fast scan rates. That is, the 'time endence' can be introduced by increasing the scan rate. The converse opern of removing the 'time dependence' of a transient voltammogram may be hematically by use of semi-integration, which is a form of fractional 84 Principles of voltammetry 11.1 Some valuable properties of the semi-integral When applied to a voltammetric experiment, semi-integration with respect to time, produces a quantity M(t) which has properties that are intermediate between those of the charge Q(t), obtained by the usual form of integration, and I(t) itself: Via this mathematical operation, and for a diffusion (linear) controlled process at a macrodisc electrode, the time (t-'I2) dependence is effectively removed from the transient voltammogram so that a sigmoidalshaped voltammogram, having many of the characteristics of a steady-state response, is obtained. Figure 2.38 shows the application of semi-integration to a reversible process, while Fig. 2.39 represents an example of applying the same mathematical processes to a quasi-reversible cyclic voltammogram. A valuable property of the semi-integral is that M(t) can be a unique function of the applied potential E(t) and, hence, be totally independent of the history by which the electrode arrives at E(t). Therefore, even the actual voltammetric technique employed to obtain the semi-integral is irrelevant as are, for example, the time or scan rate dependence of the cyclic voltammetric experimental data from which the semi-integral is derived. This valuable property is achieved when the following conditions are satisfied: (1) The voltammogram starts from a potential where the current flowing is effectively zero. (2) The electrode is planar, or effectively so. (3) Mass transport is effectively semi-infinite. Fig. 2.38 A reversible cyclic voltammogram obtained at a macrodisc electrode with mass transport by linear diffusion presented in the conventional form (a), and after semi-integration (b). Note the complete overlap of forward and reverse scans in the serni-integral form of presentation. Adapted from: Anal. Chem. 72 (2000) 3492. Semi-integvation and semi-d@eventiation r + Theoretical cyclic voltammogram for a quasi-reversible electrode process A + B neFi emi-integral as a function of potential. In this dimensionless form of presentation an k0/2/= = 0.145, a = nFv/RT, D is the common diffusion coefficient (DA = DB) and a is assumed to be 0.5. In the semi-integral, M ( t ) and M(t),,, are the semi-integral and maximum value of the semi-integral at time t. (at) is defined in Anal. Chem. 37 (1965) 1351 and J. Phys. (1972) 1160. Adapted from: Anal. Chem. 45 (1973) 1298. x (4) Convection and migration are absent, so that transport is solely diffusive. (5) The electrode reaction is of the kind A F+ B ne-. (6) The electron process generates a solution-soluble product. + e electron transfer is uncomplicated by preceding, succeeding, or adsorption reactions. n-Faradaic current is absent, or has been corrected for. compensated resistance is absent. t is this 'uniqueness' of M ( t )that has led to powedul methods of 'global analysis' of reversible or quasi-reversible cyclic voltammograms and correction for uncompensated resistance. The theoretical aspects of the use of semi-integration the useful properties of the transformed data for calculation of E:, D, ko, and cx or the potential dependence of a,associated with reversible or quasi-reversible rocesses are available in references [52-601. Measurement of uncompensated resistance by semi-integration1' e simplification of data analysis achieved by semi-integration is readily made evident by analysis of the effect of uncompensated resistance on a reversible cyclic voltammogram. The one-to-one relation between M ( t ) and E(t) in the "kidaped with permission from Anal. Chem. 72 (2000) 3492. Copyright, American Chemical Society. 86 Principles of voltammetry final condition listed above in Section 11.1 holds, even in the presence of uncompensated resistance (R,), when E(t) is interpreted as the true potential Etr,,(t) experienced by the electrode, rather than as the potential Eapp(t)that is applied to the cell. The relationship between these two potentials is Figure 2.40 shows the effect of uncompensated resistance on the cyclic voltammogram (Fig. 2.40(a)) and its semi-integral (Fig. 2.4O(b)). Figure 2.40 is scaled exactly as Fig. 2.38, so that the differences between the two arise solely from the presence of resistance. The abscissa in Fig. 2.40 is Eapp(t),though it is labeled with an unsubscripted E ( t ) ,as is common practice. Notice that in the presence of uncompensated R,, the two branches of the semi-integrated voltammogram no longer overlap, the backward branch lying above the forward branch. Consider the two points labeled m2 and ml in Fig. 2.41. ml is an arbitrary point on the forward branch of the M(t) versus E(t) curve, while m2 lies on the backward branch at the same ordinate level. The two points thus correspond to equal semi-integral values, M (tz) = M (tl). By the uniqueness property, this means that the true electrode potentials must have been equal at the two instants, tl and t2, to which the points correspond, so that Et,,(t2) = E,,,(tl). The gap between the two semi-integral branches arises from the resistance present, as comparison of Figs 2.38 and 2.40 attests. The equality of the true potentials, at the instants t2 and tl, can be combined with the general eqn (2.51), with the Fig. 2.40 A reversible cyclic voltammogram obtained at a macrodisc electrode in the presence of uncompensated resistance with mass transport by linear diffusion presented in the conventional form (a), and after semi-integration (b). Note the absence of complete overlap of forward and reverse scans in the semi-integral form of presentation, unlike the situation prevailing in Fig. 2.38 where no uncompensated resistance is present. Adapted from: Anal. Chern. 72 (2000) 3492. Semi-integration and semi-dtferentiation 87 1 Use of semi-integration to calculate the uncompensated resistance assocated with a cyclic voltammetric experiment. Adapted from: Anal. Chern. 72 (2000) 3492. subscript 'app' omitted, to give e terms I(tl)and I(t2)are the values ofthe currents at the points labeled il and i2 on the cyclic voltammogram itself. Hence, measurements of the appropriate rdinates of the four points ml , mz, il and i2, permits R, to be calculated. ince ml was selected arbitrarily, it follows that an unlimited number of simialculations may be made, ideally resulting in the same R, value. Obviously, the precision of the measurement will be greatest where the separation between the branches of the semi-integral is widest, that is, in the vicinity of Ell2. O n the s of precision, use of the mid-section of the semi-integral between (Ell4) (E314)of the wave height is recommended. Clearly, once the value of Ru is calculated, theoretical analysis of cyclic voltammograms can be undertaken inclusion of the value as shown in Fig. 2.42 for oxidation of ferrocene in igh resistance solvent dichloromethane [60]. viously, it is also possible to semi-differentiate a voltammogram to generate a symmetric peak-shaped curve from an asymmetric reversible cyclic voltammogram or indeed use any other form of operator from the field of fractional or conventional (first derivative etc.) calculus. Figure 2.43 contains an example of the asymmetrical responses obtained both in normal (Fig. 2.43(a)) and first 88 Principles of voltammetry Fig. 2.42 Voltammograms at 25OC for reversible oxidation of 0.7 rnM ferrocene at a 0.5 mm radius platinum disc electrode in dichloromethane (0.1 M Bu4NPF6)using a scan rate of 1V s-' ; (a) cyclic voltammogram; (b) semi-integral of voltarnmetric data; (c) calculation of R, using data in (b) and eqn (2.53); (d) comparison of cyclic voltammogram simulated with R, = 0 ( . . . ), with R, = 2500 ohm as calculated from data in curve (c) (- - - -) and the experimental curve (-). Adapted from: Anal. Chem. 72 (2000) 3492. derivative (Fig. 2.4307)) cyclic voltammetry which may be compared with the symmetrical semi-differential voltarnmogram (Fig. 2.43(c)).Additional details of the mathematics and other advantageous features of semi-integration and semidifferentiation (often called convolution voltammetry) are available in references [4-6,13,52-601. 12 General features associate voltammetric experiments e modelling of The difficult part of deducing an unknown mechanism from a voltammetric experiment is quantitatively extracting the chemical information from the I-E-t curve. To do this, a model must be constructed to predict the current for a given set of conditions and a postulated mechanism. An electrochemical model is concerned with the concentration distributions of chemical species (and possibly the potential distribution). If the concentration distributions of all the chemical species dissolved in the solution phase can be simulated, the current flowing at the 'working electrode' may be calculated by integrating the concentration gradient zones at the electrode surface to gwe the total flux. 12.1 Inforrmatio required to solve voltammetric theory Three pieces of information are required to define the experimental system: Kinetics The rate of electron transfer and its potential dependence can be described by the Butler-Volmer or Marcus-Hush relationships, with the former Modelling of voltammetric experiments 89 Comparison of (a) normal, (b) first derivative and (c) semi-differential forms of presentaFi tion of a cyclic voltammogram for a reversible one-electron oxidation process. Adapted from P.H. nieger, Electrochemistry, 2nd edn, Chapman and Hall, New York, 1994. being adequate on most occasions for standard voltammetric studies when the electroactive species is soluble in solution (Section 7.2). An electron transfer often initiates a cascade of homogeneous chemical reactions by producing a reactive product which could be a radical, radical cation, radical anion, or inorganic compound in an unusual oxidation state. Each step in the mechanism can be described mathematically by a rate equation, to form another part of the electrochemical model. The rate law for the overall sequence is probed by the voltammetric experiment. transport Each of the three mass transport components may be described matically, as discussed in Section 7. The effect of all three modes of mass rt may be summed giving the partial differential equation (PDE) re CA is the normalized concentration of species A (CA = [A]/[AIo). tion (2.54) is equivalent to eqn (2.19) with [A] being replaced by CA. quation (2.54) describes how the normalized concentration of species A at a given point varies with time due to diffusion, convection, and migration, relative to the bulk concentration, [Ale. This mass transport problem is the second major component of the electrochemical model and it depends only on the electrode geometry, the nature of which defines the Laplace (V2)operator. Assuming a background 'supporting' electrolyte is used in excess to eliminate migration effects from the experiment, only a diffusion-convective equation is necessary to describe the mass transport. 90 Principles of voltammetry Experiment The experimental technique controls how the mass transport and rate law are combined to form the overall material balance equation. Thus, migration effects may be eliminated by addition of supporting electrolyte, steady-state measurements eliminate the need to solve the equation in a timedependent manner and the addition of excess substrate can reduce the kinetics associated with a second-order reaction to pseudo-first-order. The material balance equations (one for each species), with a given set of boundary conditions and parameters (electrode type, cell dimensions, flow rate, rate constants etc.) define the I-E-t surface traversed by the voltammetric technique. If all three pieces of information are known, the concentration distributions of the species throughout the course of the voltammetric experiment may be described mathematically by a set of simultaneous PDEs. The way these equations are perturbed during the course of the voltammetric experiment, and the boundary conditions required to solve them, may also be deduced from these three pieces of information. 12.2 Methods used for soloing voltammetvic theory The final component of the theoretical model is the development of a suitable mathematical method to solve the relevant system of simultaneous PDEs, often as a function of time as the concentration distributions evolve during the experiment. The difficulty of solving these systems depends on the complexity of the material balance equations and as to how they are linked to each other by the kinetic terms. For a simple electron-transfer reaction (e.g. eqns (2.1) and (2.2)), it is often possible to solve the diffusion-only limiting current relationship analytically under steady-state conditions. For example, the analytically deduced limiting current steady-state microdisc equation for a spherical electrode is given by eqn (2.55) Ilim = 4nnFD[AIoy, (2.55) For hydrodynamic electrodes, in order to solve the diffusion-convective equation analytically for the steady-state limiting current, it is necessary to use a first-order approximation of the convection function(s) (such as the Lkvcque approximation for the channel electrode). Approximate expressions for these hydrodynamic steady-state mass-transport-limited currents, as noted previously, are contained in Table 2.3. For planar or spherical electrodes, and under conditions where the mass transport is a diffusion function in only one dimension, it is possible under some circumstances to solve, analytically, the diffusion equation for the reversible process as a function of time to give, for example, the peak current expression for a linear sweep voltammogram (eqn 2.34). It is also possible to solve the material balance equations for the spherical electrode at steady-state for a few first-order mechanisms [61]. In order to tackle problems involving secondorder homogeneous reactions or kinetics, or more complex mechanisms, or to solve time-dependent equations or model geometries with more complex mass Summary of principles of voltammetry 91 transport, it is necessary to resort to numerical methods, a vast number ofwhich are available. ver the past few years, several commercial electrochemical simulation packages have appeared. ' ~ h e s epackages are currently only capable of simdating mass transport in one spatial dimension and are therefore restricted to modelling vo1tammeG-y at large planar and rotating-disc macroelectrodes, or spherical & hemispherical electrodes of any size (macro or micro). Speiser [62] has undertaken a thorough assessment of these simulation packages in his recent review. Use of a commercially available package to simulate the cyclic voltammograms for a complex reaction mechanism is given in Chapter 3. or many mechanisms, the steady-state Ell? or NeKvalue is a function of just one or two dimensionless parameters. If simulations are used to generate the 'working curve' to a sufficiently high resolution, the experimental response may be interpolated for intermediate values without the need for further simion. A free data analysis service has been set up [63] via the World Wide b (http://physchem.ox.ac.uk:8000/wwwda.htrd) based on this method and currently supports spherical, microdisc, rotating-disc, channel, and channel microband electrode voltammetry for a range of mechanisms. receding discussion in this chapter has been aimed at providing the reader book with a broad understanding of the experimental and theoretical considerations related to the case of the techniques of voltammetry when the electroactive species are soluble in the solution phase. It is now possible, appropriate, to briefly summarize the general features that are inherent 11 voltammetric techniques so that general principles are emphasized and techniques of voltammetry discussed above employ a form of electrolysis, t an appropriate form of Faraday's law is coupled with the mass transport ons to give the theoretical description of the voltammogram. -1 Application ofFavadayJs law Consider an electrode-solution interface as in Fig. 2.44 and then apply Faraday9s aw to the electron flow (current) in the circuit for the electrode process A B ne-. At the electrode-solution interface [13] + 92 Principles of voltammetry electrode solvent (electrolyte) electrode reaction: A+B+ne- Fig. 2.44 Transport processes occurring at the electrode-solution (electrolyte) interface for the reaction A + B ne-. Provided by courtesy: K.B. Oldham, Trent University, Peterborough, Canada. + -Ji where and J; are the flux densities (mol cm2s-') of A and B respectively at the electrode surface and other symbols are as defined previously. It follows from the equalities in eqn (2.57) that the flux density, and, therefore, the mass transport ofA and B, are intimately related to current by Faraday's Law; this is why it is essential to understand the nature of transport processes or how species move to and from electrode surfaces in electrochemical systems. 13.2 A general approach to undevstanding a voltammetvic pvoblem In trying to understand any voltammetric problem, the following matters related to mass transport need to be taken into account: (1) Which species present at the electrode-solution interface are transported? (2) What kind of transport mechanism is important in the problem being considered? (3) What is the relative contribution of the different kinds of transport in the problem being considered? (4) How is the voltammetric current controlled by the transport? (5) How is the size of the electrode related to the transport? (6) How are the transport, and heterogeneous and homogeneous chemical reactions combined? 13.2.1 identifying the species transported Let us consider some typical electrode processes [13] and identifj. the chemical species that must be transported by use of bold type and those that do not by use of italics. Example 1 The electrodeposition of metallic copper onto a solid electrode Summary ofprinciples of voltammetry 93 Example 2 The electrodeposition of metallic copper into a mercury electrode to form an amalgam. Unlike example 1, metallic copper can now diffuse into the mercury electrode and is therefore transported into the electronic conductor. In this case both the c u 2 + and Cu+ ions are soluble in solution and are Example 4 Ag(so1id) + C1- (solution) ---+ AgCl(so1id) + e- In all these examples, and generally for all reactions, including those involving attached to electrodes (see later), at least one ion must be transported in to balance the charge with that of e-. Thus, the total number of species orted is always 2 1. The transport mechanisms tion (ions only) occurs in response to a gradient of potential. sion (ions and molecules) occurs in response to a gradient of concentration. (3) Convection (ions and molecules) occurs in response to a gradient ofpressure. .3 A comparison of transport mechanisms (1) The migration current, which is applicable to charged species only, and is generally not large in magnitude, can be modelled mathematically with relative ease via the Nernst-Einstein equation and can be avoided by the resence of excess supporting electrolyte. iffusion, like the migration current, is generally small in magnitude, is mathematically easy to model via use of Fick's Laws, and is always present. (3) Convection may give rise to large currents, is mathematically difficult to model, but can be avoided by eliminating solution motion. or the RDE the general mass transport equation in the absence of homogeneous chemical kinetics is given by 94 Princlplesofvoltammetry where r, x and 6' are cylindrical polar coordinates (see Fig. 2.23), and v,, v,, and v~ are the respective components of the solution velocity. For the channel electrode, the mass transport equation also contains convection and diffusion in the absence of homogeneous chemical kinetics and is given (see Fig. 2.25 and Section 9.2 for an explanation of symbols) by Other voltammetric techniques have mass transport equations described above or else they are available in references [5,6] or [9]. 13.2.4 Facton that control the current in a voltammetric experiment (1) Transport control by migration, diffusion, and convection. (2) Control by the chemistry of the redox reaction which may be thermodynamic (reversible process obeying the Nernst equation on the voltammetric time-scale within experimental error) or kinetic (heterogeneous or homogeneous rate laws). (3) Mixed transport and chemical control (usually the case). 13.2.5 The (I-E) voltammetric cuwe In any form of voltammetric experiment, the dependence of I (t) on E (t) needs to be known, with I(t) being measured and E(t) being imposed (sometimes vice versa). For example, in the simple potential step experiment shown in Fig. 2.45(a), where A is converted to B, current control will occur solely by diffusion when the rate of the A -+ B e- heterogeneous electron-transfer step for the oxidation reaction is inherently so fast that it is not rate-determining. This will be true at potentials in the limiting current region, where I(t) is measured as in Fig. 2.45(b) (macrodisc electrode, transient case). Furthermore, if A is not a charged species, it cannot be transported by migration, so that mass + Fig. 2.45 A potential step experiment (a) which causes the reaction A -+B diffusion-controlled manner (b). + ne- to occur in a Comparison of voltammetric techniques 95 transport occurs solely by diffusion. Under these conditions I (t) depends on the electrode size and has a characteristic mass transport time A I D (A, electrode area; D, diffusion coefficient). For a typical value of D cm2s-l) and for a rnacrodisc electrode having an area of 10 mm2 rV A/D(macroelectrode) 10-I cm2 -- lop5 cm2 s-l % 20 min which is a long experimental timescale. In contrast, for a microdisc electrode of area 10 pm2 &ich is a relatively short time-scale for the mass transport process. An analogous result based on consideration of time-scales also occurs r conditions of cyclic voltammetry. Thus, under both the potential step itions described above and when the current is changing rapidly with potential (cyclic voltammetry) the current is often diffusion-controlled at a macrodisc electrode, but under control of both the electron transfer, and transport by diffusion at a microdisc electrode. For a macrodisc electrode, the purely diffusive component of the experiment is given by the CottreIl ( n whereas for a microdisc electrode, equation, I(t) = FAD^''^ [ ~ ] ~ /t)'I2, the time-independent steady-state equation, Ili, = 4nFreDA[AIo,applies. If a combination of electron transfer and diffusion control occur under linear potential sweep conditions, the resultant voltammetric response is constructed from the two terms that may control the experiment (Cottrell and steady-state ressions), with the measured value of the current at a given potential being roximately given by whichever of the possible current terms is smaller at that potential, that is, whichever of the steps in the process is rate-determining. n any quantitative evaluation of the mechanism and kinetics of an electrode process, the experimental technique and electrode geometry must be selected match the kinetic time-scales. The time domain over which a first-order mogeneous chemical process occurs, and which needs to be matched by the voltammetric experiment, for example, would be l l k , where k is a firster rate constant. As concluded in the preceding qualitative discussion, this matching of electrochemical and chemical time domains is achieved by varying the rate of mass transport via convection, electrode size/shape, or potential scan rate. The access to solution to theoretical models and solutions for all techniques, made possible by numerical mathematical methods (Section 12), enables a quantitative comparison of the kinetic discrimination of various voltammetric techniques to be developed. 96 Principles of voltammetry 14.1 A quantitative comparison of the kinetic discn'mination of homogeneous reactions at common electrode geometries under vokammetric steady-state conditions Each of the electrode geometries and voltammetric techniques has a characteristic time-scale parameter (t,) which is a function of the time required to reach a steady-state [9,61]. For example, for an EC or ECE mechanism, dimensionless homogeneous rate constants (K) for a first-order reaction and dimensionless time (r)both may be formulated [9] using a characteristic time-scale, as in eqn (2.62) K = kt,; where k is the first-order homogeneous rate constant and t is the time. The dimensionless homogeneous rate constant, K , is the unique parameter on which the steady-state NeEor Ell2-values depend. Thus, the so-called 'working curve', deduced from numerical modelling of the process, generates a plot of Ell, or NeEversus log K ,in order to completely define the steady-state behaviour for a particular mechanism at a specific electrode geometry and voltammetric technique. For example, the 'working curve' consisting of a plot of Neg versus loglo (kr;/D), shown in Fig. 2.36, represents the case for a microelectrode of radius re under steady-state conditions for a species undergoing an ECE mechanism where the initial material in bulk solution has a diffusion coefficient D and a first-order rate constant k. Thus, the term ~ $ Z / Dused in this plot is dimensionless, as required; here r;/D is the characteristic time-scale parameter. The equivalent parameters for other steady-state techniques are available in reference [9]. The recent availability of working curves for a range of common mechanisms at a number of electrode geometries [9,61], allows a broad quantitative comparison of the kinetic discrimination of common electrode geometries to be made for both first- and second-order homogeneous processes. For example, Table 2.4 shows the approximate range of time-scales and rate constants (for ECE and ECzE reactions) that may be measured under conditions of steadystate voltammetry at various electrode geometries [9,61]. The range of rate constants given in this table has been calculated from the values of the relefrom vant dimensionless rate constant which give values of 1.1 and 1.9 for the 'working curve' for each geometry and are considered to represent suitable thresholds between which a kinetic process is 'voltammetrically visible' [64]. The calculations undertaken to obtain the results contained in Table 2.4 are based on the following (typical) assumptions related to the range of experimental parameters available with the relevant techniques: (1) All species present in the bulk solution have diffusion coefficients of 1 x loH5cm2s-'. The concentration of the electroactive species present in the bulk solution is 1 x lov6mol ~ m - The ~ . kinematic viscosity of the solvent is in the range 1 x lop3-1 x cm2 s-'. (2) Microdisc electrodes of radii 0.6-70 pm are used for steady-state measurements without problems associated with natural convection. The upper limit le 2.4 A comparison of the kinetic time-scales accessible with steady-state voltammetry using common electrode configurationsa Electrode configuration Range of accessible time-scales (t,) Range of log [dimensionless rate constant (K)] Range of rate constants (k) which can be measured ECE EC2E ECE(S-') E C 2 E (mol-' cm3 s-') 6 x lo3-2 x 1012 1 x lo4-6x 1012 6 x lo4-2 x 10'' 4 x lo1-8 x 1012 Hemispherical Microdisc Rotating-disc Wall-j et 400 ps-5 s 400 ps-5 s 0.2-1 0 s 1 ms-100 s 3.82 3.93 2.47 3.03 4.31 4.47 3.71 3.93 2 x 10-~-2 x lo5 6 x 1 0 - ~ - 7 x lo5 9 x lop2-1 x lo3 2 x l0-~-2 x lo5 Channel Conventional Microband Fast flow 0.1-1 0 s 3 ms-0.5 s 10 ps-10 ms 2.45 2.75 2.45 3.43 3.47 3.43 1 x lop2-5 x lo2 1 x lo4-4 x lo9 2 x 10-'-1 x lo6 3 x lo5-4 x 10" 2 0 ~ 1 0 ~ - 4 ~ 1 10 ~~ 1 0 ~ - 3 ~ 1 0 ~ ~ aAdapted from Adv. Phys. 0%.Chem. 32 (1999) 1. Principles of voltammetry has been chosen as 70pm, above which natural convection becomes significant. Dimensionless rate constants for spherical and microdisc electrodes were interpolated from the working curves of Alden and Compton [61]. Hemispherical electrodes are experimentally realized using hanging mercury drops for macroelectrodes and mercury-coated microdisc electrodes of radii (0.6-70 pm) for microhemispheres. For the RDE, the operating range of rotation frequency is assumed to lie between 1 and 50 Hz and a typical electrode radius is 0.25 cm. Again, dimensionless rate constants were interpolated from working curves. In the case of the wall jet electrode, experimentally accessible flow-rates are assumed to lie in the range 1 x 1o-~-I cm3 s-' , with a typical jet diameter 0.3 mm impinging on an electrode of radius 0.1-1 cm. Dimensionless rate constants were interpolated from the working curves simulated using the Backwards Implicit method [65]. MacPherson et al. [47,48] have recently miniaturized the wall jet electrode so that this technique can be applied to a uniformly accessible microelectrode system to give a micro-jet electrode. cm3 s-' through Flow-rates are reported in the range 2 x lop3-5 x a nozzle of radius 30-60 pm at distances varying from tens to hundreds of microns from the microdisc electrode. For the channel electrode, the following typical parameters were used: d = 0.6 cm; 2h = 0.06 cm; w = 0.4 cm; x, = 0.1-0.4 cm; Vf = 1 x 10-~-0.3 cm3 s-' . In the case where a microband electrode was used, the smallest microband which could be fabricated reliably (x, = 1pm) was used. Dimensions used for the fast-flow-cell were: d = 0.2 cm; 2h = 0.01 cm; w = 0.15 cm. This can accommodate band electrodes of xe = 1-1 00 pm, and flow-rates of 1 x 10-~-2.5 cm3 s-l. Dimensionless rate constants for the channel electrode method were interpolated from the surfaces of Alden and Compton [63]. The results of calculations of the kinetic discrimination for a range of steadystate techniques considered in this book and using the above-listed experimental parameters and approximations are summarized graphically in Figs 2.46-2.48. The overall rate constant 'window' (Fig. 2.36) of each geometry is the product of the range of kinetic visibility at a particular geometry (Fig. 2.35) and the range of time-scales that can be accessed (Fig. 2.34). It is clear from Fig. 2.34 that the hydrodynamic electrodes have a narrower kinetic 'window' (i.e. less inherent kinetic discrimination) than diffusion-only systems, but that convection allows shorter time-scales to be accessed. 14.2 A comparison of the homogeneous kinetic discrimination of steady-state and transient experiments Extremely high scan rates of potential can be used to accelerate the linear sweep or cyclic voltammetry time-scale beyond that of steady-state methods. The time-scale accessible by cyclic voltammetry is given by the expression Comparison of voltammetric techniques 99 ~ ' 1 s tflow channel Microband channel Channel Micro-jet Wall-jet Rotating-disc Microdisc Hemisphere -2 -3 1 0 -1 2 log (Tirnescale (s)) 2.46 Time-scales accessible by steady-state voltammetry at common electrode geometries. Adapted from Adv. Phys. 0%. Chern. 32 (1999) 1. Fast flow channel Microband channel Channel Wall-jet Rotating-disc Microdisc Hemisphere -2 -1 0 1 2 3 4 5 6 7 log (Tirnescale (s)) Fig. 2.47 Range of rate constants that can be measured by steady-state voltammetry with common electrode configurations for an ECE process. Reproduced by courtesy: Adv.Phys. 0%. Chern. 32 (1999) 1 . Copyright, Academic Press. 100 Principles of voltammetry Fast flow channel 1 Microband channel Channel Wall-jet Rotating-disc Microdisc Hemisphere log (Timescale (s)) Fig. 2.48 Range of rate constants that can be measured by steady-state voltammetry with common electrode configurations for an EC2E process. Reproduced by courtesy: Adv. Phys. 0%.Chern. 32 (1999) 1. Copyright, Academic Press. RT/ F v [5]. Typically, scan rates in the range of 10-1 0,000 V s-I are used in cyclic voltammetry as the upper limit of the scan rate used when macrodisc electrodes are employed which correspond to timescales in the p s range. However, it should be noted that when microdisc electrodes are used in the transient regime, scan rates as fast as 1 x lo6 V s-' have been used, which achieve a time-scale in the region of 10 ns [29-3 11. The price paid for use of very fast scan rates in cyclic voltammetric experiments is precision. In this, and other, transient methods at short time domains, the current changes so rapidly with time, that a small error in the measurement of the time at which the current is sampled, introduces a large error in the calculated rate constant. Of course, analogous problems arise with precision when steady-state methods are pushed to their limits (e.g. turbulent flow conditions are associated with the use of extremely high flow-rates in hydrodynamic voltammetry). Transient methods, as previously noted, are also complicated when short time domain measurements are undertaken in the presence of large capacitive currents. Some of the practical difficulties related to the use of the different voltammetric techniques are outlined in Table 2.5. Electrochemical synthesis and subsequent isolation of gram or greater amounts of a pure sample of product B, via the electrode process A -+ B ne-, requires + Parameter Cyclic voltammetry (transient) Precision Time errors; capacitive currents become large at high scan-rates Reduced IR, drop; significant errors in electrode dimensions Modelling Time-dependent; high-dimensional (I-E-t) working surfaces Two-dimensional diffusion requires use of sophisticated numerical methods of analysis Use with hybrid methods, e.g. spectroscopic detection A relatively large cell is required to maintain bulk concentration which may present practical difficulties Reduced cell size is compatible with most spectroscopic apparatus. May pick up electrical noise from other equipment Electrode: practical considerations Static solution means that passivating films may deposit on the electrode. However, electrode is easily removed and cleaned. Electrolysis products may build up in the bulk solution. Natural convection may become significant at low scan-rates Apparatus considerations Ohmic drop compensation necessary at high scan-rates Difficult to fabricate desired electrode dimensions accurately. Electrode elevation and recession is much more significant. Lithographically fabricated microbands are very fragile and cannot be cleaned mechanically. Natural convection may interfere with diffusion-only responses of larger electrodes (e.g. >25 pm) Small currents require high amplification and shielding to eliminate noise "Adapted from Adv. Phys. Org. Chem. 32 (1999) 1. icroelectrodes (steady-state) ydrodynamic Flow profile is perturbed by electrodes which are not flush or smooth Generally steady-state. Apart from RDE, models are two-dimensional due to convection Spectroscopic and photochemical methods are easily incorporated into the small, transparent channel flow cell. R D E is less versatile If electrode becomes passivated and mechanical cleaning is necessary, the cell must be disassembled (introducing cell height or electrode-jet distance variation). For ChEs by-products formed at the counter electrode cannot reach the working electrode Flow-regulation apparatus must be calibrated. Cell must ideally be designed to ensure laminar flow in order to simplift modelling. R D E rotation must have stable frequency and be axially symmetric 102 Principles ofvoltammetry exhaustive or bulk electrolysis of electroactive material A at a large-size working electrode, although, of course, exhaustive electrolysis of A is frequently achieved on the microscale (mg to pg) level in mechanistic studies, at smallersized electrodes. Thus, bulk electrolysis can be a useful large-scale synthetic tool and, indeed, is widely used for commercial production of metals such as Cu, Zn, and A1 (Chapter I), and for synthesis of some important organic compounds. Bulk electrolysis experiments, when the data are analysed in a coulometric form, also enable the n-value in a voltammetric electrode process to be determined, provided no additional reactions occur on the longer time-scale (typically minutes to tens of minutes) associated with such experiments. The bulk electrolysis method may be applied in a constant potential (potentiostatic) or constant current (galvanostatic) modes. 15.1 Theory of bulk electrolysis In a controlled potential electrolysis (CPE) experiment, the working electrode is held at a constant potential until the solution is exhaustively electrolysed. The electrolysis potential is usually chosen to be slightly more positive than the Ell2 value of a species being oxidized or slightly more negative than the Ellz value of a species being reduced, and hence just into the limiting-current region of a hydrodynamic voltammogram. A galvanostatic experiment, as the name implies, is one in which the current is maintained at a constant value for the desired period of time. In a coulometry experiment, usually undertaken during the course of bulk electrolysis, the current passed as a function of time is integrated by means of an electronic integrator or coulometer to give the charge. Faraday's law of electrolysis requires that the quantity of electricity passed or charge (coulombs) is directly proportional to the amount of chemical reaction (equivalents) that has taken place at an electrode. Thus [66], where I is the current at time t and Q is the charge or number of coulombs passed during the course of the electrolysis experiment. Alternatively, this equation may be expressed as N = Q/nF (2.64) where N is the number of moles of electroactive material oxidized or reduced, F is Faraday's constant and n is the equivalents per mole, that is, the number of electrons transferred per molecule or ion that has undergone electrolysis. It can be seen from eqn (2.64) that coulometric monitoring of the bulk electrolysis experiment involving the reaction A -t Bfne- can be used to calculate n, ifthe number of moles ofA initially present in the bulk solution is known. Conversely the equation may be used to calculate the number of moles of species A intially present, and hence the concentration of A in solution (provided the solution Bulk electvolysis 103 volume and n are known). It also follows from eqn (2.64) that in any experiment in which the current is kept constant for the duration of the bulk electrolysis. hen a constant potential exhaustive electrolysis is carried out under conditions where a constant level of convection is maintained for the duration of the experiment, and the background or non-Faradaic current is relatively insignificant, the Faradaic current, I, for a simple A -+ B ne- process decays exponentially with time, t , according to the relation [66] + I = Ii exp (-pt) (2.66) where Ii is the initial Faradaic current and p is the mass-transport-controlled rate constant for the reactant species undergoing electrolysis. Typical current charge versus time plots for this simple mechanism are shown in Fig. 2.49. For efficient electrolysis, a high value of p or very efficient mass transport by convection is desirable. When the potential is held at a value corresponding to the limiting current regime of a hydrodynamic voltammogram, p can be where k,,, is the mass transport parameter for the reactant species, A is the area of the electrode and V is the volume of the solution. The mass transport parameter depends on the reactant diffusion coefficient, the solution viscosity and the relative velocities of the solution and electrode surface, that is, the rate of stirring or flow rate of the solution or rotation rate of the electrode. T o have a large value ofp, the solution or electrode must be rapidly stirred and the cell must have a high A/V ratio. rovided there is only a negligibly small background current present, and unimass transport conditions operate throughout the course of the electrolysis t, the current is proportional to the concentration of electroactive the process A -+ B ne-. Thus, when the current has decayed to a value of approximately 0.1 per cent of its initial value, the electrolysis is 99.9 per cent complete. Due to the exponential relationship of the decay of the current with time, the rate of electrolysis decays with time as illustrated + (a) Faradaic current and (b) charge versus time plots obtained for CPE experiments under constant convection conditions. 104 Pvinciples of voltammetvy in Fig. 2.49. If mechanistic nuances are present, as is the case with ECE and related reactions, the current-time and current-charge curves may, of course, become much more complex but in principle may be analysed to enable the rates of homogeneous reactions coupled with the electron-transfer reaction to be calculated [66]. 15.2 Cellsfor bulk electrolysis Two different cells routinely used for CPE in the author's laboratories [67] are described in detail in this book: (a) a large-volume cell (100mL) for electrosynthesis of gram quantities of material; (b) a small-volume cell (5 mL) for electrolysis of relatively small amounts of material (up to 200 mg); this is predominantly used for coulometry with voltammetric and/or spectroscopic monitoring of the products formed. 15.2.1 Large-volume electvolysis cellfov electrosynthesis A schematic diagram of a large-volume cell used for electrosynthesis is given in Fig. 2.50. The large-volume GC cup serves as the working electrode and also holds the solution to be electrolysed. The reference electrode is contained Fig. 2.50 Schematic diagram of CPE cell and associated experimental arrangement used for electrochemical synthesis experiments: (a) nitrogen gas bubbler (b) reference electrode (c) spring clamp (d) Teflon o-ring (e) platinum basket auxiliary electrode within inner solution compartment (f) 1.0-1.7 pm porosity glass frit (g) magnetic stirrer bar (h) glass outer housing (i) GC cup working electrode forming outer solution compartment, and 6) glass supports for counter electrode compartment. Reproduced by courtesy: J. Chem. Sol. Perkin Trans. 2 (1995) 1365. Copyright, Royal Society of Chemistry. Bulk electrolysis 105 in the solution which is in contact with the working electrode. The auxiliary electrode consists of a platinum gauze basket which is arranged symmetrically inside the working electrode. Separating the working and auxiliary electrodes is a glass cylinder with a porous glass frit in the base within which the platinum auxiliaty electrode sits. The separation of these solutions is required to prevent product generated during the course of the electrolysis at the auxiliary electrode reacting with the products of interest that are formed at the working electrode. The design is similar to that described by Moinet and Peltier [68], and Fry [69]. p he important features of the cell are given below. ( 3 ) There is a porous glass frit, separating the working and auxiliary electrode compartments, which has a surface area of approximately 20 cm2. The large frit surface area enables adequate current to be passed between these two electrodes which in turn allows fast electrolysis times to be achieved. owever, the use of a large frit also increases the amount of leakage between the two compartments. In order to test the level of mixing of solutions that occurs between the two compartments, fluorescein dye may be added to the working electrode compartment, and the change in colour of the auxiliary electrode compartment can be monitored as a function of time by UVspectroscopy. An experiment of this kind shows that after six hours electrolysis conditions, 10 per cent mixing of the solutions occurs using a 1.O-1.7 pm porosity glass frit (porosity no. 5) and the cell epicted in Fig. 2.50. In contrast, a 10-20 pm porosity glass frit (porosity o. 4) allows a much larger level of mixing of nearly 40 per cent to occur over a three-hour period, making the use of the larger porosity glass frit unacceptable with this particular cell design. The higher porosity frit does, of course, permit a slightly higher current to flow, thereby allowing shorter electrolysis times, but generally the disadvantage of a large increase in solution mixing between the two compartments more than offsets the advantage gained by a faster electrolysis time. (2) The working and auxiliary electrodes are arranged as symmetrically as posh respect to each other to assist the attainment of an even potential ent distribution over the surface of the working electrode [70]. The volumes of the working and auxiliary electrode compartments in the cell are approximately 100 mL and 65 mL, respectively. The IR, drop which is always present in any bulk electrolysis experiment, should be distributed as uniformly as possible over the electrode surface. This requires that the frit separating the two compartments, ideally, should also be arranged as symmetrically as possible. For practical reasons the highest possible symmetry condition is not achieved, mainly because of leakage problems and the difficulty in obtaining a cylindrical frit of optimal diameter and pore size. The asymmetry present in the cell in Fig. 2.50 results in a higher current density and, therefore, more electrolysis occurring at the base rather than at the sides of the GC working electrode cup, and also in a lower overall current ow than the maximum which is theoretically possible. For this particular cell, conditions are set so that current levels at the start of the electrolysis are 106 Principles ofvoltammetvy in the 0.2-1 A range, the exact value depending on the concentration of the species being electrolysed. In order to limit the amount of mixing between the working and auxiliary electrode compartments, exhaustive electrolysis experiments must be completed in less than two hours. This means that for species with molecular weights of the order of 1000 Da, gram quantities of electrolysed product may be obtained. (3) The reference electrode, for example, A ~ / A ~(0.05 + M AgNO,; CH3CN) for electrolysis in acetonitrile solvent, is positioned as close to the surface of the working electrode as possible to ensure a potential control which is as uniform as possible [7I]. (4) The working and auxiliary electrode compartments are stirred using a magnetic stirrer bar to increase the value o f p (see eqn 2.64). (5) The working and auxiliary electrode compartments are easily degassed. (6) Large currents of up to 1 A can be obtained with this cell configuration when a standard 0.1 M concentration of supporting electrolyte is present. However, that rate of electrolysis may slow down prematurely in some situations unless an adequate concentration excess (at least 1.5 times) of supporting electrolyte to compound being electrolysed is used. This premature rate decrease is highly significant when ion pairing occurs between charged products of the electrolysis and the electrolyte, thus decreasing the effective electrolyte concentration and lowering the overall conductivity of the solution. The impact of precipitation of insoluble products containing electrolyte ions may also need to be considered, for similar reasons. (7) The cell can be easily assembled and dismantled for cleaning. (8) The potential required for the electrolysis may be determined by taking an aliquot of solution from the working electrode compartment, diluting to approximately 1 mM, and recording a cyclic voltammogram, using, for example, a 1-mm diameter macrodisc working electrode made from the same material as the bulk electrolysis working electrode along with exactly the same reference electrode as that used in the large-scale electrolysis cell. The electrolysis experiment may also be monitored ex ritu by periodically taking samples hom the working electrode compartment and recording voltammograms or spectra (electronic, infrared (IR), NMR, etc.) in the usual manner. 15.2.2 Small volume cell for coulometry and in situ voltammetnc or spectroelectvochemical measurements For coulometry measurements used to determine n-values associated with an electron-transfer process, a smaller solution volume cell, which retains most of the design features of the cell described in Section 15.2.1, can be used. In the smaller volume cell, the 5-mL volume inner compartment contains a GC cylindrical working electrode (area approximately 28 cm2) as the working electrode and a reference electrode separated by a 1.0-1.7 pm sintered glass frit from a platinum mesh cylindrical auxiliary electrode. Solutions are again purged with Spectroelectrochernistry 107 1 Cell for bulk electrolysis at a platinum gauze electrode. The working electrode compartment 13 sits inside the auxiliary electrode compartment A. (a) Pt mesh basket working electrode (b) clip to pressure seal cell and lid (c) Pt mesh basket working electrode (d) porosity 5 glass frit (e) magnetic stirrer bar, and (f) reference electrode. Reproduced by courtesy: Anal. Chem. 67 (1995) 1691. Copyright, American Chemical Society. an inert gas prior to and during electrolysis and are stirred with a magnetic stirrer bar. In this cell, sufficient space is available so that the standard elecarrangement used for voltammetric experiments may be inserted into the ing electrode compartment and hence cyclic, rotated-disc or microelece voltammograms may be recorded during the course of the electrolysis. tu spectroscopic (infrared, electronic, etc.) monitoring of products of elecis is also possible using detection aided by fibre optics transmission of (Section 16). Of course equivalent designs with platinum or other metal (Fig. 2.51), rather than GC working electrodes and porous vycor or other materials (e.g. membranes) rather than sintered glass frits can be made using the principles described in Section 15. ee ist Comparisons of voltammetric experiment and theory frequently provide significant clues to the mechanisms of an electrode process, but only rarely can the identity of intermediates and products be deduced solely from voltammetric ata. Consequently, the characterization of intermediates and final products proposed in a mechanism, whenever possible, should be confirmed by spectroopic identification (Fig. 2.6). Ex situ spectroscopic measurements made after lk electrolysis experiments can obviously be used to identify stable products tion 15). However, because in situ spectroelectrochemical measurements y to much shorter time domains, they provide a powerful method of ideng the nature and even structures of intermediates involved in reaction hanisms. The nature of the spectroelectrochemical technique should be 108 Principles of voltammetry appropriate to the problem [72]. Thus, for example, electron spin resonance (ESR-also called electron paramagnetic resonance (EPR)) spectroelectrochemical techniques are likely to be ideal for identifying radicals that are formed by one-electron oxidation or reduction of diamagnetic organic species. 16.1 E S R spectroelectvochemistvy Undertaking an electrolysis experiment on a flowing solution which moves over a channel electrode and then passing the electrolysed solution into an ESR, Raman, Infrared, UV-visible, or other kind of spectrometer (including an electrospray (ES) mass spectrometer), represents an ideal method of detecting and identifying moderately stable species generated upstream at the electrode surface. Figure 2.52 depicts an in situ channel-electrode cell design that has been used in the ESR form of spectroelectrochemistry [73]. Alternatively, designs can be achieved in which the entire electrochemical cell [74-761 may be placed inside the cavity of the ESR spectrometer (Fig. 2.53) and when a microelectrode working electrode is employed (Fig. 2.54), simultaneous ESR-voltammetric experiments may be undertaken in situ using electrolysis in very small volumes of solution [74]. Data illustrating responses obtained from channel electrodes and in situ small volume microelectrode techniques are contained in Fig. 2.55 for the reduction at a platinum electrode of dipropylpyridine-2,4-dicarboxylateto its anion radical [77]. Inspection of Fig. 2.55 reveals that the channel flow-cell experiments (Fig. 2.52) display a markedly greater sensitivity as shown by the much enhanced Fig. 2.52 Channel flow-ESR spectroelectrochemical cell. Reproduced by courtesy: J. Electroanal. Chem. 144 (1983) 87. Copyright, Elsevier. Spectroelectrochemistry 109 Electrolytic cell Lock-in I Resonator Electromagnet 80 H signal . 2.53 A highly sensitive microelectrode-ESR detection system obtained by placing the electrochemical cell within the ESR cavity. Reproduced by courtesy: Chem. Lett. (1995) 919. Copyright, Japanese Chemical Society. signal-to-noise ratio and the better developed hyperfine splitting patterns observable. The significant improvement in sensitivity is largely attributable to the relative electrode sizes. In the small volume cell (Fig. 2.54),spins are injected through a 70-pm diameter microdisc electrode. In contrast, channel electrodes typically have approximate dimensions of 4000 pm x 4000 pm, so that the difference in electrode areas is approximately 4 x lo3 although this relative advantage may be partly offset by the effect of convection in sweeping radicals out of the ESR cavity once they are formed. The effect of convection on the intensity S , of the ESR signals generis demonstrated in ated by reduction of dipr~p~lpyridine-2,4-dicarboxylate ig. 2.56, which shows signal/flow rate (Vi)/current (I data analysed according Pn'nciples of voltammetry Cu rods Soldered connections Nylon support B7 joint (quartz socket, pyrex cone) o-ring average filling level (approx. 0.25 ml) counter electrode (250 pm Pt) Sensitive region of cavity Reference electrode (70 pm Pt, coated with Ag/AgCl) 1 \ Working electrode (70 pm Pt) Fig. 2.54 Small-volume microelectrode cell for simultaneous voltammetric-ESR experiments inside the ESR cavity. Dimensions are given in mm. Adapted from: J. Electroanal. Chem. 404 (1996) 303 and J. Electrochem. Soc. 142 (1995) 863. to eqn (2.68) which is known to apply to a stable radical in the laminar channel flow cell [77]). Specifically, a plot ofloglo{S/I}against loglo{Vf}is seen to be linear with a slope of (-213) as predicted by eqn (2.68). This result provides clear evidence that the radical is stable on the time-scale of the channel electrode ESR experiment (that is, there is no time for decay before the radical leaves the ESR cavity). In practice, given the range of solution flow rates normally employed in channel electrode ESR work, this means that the anion radical has a lifetime in excess of 5-10 s. Clearly, mechanistic information is accessible via channel electrode measurements in which the ESR signal is monitored as a function of the flow rate and electrode current. Radical instability is revealed by curvature in plots of the type Spectroelectrochemistry (a) 200 111 0 I3470 3480 3490 3500 Field (G) . 2.55 ESR spectra resulting from the reductive electrolysis of dipropylpyridine-2,4-dicarboxylate in acetonitrile solution; (a) 15 rnM (b) 5 mM using the small volume cell (Fig. 2.54), and (c) 1.5 mM using the channel flow cell (Fig. 2.52) and a flow rate of 4 x 10-'cm3 s-l. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 303. Copyright, Elsevier. displayed in Fig. 2.56 and as shown schematically in Fig. 2.57. Such plots can be analysed to provide information concerning the mechanism of the radical decay and the associated kinetics. Various EC, ECE and disproportionation processes have been quantitatively studied in this manner [73,78-841. The small volume cell does not readily permit the direct interrogation of electrode reaction mechanisms in an analogous way through the ESR signal. However, because of the short time constant of the cell, fast scan cyclic voltammetry is viable, and may 1 12 Principles of voltarnrnetry Fig. 2.56 Variation of the current normalized ESR signal intensity ( S I I ) with solution flow rate (Vf) for reduction of dipropylpyridine-2,4-dicarboxylatein a channel flow cell. The line shown has a slope in agreement with eqn (2.68). Reproduced by courtesy: J.Electroanal. Chem. 404 (1996) 303. Copyright, Elsevier. 1% S A '--, I Stable radical R- 1% Vf Fig. 2.57 Schematic behaviour of ESR signal-flow-rate-current data for stable and unstable radicals. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 303. Copyright, Elsevier. be used to interrogate the electrode process in the conventional manner [73,77] without recourse to the ESR signal. Cyclic or linear sweep voltammetry at channel electrodes is restricted by the much larger time constant of the electrode, although the relevant theory which takes into account the influence of the convective flow has been derived [85]. Instead, hydrodynamic voltammograms are normally recorded under steady-state conditions, and the variation of the half-wave potential, and/or the transport-limited current, with solution flow rate is used to derive kinetic and mechanistic information [86]. It is noteworthy that the demands of high sensitivity, which dictate as large an electrode area as possible, are in direct conflict with those essential for undistorted cyclic voltammetric studies. Finally, it can be noted that the channel flow cell is not readily amenable to low-temperature work and that it is prone to consume relatively large quantities of electrolyte. Both these deficiencies are remedied in the design considered in reference [74]. n summary, the advantages of the channel electrode flow through cell, introduced by Coles and Compton [73], are as follows: the deduction of kinetic and mechanistic parameters is readily accomplished using the ESR signal and its dependence on flow rate and electrode current. he advantages of the microelectrode, stationary solution, in situ cell designed by Fiedler, Koppenol and Bond [74] are as follows: only a small volume of solution is required (0.2 mL); easy to work at variable temperature; the electrode has a short cell time constant permitting, for example, fast scan rate cyclic voltammetry; the cell is of all-glass construction and is therefore usable in almost all solvents. eferences [72,76,77,87,88] provide useful overviews of the subject of ESR ectroelectrochernistry. learly infrared spectroelectrochemical monitoring is likely to be excellent for electrochemical studies on compounds where intermediates and/or final products exhibit strong infrared bands. Figure 2.58 illustrates what effectively acts as a very small volume thin-layer cell design in order to achieve very efficient electrolysis at a platinum macrodisc electrode [89,90]. With this design, infrared iation only has to pass through a very thin layer of solution and after being rbed by the species of interest can be reflected off the platinum electrode and then detected by the I R spectrometer. The method is based on the use of a modified infrared reflection-absorption spectroscopy (IRRAS) cell which is mounted on a specular reflectance accessory located in the sample of a Fourier Transform Infrared (FTIR) spectrometer [89,90]. Transition metal carbonyl complexes have intense infrared bands in the 2000 cm-' region and so studies on this class of compounds gain enormously from the use of the infrared spectroelectrochemistry approach. Figure 2.59(a) shows that the oxidation of Cr (CO), (C6Me6), under conditions of cyclic voltammetry at a platinum macrodisc electrode, is chemically reversible (scan rate = 100 mV s-l) at room temperature in dichloromethane. Monitoring the course of this reaction by the IRRAS spectroelectrochemical method gives the result shown in Fig. 2.59(b). The shift in the carbonyl infrared bands to higher wave numbers is exactly as expected if [Cr(CO), ( c 6 ~ e 6 ) ]is' generated via the electrode process Cr(CO), (C6Me6)+ [Cr (CO), (C6Me6)] e- . In the experiment in Fig. 2.59(b), application of a constant applied potential of 1000 mV versus Ag/AgCl is adequate to oxidize Cr (CO), (C6Me6)and FTIR + + 1 14 Principles of voltammetry to micrometer cooling gas in - ---c cooling gas out platinum wire B14 sept platinum disc working electrode \ alkali halide/quartr window Fig. 2.58 Infrared spectroelectrochemical experiments based on the use of a modified infrared reflection-absorption spectroscopy (IRRAS) cell [87,88]. A flow of cold nitrogen gas is maintained for low-temperature experiments. Adapted from J. Chem. Soc. Dalton T m s . (1996) 2945 and provided by courtesy of D.G. Humphrey, Monash University, Victoria, Australia. spectra can be recorded rapidly to monitor the course ofthe electrolysis. Spectral runs 0, 4, 8, and 9 are shown in Fig. 2.59(b) and because the differential adsorbance is used to subtract the contribution from the solvent, the initial spectrum (rc.0, in Fig. 2.59(b)) is inverted relative to the usual display format used in infrared measurements. Consequently, the infrared spectrum of the unoxidized form of the compound C T ( C O )(C6Me6) ~ lies below zero and decays towards zero as the extent (time) of electrolysis increases, while that for the lies above zero and increases with time. product [Cr(CO)3(C6Me6)]+ Spectroelectvochemistry 2200 2100 2000 1900 115 1800 Wavenumber (cm-1) 2.59 (a) Cyclic voltammogram (scan rate 100 mV s-l, platinum macrodisc electrode) for the oxidation of C S ( C O ) ~ ( C ~ in M dichloromethane ~~) (0.2 M Bu4NPF6) at room temperature. (b) Infrared measurements obtained during the course of oxidation electrolysis using the cell described in Fig. 2.58. Provided by courtesy of D.G. Humphrey, Monash University, Victoria, Australia. Clearly, far more complex reaction schemes can be unravelled by infrared troelectrochemistry in the IRRAS mode, particularly when the low temture mode of operation is employed in this thin-layer electrolysis cell. tensive use of this method is described in references 191-931. As an alternative to use of a thin-layer electrolysis method, systems based on e use of fibre optic cable for transmission of infrared radiation (Fig. 2.60) may e used in an in situ dip probe made for monitoring the course of conventional ulk electrolysis experiments [94]. Unlike thin-layer cell methods, this spectroctrochemical technique requires no cell design compromises which diminish e accuracy of the voltammetric data that may also be obtained during the course of the electrolysis. In the design described by Shaw and Geiger [94] a bifurcated 1-m fibre-optic alcogenide cable mounted on the exit port of a FTIR spectrometer carries radiation into the electrolysis cell and returns it to a HgCdTe detector. he probe terminates in a tip into which the analyte solution is allowed to ow freely through entry holes (Fig. 2.60). Infrared light enters the solution \ screw threads I------8 mm------1 Fig. 2.60 Infrared spectroelectrochemistry based on the use of sampling probe head at the end of the fibre-optic cable. The portion shown schematically is immersed in the electrolysis solution, and solution enters the sample chamber through holes in the stainless steel probe wall. Reproduced by courtesy: Organometallics 15 (1996) 13. Copyright, American Chemical Society. from the cable, bounces off a gold reflecting mirror attached to the end of an adjustable screw, and is returned to the detector by the cable. The optical path length may be changed (c.1-5 mm) by adjusting the screw. The oxidation of 1.0 rnM acetylferrocene ( E ~ O = 0.27 V versus FC/FC+) was studied using this infrared spectroelectrochemical method in CH2C12(0.1 M NBu4PF6)at 273 K by monitoring the position and intensity of the organic carbonyl band as the reversible electrolysis to the cation proceeded at Eappl = 0.53 V (v,, 1666 cm-' for acetylferrocene, v,, 1700 cm-' for the cation) again as difference spectra (Fig. 2.61 (a)). Progress of the conversion to the oxidized cation was also followed by voltammetry and coulometry [94]. Steady-state voltammograms at a 25-pm diameter Pt disc electrode (Fig. 2.61(b)) were recorded at approximately the same time as the infrared spectra in Fig. 2.61 (a). Moreover, the absorbance of the infrared bands was directly proportional (1700 cm-', product) or inversely proportional (1666 cm-' , reactant) to the amount of charge passed during the course of electrolysis as shown in Fig. 2.61 (c). 16.3 UV-visible spectroelectrochemistry UV-visible spectroelectrochemical monitoring of the course of electrolysis has been in widespread use for many years [72]. Thus, optically transparent gauze minigrid gold or platinum (Fig. 2.62) or optically transparent tin or iridium oxide semiconductor electrodes have been commonly used for in situ UV-visible spectroelectrochemical measurements over very wide temperature Spectroelectrochemistry 117 ranges. Alternatively, flowing solution channel electrode techniques can be used conveniently (Fig. 2.63) with detection by UV-visible spectrophotometry in a manner akin to their ESR and I R spectroelectrochemical analogues. The result obtained in a UV-visible spectroelectrochemical experiment is shown in Fig. 2.64 for the reversible one-electron reduction of l-bromo9,lO-anthracenedione to its anion radical [95]. The series of isosbestic points, expected for a simple reaction of this kind, is readily observed, as are parallel absorbence and current transients in a potential step experiment (Fig. 2.65). Further examples of the use of UV-visible spectroelectrochemical techniques are provided in Chapter 3. 6.4 N M R spectroelectvochemistry Coupling of solution-phase electrochemistry and N M R spectroscopy has proved difficult even though the great value of N M R as a structural tool is well recognized [96]. The desirability of spinning the N M R tube while simultaneously undertaking an electrolysis experiment represents a far more difficult technical problem than that encountered in the ESR, IR, and UV-visible in situ spectroelectrochemicaltechniques described in Sections 16.1-1 6.3. A solutionphase N M R spectroelectrochemical technique has been described by Prenzler et al. [96] using the cell described in Fig. 2.66, which allows solution electrolysis to occur in the receiving coil region of a superconducting, high-field N M R spectrometer. Although the idea of coupling electrochemical generation with M R detection is not new [97-1011, this cell is unique in that: the N M R spectra may be accumulated as the electrolytic current is flowing; the electrolysis products are generated directly at the receiver coil; the outer tube spins keeping the inner tube strictly centred and the sample mixed as electrolysis occurs; and finally, the unit is designed to work in a commercial probe-that is, no custom built probe is necessary. Figure 2.67 illustrates 'H N M R spectroelectrochemical results obtained for the two-electron, two-proton reduction of p-quinone to (di)hydroquinone in acidified DzO. Both 0 = C 6 H 4 = 0 and 0- C6H4-OD are diamagnetic with a single, one line 'H N M R signal in the aromatic region, and even though the two lines are quite close (10 Hz apart with 300 MHz N M R instrument) excellent resolution is achieved under electrolysis conditions. 6.5 Combining mass spectrometry and electrochemistry An almost unlimited range of in situ and ex situ spectroelectrochemical techniques have been reported in the literature [72] and have become an essential tool of the electrochemist's trade. Obviously, products obtained during or after completion of an electrolysis experiment may also be examined by mass spectrometry, and masdcharge ratios and isotopic composition of charged products determined. Wavenumber 400 , Volt vs Fc/Fci 0 1000 2000 Charge (mC) o acetylferrocene (1666 cm-l) 3000 r acetylferrocenium (1700 cm-l) Spectvoelectvochemistvy 119 he advantages of mass spectrometry (MS) as an analytical technique have long been recognized. The high sensitivity and selectivity are particularly useful fOl-the identification of trace levels of analyte in complex gaseous and solid mixtures, but, until quite recently, a limitation of the technique was the inability to routinely determine non-volatile species present in solution, as is required for identification ofproducts formed by electrolysis in the solution phase. However, following its initial development in the late 1970s [I021, thermospray MS has been widely used for the identification of solution-based species [lO3,lO4]. Not risingly therefore, the online coupling of electrochemistry and thermospray has been reported for monitoring of electrochemically-generated species in aqueous solution [I 041. lectrospray MS (ESMS) has rapidly risen in popularity over the past fifteen years [105-1071, and is clearly now the preferred MS technique for detection of charged species present in solution. It is the 'softest' method for transfer of ions from solution to the gas phase and has the advantage of minimal decomposition and fragmentation of ions. Thus it is ideally suited for the determination of charged solution species which are frequently generated in electrochemical experiments. The ability to identify the charged products of electrolysis reactions in solution by ESMS is very desirable, in both off-line and on-line modes. However, a basic incompatibility exists between the two techniques, and this problem has to be solved. Electrolysis reactions are normally carried out with high concentrations of supporting electrolyte (typically about 0.1 M) ith an approximately 100-fold excess of electrolyte over electroactive und, whereas in ESMS, high concentrations of ions are very undesirusing problems of peak suppression [I081 and fouling of the interface ates and lenses. This problem has limited the coupling of electrochemistry and S. Dupont and co-workers describe the ESMS of products produced with electrolysis of fullerenes [I091. Using 10 rnM Bu4NPF6 as electrolyte pM fullerene, optimized conditions gave ESMS signals with the loss of signal intensity relative to that expected under other conditions being attributed the high concentration of supporting electrolyte. Zhou and Van Berkel also ve reported the use of electrochemical cells online with ESMS [I 101. In this study, the problems of high electrolyte concentrations were minimized by use of an uncommon type of electrolyte, that is, one incorporating a small metal-ion and a relatively volatile anion (for example, 20 rnM lithium triflate). . 2.61 Infrared monitoring of oxidative bulk electrolysis of l.0mM acetylferrocene in CH2C12(0.1 M NBu4PF6) at 273 K. An increasing amount of the acetylferrocenium cation is produced in the sequence A-F. (a) Difference infrared spectra; (b) Steady-state voltammograms (scan rate 5 mV s-I at a 250-pm diameter Pt disc electrode) of solutions A-F like those in (a). Scan A is that of 1.0 mM acetylferrocene and scan F that of nominally 1.0 mM acetylferrocenium cation. (c) Absorbance changes observed in (a) plotted against the total amount of charge passed. Passage of 1 Faraday mol-I required 3300 mC in this experiment. Reproduced by courtesy: O~anovnetallics15 (1996) 13. Copyright, American Chemical Society. Principles of voltammetry Flow in Flow out Platinum mesh Platinum wire Low-temperature melting glass sheet \ s +Silica plate Fig. 2.62 Schematic diagram of an optically transparent platinum-mesh-electrode-thin-layer cell design. The assembled cell can be placed in the sample holder of a UV-visible spectrophotometer and electronic spectra recorded during the course of electrolysis. Diagram provided by courtesy of G.A. Heath, Australian National University, Canberra, Australia. Downstream Pt counter electrode Au minignd. Length of grid was dictated by Ag paint connection to Cu wire I t-7 mm-i t-9mm -I -I 12.5mm 4 Upstream Ag wire quasi-reference electrode Fig. 2.63 Schematic representation of a flow-through cell used for UV-visible spectroelectrochemistry. Reproduced by courtesy: Anal. Chem. 61 (1989) 1787. Copyright, American Chemical Society. Spectvoelectrochemistry 300 400 500 Wavelength (nm) 12 1 600 Development of the thin-layer spectrum with time when the cell depicted in Fig. 2.63 is used after solution flow is stopped for the reduction of 1.1 x ~ o - ~ M B in A acetonitrile (0.1 M Et4NC104) at 25°C: (-) BA at t = 0, (- - -) BA and BA0- at t < 130s, BAe- at t = 130s. The time elapsed to reach exhaustive electrolysis was 130 s. and (. (BA = 1-bromo-9,1 O-anthracenedione). Reproduced by courtesy: Anal. Chem. 61 (1989) 1787. Copyright, American Chemical Society. a ) 0 60 120 180 Time (s) 240 300 2.65 Parallel current and absorption transients using the cell depicted in Fig. 2.63 with a stationary solution: (a) Absorption against time at 565 nm; (b) current against time. At (i) the potential was stepped from 0 to -0.9 V versus a Ag wire pseudo-reference electrode, and at (ii) the potential was stepped back to 0 V. The initial step (i) corresponded to stepping from a zero current to what would be a limiting current under flowing solution conditions. Reproduced by courtesy: Anal. Chem. 61 (1989) 1787. Copyright, American Chemical Society. 122 Principles of voltammetry Reference Working electrode -------- J - Counter electrode 10-mrn NMR -+ Tube Receiver coils Fig. 2.66 Schematic diagram of an N M R spectroelectrochemical cell. Reproduced by courtesy: Electrochem. Comm. 2 (2000) 5 16. Copyright, Elsevier. Fig. 2.67 N M R spectroelectrochernical two-electron, two-proton reduction of diamagnetic p-quinone to diamagnetic hydroquinone using an applied potential of -0.5 V versus A /AgC1 in aqueous 0.1 M quinone (0.1 M KC1, 0.3 M DC1) inside a 300 MHz N M R spectrometer. H spectra recorded for 130 min at 10-min intervals. Reproduced by courtesy: Electrochem. Comm. 2 (2000) 5 16. Copyright, Elsevier. F More recently, work in the author's laboratory [I 111 has shown that off-line (electrolysis in cell described in Fig. 2.5 1, but using very dilute electrolyte), and, online ESMS electrochemical methods, again with low concentrations of supporting electrolytes, can be used (Fig. 2.68). For online electrolysis with ESMS detection of product, a syringe pump was used to transport the electrolysis solution through the flow cell, the outlet of which was connected directly to the fused silica capillary of the ESMS interface. A schematic diagram is given in Fig. 2.68. The electrochemical flow cell consisted of two 10-cm lengths of Pt microtubing (internal diameter 100 prn) connected by Voltammetry at variable pressure and temperature 123 Diagram of online electrochemical cell where products of electrolysis can be fed directly into an ES mass spectrometer. (a) Syringe (b) syringe needle (c) Teflon tubing (d) Pt microtubule (,) metal connector (0fused silica capillary of spectrometer (g) syringe pump and (h) constant ~oltagepower supply. Reproduced by courtesy: Anal. Chem. 67 (1995) 1699. Copyright, American chemical Society. 3 cm of Teflon tubing. The microtube closest to the mass spectrometer funcas the working electrode and was connected to the positive terminal of a high-voltage power supply. A constant potential was applied across the two microtubes to cause electrolysis to occur. This very simple flow cell has ) ~acetonitrile been shown to afford efficient electrolysis of 0.2 rnM N i ( E t 2 d t ~in Bu4NPF6).Prior to electrolysis, the positive-ion mass spectrum in Fig. 2.69(a) was recorded, and clearly verifies the presence of the Bu4Nf electe cation. After applying 200V across the two Pt microtubules, with the closest to the mass spectrometer as the working (positive) electrode, and after allowing time for the electrolysed solution to reach the mass spectrometer r, the spectrum shown in Fig. 2.69(b) was obtained. Clearly, the prod(Et2dtc)3]+,is readily detected via its m / z value (masdcharge anion) and the comparison of experimental and predicted isotopic patterns, after generation by oxidative electrolysis. Thus, the ESMS data support previous proposals that the electrochemical oxidation of Ni(Et2dtc)2occurs [I 121 via the overall reac-+ 2 [ ~ i ( d t c ) ~ ] +Ni2+ 4e-. The advantage of the online i(Et2dt~)2 e is obvious: the flow line can be introduced to the mass spectrometer modification of the instrument; for air-sensitive species, the solution can be degassed prior to being introduced into the syringe; the required sample volume is small. In contrast, in the off-line method, larger volumes of solution are required, products must be stable in longer time domains, and prevention with adventitious oxygen is difficult. sly, gaseous products formed during the course of electrolysis may erized by mass spectrometry [I131 and, of course, products of bulk electrolysis may be identified with assistance from the relevant chromatographic separation techniques such as gas or liquid chromatography, or electrophoresis, etc. + + he equations relating to the thermodynamics (AE' or E: values) of an electrochemical cell, operating under equilibrium conditions, have been described 124 Princivles of voltammetry 1 [Ni ( ~ t ~ d t c ) ~ ] 502 ' 495 500 505 510 515 m/z Fig. 2.69 Positive-ion ES mass spectra, obtained using the online electrochemical-ES mass spectrometer flow cell shown in Fig. 2.68 for an acetonitrile solution containing equimolar (0.02 mM) = diethyldithiocarbamate) and Bu4NPF6 (a) before electrolysis and (b) during Ni(Et2dt~)2(Et2dt~ oxidative electrolysis. Reproduced by courtesy: Anal. Chern. 67 (1995) 1699. Copyright, American Chemical Society. as a function of pressure and temperature in Section 4 of Chapter 1. Voltammetric experiments may also be conducted at variable temperature and pressure, and it, therefore, follows that the dependence of the kinetics of a reaction on these parameters can be used to deduce the activation parameters [volumes (A V*), energies (E,), enthalpies (AH*), and entropies (AS*) of activation] of heterogeneous and homogeneous reactions associated with electron-transfer reactions, in addition to the thermodynamically important reaction volumes (A V), enthalpies (AH) and entropies (AS). ~fo,kO,u Consider again a voltammetric process of the kind, A B e-, where E,O and ko (and in principle a) can be measured as a function of pressure or temperature. Figures 2.70(a) and (b) illustrate the voltammetry observed for the reduction of some iron complexes [I 141 as a function of pressure, and the shift in the position of cyclic voltammograms with pressure can be noted via data contained in Fig. 2.70(c). If the process remains electrochemically and ++ Voltammetry at variable pressure and temperature 125 chemically reversible as the pressure is varied at constant temperature, then the position of the cyclic voltammograms essentially moves along the potential axis. small changes due to the dependence of the diffusion coefficient on pressure are likely. Under these conditions, the value of the reversible potential will reflect the dependence of the thermodynamics of the overall process (combination of working electrode and reference electrode half-cell reactions, Chapter 1) essure. In contrast, if the temperature is varied at constant potential, and ocess remains reversible at all temperatures studied, then the value of the reversible potential may also vary with temperature, but in this situation a change in shape of the voltammogram is predicted to occur as a result of the nF term present in the theory. the process is kinetically controlled by the heterogeneous charge-transfer step (kO value) rather than being reversible, then k0 will change as either the pressure or temperature is varied, assuming E, or A V* and AS* are not zero. [Fe (phen) (cN)~]I-/'- .+: Fig. 2.70 Continued 126 Principles of voltammetry $-@(,.I a,) (n1Y [Fe (cN)~]~-' 0.0 25.0 50.0 75.0 100.0 125.0 Pressure (MPa) Fig. 2.70 Dependence of voltammograms and reversible potentials on pressure. (a) Voltammograms ofthe [Fe(phen)(CN)4]1-/2-couple (phen = phenanthroline) in 1 M K N 0 3 at 0.1 Mpa (-), 36.2 Mpa (. . . ), 70.3 Mpa (- - -), and 105.2Mpa (- . -.) at a gold disc electrode using a Ag/AgN03 (0.01 M); 1.0 M K N 0 3 reference cell. Scan rate = 0.057 V s-'; T = 298 K. (b) Voltammograms of the [ F ~ ( O X ) ~ couple ] ~ - / ~(ox = oxalate) in 0.10M NH4HC204at 0.1 Mpa (-1, 35.7Mpa (. . .), 69.7 Mpa (- - -), and 104.5 Mpa (- - -). Conditions as for (a), but using a Ag/AgN03 (0.01 M); 0.1 M K N 0 3 reference cell. (c) Variation of formal potential with pressure for [ F ~ ( c N ) ~ ] ~ - / ~ ] (empty circles), and (filled circles), [Fe(bpy)(cN)~]'-I2- (empty squares), [ ~ e ( b p y( )c~N ) ~ '+I0 Fe(bpy):+I2+ (filled squares) couples (bpy = 2, 2'-bipyridyl) relative to the formal potential at 0.1 Mpa. Ionic strength = 1.OM; T = 298 K. Reproduced by courtesy: Inorg. Chem. 33 (1994) 6180. Copyright, American Chemical Society. The value of ko would, of course, be expected to decrease with temperature as the rates of almost all reactions slow down as the temperature decreases. An analogous situation with respect to temperature dependence applies, if a rate-determining homogeneous chemical step accompanies a reversible chargetransfer process. Thus, consider the EC reaction Voltammetry at variable pressure and temperature c.) A 0 0.4 0.8 1.2 Volt vs Ag/Ag C1 127 1.5 0 0.4 0.8 1.2 1.6 Volt vs Ag/Ag C1 Cyclic voltammograms for oxidation of [Cr(CO)51] in acetone at a platinum electrode: (a) T = 20°C; scan rate = 200mV s-'; electrolyte = 0.1 M Et4NC104 (b) T = -70°C; scan rate = 200 mV s-l; electrolyte = saturated Et4NC104.Reproduced by courtesy: Inorg. Chem. 13 (1974) 602. Copyright, American Chemical Society. As can be deduced from the discussion in Section 12, simulation of each of the voltammetric responses obtained under the relevant conditions will enable kl [ f ( T ) ]to be calculated as a function of pressure,f (P),or temper, respectively. The direction of change of kl with pressure variation tive or negative. However, as the temperature is decreased, the maghe homogeneous reaction kl is expected to decrease. In Fig. 2.71, on of [ C r ( C 0 ) 5 1 ]in acetone is shown under conditions of cyclic voltammetry [I 151 at a scan rate of 200 mV s-' at both 20°C and -70°C, using on-isothermal cell (reference electrode temperature maintained at 20°C). As temperature is lowered it may be easily observed that the reaction scheme, products which the second process is chemically irreversible converts at 20°C to the ly reversible scheme, hat is, at -70°C, the value of kl decreases to the point where it becomes too slow to be rate-determining on the voltammetric time-scale. Quantitative measurements of the relevant rate constant as a function of pressure [I 141 will give the volume of activation for the appropriate process via use of the relationship where j stands for the relevant heterogeneous (ko) or homogeneous ( k l ) rate constant. The AS* value is analogously given from measurement of kj as a function of temperature and use of the equation The values of A V* and AS* are extremely valuable in assigning the nature of a mechanism (inner sphere, outer sphere, associative, dissociative, twist, etc .) , and complement the measurement of thermodynamically significant A V and AS values as described in Section 4 of Chapter 1. Voltammetric measurements at very high pressures are, of course, potentially, highly dangerous and require the use of carefully designed cells that can be operated safely. Figure 2.72 gives an example of a variable pressure electrochemical cell that has been used to study a range of systems by voltammetry. A recent review by Swaddle and Tregloan [I 161 details the theoretical and experimental aspects of voltammetry at high pressure. Variable temperature studies are more readily implemented than variable pressure ones. Commonly, a non-isothermal electrochemical cell arrangement is employed in variable temperature voltammetry in which the reference electrode compartment remains at ambient temperature, while the temperature of the working electrode compartment is varied [I 17,1181. If thermodynamic calculations are being undertaken, then, of course, the relevant junction potentials and reference electrode behaviour as a function of temperature need to be extremely well characterized. The use of a non-isothermal cell provides some simplification with respect to the measurement of the temperature-dependent terms that are of voltammetric significance. Details of experimental arrangements and data that can be obtained use of variable temperature measurements for a range of reactions are available in references [I 17-1 2 I]. 18.1 General aspects Either explicitly or implicitly, voltammetric studies referred to above apply to B ne- process are soluble in the a process where both species in the A solution phase. However, if both A and B in thick solid or thin-film formats + + Voltammetric studies o n solids 129 Vertical section Pt auxiliary electrode Electrical connection through to high-pressure seal and detection Kel-F threaded electrode mount Teflon seal Disc working electrode Ag reference electrode and compartmens Vycor junction and piston Kel-F cell body Section at AA' Auxiliary electrode Reference electrode Disc workmg electrode . 2.72 Schematic representation of the high-pressure electrochemical cell. Reproduced by courtesy: Inorg. Chem. 33 (1994) 6180. Copyright, American Chemical Society. are attached to an electrode surface, which is in contact with a solvent (electrolyte) solution phase, then an electron-transfer reaction could occur within e solid phase to give a diffusionless system, at least with respect to the solution (electrolyte) phase in which the electrode is placed. However, in these circumstances, charge transport across the redox active solid(s)-electrode-solution (electrolyte) interface must still occur to achieve charge neutralization so that both ionic and electron transport processes must occur within the attached solid phase(s) as part of the mechanism of the electrode process. In the absence of a solution phase, mass transport process being a ratedetermining step, voltammetry at stationary or rotated macro- or microdisc electrodes can be inherently similar, since it is the charge neutralization or electron-transfer step within the solid that is likely to be rate-determining. This is about the only simplification, with respect to the theory, that is achieved when studying the voltammetry of a surface confined process, as almost every other aspect of the problem becomes inherently far more complex than when the redox components are soluble in the solution phase. For example, the solid 130 Princijdes of voltammetry may be adsorbed or attached to the electrode by chemical or physical process to give thin films of monolayer or sub-monolayer coverage or thick films where each layer has a separate level of activity. Alternatively, the solid may be attached to the electrode as arrays of microcrystals or exhibit completely non-uniform or random forms of electrode coverage and, of course, several phases may exist simultaneously on the surface. Numerous permutations and combinations of electrode (metal, chemically modified, conducting polymer) and attached solid have been reported and all have nuances which need to be considered when generating a theoretical description of the voltammogram. Finally, of course, chemical transformations may occur that are related to the EE, EC, ECc,t,I,,ic classes observed when the redox active species are solely present in solution. Clearly, the C step when the redox active species is attached to the electrode can be a heterogeneous solid-solution-phase reaction rather than a homogeneous reaction. Since it is not practical to consider every aspect of the voltammetry of surfaceattached species, only the simplest case of the redox transformation of a thin film (monolayer or sub-monolayer) of non-interacting surface confined material will be considered in Section 18. In Chapter 5, the significantly more complex situation when microcrystals (thick film) are adhered to an electrode surface will be considered. Treatment of this moderately simple thin-film case provides a basis for comparison with studies where reactants and products of an electrode process are soluble in the solution phase as in previous sections of this chapter. From a fundamental viewpoint, metalloprotein-films of the kind prepared by Armstrong and colleagues [I221 come as close to fulfilling the conditions required for so-called ideal thin-layer voltammetry. The beauty of electron-transfer metalloproteins is that they are designed to accommodate very fast rates of electron transport over long distances, and the interactions between molecules present in thin films of these molecules are relatively small. Figure 2.73 provides an idealized representation of a film of redox active protein ox + e-A kred red red kox Cell solution ox + e- redox centre [EOflsurf Fig. 2.73 Idealized diagram of a layer of redox active protein adsorbed onto an electrode surface. All centres are assumed to have the same value and exhibit identical electron-transfer characteristics. Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. (EF)~~~ Voltammetric studies on solids 131 Cyclic voltammogram obtained for reduction of a thin film of the 'blue copper' proomonas aeruginosa Azurin, at a pyrolytic graphite electrode using a scan rate of 500V s-' (pH = 8.0, T = O°C). The potential axis is V versus SCE. Baseline subtracted peaks (not to le) are shown in the centre of the voltammogram. Reproduced by courtesy: Chem. Soc. Rev. (1997) 169. Copyright, Royal Society of Chemistry. adsorbed as a monolayer onto an electrode surface, while Fig. 2.74 gives an erimentally obtained cyclic voltammogram for a thin film of azurin attached to a carbon electrode. In this ideal situation, a homogeneous electroactive olayer of a metalloprotein such as azurin is formed to give a coverage tween 10-l1 and 10-l2 rnol a n A 2 . Thus, only minuscule quantities of sample are required to obtain data related to interfacial electron-transfer kinetics, information on chemical reactions coupled to the charge-transfer process, including biologically important catalytic reactions, and reversible potentials of biologically important processes [122,123]. However, it needs to be recognized that kinetic and thermodynamic parameters obtained from voltammograms of surface-attached species need not be the same, even with respect to units, as for the solution-phase electroactive species. -2 Electron transfer i n ideal redox active thin$lms attached to electrode su faces et us assume that species A (now labelled 'red' when in film form) can be oxidized to species B (now labelled 'OX' when in film form) while attached to an electrode surface placed in a solution (electrolyte) medium without dissolution of red or ox. Let us also assume that the entire thin-film layer consisting of redox ~~, active species red and ox has the same single reversible potential [ E ~ O ] ~ and that for a given potential E, all values of the charge-transfer rate constants for oxidation k,,, and reduction kred are equal. That is, red and ox are considered 132 Principles of voltammetry to be non-interacting redox active centres. By analogy with the solution phase case, if k,, and kred are both fast enough to maintain equilibrium as the potential is scanned, then the potential of the electrode with surface-attached material will be governed by the Nernst equation in its surface attached rather than solution-phase form. Thus, is used to denote the fraction of the surface coverage where the symbol rred of the reduced form of the compound, and r,, the fraction of the oxidized form of the compound. This is equivalent to stating that the activities of red and ox are proportional to their mole fractions in the ideal thin film, assumed to be present on the electrode surface, unlike the case of a pure solid where the activity is usually assumed to be unity. Other symbols in eqn (2.74) have their usual meaning. For this reversible process and with the above assumptions, the on the electrode surface will be governed by the distribution of I?,, and rXd Nernst equation to give the fractional coverage shown in Fig. 2.75 as a function of potential. This thin-layer model effectively assumes that the solid is adsorbed or otherwise attached to an electrode to give a planar uniform surface and that attachment to the surface of ox and red is analogous to that which occurs in the Langmuir model of gas adsorption when all sites are identical and behaviour akin to a monolayer is observed. In this circumstance, and when no interaction between redox centres occurs, it is reasonable to assume that the oxidation and reduction components of the experiment vary uniformly with potential so that the charge-transfer coefficient (Section 7 -2) is 0.5. Fig. 2.75 The variation of fractional coverage of the oxidized species with respect to potential, for a reversible process when the ideal thin-layer model given by eqn (2.74) applies for the process red + ox e- at 0°C. The potential axis is V relative to [ ~ f o ] , , ~ . Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. + Voltammetric studies on solids 133 18.2.1 ideal thin-filmvoltammetry and reversible electron transfer For a diffusionless reversible (Nernstian) reaction involving the simultaneous transfer of n electrons at the same potential, the reaction schemes red + ox + ne- ox + ne- or (2.75) red + + nlay now be used to distinguish them from the A + B new or B new + A reactions given for the solution-phase. In eqn (2.75), charges again are omitted for simplicity as is the ion that must be transported across the thin-film-solvent (electrolyte) interface, even though this ion transport rather than electron transfer may be rate-determining in a kinetically controlled process. The role of the ion transport required for charge neutralization will become clearer in Chapter 5 when voltammetric studies on microcrystals attached to an electrode surface are considered. or a cyclic voltammetric experiment, assuming the scan rate is constant, the change of potential is linear in time and, therefore, the equilibrium current (i.e. ed for suitably low scan rate/high electron-transfer rates) is simply given rate of change of the redox state of the redox centers shown in Fig. 2.73. Thus (Section 13.1) ence except for the sign of the current12,a symmetrical result is obtained for oxidation and reduction components of the experiment. Thus, combining the = ernst eqn (2.74), and the relationship for the total surface coverage rtot yielding, via use of eqn (2.79) and substitution of the expression for the scan rate, v = dE/dt. 1 2 ~ hpositive e sign required by convention for the oxidation current and the negative sign for reduction current can be achieved in several ways. Equations (2.77) to (2.80) represent one of the formats used in the literature to obtain this outcome. 134 Principles of voltammetry Normalized - Fig. 2.76 A reversible voltammogram for a surface confined ideal one-electron thin-film reaction at 0°C. Note that the peak separation is zero, the current has been normalized to the peak current and the potential axis is V relative to [ E ~ O ] , , ~ . Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. The peak heights [IpIsud,for oxidation and reduction can be calculated from the expression (dI/dE,,,) to give = [P ' IS"" n2F~ VAL,, which has a positive value for oxidation and a negative one for reduction.13 Furthermore, for this reversible process, the peak current for both the oxidation and reduction components of a cyclic voltammogram occurs at the potential [Ep],,d where E = [E~O],,,~.A convenient form of presentation of the resulting process may be obtained by plotting the normalized current value (I/[IplSud) versus potential E to give the voltammogram shown in Fig. 2.76. Note that the areas under the peaks are related to the total number of electrons transferred (or number of adsorbed molecules) as in eqn (2.82) Area under peak v = nFAr,,, where v is the scan rate in V s-' and the left-hand side of eqn (2.79) gives the number of Coulombs (normalized with respect to scan rate). The peak 131n deriving the thin film theory, the scan rate is assumed to be positive for oxidation and negative for reduction. However, ifthe scan rate is only regarded as having a magnitude and hence always positive, formats required as in solution soluble theory presented in Section 8, then different formats are required for presentation of all equations containing the scan rate term. Voltammetricstudies on solids 135 %tidthat half-height width, W'p, is also an important experimental parameter in thin-film voltammetry and for a reversible process or about 9 0 / n rnV at 25OC. is the case with solution-phase voltammetry, when equilibrium cannot be maintained, the thin-film voltammetric process is no longer reversible. This situation will arise either when the scan rate (rate of change ofpotential) is increased or when the electron-transfer rate is too slow for equilibrium to be maintained. Under this non-equilibrium condition (within relevant experimental domain) the process is now termed irreversible or quasi-reversible in the intermediate regions when the response lies between the reversible and irreversible. Since the rate of change of potential is now faster than the rate of adjustment of the redox centres, the current lags behind the potential, and as in the solution-phase case, enhanced separation of the reductive and oxidative peaks is observed. An of a non-reversible process is given in Fig. 2.77. the dependence of the peak separation on scan rate, and also from the wave shape, it is possible to derive the magnitude and the potential dependence of the thin-film charge-transfer rate constants. However, for a non-reversible process, an analytical theoretical solution is not available and a 'finite difference' simulation is required, using a model of the potential dependence of the electron-transfer rate constants, rather than the Nernst equation [122]. Normalized current 'T - Potential -77 An example of a non-reversible voltammogram for a surface confined ideal one electron thin-film reaction at 0°C. Note that the oxidation and reduction peaks have separated, the peak height has decreased and the peak width has increased relative to the reversible process in Fig. 2.76. The current axis is normalized with respect to the reversible process. The potential axis is V relative to [ E ~ O ] , , ~ . Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. 136 Principles ofvoltammetry 18.2.2 Thin-film voltammetry and non-reversible electron transfer using Butler- Volmer theory The simplest model used to describe electron transfer between a thin film of adsorbed redox centre and an electrode is based on Butler-Volmer Theory, and hence the behaviour is phenomenologically closely related to that used when the compound undergoes oxidation or reduction in the solution phase. This model, as noted in Section 7.2, is based on a transition-state approach to the electron-transfer process and the equations for the electron-transfer rates therefore takes on a simple Arrhenius-like form (eqns 2.84 and 2.85) ko, = ko exp ( -anF kred = ko exp KT ( E - [':lSud)) The important kinetic parameter in this equation is ko, the rate constant at E = [ E ~ ] , , ~It.is important to note that the units of ko, k,, and kred are now s-' rather than cm s-' as is the case for the heterogeneous charge-transfer rate constant that is relevant when electron transfer takes place between a solution-soluble redox active species and an electrode. The symbol ko is used for surface rate constant to distinguish from kO used for heterogeneous charge-transfer reactions, while the analogous parameters to k,, and kred in thin-film voltammetry are kfet and kEt (see Section 8.1.2) in solution-phase reactions. The parameter a (Section 7.2) again represents the degree of conversion between the initial and final states in = 1 . For a 'symmetrical' the transition state, and it is assumed that (a,, ared) electron transfer in the oxidative and reductive directions, a is equal to 0.5. The dependence of the rate constants k,, and kred on potential, as predicted by the Butler-Volmer theory is given in Fig. 2.78. + P Potential Fig. 2.78 The exponential dependence of the Butler-Volmer rate constants on potential for a surface confined ideal one-electron thin-film reaction. The rate constant at [~fo],,& is ko( = 600 s-l) and cx = 0.5. The potential axis is V relative to [E:],,~. Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. Voltammetricstudies on solids 137 The dependence of voltammograms for a surface confined ideal one-electron thin-film reaction on scan rate as modelled by Butler-Volmer theory. As the scan rate is increased the eaks separate and broaden as predicted for irreversible electron transfer. In this example ko is 600 s-' and the scan rates are 1 V s-' (lower scan rates are superimposed), 10 V s-' , 100V s-I ,1000 V s-' and 10 000 V s-' and the potential axis is V relative to Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. [~fo],,~. igure 2.79 contains a set of voltammograms predicted when the Butlerer thin-film relationship, combined with theory contained in Section 17.2.3, is used for a range of scan rates, with the same ko value, with the current normalized to the value predicted for a reversible surface confined process. As expected, increasing the scan rate has the same effect as decreasing ko. At the lowest scan rates considered, the Nernstian response is observed with the noralized peak height, K , being, of course, unity. As the scan rate is increased, peaks separate, but also decrease in height and broaden. With use of Butlerlmer theory, the peaks reach an 'irreversible' limit (Fig. 2.80) (e.g. at O°C, p = 116 mV and K = 0.74) beyond which no further broadening occurs. This dependence on the reversibility can be more easily visualized by plotting the relevant parameters as a function of loglo (v). As also, shown in Fig. 2.80, with increasing scan rate, peak positions separate symmetrically from [ E O ] , , ~ , eak widths at half-height increase and peak heights decrease. Finally, this concept may be generalized by normalizing with respect to ko as shown in Fig. 2.81, to provide results that hold for all values of scan rate and ko. 18.2.3 Application of the Butler- Volmer and Marcus theories to thin-film voltammetry As noted above, metalloproteins spontaneously attached to electrodes exhibit almost ideal thin-film voltammetric behaviour (Fig. 2.74) and non-reversibility may be approximated by Butler-Volmer theory [122]. In contrast, while selfassembled monolayer (SAM) structures of the kind shown in Fig. 2.82 may also 138 Principles of voltammetry Fig. 2.80 Variation of peak position (a, Epeak), normalized peak height ( b , ~ )and , peak half-height width (c, W1/2) predicted by the Butler-Volmer theory with loglo(scan rate). Note the attainment of an 'irreversible limit' in peak height and peak half-height width and that the peaks appear to separate linearly with log(v) at high scan rate. The example shown is for ko = 600 s-l. Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. exhibit close to ideal thin-film behaviour [122], usually, for these systems, the rate of electron transfer is much slower than for metalloproteins and under these circumstances it has been reported that Butler-Volmer theory is not adequate and the more complex Marcus theory needs to be adopted. Several groups have studied the electrochemical kinetics of SAM structures consisting of ferrocenes Voltammetric studies on solids 139 . 2.81 Peak positions (a), normalized peak heights (b), and peak half-height widths (c) as a function of log lo(norma1ized scan rate,v/ko), which provides a unique parameter applicable to all data sets. Other symbols are defined in caption to Fig. 2.80. Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. linked to a gold electrode surface through alkane thiols of varying chain length. Typically, the electrode is a gold mirror surface prepared by sputtering on silica wafers. Notably, Chidsey [I241 was able to detect the Marcus theory prediction of the variation of electron-transfer rate with free energy and temperature, and his conclusions have been supported and extended in studies by Murray and co-workers [I 251 and by Weber and Creager [I 261. 140 Principles of voltammetry X is redox group, e.g. fenocene or functionality interacting with protein X X X X X X Distance fixed by number (n) of (CH2),,in spacer S S S S S S Au electrode Fig. 2.82 Cartoon showing the structure of electrode surfaces modified with a monolayer of functionalized alkanethiolate. The group X may be redox active or a functionality such as carboxylate that is capable of interacting with the surface of a redox active protein. Reproduced by courtesy: Chenz. Soc. Rev. 26 (1997) 169. Copyright, Royal Society of Chemistry. The voltammetry of osmium complexes adsorbed on platinum electrodes [127,128] also supports the use of the Marcus model. Monolayer coverage of [O~(bipy)~Cl(X)] (bpy = 2,2'-bipyridyl; X = 4,4'-bipyridyl or analogues with two or three CH2 groups spacing the pyridyl rings) is achieved at platinum microelectrodes utilizing the pendant pyridyl-N atoms from ligands X as anchors. The relatively ideal response obtained with this system has allowed detailed investigation of the effects of electrolyte, solvent, temperature and electron-transfer distance to be undertaken. At a sufficiently large overpotential, electrochemical rates were observed to become independent of driving force, indicating the need to use Marcus rather than Butler-Volmer theory. However, in this study, and in the work on metalloproteins [122], some features of the voltammetry are not predicted by either the Butler-Volmer or Marcus theories. For example, a finite peak separation always remains at the lowest scan rates and the rate constant is approximately, but not completely, independent of ionic strength, giving rise to the possibility that ion transport/binding effects cannot be neglected, as has been assumed. The work on the SAMs and osmium complexes, as noted above, supports the use of the Marcus rather than the Butler-Volmer theory. The Marcus theory takes into account the dependence of the rate of electron transfer on distance of the redox active centre to the electrode, and the re-organization energy, A, defined as the energy required to change the nuclear coordination from the equilibrium position of the reactant and product, without allowing electron transfer to occur. Marcus theory also requires [5] that: (i) the electron-transfer reaction can occur both from and to all Fermi levels in the electrode, not just between two defined levels; (ii) the rate of the electron-transfer reaction is affected by the occupancy of the Fermi levels involved in the reaction; (iii) the . free energy or driving force is a direct result of potential differences. A direct comparison of theoretical linear sweep and cyclic voltammograms, predicted on the basis of the Butler-Volmer and Marcus models, has been provided in references [122-1 24,1291. Adopting the simple formalism used in , Voltammetric studies on solids 141 [I251 provides the following brief comparison of the two models14: For a simple, reversible one-electron charge-transfer process between an electrode and a surfice-attached redox active species red +ox + eko* the dependence of kox and kKd (the forward and reverse potential-dependent half-reaction-rate constants) on the overpotential, q, as expressed by the ButlerVolmer relations is: k,, = ko exp (2i:T These are the same relations given in eqns (2.84) and (2.85); here q = E [~fo],,,~, kg is the Boltzmann constant ( F I R = elkB), e is the charge on the electron, the charge-transfer coefficient, a , is assumed to be equal to 0.5, and a one-electron charge-transfer process is considered. The analogous Marcus relations [I251 to the Butler-Volmer equations when q/h << 1, with h being the ization energy. Thus, the Marcus relations applied to electrode reactions that, as 11 approaches h, the rate constants do not continue to increase nentially with r,~(as they always do in the Butler-Volmer formulation) but mize at q = fh and actually decrease at larger q (classicalMarcus 'inverted' region) [I24,13O,l3 11. Examples of differences resulting from the two forms of relations are summarized in Fig. 2.83, while the impact of the difference on ersible voltammograms is shown in Fig. 2.84. owever, use of eqns (2.89) and (2.90) are not rigorously correct since, when electron transfers occur at a metal interface it is necessary to account for the energy distribution of electrons about the Fermi level in the metal which, eference [I291 is a review using conventional electrochemical symbols, which can be consulted for a more detailed comparison of the different electron-transfer models. 142 Principles of voltammetry Fig. 2.83 Comparison of electrochemical rate constants predicted by Marcus and Butler-Volmer theories. (a) and (b) Marcus theory rate constants for small (0.2 eV) and larger (0.4 eV) reorganization energies respectively, the same plateau level (2 x lo5 s-') is achieved in each case; (c) the Butler-Volmer dependence with ko the same as for (b). Reproduced by courtesy: Chem. Soc. Rev. 26 (1997) 169. Copyright, Royal Society of Chemistry. Normalized 0.8 current I I Fig. 2.84 A comparison of the waveshapes premcted by Marcus theory (-) and Butler-Volmer theory (--) for an irreversible reaction with equal ko values. The Marcus reorganization energy is 0.2 eV and the Butler-Volmer ol is 0.5. Potential axis is V vs [E;],,~. Reproduced by courtesy: Chem. Soc. Rev. 26(1997) 169. Copyright, Royal Society of Chemistry. following Chidsey [I 241, leads to OX = P P ~ T B " exp{-(x - e(h - ~ ) / k ~ T ) ~ ( k ~ ~ / 4 h ) } 1 + exp (x) dx (2.91) Voltammetric studies on solids 143 x is the electron energy relative to the Fermi level, p is the distance- ent electronic coupling between the electrode and redox sites, and p is ity of electronic states in the metal electrode. p is anticipated [I321 to pelld exponentially on distance, d, according to the relation P = Fo exP (-m) (2.93) is the coupling at zero edge-to-edge reactant separation, and the decay ,f3 depends on the details of the structure through which tunnelling occurs and which has been reported, for example, to be -1.07 per CH2 group for ferrocene alkanethiol monolayers on gold electrodes [125]. The relations in eqns (2.92) and (2.93) are referred to as the heterogeneous Marcus equations to distinguish them from the Marcus equations given by eqns (2.90) and (2.91). Assuming values of two of the three parameters, ko, A, or p p , automatically fixes the value of the third. Figure 2.85 gives the dependence of k,, on q , as calculated from eqn (2.92) at 273 K, for a fixed value of ko(l.Os-l) and a series of values of h (and a corresponding series of p p values). At small values of ( E d), these curves are the same as the exponentially increasing reaction rates ted by the Butler-Volmer relationship (eqn 2.88) for the same ko value, but at larger overpotentials and at smaller values ofh, eqn (2.92)predicts reaction -85 Calculated log(k,,) versus (E- [E:],,~)at 273 K and ko = 1.0 s-l, based on heterogeneous s kinetics (-), top-to-bottom h = 1.00,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2, and 0.1 eV. (- - -) Butler-Volrner calculation for ko = 1.0 s-* and a = 0.5. Reproduced by courtesy: Anal. Chem. 66 (1994) 3 173. Copyright, American Chemical Society. 144 Principles of voltammetry rates that increase less than exponentially with (E - [E:],,~). At sufficiently large q, and/or small A, the heterogeneous electron-transfer rate constants fold over to become, at q > A, essentially independent of overpotential. However, the heterogeneous electron-transfer rates do not decrease at q > A, as predicted in homogeneous solutions in the classical Marcus 'inverted' region, because of the continuum of electronic states in the metal electrode [124,125,133]. The limiting rate constants (at large q) in Fig. 2.85 are determined by the value of ,xp, which in the series of calculations presented at constant ko and decreasing A, decrease in accord with A. Calculation of voltammograms in which the reaction rate is controlled by either the Butler-Volmer eqns (2.87) and (2.88) or different forms of the Marcus theory (eqns 2.89 and 2.90 or 2.91 and 2.92) are made using principles analogous to those for the reversible case (Section 17.2.1). The difference is that the current for first-order reaction of a diffusionless electroactive species is now given by where the reaction rate constants k,, and kred are given by eqns (2.84) and (2.85), or (2.87) and (2.88)' or (2.89) and (2.90) and To, and rred are the instantaneous surface coverages of the oxidized and reduced forms of the redox surface confined species, respectively. The applied potential, relative to E:, is q = q* v t where q* is the initial potential, v is the scan rate (V s-l), and t is time. The mass balance relationship in eqn (2.95) again applies so that + and where r,,, is total surface coverage and the initial surface coverages are given by the Nernst equation (see Section 17.2.1). To calculate voltammograms, q can be changed in small increments of dq ( < l mV, sufficiently small so that calculated currents are independent of the chosen dq) thereby allowing the reaction to proceed during time intervals of dt = dqlv at rates according to eqns (2.84), (2.85), or (2.87)' (2.88), or (2.89), (2.90). The instantaneous values of r,, and I-',d at each potential are then calculated from their initial values and the oxidative or reductive charges passed since initiation of the potential sweep. Finally, the current is calculated from eqn (2.94). It has already been shown (Fig. 2.84) that cyclic voltammograms calculated with the simplest form of the Marcus model may differ substantially from those predicted on the basis of classical Butler-Volmer kinetics. Figure 2.86 shows a comparison of Butler-Volmer voltammograms calculated for several values of log[v/ko] as the applied q is swept from -0.2 to 1.O V. (Increasing v is completely equivalent to decreasing ko in these calculations as shown previously.) Clearly, the traditionally used Butler-Volmer formalism does not take into account the nature of the electronic states involved. Further, at least two significant major assumptions that cause limitations in the application of the theory Voltammetric studies on solids 145 Calculated, normalized voltammetric waves based on (bottom, a = 0.5) Butler-Volmer kinetics and (top, h = 0.85 eV) heterogeneous Marcus kinetics, at 273 K, for left-to-right values of log[v/ko] = -1,0,1,2, and 3. Reproduced by courtesy: Anal. Chern. 66 (1994) 3173. Copyright, American Chemical Society. are made. First, it is assumed that the reaction surface is linear, so that potential energy varies linearly rather than parabolically along the reaction coordinate, and, second, that all electrode energy levels, apart from the Fermi level are ignored. As a result of these assumptions, the variation of electrochemical rate constants with overpotential is incorrect: Butler-Volmer theory predicts an ever (exponentially) increasing electrochemical rate constant, whereas in fact (and correctly predicted by Marcus theory) the rate reaches a constant level (independent of applied potential) at high overpotential, as shown in Fig. 2.83. This 'plateau' is the electrochemical equivalent of the inverted region described in homogeneous solution-phase electron-transfer reactions at large driving forces [I241. The differences in the theories translate into important aspects of voltammeus for example, Butler-Volmer theory predicts that even a very sluggish electron-transfer reaction should exhibit a relatively sharp waveform (since the electron-transfer rate increases exponentially), the irreversible limiting value for Wl/2(width at half-peak height) being 6 2 . 5 1 mV ~ ~ at 25"C, which is 125 mV 0.5. Broadening could, of course, with this model, be attributed to lity, an obvious example being kinetic dispersion in which different orientations of molecules attached to the electrode surface display a spectrum of rate constants [134]. However, Marcus theory predicts broadening even for an ideal, homogeneous array, since the rate of a process having a small reorganization energy quickly ceases to respond to an increase in driving force. This is 146 Principles of voltammetry illustrated in Fig. 2.84, which compares wave shapes expected, in this situation, for ~utler-Volker and Marcus models having ;he &me value of ko. Essentially, the heterogeneous Marcus model predicts electrochemical rate constants by summing over all the individual rate constants for each Fermi level in the electrode, where the separate rate constants are the standard Marcus long-range electron-transfer rate constants specific to two energy levels. The actual rate of electron transfer from or to a specific level is influenced by the probability of occupancy of that level as predicted by the Fermi-Dirac distribution 11241. In principle, the cyclic voltammetric behaviour of systems having poor electronic coupling and low reorganization energy, such as metalloproteins, should be better accounted for by the Marcus model than by the Butler-Volmer model, particularly under conditions offast scan-rates where the peaks occur at higher qvalues and hence lie closer to the plateau region. However, because of the rather fast values of ko for metalloproteins, data, usually, can be matched fairly well with the Butler-Volmer theory [122]. In the case of the Chidsey type experiments [124-1261, systems of the kind given in Fig. 2.82 are employed and because of the large electron-transfer distances, ko values are much smaller than for metalloproteins and use of the Marcus model is always required. Figure 2.74 contains an example of a voltammogram of surface-confined metalloprotein azurin which shows that even at a scan rate of 500 V s-l, the peak-to-peak separation is not large. In contrast, the separations in peak potential for the thiol system attached to a gold electrode (Fig. 2.87) show a very significant scan rate dependence with peak-to-peak separations being above 1 V at a scan rate of 1000 V s-' . A number of recent papers in the area of thin-film voltammetry have considered doublelayer and other effects [ I D ,135-1371. Thus, the overview given above still does not necessarily incorporate all the nuances. Further, only the ideal monolayer coverage is considered so that the probability of real systems exactly matching theory presented in Section 18 is still problematical, and, not surprisingly, several aspects of the theory [I 29,135-1401 are being debated in the literature. 2 18.3 Chemical reactions coupled to ideal thinjilm electron-transfer process As is the case when solution-phase electrochemistry is being considered, chemical steps may accompany charge-transfer processes when solids are attached to electrode surfaces. The majority of studies on adsorbed proteins have been carried out using cyclic voltammetry which is the most 'visual' of the dynamic methods, revealing the potential and time perspectives in an interactively simple manner. The scope for studying EC and more complex catalytic mechanisms associated with surface-attached films is illustrated in Fig. 2.88. Three situations are considered in this figure, each of which is simplified by being reversible in terms of interfacial electron transfer, but they differ in how the E step is coupled by C steps to further chemical processes. Figure 2.88(a) shows the voltammogram expected for a simple, reversible electron-transfer reaction for a thin-film surface-confined species as described in Section 18.2. Thus, as explained previously, oxidative and reductive components of the cyclic voltammogram are symmetrical, and currents reach a Voltammetric studies on solids I I I -0.5 0.0 0.5 1.0 +-----,----0.0 0.5 -0.5 E(V) vs Ag wire -0.5 0.0 0.5 E(V) vs Ag wire 1.0 E(V) vs Ag wire E(V) vs Ag wire -0.5 0.0 0.5 E(V) vs Ag wire 1.0 2.8'7 Effect of sweep rate on voltammetry of mixed Fc - C O N H - Cl5 - SH/HO - Clh- SH ~ )aqueous 1.0 M HCIOl at room temperature. thin-film monolayer (r = 9.5 x lo-" mol ~ m - in Currents have been normalized by the factor vQF/RT, where v is the sweep rate and Q the charge under the voltammetric wave. Sweep rates were (a) 0.1 (b) 1.0 (c) 10.0 (d) 100.0, and (e) 1000V s-'. Reproduced by courtesy: Anal. Chern. 66 (1994) 3164. Copyright, American Chemical Society. aximum value at the reversible potential [E~O],,~, thereafter decreasing to zero as all of the finite number of redox centres are transformed from one redox level to the other. The separation between peaks (AE,) is zero, the half-height eak width Wl12 is 3.53RTlnF and the peak current I, = PZ~F~VAI',,,/~RT. bviously, on the basis of these relationships, a two-electron (n = 2) reaction gives rise to a much more prominent signal than a one-electron (n = 1)process since Ip is proportional to n2 and Wl12 varies as l l n . Integration of the I-E curve gives the number of electrons transferred and hence direct calculation of the electrode coverage (peak area = nFvAr,,,). For a protein of molecular mass of 100 000 Da, maximum (monolayer) coverage is in the region of 3 x 10-l2 mol cm-2 [122]. 148 Pvinciples of volturnmetry . .:. .. .. '"'. E (V) -1 eox +-!+ red + OX*. ............. red* product substrate Fig. 2.88 (a) The ideal response expected from a thin-film monolayer of adsorbed electroactive species when the electron transfer is reversible. Current values are normalized to n 2 ~ 2 ~ ~ l ' / ~ (b) A response obtained when the electron transfer is followed by chemical conversion to a more stable electroinactive species. (c) Conversion of a one-electron reversible wave to a one-electron reversible catalytic wave on addition of substrate. Potential scale is V vs [~J],,fi. Reproduced by courtesy: Chem. Soc. Rev. 26 (1997) 169. Copyright, Royal Society of Chemistry. An illustration of what happens when the electron transfer is coupled to a first-order chemical reaction is shown in Fig. 2.88(b). The example given for an electron transfer, coupled chemical reaction, is the thin-film version of the well-known square-scheme model [I 41,1421, where the electrochemical and chemical reactions are assumed to occur separately. The kinetics of the chemical transformations, as in all electrochemical mechanistic studies, are investigated by varying the experimental time-scale, for example by using a range of scan-rates under conditons of cyclic voltammetry. The situation depicted in Fig. 2.88(b) is one in which the time required for interconversion of reduced red (isostructural with ox) to the thermodynamically more stable species red* (different structure to red) is comparable with the experimental time-scale, and where red* is electroinactive within the experimentally examined potential range, all species being surface confined. Obviously, under these conditions the reductive and oxidative components of cyclic voltammograms are no longer symmetrical and the reduction peak potential now contains a contribution from the thermodynamics associated with interconversion of red and red* instead of solely red reflecting the properties of the elementary electron exchange ox ereaction. Hence, the reductive wave is shifted to a less negative potential and sharpened as the position of equilibrium for the primary electron-transfer process is modified by removal of red. In the example given, the re-oxidation of red* is effectively gated because before any oxidation current can be observed, it must convert back to red. However, as the scan-rate is lowered, further time is + + Voltammetric studies on solids 149 available for red* to be in equilibrium with red. If a slow enough scan-rate can be achieved so that equilibrium between red* and red is achieved, the response will revert to being symmetrical and the reduction potential under these circumstances will reflect the thermodynamic distribution of species. Other complex heterogeneous-homogeneous processes that have been considered include dissolution/crystallization and more complex surface bound ECE type reactions in which the electron-transfer step may be connected with the solid or solution hase reactions [I 43-1 471. Figure 2.88(c) shows the voltammogram expected when reversible electron transfer is coupled to a catalytic scheme involving reaction of red with a substrate present in solution. Thus, ox is electrochemically transformed to red (in this case it is reduced) and then restored (re-oxidized) to the initial state by the substrate, whose mass transport in the solution phase can be controlled hydrodynamically by, for example, rotating the electrode. Hence, electron ort is no longer confined to the adsorbed film, and the balance produced en electrochemical and catalytic redox transformation results in a steadystate voltammetric response. It is important to note that rotating the electrode not affect the voltammetry of completely surface confined reactions. How, the catalytic redox scheme considered in Fig. 2.88(c) does involve a solution-phase component, so the rotation rate is important. A wide range talloprotein thin-film substrate catalytic schemes have been investigated and the relevant kinetic parameters determined from the dependence of limiting currents on rotation rate and substrate concentration [148]. 8.4 Nuances associated with adsorption n the above discussion, thin films of adsorbed or surface-attached material are strongly and irreversibly attached to the electrode surface. However, if an electrode is placed in a solution containing redox active material, a wide range of possibilities other than monolayer or sub-monolayer coverage of red and ox may ccur. Generally, these alternative situations give rise to complex voltammetry. or example, if adsorption of the oxidized or reduced species is weak, or if only either the oxidized or reduced form of the compound are adsorbed, then mixture of surface confined and solution-phase voltammetric responses may e observed which will be related to the free energies of adsorption and the nature of the adsorption isotherm(s). Figures 2.89-2.9 1 provide examples of voltammograms observed when different levels ofproduct (eqn 2.96) or reactant (eqn 2.97) adsorption are present, so that both surface confined and diffusioncontrolled components are simultaneously present. -ne - A(so1ution)6B (solution) OX (adsorbed) (2.96) +ne- +A(so1ution)+B (solution) -ne red(adsorbed) Sne- (2.97) 150 Principles of voltammetry Fig. 2.89 Examples of the influence of adsorption in (a, b) linear sweep and (c) cyclic voltarnrnetry for the process given in eqn (2.96). (a) Effect of variation of concentration for a reaction in which the product is adsorbed. Relative concentrations C : B :A are 1 : 4 : 16. (b) Variation of voltammograms with product strongly adsorbed as a function of free energy of adsorption. Free energies of adsorption are 29.4, 24.8, 20.2, and 15.6 kcal mol-', respectively, in curves A to D. (c) Influence of scan-rate on cyclic voltammograms with product weakly adsorbed. Relative scan-rates A : B : C are 4 x lo4 : 2.5 x lo3 : 1. Adapted from: Anal. Chern. 39 (1967) 1514. Copyright, American Chemical Society. An electrode may be modified, as in Fig. 2.82, by adsorption of a long chain of alkanethiolate or other related species not having an electroactive group. If this occurs, and an electroactive species is in solution, then the diffusioncontrolled response can be modified, as, effectively, electron transfer to and from the electrode surface has to occur over a rather long distance and also the double-layer region of the new interface at the chemically modified electrode is significantly different from that at the bare unmodified electrode. Miller et al. [149,150] have considered this situation and voltammograms of the kind shown in Fig. 2.92 are observed for reduction of cytochrome c when long and short chain alkane thiolates are used to modify the electrode and reduction occurs according to the schematic diagram in Fig. 2.93. Of course, the chemical modifier may also act as an insulator which will prevent any Faradaic current being observed, although if pin holes or other imperfections are present at such an electrode surface, then a small amount of material may still reach the Voltanzmetric studies o n solids 151 . 2.90 Theoretical cyclic voltammograms for electrode processes involving adsorption: (a) reactant weakly adsorbed; (b) product weakly adsorbed; (c) reactant strongly adsorbed; (d) product strongly adsorbed. Dashed lines indicate behaviour for uncomplicated Nernstian charge transfer. Reproduced by courtesy: Anal. Chem. 39 (1967) 1514. Copyright, American Chemical Society. I I I I -0.3 -0.2 -0.1 0.0 Volt vs SCE ig. 2.91 Cyclic voltammograms for reduction of methylene blue in buffered aqueous solution M; (c) 0.40 x lop4 M. Reproduced (pH 6.5; u = 44.5 mV s-l): (a)1.00 x lon4M; (b) 0.70 x by courtesy: Anal. Chem. 39 (1967) 1527. Copyright, American Chemical Society. Principles of voltammetry Potential vs SCE (V) Fig. 2.92 Cyclic voltammograms ofyeast cytochrome c at a modified gold electrode. (a) With a thin SAM, HO(CH2)3SHmodified electrode, the voltammetry reveals a well-formed almost reversible response. (b) When the SAM is thicker [HO(CH2)11SH] the rate of the electron transfer process is much slower, as evidenced by the appearance of a large shift in potential of approximately -0.6 V. The flattened shape of the reduction peak is predicted by Marcus theory. Experimental conditons: v = 0.5~s-lA ; = 0.13 cm2; T = 0°C; 1.1mM cytochrome c, 2 m M phosphate buffer (pH 7.1) with 1.O M KC1. Reproduced by courtesy: J.Am. Chem. Soc. 118 (1996) 7857. Copyright, American Chemical Society. bare electrode surface by radial diffusion to give voltammograms of the kind described in references [I 5 1,1521. Alternatively, if cytochrome c is adsorbed or attached [I531 onto the modified electrode surface to give the voltammogram shown in Fig. 2.94, then the distance dependence is given as in Fig. 2.95. 19 Techniques information on r voltammetry of s s associated with the -attached species Clearly, the theory applicable to the eletrochemistry of surface-attached species is almost invariably complex. In the discussion above, no consideration was given to the possibility that the rate of a process in a film is limited by the incorporation or expulsion of ions from the surface-attached layer as must occur to achieve charge neutralization. Additionally, significant problems with correction for uncompensated resistance, capacitance current and the modified double layer have not been addressed, nor have problems that arise when more than a monolayer coverage of electroactive film is present, when more than a single phase is attached to the surface, when microcrystals rather than films are attached to the electrode surface, or when electrocrystallization is coupled with electron transfer. Thus, it is probably not surprising that comparisons between experimental data and inherently approximate theory are often relatively poor when electrochemical data related to surface-attached species are scrutinized over very wide time domains. Obtaining moleculav level information 153 3 Cartoon of adsorbed cytochrome c on a COOH-terminated modified gold electrode. A crystalline region for a SAM HS(CH2)lsCOOH film exhibiting a 30" alkyl chain tilt angle is depicted. Alkanethiol molecules are represented as end-capped cylinders with a C O O H terminus (black) and a thiolate (grey) attachment to the gold electrode. Polypeptide line diagrams of cytochrome c molecule are shown in an electrostatically favoured orientation. For clarity, the haem group has been blackened. Reproduced by courtesy: Electmchern. SOC.liztegace 6(4) (1997) 40. Copyright, The Electrochemical Society. The determination of what occurs in a chemical or physical sense on an electrode surface when electron-transfer reactions occur with surface-attached species, requires the use of spectroelectrochemical (ESR, IR, UV-Visible, etc.) techniques in surface suitable formats, surface analysis techniques [I541 (e.g. electron microprobe) and microscopy (e.g. electron scanning microscopy, atomic force microscopy (AFM)).That is, a battery of surface science techniques are available to address the 'surface' problems that are present. A difficulty in relying solely on data obtained from voltammetrically based experiments is that since the electrochemical response usually reflects only the average response of numerous processes, the details of the chemical or physical changes that occur 154 Principles of voltammetry Fig. 2.94 Diffusionless cyclic voltammograms of yeast cytochrome c monolayers prepared by adsorption onto COOH-terminated gold electrode modifiers of different thickness. Conditions: pH 7.0 phosphate buffer of ionic strength = 50 mM; sweep rate is 100 mV s-'. (a) HS(CH2)loCOOH (b) HS(CH2)5COOH.Reproduced by courtesy: Electrochem. Soc. Inte6ace 6(4) (1997) 40. Copyright, The Electrochemical Society. Fig. 2.95 Dependence of the electron-transfer rate on distance for horse cytochrome c adsorbed on COOH-terminated alkanethiol gold electrode. The logarithm of the standard electron-transfer rate constant is plotted versus the number (n) of rnethylenes in the SAM HS(CH2),COOH alkyl chain. Reproduced by courtesy: Electrochem. Soc. Inte6ace 6(4) (1997) 40. Copyright, The Electrochemical Society. on the surface are unlikely to be unravelled by voltammetric studies alone. As well as utilizing knowledge gained from solid state spectroelectrochemistry, it can be noted that a mass change invariably occurs when a surface confined solid undergoes a redox reaction, and therefore the ability to 'weigh' the mass Obtaining molecular level information 155 change, via use of the electrochemical quartz crystal microbalance (EQCM), can be a very powerful tool to apply as an aid to understanding the nuances of solid state electrochemical studies. The surface spectroscopic, surface elemental analysis and electron microscopy techniques are well-established methods used in many branches of surface science and do not need special discussion in this book devoted to electrochemistry. In Chapter 5, important knowledge readily gained in electrochemical studies of surface-attached solids, by employing these surface science techniques in conjunction with voltammetry, will be demonstrated. In this chapter, only brief details are provided on the use of scanning probe microscopy techniques, which enable changes at atomic resolution of species on surfaces to be observed at the same time as voltammetric experiments are undertaken, and the in situ M method that enables the changes in mass taking place on an electrode e during the course of a voltammetric experiment to be measured. Both these techniques have been responsible for significant advances in the understanding of additional processes that need to be taken into account relative to those present in the idealized thin-layer model in Fig. 2.73. Indeed, as will e seen later, it is amazing that when electrode surfaces containing attached solids are examined in molecular or atomic level detail, as is now possible, that models based on Butler-Volmer or Marcus theoretical concepts provide even a reasonable description of the voltammetry! -1 The use of scanning probe microscopies in electrochemistry e ability to actually 'observe7what happens on an electrode surface during e of a voltammetric experiment has become possible via application family of scanned probe microscopies (SPMs) that were developed in s (see references [155,156], for example). Prior to the advent of these s, only methods such as electron microscopy and X-ray diffraction were available to obtain resolutions approaching molecular dimensions, and ese methods usually had to be applied in an ex situ mode. The new class of microscopes that have become an invaluable tool of the electrochemist7strade are typified by the scanning tunnelling microscope (STM) for which Binnig and Rohrer [157,158] received a Nobel Prize in 1986. These techniques examine surfaces at very close range with a probe that may be t a single atom across and may detect features on electrode surfaces at sizes roaching, or even reaching, molecular dimensions. Figure 2.96 represents a schematic diagram of the basic components of many forms of SPM instrumentation. In an STM, the tungsten probe or tip is ground so fine that it may consist of only a single atom [155,156]. Piezoelectric controls manoeuvre the tip within a few nanometres ofthe surface of a conducting sample 2.97(a)). At these short distances there is overlap of the electron cloud of toms of the probe tip, and of the nearest atom of the sample being probed. n a small voltage is applied to the probe tip, electrons tunnel across the gap, generating a minuscule tunneling current. X and Y piezoelectric controls move the probe back and forth across the sample surface in a raster pattern. The 156 Principles of voltammetry Feedback electronics Light or current detection Computer system Fig. 2.96 Schematic diagram of the basic components of a Scanning Probe Microscope system which consists of an X,Y piezoelectric scanner, a sensor to monitor movement ofthe probe, feedback circuits for controlling the Z-piezo and a computer system on which results can be displayed and analysed. Reproduced by courtesy: Coord. Chem. Rev. 200-202 (2000) 41 1. Copyright, Elsevier. probe is moved up and down as it tracks the topography of the surface using a feedback mechanism which senses variations in the tunneling current and varies the voltage applied to a third, piezoelectric control, Z. The Z control moves the probe vertically to stabilize the current and maintain a constant gap between the probe tip and the surface. The image produced by this STM technique is not the true topography, but a surface of constant tunneling probability, although often the two are closely related. Figure 2.97(b) shows an STM image of highly oriented pyrolytic graphite, while Fig. 2.98 illustrates what happens to this graphite surface during cycling of the potential [159]. The ability to 'see' an electrode surface at molecular levels of resolution is a great aid to the interpretation of electrochemical phenomena [160]. The STM microscope can be used only to create images of conducting materials. In contrast the atomic force microscope (AFM), shown in Fig. 2.99, does not require a conducting material to create an image. In this case, the probe tip is an atomically sharp diamond mounted on a strip of metal foil which is moved over the surface. An AFM records contours of 'force' rather than tunnelling current. The 'force' is the repulsion generated by the overlap of electron clouds of the tip, with the electron clouds of the surface atom. However, caution in the interpretation of data is always required in SPM measurements because the tip may damage the surface and artefacts may occur in the measurement [I611. The AFM can image a wider range of materials than the STM and can be used under water or other solvents in an in situ mode with voltammetric experiments. Figure 2.100 shows AFM images of Cao (buckyball) obtained before and during the course of reduction of the solid at a Cao-GC-acetonitrile (electrolyte) interface [I 621. Other forms of SPM have also been developed which include [155,156] the laser force microscope (LFM), the magnetic force microscope (MFM), the electrostatic force microscope (EFM), the scanning thermal microscope (detects Obtaining molecular level information 157 z Piezo ig. 2.97 (a) Schematic view of an STM. The tip, shown as a rounded cone, is mounted on a piezoelectric X, Y, Z scanner. A scan (dashed line) of the tip over the sample can reveal contours of the surface down to the atomic level. (b) An STM image showing carbon atoms in a sample of highly oriented pyrolytic graphite. This is a line scan image displayed as observed by a viewer 45' above the surface. An STM image is made up of a series of line scans, each displayed in Y from the previous one, and displays the path the tip followed over the surface. surface-temperature variations as small as ten-thousandth of a degree), the scanning ion-conductance microscope (SICM) and the scanning electrochemical microscope (SECM) [I 631. Since the SECM technique is based on detection with a microelectrode of the kind used in voltammetric studies (Section 10) and, therefore, is of direct interest to electrochernists in a fundamental sense, it is discussed in more detail. The technique of SECM was developed by the Bard group [163,164] as a novel Fig. 2.98 Constant-current STM images of the oxidation of highly oriented pyrolytic graphite (HOPG) in 0.1 M H S 0 4 at 0.05V versus a Ag quasi-reference electrode. KIP = -50 mV, l;,nn,l= -7 nA. Scan speed = 260 A s-l. (a) HOPG topography before oxidation. (b) HOPG topography after 20 potential cycles. (c) HOPG topography after further oxidation of the surface. Reproduced by courtesy: J. Phys. Chem. 92 (1988) 5563. Copyright, American Chemical Society. Obtainin, rnoleculav level infoormation 159 Laser Optical deflection sensor El- Cantilever and tip Image Piezo scanner 2.99 An AFM scans a sample with a shard of diamond mounted on a thin metal arm. The electron cloud of the diamond tip (which may end in a single atom) presses against the clouds of individual atoms in the sample, generating a repulsive force that varies with the surface relief. The force deflects the tip, whose movements are monitored by a laser beam reflected from the top of the arm to a photodiode sensor. A feedback mechanism responds to the changes in the beam's path by activating a piezoelectric control, which adjusts the sample's height so that the deflection of the arm remains constant. The sample's movements are translated into a surface profile. Unlike the STM, the AFM can readily image electrical insulators. Provided by courtesy: R.G. Compton, University of Oxford, England. variant on the use of voltammetric microelectrodes. Exact positioning of the icroelectrode and measurement of features of an electrochemical process in e spatial region behind the tip of the electrode surface and the surface, allows resolution of surface features down to approximately 30 pm. Figure 2.101 shows a schematic diagram of the typical apparatus used in the SECM method. n a typical configuration [I651 the 10-50-pm diameter microelectrode is formed from a glass sheath with a narrow central pore. A platinum wire is then sealed into the pore with epoxy resin, and the end is polished flat. The position of the electrode can be controlled at two levels. First, a three-dimensional microstage allows the microelectrode to be positioned manually in increments of a few pm. The electrode tip is moved into an initial position using the icrostage and with the aid of an optical microscope the area of the substrate to be investigated is selected. The piezoelectric translator then allows fine positioning of the electrode with sub-micrometer resolution. The electrode may thus be accurately positioned over the substrate. The SECM may be operated in a variety of modes. In the 'collection' mode B n e is used to monitor the current, for and when the solution process A example, [ F ~ ( c N ) , ]+ ~ [ F ~ ( c N ) , ] ~ - e-, the substrate is held at a potential where the species A in solution will be oxidized to B. The electrode tip is held at potential Et, which causes the species B to be reduced back to A. The tip current is then monitored as a function of time at constant height above the substrate. Variations of this technique are usually related to whether E, is + + + Obtaining molecular level information 161 held at a constant value while E, is stepped, as in a potential step experiment, or whether the substrate is held at constant potential and E, is cycled. In the 'AC generation/collection7 mode, an alternating signal is generated and applied to the substrate and a lock-in-amplifier is used to analyse the tip response with reference to the substrate signal. In the 'feedback' mode, a potential sufficient to drive a redox reaction is applied to the tip of the electrode and the current is measured as a function of tip position. As the tip approaches an insulating substrate, the diffusion layer around the tip is obstructed and the current response is diminished. At conductive substrates, the redox reaction may be reversed, as the electrogenerated species will be in excess relative to the bulk solution to which most of the conductive domain will be exposed. This 'reflected9material will then react at the electrode again, and the 'feedback' between the tip and the conductive substrate will enhance the current observed. This 'feedback7mode is used to image the conductivity of surfaces. Variations in the current or potential at the tip of the microelectrode, during the scanning of the surface, produce the images. Figure 2.102 provides a summary of the basic principles of SECM, while Fig. 2.103 represents a conventional height image of a portion of a composite el-F/Au surface which obviously contains a mixture of conducting and nonconducting substrates [I 661. The constant-current image of the same Kel-F/Au surface is shown in the upper half of Fig. 2.103. The constant-current image shows more detail than the constant-height image and provides the topography with higher accuracy. Scanning photochemical techniques [I 67-1691 use, as a source of contrast, the thermal effect associated with a focussed laser beam on the current or potential variations associated with an electrochemical process. This technique is essentially a temperature jump experiment and it is complementary to the SECM method in the sense that an electrochemical process is inherently associated with the ability to obtain a high-resolution image. For irreversible processes, the photothermal response is due to thermally induced changes in the rate of electron transfer, with contrast arising from local variations in dark current density, activation energy, and temperature change due to spatial variations in the absorption coefficient of light. For reversible processes, the signal arises from the thermally induced shift of the standard electrode potential, with contrast arising from variations in the local diffusion-limited current or temperature change. Blurring and shadowing effects arise from the relaxation of the local temperature in the electrode and diffusion field in the electrolyte as the scanning spot moves on. ig. 2.100 In situ AFM images obtained at 0 V versus Ag/AgCl in acetonitrile (0.1 M Bu4NC104) showing the changes in the morphology that occur when CbOmechanically adhered as a crystalline ~ solid to a G C electrode is subjected to redox cycling experiments (scan rate 0.1 V s-l). C 6 microcrystals after (a,b) 10 potential cycles between 0 and -1.OV (c,d) after two further cycles between 0 and -1.2 V, (e,f) after eight further cycles between 0 and -1.2 V (g) after three additional cycles between 0 and -1.6 V. Scale (a) 1.5 pm (b) 0.9 ym (c) 2.2 pm (d) 0.6 pm (e) 3.0 pm (f) 1.4 pm, and (g) 0.2 ym. Reproduced by courtesy: J. Phys. Chem. B 103 (1999) 5643. Copyright, American Chemical Society. 162 Principles of voltammetuy (2) Bipotentiostat I Piezoelectric translator Electrode insulated up to tip Reference electrode I Fig. 2.101 Schematic diagram of the apparatus used in a SECM. (a) Instrumentation. (b) Expanded version of microelectrode. Provided by courtesy: N. Stevens, Monash University, Victoria, Australia. Insulating substrate Conductive substrate Fig. 2.102 Basic principles of SECM: (a) When the microelectrode (ME) is far from the substrate (d the tip-to-substrate distance is much larger than electrode radius re), diffusion of A leads to a limiting steady-state current IT,, = 4nFDr,[Alo (Section 10.1). (b) When the ME is near an insulating substrate, hindered diffusion of A leads to IT < IT,,. (c) When the ME is near a conductive substrate, positive feedback of A to the tip leads to IT > IT,oo.Reproduced by courtesy: Physical Electrochemistry (ed. I. Rubenstein), Marcel Dekker, New York, 1995, p. 210. 19.2 T h e electrochemical quartz crystal microbalance Mass changes can occur at an electrode surface under a wide range of conditions. For example, the deposition of metallic lead from aqueous solution occurs as in eqn (2.98). ig. 2.103 (a) SECM surface plot of the microelectrode tip current recorded during a constant-height scan. Scan size is 100 pm x 100 pm. Vertical axis is relative tip position in pm. (b) SECM surface plot of the Z-piezo positioner voltage recorded during a constant-current imaging scan. Scan size is 100 pm x 200 pm. Vertical axis is relative tip position in micrometres obtained from the piezo voltage. The tip position was modulated at a frequency of 160 Hz with a 100-nm peak-to-peak modulation amplitude. The negative and positive current reference levels were set at 500 and 780 pA, respectively, and IT,oo was 80 PA, implying maintenance of about 2-ym tip-substrate spacing over both conductive and insulating regions. The images were made with a 2 pm diameter Pt tip, using a 2.1 rnM solution of [ R U ( N H ~ ) ~ in ] ~a+p H 4.0 buffer as the mediator species, and a tip raster scan of 10 pm s-l. See Fig. 2.102 for definitions of symbols. Reproduced by courtesy: Anal. Chern. 65 (1993) 1373. Copyright, American Chemical Society. a 164 Principles of voltammetry For this reaction, Faraday7slaw states that the charge consumed (Q) is related to the mass deposited by the expression n F (mass) = molecular weight mass = (2.99) (molecular weight) Q nF Typically, in a voltammetric experiment, the charge, Q, is only a few hundred microcoulombs (e.g. 10 pA for 10 s). Since F is 96 485 C mol-l, masses of only up to about 5 pg are deposited under conventional voltammetric conditions. However, a metal deposition reaction involves much larger mass changes than encountered with most other forms of reaction involving interaction of a solid with an electrode. Consequently, the mass change that occurs during the course of a voltammetric experiment is oiten less than a microgram, so that very sensitive mass detection is needed. The quartz crystal (QC) microbalance can be readily used to measure mass charges in the nanogram region. Hence, when electrochemistry is combined with this mass sensor, an EQCM is constructed. In the EQCM experiment, a metal electrode (e.g. gold) is deposited onto a Q C microbalance. Then if, say, Pb is electrochemically deposited as in eqn (2.98), the interface looks like that in Fig. 2.1O4(a), whilst a voltammogram and EQCM data for deposition and stripping of lead are shown in Fig. 2.104(b) and (c) respectively. The Q C microbalance itself is a piezoelectric device in which a crystal of alpha quartz deforms when placed in an electric field (oscillates in an alternating electric field). In order to fabricate a mass sensor, a large, single, alpha Q C is cut into a wafer at a certain angle with respect to the crystalline axes to optimize the piezoelectric activity. The application of an alternating electric field to the crystal causes the crystal to oscillate. If the alternating electric field is applied at the correct frequency, the crystal will oscillate at a resonant frequency, fo, which depends on the thickness of the crystal. where tq is the thickness of the crystal, p, is the density of quartz (2.648 g ~ m - ~ ) , and p, is the shear modulus (2.947 x 10" g cm-' s-'). 19.2.1 The Sauerbvey equation For thin, uniform, and rigid films attached to a QC, the following relationship exists Arn relating the observed change in frequency to the change in mass at the surface of the crystal. The term in brackets is a constant for a certain thickness of crystal . 2.104 (a) Schematic diagram of electrode interface in an EQCM experiment in which metallic lead is deposited onto a gold-coated quartz surface. (b) Cyclic voltammograms showing deposition and stripping of lead in aqueous 0.1 M acetic acid/O.l M sodium acetate. (c) EQCM data obtained simultaneously with cyclic voltammograms shown in (b). v = 100 mV sP1 and [Pb2+] = 8 mM. Provided by courtesy: P.J. Mahon and G.A. Snook, Monash University, Victoria, Australia. 166 Principles of voltammetry and the equation is simplified to where Cf is the sensitivity factor for the crystal. Thus, a mass increase produces a decrease in the observed frequency. For a 10-MHz crystal, Cf = 2.26 x lo8 Hz cm2g-l. Equation (2.103) indicates that an observed frequency change of 1 Hz corresponds to a mass change of 4.4 ng cmP2.In principle, the need for calibration of each crystal is usually unnecessary because the 'sensitivity factor7 is only dependent upon well-known physical constants. In practice, calibration is usually undertaken via the use of a well-defined metal deposition reaction [170,171], because the frequency depends on additional factors, and a more rigorous equation is where the terms on the right-hand side of the equation refer to the effect of mass, pressure, viscosity, and roughness, respectively. In electrochemical experiments it is generally assumed that all factors, except mass, are constant. It is also assumed that species are rigidly attached to the electrode surface. In an EQCM experiment, the Q C may be mounted between two spring clips and electrical contact is made to the connector holding the clips and the crystal. A schematic diagram of an EQCM instrument of this design is shown in Fig. 2.105. In addition to the standard components required for an electrochemical experiment, there are two additional elements. The Oscillator is a circuit which enables the crystal to oscillate without interfering with the electrochemical experiment. The Frequency Counter measures the frequency developed in the Oscillator (in some instruments a frequency-to-voltage converter is used). In a common instrument design, the working electrode is wired so that it is true ground and the voltage between the two metal surfaces of the crystal also varies relative to this ground point. The oscillator circuit develops a voltage of approximately 0.4 V, peak-to-peak, across the crystal [17 1,1721. A typical Q C with deposited metal electrode arrangement is shown in Fig. 2.106. The deposited metal can be any metal that adheres strongly to the , Current in nanoamps Potentiostat I Counter electrode Quartz 45 Reference electrode nanograms \Gold working electrode Fig. 2.105 A block diagram of an EQCM. Provided by courtesy: P.J. Mahon and G.A. Snook, Monash University, Victoria, Australia. Obtaining molecular level information 167 Typically the crystal has a diameter of 13 mm. T o resonate at 10 MHz the crystal is cut so that it is 0.17 mm thick Electrical Electrical contact Metal is deposited on both sides of the crystal so that the alternating electric field can be applied across the crystal. -106 The gold-coated quartz electrode surface used in an E Q C M experiment. Provided by courtesy: P.J. Mahon, Monash University, Victoria, Australia. quartz surface. Typically Au is used, but other metals such as Ag, Al, Cu, Zn, , and Pt have also been employed. It is also possible to deposit one metal of another. Usually vapour deposition techniques are used to deposit the metal onto the quartz, but any technique can be used as long as the crystemperature stays below 573°C. Above this temperature, the piezoelectrical activity is destroyed. ri&nally it &as thought that the application of the Q C microbalance in solution-phase electrochemical studies would fail due to heavy damping of the crystal by viscous liquids. The first electrochemical application involved the three stage ex situ process of (i) measuring the frequency of the dry crystal, (ii) deposition of a small quantity of metal in solution, and (iii) measuring the frequency of the dried crystal. The first in situ application occurred in 1981 [170]. In this pioneering study, use of Faraday's law and the Sauerbrey equation enabled a simple relationship between the change in frequency (Afm) and the amount of charge (Q) passed to be obtained. Af = - (molecular weight) Cf Q nF he charge can be obtained by integrating the current (i.e. Q = J,fI dt). Alternatively, the current can be related to frequency in the following way I=- d(Af,)/dE nFv (molecular weight) Cf ere v is the scan rate (V s-l). 19.2.2 Applications of the electrochemical quartz crystal microbalance umerous applications of the EQCM method have been published in the last ecade and have been reviewed in references [172-1751. In Chapter 5 the 168 Pn'ncipler of voltammetry use of this method will be demonstrated with microcrystals adhered to electrode surfaces. In this chapter, application of the EQCM to the problem of metal deposition has already been referred to in Section 18.2 (see Fig. 2.104). To conclude this brief overview of the EQCM method, applications to studies on adsorption and desorption processes and conducting polymers will be considered. As noted above, a mass change will necessarily accompany an electron-transfer process at an electrode surface only when either the oxidized or reduced species is attached to the electrode surface, as occurs in the ~b~+(solution) 2e- + Pb(rneta1) deposition process. However, a mass change also occurs when either the oxidized or reduced forms of solution-soluble species become adsorbed onto an electrode surface (see eqns 2.92 and 2.93). For example, consider the bromide salt of the ferrocene derivative C H ~ ( C H ~ ) , ( C H ~ ) ~ N + CcontainH~FC ing a long alkyl ammonium chain of length x attached at one position. The unoxidized ferrocene (Fc) compounds are strongly adsorbed to gold surfaces and studies on the interactions with this electrode surface have been made with an EQCM [176,177]. When x = 12, and a dilute 22 yM solution of CH3(CH2)12 ( C H 3 ) 2 ~ + C H 2isFused, ~ oxidation of Fc(adsorbed) to solution) leads to an EQCM frequency increase which corresponds to a mass decrease at the electrode surface (Fig. 2.107) which is consistent with dissolution of the oxidized FC+ form of the compound. Adsorption occurs when the potential returns to less positive potentials, where Fc(adsorbed) is reformed by reduction of solution). Under these conditions, eqn (2.104) applies. + However, if the concentration is increased to 500 yM (Fig. 2.108), then not all the oxidized ferrocene dissolves and there are current contributions arising from formation of both Fc+(adsorbed)and solution), because the reaction occurs as in eqn (2.108). This situation is akin to that described in Section 17.4. In this case, the molecular weight of the material cannot be calculated by simple use of the Sauerbrey equation because an anion X from solution electrolyte enters the monolayer to compensate for the increase in charge during the Fc(adsorbed) -+ Fc+(adsorbed) component of the oxidation process, and so the frequency increase on oxidation corresponds to the difference of mass loss from dissolution and mass Obtaining moleculav level infoormation .080 I ,080 .240 .400 Potential (V vs Ag/AgCl) I I I I I .240 .400 Potential (V vs Ag/AgCl) .560 I .560 ,720 I I I .720 2.107 Simultaneous recording at a scan rate of 50mVs-' of (a) a cyclic voltammogram, and (b) EQCM frequency response for oxidation of low coilcentration (22 pM) of CH3(CH2)12(CH3)2~f CH2Fc in aqueous 1.0M H3P04. Reproduced by courtesy: Langmuir 5 (1989) 671. Copyright, American Chemical Society. increase from incorporation of X and of course, vice versa, for the reduction component of the cyclic voltammogram. The fabrication and use of polymer modified electrodes has attracted much attention in recent years [178,179]. Redox conversion in polymer film modified electrodes is associated with the simultaneous presence of electron transfer and exchange of electrolyte ions to maintain charge neutrality. The ionic switching component of the process is elegantly monitored by the EQCM method. For example, the oxidation of the ferrocene sites in poly-(vinylferrocene) in contact Pvinciples of voltammetvy .080 ,240 .400 E (V vs SCE) .560 .720 .080 .240 .400 E (V vs SCE) .560 .720 I I Fig. 2.108 Simultaneous recording at a scan rate of 50 mV s-' of (a) a cyclic voltammogram and (b) EQCM data for oxidation of a high concentration (0.5 rnM) of C H ~ ( C H ~ ) ~ ~ ( C H ~ ) ~ N + C H in aqueous 0.2 M Li2S04 (pH 3). Adapted from: Chemically Modijed Electrode Sufaces in Science and Industry, Gordon and Breach, New York, 1988, p. 377. with solvent (electrolyte) creates a highly charged polymer coating. The frequency in the ECQM experiment is observed to decrease during the oxidation process and subsequently increases to the original frequency during the reduction cycle (Fig. 2.109). The mass change corresponds to an influx of anions into the polymer during the oxidation process, in order to maintain electroneutrality throughout the polymer. During the reduction of the ferrocenium groups, the anions are expelled into the solution. In the case shown in Fig. 2.109, the mass change corresponded directly to the uptake of the electrolyte PF, anion [180]. However, use of the Sauerbrey equation requires that the solid should be attached in an acoustically rigid manner. 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However, polyoxometalates [I] represent an electrochemist's dream class of compound because it is not uncommon to have multiple charge-transfer processes taking place during the course of a single voltammogram [2,3] and several examples, where more than twenty electrons [4,5] can be added during the course of electrochemical reduction of lyoxometalate, have been established. o unravel the vast array of kinetic, thermodynamic, and synthetic information available from a voltammetric study of polyoxometalate compounds res the application of the majority of procedures described in Chapter 2. , the use of transient and steady-state studies at numerous classes of eleche use of spectroelectrochemical techniques, electrochemical synthesis, ulation techniques, as well as photoelectrochemica1and electroanalytical ions, abound in the polyoxometalate electrochemical literature. n this chapter, detailed descriptions of the very rich redox chemistry of sevoxometalate compounds are presented. In particular, the contributions ctrochemist's arsenal of techniques described in Chapter 2 are highthe establishment of the detailed picture now emerging on the redox of this important class of compound. However, studies reported are confined to cases where both the oxidized and reduced forms of the polyoxometalate species are soluble in the solvent(electrolyte) of interest. Examples of voltammetric studies where solids are attached to electrode surfaces will be emphasized in Chapter 5. olyoxometalates form a large class of inorganic cluster-like mineral comounds, known for well over a century, that have become of increasing 178 Illustvating basics ofvoltammetvy interest in recent years due to recognition of their extraordinary topological and electronic versatility, and due to their current significance in disciplines as diverse as oxidative catalysis [6-81, biology, medicine, and materials science [I ,5,9-1 I]. They are formed principally from combinations of oxide ions and transition metal cations in their do electronic configurations, held together only by metal-oxygen bonds [I ,5,11,12]. Based on restrictions placed on acceptable ionic radii ratios, only a limited number of metal-ions form these complexes (v', ~ b ' , ~ a ' , MO", and w'' ) with the latter two forming by far the largest number [I ,2,5,ll,121. The principal units that make up most polyoxometalates Atomdesignations: M = e 7 O = O , P = @ , S i = O , W = O a n d X = @ Fig. 3.1 'Ball and stick' drawings of representative structural families of polyoxometalates: (a) hexametalate structure, [M6OI9lX- (the charge, x, depends on M) ; (b) Keggin structure, [XW12040]X-(X depends on the heteroatom, X); (c) Dawson structure, [X2wlX062]x-(X depends on X); (d) Pope-Jeannin-Reyssler structure, [MPsW300110]x-(x depends on the central metal-ion, M). Reproduced by courtesy: Chern. Rev.98 (1998) 327. Copyright, American Chemical Society. Coupled electron- and proton-transfer reactions 179 6 octahedra. The 'polyhedral notation', commonly used by investigaare tors who study polyoxometalate and related materials, including metal oxides, the dominance of these octahedral units [9]. Deviations of the M 0 6 units ure octahedral symmetry can be substantial, with the metal always being ed towards the terminal or doubly bonded oxygen atoms. The M 0 6 units in polyoxometalates can be linked together by a single oxygen atom, termed a nkage. Octahedra joined in this manner are said to be 'corner sharing'. present in the same polyoxometalate molecule as the corner-sharing a are the edge-sharing octahedra. In the latter, two M 0 6 units are gether by two oxygen atoms, termed a di-p-0x0 linkage. Two large sub-categories of polyoxometalates exist: the 'isopoly' and the 'heteropoly' compounds. The former are constituted of only metal and oxygen atoms, while the latter contain one or more p-, d-, or f-block 'heteroatoms' at well-defined geometrical sites in the molecule, in addition to the metal and oxygen atoms [2]. Up to 75 per cent of the elements in the periodic table can function as heteroatoms in polyoxometalates. The heteroatoms in the heteropoly compounds can reside in either buried (not solvent accessible) or surface ent accessible) positions in the polyoxometalate structure [2]. all and stick' forms of structural representation are given for a range of polyoxometalate complexes in Fig. 3.1. Given the fact that the transition metals sent in polyoxometalate complexes are generally in high oxidation states oV1,W" etc.), and that there are non-equivalent environments for the within the structures, it is not surprising that this class of compound e extensively reduced under voltammetric conditions to give a rich array -transfer reactions aps the most widely used technique used to elucidate voltammetric mechas is cyclic voltammetry at macrodisc electrodes (see Section 8 in Chapter 2). ost all recent voltammetric studies on polyoxometalate systems contain les of the use of this technique, and if data are reported in aqueous then the pH dependence is likely to have been examined. However, only rarely are voltammograms simulated according to the postulated mechanisms reported, as recommended in Chapter 2. In this section simulationerimental comparisons for the initial processes observed in the reduction, in aqueous media, of the ~ - [ P ~ w ~ ~and o ~a ~ ]- ~ -[ ~ ~ systems ~ ~are~ presented [13] in order to demonstrate the value of undertaking a systematic interactive experiment-theory approach to achieve a realistic comparison of ' ~ d a p e dwith permission from Anal. Chem. 71 (1999) 3650. Copyright, American Chemical Society. Additional details may be obtained by consulting this reference. 0 ~ 180 Illustvating basics of voltarnrnetvy experimental and theoretical voltarnrnograms under circumstances where the mechanism is inherently complex. Limitations that may be encountered in simulation-experimental comparisons also are identified. 3.1 Reduction ofa -[P, wI8 06#Six one-electron processes are observed for the reduction of a-[P2W18062]6(Structure C in Fig. 3.1) in aqueous electrolyte media at pH values above six [14]. The processes under these conditions are summarized2in eqns (3.1)-(3.6). However, in the presence of 6 M acid, there are three, apparently, two-electron reduction events [I 4,151 instead of six, single one-electron processes. Typically, the processes obtained in strongly acidic conditions have been written as in eqns ( 3.7)-(3.9), although, as will be seen from subsequent discussion, protonation steps accompany electron transfer in acid media and more informative descriptions of the coupling of electron- and proton-transfer reactions can be developed via simulation-experiment comparisons. 3.1.1 Initial considerations The cyclic voltammetric behaviour at a 3-mm diameter glassy carbon (GC) macrodisc electrode is presented for the first four one-electron charge-transfer processes (Scheme 3.1) over the pH range 5.2-1 -0 in aqueous 0.5 M NaC1 solution (Fig. 3.2). Over the pH range 5.2-1 .O, the wave shapes and peak positions of the first two couples 0 / 1 and 1/2 do not change [15], whereas processes 21'3 and 3/ lesce (Fig. 3.2). Thus, at some pH values, very complex cyclic voltammograms 2~somericnotation as in ~ ~ ! - [ P ~ w ~and ~ o~ ~~ ~! ]- ~ [H - ~ W ~is ~commonly O ~ ~ ] ~omitted in subsequent discussion for convenience and also because the isomeric forms of reduced species are usually unknown. Coupled electron- and poton-transfer reactions I -0.75 I I I -0.5 -0.25 0 Potential (V vs Ag/AgCl) I 0.25 181 I 0.5 Potential (V vs Ag/AgCl) . 3.2 Cyclic voltammograms obtained at a scan rate of 100 mV s-I for reduction of 1 rnM [ P ~ w ~ ~ oat~a GC ~ ] macrodisc ~ electrode in aqueous 0.5 M NaC1; (-) experiment; (- - . ) simulation. The poorer fitting at the switching potential is caused by the influence of additional processes at more negative potentials. Reproduced by courtesy: Anal. Chem. 71 (1999) 3650. Copyright, American Chemical Society. are observed, but it will emerge that this does not correspond, in this case, to the onset of either electrochemical or chemical irreversibility. The simulation will e shown to be critical to gain an understanding of the pH-dependent factors that govern the coalescence of these processes. Illustrating basics of voltammetry Scheme 3.1 Summary of the first four basic charge-transfer processes associated with reduction of [ P ~ w ~ ~ in o aqueous ~ ~ ]0.5 ~MNaCI. Experimental E;,? values are given in parentheses in rnV versus Ag/AgCl. 3.1.2 Stepwise approach to the simulation Even the simulation of the four uncomplicated one-electron charge-transfer processes at pH 5.2 (Fig. 3.2(a)) requires the input of a large number of parameters, some of which are derived from the considerations in points (1) to (11) below: (1) Experimental conditions The potassium form of the polyoxometalate salt was dissolved in an aqueous solution of 0.5 M NaCl at a known concentration (1 or 5 mM). The pH value was adjusted with aqueous NaOH or HCl. (2) E;,2-values for simple one-electron steps These were estimated from cyclic voltammetric data as the average value of reduction and oxidation peak potentials [ ( E ; ~ E y ) /2] (Section 8.1 in Chapter 2) in solutions of sufficiently high pH (Table 3.1, Scheme 3.1). (3) Uncompensated resistance arisingfvom I R drop between the working and reference electrodes A value of 200 ohm was measured by impedance techniques and found to be suitable for use in simulations over the scan rate range of 50-1 000 mV s-* . Farad cm-2 was assumed, (4) Double-layer capacitance A value of 2 x on the basis of agreement between experiment and theory of the background electrolyte. Parameters (3) and (4) were optimized values deduced from measurements at higher pH values where protonation effects were minimal. (5) Temperature The simulation temperature was set to 298.2 K. Small differences with experimental data obtained at temperatures between 20°C and 23°C are not critical for this system. (6) Charge-transfercoeficient a Assumed to be 0.5. (7) Area of the working electrode This parameter was determined to be 0.0893 cm2 by application of the Levich equation (Table 2.3) to rotating-disc voltammograms at the GC electrode obtained for oxidation of solutions of 1.0 mM ferrocene in CH3CN(0.1M Bu4NC104). Each process (8) Standard heterogeneous charge-trans& rate constants at E ; , ~ ( ~ O ) was considered to be essentially diffusion controlled in the scan rate range v = 50-1000 mV s-'. Consequently, the ko values were assumed to be fast and were set at 1cm s-' for the purposes of the simulation. This implies that the processes were assumed to be reversible on the cyclic voltammetric time-scale. + Table 3.1 Parameters used in the simulation of the cyclic voltammetry of 1 rnM solutions of polyoxometalate in aqueous 0.5 M NaCl Couples [ P ~ w ~ ~ o(Scheme ~ ~ ] ~ -3.4) 2/3 3/4 [H~wI~o~c$- (Scheme 3.5) 3h/4h Of/1' 11/2' lth/2'h -490 -555 -755 -585 65 72 101 Protonic equil. K~~ (M-I) 50 Dispropn. equil. 2 3 t,2 + 4 Equil. const 9.1 x lo-4 Diffusion coeff. Dan;,, Kllh 2.8 x 103 2 1' t, 0' 4 x lo-4 Danion K2'h 2.4 x lo6 1' 1' h t, 0' lo6 cm2 s-I 2.0 33/2(mV) AEp (mv) 2.5 + 2' + 0.35 DH+ 19 + 2'h K2'h2 3.0 x 103 2 l'h t,0' 0.38 + 2'h2 184 Illustvating basics of voltammetvy (9) Dfusion coefficients of [P2W180 6 2 ] x ( x= 6-10) These were assumed to be independent of x. A value of Danion= 2.0 x loh6cm2s-' was estimated for [ P ~ w ~ ~ viaouse~ of~ hydrodynamic ] ~ voltammetry and the Levich equation at a RDE (Section 9.1 in Chapter 2). Allowing variation of the single variable Danion,generated the simulated voltammogram in Fig. 3.2(a) with Danion optimizing at 2.5 x 1o - ~cm2 s-' . As noted above, the first and second processes remain unaltered as the pH of the solution is lowered from the initial value of 5.2 (Fig. 3.2). In contrast, the fourth wave appears to collapse and merge with the third wave (Fig. 3.2(b) and (c)).At pH 3.0, and when the solution concentrations of H+ and [P2W18062]6are equal, only a single broad wave is detected, with an apparent peak-to-peak separation, AE,, of 115 mV (Fig. 3.2(d)). As the pH value is further lowered, this process gradually sharpens and, below pH 2.20, begins to move to more positive potentials (Fig. 3.2(e)). By the time a pH-value of 1.0 (Fig. 3.2(f)) has been reached, AE, is 44 mV, and hence consistent with two unresolved one-electron processes (28.5 mV is expected for a reversible couple when two electrons are transferred simultaneously and reversibly at the same potential at 298 K). In order to simulate this complex, pH-dependent, voltammetric behaviour, the following stepwise approach is recornmended. Initially, a protonic equilibrium involving 4, presumably the most basic species (charge lo-), was included into Scheme 3.1 to give Scheme 3.2. Scheme 3.2 Subsequently, additional parameters associated with other added equilibrium reactions need to be introduced as the proton concentration increases. (10) The apparent dzjiusion coeficient of^+ In principle, the diffusion coefficients of four polyoxo anions need to be defined, as well as that of the proton. In (9) it was decided to make the diffusion coefficient of all the polyoxo anions equal to that measured for [ P ~ w ~ ~ o ~Further, ~ ] ~ - significant . ion-pair formation [16], that is likely to result from the combination of a high sodium cation concentration and negatively charged polyoxo anions, was neglected. These simplifications necessitate the use of an optimal apparent value of DH+ rather than a measured value. In pure water at 25°C [17], DH+ = 9.3 x cm2 s-* . Its value in aqueous NaCl (0.5 M) is not known but is 7.5 x cm2 s-* in 0.54 M NaCl at 25°C [18]. In contrast, a value of 1.0 x lop5cm2 s-' was found Coupled electron- and proton-transfer reactions 185 give excellent agreement between experimental and simulated voltammograms in the pH range 1-6. This value was optimized in the intermediate pH range, as the contribution from protonation was insignificant at higher values and the electrochemistry was not sensitive to DH+at lower values. Clearly, both approximations introduced above play a role in the apparent value of DH+ used to optimize the simulation. That is, DH+is subject to accumulation of errors and hence may contain considerable uncertainty with respect to systematic error. Thus, while no great precision can be attached to the apparent value H+, 1.0 x cm2s-l, and indeed it is lower than that predicted from the in literature [17,18], the important aspect is that this value is much larger than that derived for the anions, a feature critical for the creation of a high pH gradient close to the electrode in unbuffered media. This feature is essential in order to achieve agreement between simulated and experimental data. Ideally, input of independently measured diffusion coefficients and ion pairing equilibrium constants for all species and equilibria would improve the accuracy of the simulation. Since such measurements could not be achieved, an optimal, rent value of DH+was used over the entire pH range to minimize the ut parameters. Errors in estimation of the area of the electrode to the uncertainties in the diffusion coefficients. mogeneous rate constants The rate constant for protonation, kqf (foreaction) of 4, was assumed to be extremely fast and arbitrarily set to , which corresponds to an essentially diffusion-controlled value. The back rate constant k4b was allowed to vary and therefore to determine the of the equilibrium constant: K4h = k4f / k4b. e parameters designated above, when used in the initial simulation, prod an acceptable fit to experimental voltammograms in the pH range 6.0-3.0 3.3; K4h = 5 X lo4M-l) but not at pH 1.0 where the simulated value was too large, and the simulated peak potentials too negative, relative to experiment (Fig. 3.4). Reducing K4h exacerbated these effects, and allowing it to increase caused the wave to become too 'irreversible'. The latter effect is traced to the constraint of assuming protonation to be Thus, increasing Kqhreduces kqb. Consequently, less 4 s converted to 4 during turn sweep leading to an unacceptably low cur e inconsistencies between simulations based on Scheme 3.2, particularly at be overcome by introducing an alternative route for the convervia 3h, the protonated form of 3 (Scheme 3.3). In the simulation , the Eil2 value for the [ P ~ w ~ ~ o ~couple ~ ] ~in-Scheme ~ ~ ~ 3.2, ) remains fixed at the experimentally determined value, and K3h and Kqh are allowed to vary. The Nernst equation ensures that these three quantities define ) = E(3/4) - (2.303 RTInF) log (K3h/Kqh) /4h) is the Ei12 value for the [ ~ ~ 2 ~ 1 8 0 6 2 ] ~couple. -/~- Illustrating basics of voltammetry 186 -0.50 -0.25 -0.00 Potential (V vs Ag/AgCl) 0.25 0.50 Fig. 3.3 Cyclic voltammograms obtained at a scan rate of 100 mV s-' for reduction of ~ oa GC ~ ~ macrodisc ] ~ electrode in aqueous 0.5 M NaC1 (pH 3); (-) experi1 ~ M [ P ~ w ~ at ment; . .) simulation; employing Scheme 3.2 with K4h = 5 x lo4 M-' . Reproduced by courtesy: Anal. Chem. 71 (1999) 3650. Copyright, American Chemical Society. ( 0 At pH 3.00, the experiment shows that the two waves have merged to a broad, single wave (Fig. 3.2(d)).For this to occur, E(3h/4h) 5 E(2/3) and as, experimentally, E (213) - E(3/4) = 180 m v , eqn (3.3) requires that K3h/K4h < This constraint allows a systematic search to be undertaken for the estimation of K3h and K4h. Values which provided acceptable simulation at individual pH values could be defined but were not transferable (e.g. pH 5 3.0 : K3h = lo2M-l, K& = I O ~ M - '(Fig. 3.2(a-d)); pH = 1.0 : K3h = IOM-', K4h = I O ~ M - ' ) .Consequently, the next step undertaken in order to seek good agreement between simulated and experimental cyclic voltammograms was to include protonation of 4h (Scheme 3.4). This seems desirable because: (a) the fact that K4h2 depends upon [H+12 means that inclusion of this equilibrium reaction need only affect voltammetric behaviour at the lower pH values where discrepancies presently exist with use of Scheme 3.3; Coupled electron- and proton-transfer reactions 187 Potential (V vs Ag/AgCl) Cyclic voltammograms obtained at a scan rate of 100mVs-' for reduction of 1 rnM [ P ~ w ~ ~ at aoGC ~ macrodisc ~ ] ~ - electrode in aqueous 0.5 M NaCl (pH 1); (-1 experiment; (. . - .) simulation; employing Scheme 3.2 with &, = 5 x lo4MM-'.Reproduced by courtesy: Anal. Chem. 71 (1999) 3650. Copyright, American Chemical Society. Scheme 3.3 (b) anionic charge considerations and the expected increasing basicity, predicted to occur as extent of reduction increases, suggest that if equilibrium 3 tz 3h is important, then 4h tt 4h2 also should be included. ystematic searching leads to a set of parameters (Table 3.1) which fitted the cyclic voltammetric behaviour optimally in the pH range 6.0-1.0 (Fig. 3.2). 188 Illustrating basics of voltammetry Scheme 3.4 E(3h/4h) is calculated to be -0.480 mV, some 10 mV more positive than E(2/3), as required. Thus, a single set of three equilibrium constants can be used to fit this complex voltammetric behaviour over a range of five orders of magnitude in proton concentration. Disproportionation reactions are known to be important in the chemistry of polyoxometalates [5]. Relevant equilibrium constants related to disproportionation of reduced forms of the [ P ~ w ~ ~ osystem ~ ~ ] can ~ - be derived from Table 3.1 (see Scheme 3.4 and eqns (3.11) and (3.12)): As expected for a reaction scheme in which all electron-transfer steps and acidbase reactions are reversible, incorporation of these cross reactions had no impact on the simulated cyclic voltammetric behaviour over the pH range 6.0-1.0. 3.1.3 Additional verification o f t h e acceptability of calculated parameters The simulation parameter values established above have all been derived from 1mM solutions of polyoxometalate anion. A crucial test of their validity, is their ability to be used to correctly predict voltammetric behaviour at different polyoxometalate concentrations. Predictions for 5 mM solutions were surveyed and the data suggested that significant differences in wave shapes were expected at pH 3.45. A comparison of experimental behaviour and simulation at this o ~ ~ ]in~ Fig. 3.5. Peak pH for 1 and 5 mM solutions of ~ ~ ! - [ P ~ w ~ is~ shown positions still match closely but current intensities reveal discrepancies. The value current magnitude may be fitted almost exactly by changing the D,,, from 2.5 x cm2 s-' (derived cm2 s-l to the experimental value of 2.0 x from rotated-disc voltammetry at 1mM concentration). A rationale for this change is that an increase in anion concentration and a concomitant increase Coupled electron- and proton-tranrfer reactions I -0.75 I I I I I -0.5 -0.25 0 0.25 0.5 189 Potential (V vs Ag/AgCl) . 3.5 Cyclic voltammograms for reduction of [P2 W18 0 ~ ~ (a)1 5~mM; ~ (b) ; 1mM. Other conditions are as in Fig. 3.2. Reproduced by courtesy: Anal. Chern. 71 (1999) 3650. Copyright, American Chemical Society. ion pairing for these highly charged species is expected to decrease Danion. owever, it can be noted that changing the electrode area slightly, assuming a small amount of blockage has occurred, would also lead to a lowered current agnitude and good fitof the data. The value of DH+was not altered in the even though simulation, when charging the concentration of a-[p2wI8 is species is expected to be a function of the ionic strength and environment. A word of caution is needed to conclude this Section. With enough variables available, it is of course possible to simulate the proverbial camel, so that a sysatic and chemically 'reasonable' strategy needs to be adopted when varying parameters that may be input into a simulation. Thus, it is considered that simulation of the [ P ~ w reduction ~ ~ sequence ~ ~ ~represents ] ~ the limit to ich it is 'reasonable' to push the extent of credibility of a simulation of a comx problem if the data obtained from the simulation are to be quantitatively lievable. Clearly, the more the number of available, independently measured ameters, the better. Use of sensitivity analysis and smart statistical methods calculation of the significance of each parameter [19] will assist in assessing e reliability. Major weaknesses in the above simulation, as it presently stands, es with uncertainties in the diffusion coefficients of D,;,,, and DH+and, to lesser extent, with the electrode area. Setting the protonation reaction (e.g. 190 Illustrating basics of voltammetry forward reaction k4f) at a value expected for the diffusion-controlled rate of 10'' M-' s-l is also somewhat arbitrary. Finally, it is never possible to guarantee that a unique solution to a mechanism has been achieved. In all senses, then, ultimately, an improved simulation may emerge in the voltammetry than that presented above, despite the relatively impressive results in Section 3.1. 3.2 Reduction ofa -[H2W I 2od016The initial definition of the reduction chemistry of ( . u - [ ~ 2 ~ 1 2 0 4 0by ] ~Pope and Varga [20] was followed by examination of its extended redox chemistry which apparently involves addition of up to 32 electrons [20-241. At pH above 4.0, the initial reduction processes O r / l ' and 1'/2' for this metatungstate anion each involve transfer of one electron (Scheme 3.5) and as expected their reversible potentials measured under these conditions are independent of p Experimental E;,2 values in Scheme 3.5 are given in mV versus Ag/AgCl. The metatungstate ion features two protons trapped in an internal cavity. Extra protons present on reduced species are probably bound externally. However, the two classes of protons are not differentiated in this reaction Scheme. The voltammetric behaviour for reduction of 1mM solution of [H2Wl2O4()] in the pH range 6.9-2.0 in aqueous 0.5 M NaCl is shown in Fig. 3.6. As the pH value is decreased below 4.0, process l f / 2 ' diminishes in current intensity whereas the current intensity of O f / appears to increase. At pH 3.4, a single wave (AEp = 87 mV at v = 100 mV s-l) is observed. This wave gradually sharpens and begins to move to more positive potentials as the pH is decreased below pH 3.2. At pH 1.1, A Ep = 55 mV, consistent with a chemically reversible, apparently two-electron process constituted from two non-resolved one-electron charge-transfer processes. The approach to the simulation presented below follows that for the [ P ~ w ~ system ~ o ~and ~ is] based ~ on Scheme 3.5. The simulations are presented Scheme 3.5 Coupled electron- and pvoton-transfer reactions -1.0 -0.8 -0.6 -0.4 -0.2 Potential (V vs Ag/AgCl) 0.0 -1.0 -0.8 -0.6 -0.4 -0.2 191 0.0 Potential (V vs Ag/AgCl) . 3.6 Cyclic voltammograms obtained at a scan rate of 100mV s-' for reduction of 1 rnM W12040]at a GC macrodisc electrode in aqueous 0.5 M NaC1; (-) experiment; (. . . ..) simulation. Reproduced by courtesy: Anal. Chem. 71 (1999) 3650. Copyright, American Chemical Society. in Fig. 3.6 and derived parameters listed in Table 3.1. Specific considerations included: (1) At v = 100 mV s-', processes 0'/1' and '/2' exhibit peak-to-peak separations, AE,, of 70 and 100 mV respectively, versus 57 mV expected for a reversible one-electron couple at 298 K). Satisfactory simulation (Fig. 3.6(a)) of these processes was achieved by using values of 0.50 and 0.55 for a and 0.06 and 0.003 crn s-I for ko, respectively. These electron charge-transfer 192 Illustvating basics of voltammetry steps may therefore be termed quasi-reversible, rather than reversible, as was the case for the [ P ~ w ~ ~ osystem; ~ ~ ] ~ (2) The experimental value of D,,, 2.0 x low6cm2s-', was employed while cm2s-' at intermediate pH values; DH+was optimized at 1.9 x (3) Relevant disproportionation reactions (eqns 3.13 and 3.14) were considered (Table 3.1): + l'h --+0 + 2'h 1 h' + l'h + 0 + 2' 1' K = 1.3 x (3.13) K = 0.35 (3.14) Inclusion of disproportionation of lh' (eqn 3.14; kf = 100 M-' s-') significantly improved the fitting below pH 4; (4) Predictions, based on parameters derived at 1mM anion concentration, of behaviour for solutions of 5 m M concentration indicated that coalescence of the one-electron processes O'/lf and 1\12' should occur at about one pH unit lower at the higher [Hzw12 040]6- concentration. Simulations fitted experiment well for pH values above 3 but increasingly poorly below pH 3. Additional complexity could be introduced into the simulation to provide an apparently better fit with experiment. However, reality may soon be left behind and limitations in present levels of understanding of this system have been reached. 3.3 Discussion of results obtainedfrom the simulation ofthe reduction of w-[p2w ~ ~ oand~a!-[~ & ]w~ ~- ~ o ~ ~ ] ~ The comparisons of experiment and theory made in Figs 3.2 and 3.6 indicate that the behaviours of both [ P ~ w ~ ~ oand ~ ~[ ]H~ -~ w ~ in ~ aqueous ~ ~ ~NaCl ] ~ (0.5 M) in the pH range 6.0-1.0 can be accounted for, in the main, by related Schemes 3.4 and 3.5 respectively. Importantly, it is apparent that while the observed voltammograms differ significantly in shape and apparent complexity as the pH varies, this need not imply the onset of chemical irreversibility. Definition of three protonation constants for each system, combined with experimental values of E;,, for the two simple one-electron couples involved (Table 3. I), provides a cdmplete thermodynamic description. The assumption of fast protonation rates in all cases appears to be justified. In addition, the protocol available in the simulation [25] successfully handled the fact that the simple one-electron couples O f / l ' (AE, = 72 mV; cx = 0.50; ko = 0.06 cm s-') and lf/2' (AEp = 101 mV; cx = 0.55; ko = 0.003 cm s-') can be quasi-reversible for reduction of [ H ~ w ~ ~ rather ~ ~ ~ than ] ~reversible, - , as deduced for process 2/3 and 314 ' in the [ P ~ w ~ ~ osystem. ~ ~ ] ~Minor contributions from uncompensated resistance (200 Ohm) and capacitance (2 x Farad ~ m - ~which ), also give rise to non-ideality, are also accommodated by the simulation. The assumption that the initial forms of the anions ( [ P ~ w ~ ~ o (2), ~~]~Scheme 3.4; [ H ~ w ~ (Of), ~ ~Scheme ~ ~ 3.5) ] ~ are - not protonated is justified by Coupled electron- and proton- tranrfer reactions 193 the results and in the case of 0'by the fact that fully oxidized polyoxometalates are characteristically strong acids (pK,, 0-2) [26,27]. Schemes 3.4 and 3.5 are also consistent with the observed two-electron-two-proton [20,26] (eqns 3.15 3. and 3.16) Nernstian dependence of E;,, for the coalesced waves at pH i A significant weakness may be the need to assume that the diffusion coefficient Danionis independent of the redox and protonation state of the anion and that Dani,, and DH+are independent of pH in aqueous 0.5 M NaCl. Thus, optimization of these parameters within chemically sensible ranges was necessary to simulate successfully the current magnitudes at anion concentrations of 1 and 5 mM (Fig. 3.5). The detailed reasons for the significant differences in wave shapes as a function of pH and concentration of polyoxometalate can be discerned from examination of plots of species concentration versus distance from the electrode [25]. Figure 3.7 presents simulated surface concentration data for reduction of 1 and ~ ] ~ - of -0.74 V, which corre5 mM solutions of ( ~ - [ P ~ w ~ ~ato a~ potential sponds to a value just beyond the peak potential for the most negative process considered in this study. For the 5 mM concentration case (Fig. 3.7(a)), this potential corresponds to the reduction of 3 to 4 (also compare the morphology of the inset in Fig. 3.7(a) with that of Fig. 3.2(a) for 1 mM concentration at pH 5.20). Note that at the 5 mM concentration, conversion of 4 to 4h to achieve their equilibrium values has expended virtually all the available protons, which leaves only a very low residual concentration of H+ at the electrode surface (Fig. 3.7(a)). Hence, non-protonated 4 is the dominant species at the electrode surface. In contrast, for the 1 mM bulk concentration (Fig. 3.7(b)), the surface concentration of H+ no longer falls to anywhere near zero, even though [H+]/[anion] 1 : 3. This is because the diffusion coefficient DH+ 4D,,,,, in the simulation, so that H+ diffuses to the surface faster than the anion, thereby enabling a significant surface proton concentration to be maintained during the entire forward sweep of the voltammogram. Consequently, under these conditions 4h, rather than 4, is now the dominant polyoxometalate species present at the electrode surface and the change in voltammetric shape relative to that when the bulk anion concentration is 5 mM reflects this feature. It is apparent that the differences in wave shapes as a function of anion concentration are with any effect of ion pairing driven by the ratios [H+]/[anion] and DH+/ Damon, being neglected in this discussion. Thus, the fact that DH+is always significantly larger than any other species present, is a significant feature in voltammetry of electrode processes involving acid-base equilibria coupled to electron-transfer processes. In many simulations it can be assumed that the diffusion coefficient of all species participating in the electrode process are equal, but not when protons participate in the redox process. 194 Illustrating basics of voltammetry 100 Distance (prn) 200 Fig. 3.7 Simulated speciation as a function of distance from the electrode surface for reduction of [ P ~ w ~ ~ o(a)~ 5~mM; ] ~ (b) - 1mM in aqueous 0.5 M NaCl at pH 3.45. Insets show cyclic voltammograms obtained at a scan rate of 100 mV s-l terminated at a potential of -0.74 V versus Ag/AgC1, the sampling point for the calculation of the concentrations of each species considered in the simulation. Reproduced by courtesy: Anal. Chem. 71 (1999) 3650. Copyright, American Chemical Society. [p2w18 0 ~ ~ 1and [ HwI2 ~ 0 4 ~ 1 formally carry the same negative charge. However, the EiI2 values of the first two simple one-electron couples for the latter species are more than 600 mV more negative (Schemes 3.1 and 3.5), a situation probably related to the higher surface charge density on the smaller 6- o ~ ~ ] [ H ~ w ~ ion. ~ ~In ~fact, ~ the ] ~ first- two reduction processes for [ P ~ w ~ ~ are insensitive to pH in the range 6.0-1.0 (Fig. 3.2), in stark contrast to Electrochemical reduction ofa-[S2Mo180621~- 195 the equivalent situation in the [ H ~ w system ~ ~ (Fig. ~ 3.6). ~ ~ In ] addi~ tion, the derived protonation constants for [H2w ~ ~ o ~and ~ [] ~H - ~ w 8- ~ ~ ~ ~ (Scheme 3.5; Table 3.1) are two orders of magnitude larger than those for 180621~- and [ P ~ w ~ lo-, ~ o despite ~ ~ I the lower anionic charges. However, the pattern of relative values of the constants within a given system (eqns 3.17 and 3.18), does reflect expectations based on the anionic charge: K3h K4h2 and K3h/K4h (3.17) n summary, a systematic approach to the simulation of the cyclic voltammetry for reduction of the a-[p2w ~ ~ o ~and ~ a] ~- - [ ~ ~ ~ polyoxomet~ ~ 0 ~ ~ ] ~ alates in aqueous solution, based upon an established program [25], provides a reasonably detailed understanding of the coupled electron-proton transfer chemistry. Further refinement of the model to incorporate ion-pair formation and phenomena related to media effects, and their influence on diffusion coefficients is probably required to afford a complete description. However, without access to independent experimentally derived measurements of some of these parameters, and their dependence on the medium, it is not clear that unique ulations will be obtained if the complexity of the simulation is enhanced for sole purpose of providing greater agreement with experiment. The reader is therefore again cautioned against over-interpretation of the quantitative significance of a simulation involving the input of more than a few unknown parameters. Thus, as noted in Chapter 2, while advances in the use of more isticated forms of statistics can be expected to improve the level of confie in the results of simulations in the future, every effort should always be e to evaluate any input parameters that can be independently measured, so he number of parameters that have to be deduced from the simulation are ept to the absolute minimum. he successful simulation of experimental cyclic voltammograms obtained for o ~a ~ -] ~[ - ~ ~ ~ has ~ helped ~ 0 to~quantify ~ ] sev~ reduction of ( ~ - [ P ~ w ~ ~and eral aspects of the proton-transfer reactions that can accompany the electrontransfer processes of polyoxometalate compounds in aqueous media. In essence, as reduction proceeds, the anions acquire an increasingly negative charge, which increases the basicity of the reduced form, and encourages protonation. In turn, protonation lowers the negative charge, encouraging further reduction, so that very high levels of polyoxometalate reduction can occur under acidic conditions. However, cyclic voltammetry represents only the application of one 3 ~ a r tof s Section 4 have been adapted with permission from Inoy. Chem. 32 (1993) 2416; 36 (1997) 2826; and 36 (1997) 4227. Copyright, American Chemical Society. Additional details may be obtained by consulting these references. 196 Illustrating basics of voltammetry technique of electrochemistry and, in its own right, does not lead to unequivocal identification of structures or properties of highly reduced species. In the case studies have been undertaken in both protic and aprotic of media, in which many of the voltammetric, spectroelectrochemical, and electrochemical synthetic techniques described in Chapter 2 have been employed. In this section, a review of data available on the reduction of a-[S2Mo18062]4is provided to highlight the advantages and limitations of the various electrochemical techniques and, also, to further illustrate how data obtained'from the use of a wide range of techniques may be used in an interactive manner to understand inherently complex redox chemistry. ~ ~ (Fig. o ~3.8) ~ has ] ~approximately D3hpoint The idealized a- [ s ~ M ~ anion symmetry [28-321. Two hexagonal belts of, alternately, point- and edge-sharing M o o 6 octahedra are each capped by an edge-shared Mo3Ol3 unit. The belts are linked by six bridging 0x0 ligands located on the horizontal plane of symmetry. Since there are different Mo(V1) environments in this polyoxometalate species, the location of electrons in reduced states is of considerable interest. In principle, ~ - [ s ~ M ~ ~might ~ o be ~ ~expected ] ~ - to accept a total of at least 18 electrons, formally reducing each Mo(V1) (do electronic configuration) centre to the Mo(V) (dl electronic configuration) state. Structural considerations noted above, imply that reduction would occur over a range of potentials and not as a single 18-electron process. Even more extensive reduction to generate, formally, Mo(IV) (d2 electronic configuration) centres could be expected on the basis that to the meta-tungstate ion, a - [ ~ ~ ~ considered ~ ~ 0 in~ Section ~ ] 3~is reported - Fig. 3 -8 Polyhedral form of structural representation of ~ - [ s ~ M0o6I2 ~1 ~ ~ . Electrochemical reduction Ofa -[S2Mo18o62I4- 197 accept at least 24 electrons, together with charge-compensating protons [20-241, which formally, therefore, corresponds to reduction of all 12 W(V1) sites to the ~ ~ more ] ~ - , elec(IV) oxidation state. Apparently, with a- [ H ~ M O ~ ~ Oeven trons can be accepted into the polyoxometalate framework [24,32], so that very extensive addition of at least 36 electrons (do to d2 for each of the 18 Mo atoms), and probably more, is predicted to be available in the case of reduction of ~ ~ - [ s ~ M o ~ Electrochemical ~ o ~ ~ ] ~ .studies in protic and aprotic media presented below reveal the details of the extensive redox chemistry associated with - [ ~ ~ ~ o ~ ~ 0 ~ ~ l ~ - . 4.1 Voltammetry of a - [ S ~ M Oob214in aprotic acetonitvile media4 deally, the fundamental nature of the electron-transfer properties of the [ s ~ M ~ ~ ~system, o ~ ~free ] ~from - complicating, coupled protonation reactions, should be revealed by voltammetric studies in aprotic solvents. The problem with this concept is that traces of adventitious water and, hence, protons invariably present in aprotic media can cause complications, as also can interactions with the high concentration of electrolyte anions (ion-pair formation). All these facets of polyoxometalate redox chemistry studies are revealed in the voltammetry of [ s ~ M ~ in ~ nominally ~ o ~ ~aprotic ] ~ CH3CN. Figure 3.9 shows the reduction of [ ~ ~ ~ ounder ~ ~conditions 0 ~ ~ of cyclic ] ~ voltammetry at a 1-mm diameter GC macrodisc electrode in 'dry' CH3CN (0.2 M Bu4NC104)over the potential range of about +1.0-3.OV versus Fc/Fc+ at scan rates of 0.05, 0.5, and 10 V s-l (ion pairing ofpolyoxometalate anions with the Bu4N+ cation appears to be small) [16]. Clearly, an extensive and complex reductive chemistry is available in this solvent. An initial goal is to identify the primary electrontransfer processes and establish their reversible potentials; this may be achieved in CH3CN (0.2M Bu4NC104)by a combination of fast scan rate and lowtemperature conditions which enable protonation reactions from adventitious water or other impurities to be minimized. 4.1.1 Dependence of cyclic voltammetry on scan rate, switching potential, and temperature Initially, voltammograms, obtained only in the potential region where the first four charge-transfer processes occur, are considered. These processes are summarized in eqns (3.19)-(3.22) and designated I, 11, I11 and IV respectively. 'AS in Section 3.1 the a isomeric notation is now commonly omitted for convenience and also because the isomeric forms of the reduced species are again usually unknown. 198 Illustrating basics of voltammetry 1 1 1 1 1 1 1 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 1 1 1 0 +0.50 +1.00 Potential (V) Fig. 3.9 Cyclic voltammograms for reduction of 2.0 rnM [ s ~ M o I ~ o ~ in ~ ] ~CH3CN (0.2 M Bu4NC104)at a 1.O-mm diameter GC macrodisc electrode at 22OC; potentials versus FC/FC+; scan rate (V s-I): (a) 0.05; (b) 0.50; (c) 10. Reproduced by courtesy: Inog. Chem. 36 (1997) 2826. Copyright, American Chemical Society. Experiments as a function of scan rate at GC electrodes for these initial four processes involved switching the potential between the various processes. Scanning the potential regions of only process I or just processes I and I1 produced almost ideal reversible one-electron reduction responses (after allowance for Ohmic drop) for scan-rates in the range 0.02-1 0 V s-' (Fig. 3.10). Thus, the voltammetric characteristics were initially indistinguishable from the known reversible one-electron ferrocene (FC/FC+)oxidation process under the same conditions. However, when the potential is switched after processes I11 or IV, small deviations from ideality emerge in the form of a dependence Electrochemical reduction ofa -[S2Mo180621~- I I I I I -1.00 -0.50 0 0.5 1O .O 199 Potential (V) ig. 3.10 Cyclic voltammograms for reduction of 2.0 rnM [ s ~ M ~ ~ ~when o ~ the ~ ]potential ~ is switched after process 11; other conditions as for Fig. 3.9. Reproduced by courtesy: Inorg. Chem. 36 (1997) 2826. Copyright, American Chemical Society. of on scan rate, and the appearance of minor processes (Fig. 3.11). In particular, a new chemically reversible process is present at potentials just after process IV and new processes are evident between I1 and 111. However, at a fast scan rate of 10 V s-' , four, almost ideal, reversible, one-electron reduction processes are observed (Fig. 3.1 1). Deliberate addition of water amplifies the relative magnitude of the minor processes, implying that the three- and fourelectron reduced anions [ ~ ~ ~ o ~ ~ the 0 ~presumed ~ ] ~ -products . ~ - of , processes 11 and IV, are extremely basic and readily protonated by adventitious water present in acetonitrile. 200 Illustrating basics of voltammetry I I I I I -2.00 -1.05 -1.00 -1.50 0 Potential (V) I I 0.50 1.00 Fig. 3.11 Cyclic voltammograms for reduction of 2.0 mM a - [ ~ ~ ~ when o ~the~potential 0 ~ ~ is switched after process IV; other conditions as for Fig. 3.9. Reproduced by courtesy: Inorg. Chern. 36 (1997) 2826. Copyright, American Chemical Society. Processes observed at more negative potentials than reduction waves I to can now be considered. Clearly the complexity increases as more highly redu species are generated (Fig. 3.9). The effect of scan rate variation on process is illustrated in Fig. 3.12. At slow scan rates, V has a peak current considerably larger than that expected for a one-electron reduction process (Fig. 3.12(a)). the scan rate increases, the peak height of V approaches that of processes I(Fig. 3.12(b) and (c)).This feature is consistent with protonation accompanying processes V and VI, thereby causing them to coalesce into a single two-electron reduction wave (see analogous reactions in Section 3). However, at fast scan rates, insufficient time is available for complete protonation to take place, so that processes V and VI are resolved. ] ~ Electrochemical reduction of~x-[s~n/ilo~~ o62I4- I I I I -2.00 -1.05 -1.00 -1.50 I 0 Potential (V) I I 0.50 1.00 . 3.12 Cyclic voltammograms for reduction of 2.0 rnM [ ~ ~ ~when o the~ potential ~ 0is switched after process V; other conditions as for Fig. 3.9. Reproduced by courtesy: Inoq. Chem. 36 (1 997) 2826. Copyright, American Chemical Society. Even more complex voltammograms are seen upon switching the potential after process VI (not shown). Like V, process VI is only detected as a oneelectron reduction process at very fast scan rates when, presumably, the influence of following chemical reactions is minimized. Very dry acetonitrile is required to achieve even this fast scan rate result, and deliberate addition of water enormously increases the complexity of the cyclic voltammetry at negative potentials. While processes V and VI observed in 'dry' acetonitrile (0.2 M Bu4NC104) are not completely reversible in the chemical sense even at very fast scan rates, simulations show that under this circumstance the reversible reduction potentials ~ ~ ] 202 Illustuating basics of voltammetry Table 3.2 Cyclic voltammetric dataa for reduction of 2.0 rnM [ s ~ M ~ ~ in~ o ~ ~ ] ~ CH3CN(0.2M Bu4NC104) I I1 I11 IV v v VII VIII v = 10 V s-' ; 1 rnrn diameter GC macrodisc working electrode. v v~ FC/FC+. CAE1I2= difference in Ell2 between consecutive electrode processes. a + measured as (Erd E y ) / 2 will not be significantly shifted from their true values. Thus, it can be concluded that E;,, values for I and 11 differ by -0.24V and that similar differences also apply for the pairs 111, IV and V, VI. Based on a separation of about -0.6 V between individual pairs (Table 3.2), the first process for the next reversible pair (process V ) is predicted to occur at about -2.50 V versus FC/FC+.However, switching potential just prior to the solvent limit of -3.0 V versus FC/FC+ in acetonitrile at 20°C shows very complex behaviour (Fig. 3.9) and, hence, this experiment provides no direct evidence for the anticipated additional pair of one-electron charge-transfer processes. At the lowered temperature of -30°C, on the other hand, direct found for the predicted seventh and eighth processes, VII an close to the predicted potentials. Lowering the temperature t o ~water, ~ ~ ~ ~ ] to slow the rate of reaction of reduced forms of o l - [ ~ ~ ~ with and possibly also lower the activity of water. Data presented so far imply that in the absence of significant concentrations s of protons, or ion pairing with the electrolyte, processes as detected at a GC electrode, also correspond to simple extension of the electron-transfer series (see eqns (3.19)-(3.26)). Electrochemical reduction ofa -[S2 Mo180 ~ ~ 1 ~203 - ~ h u s eight , one-electron reversible charge-transfer processes appear to exist for reduction of [ S 2 ~ 0 1 8 0 6 2 in ] ~aprotic media at potentials up to -3.0 V versus c+, and these are summarized in the overall eqn (3.27). resumably, even more one-electron processes would be detected if a more negative potential range could be accessed in a highly pure (water-free) aprotic solvent medium. 4.1.2 Steady-state voltammetry e the transient cyclic voltammetric data provide some of the basic ation, complementary studies using steady-state conditions are always recommended to both confirm findings made by the transient method as well as to provide additional details. For the reduction of [ ~ ~ ~ o it turned ~ ~ 0 out that the need to use slow scan rates to obtain the steady-state condition t electrode 'fouling' in the negative potential region where I are expected. Nevertheless, useful additional data associated V can be obtained. i I -1.50 -1.00 -0.50 0 Potential (V) 0.50 f I 1 I I I 1.00 -3.00 -2.50 -2.00 -1.50 -1.00-0.50 1 0 I I 0.50 1.00 Potential (V) 3.13 Steady-state voltammograms obtained at a scan rate of 0 . 0 0 5 V ~ - for ~ reduction of 2.0rnM [ s ~ M ~ ~ ~ino CH3CN ~ ~ ] ~(0.1 - M Bu4NC104) at 20°C; (a) 50pm diameter platinum microdisc electrode; (b) 2.8 mm diameter GC RDE; rotation rate of 500 rpm. Reproduced by courtesy: Inorg. Chern. 36 (1997) 2826. Copyright, American Chemical Society. ~ ~ ] 204 Illustrating basics of voltammetry Microdisc Electrode Figure 3.13(a) shows a near steady-state voltammogram obtained at a platinum microdisc electrode (50 pm diameter) over the potential range encompassing waves -1V. While Ell2 values obtained and I1 are the same as thos found by cyclic voltammetry (T technique-dependent variations in Ell2 are evident for processe vary stea addition, the magnitude of the limiting currents (Ilim) > IV (Fig. 3,.13)implying that the steady-state voltammetry does not in fact solely consist of simple mass-transport-controlled, reversible processes under these near steadyitions. The current contribution from minor 3.13) accounts for the majority of the processes seen between I. However, the magnitude of Ilim for 'missing' current for process process IV is too low to be consistent with simple mass-transport-controlled conditions. For electrochemically reversible processes, plots of E versus ln[(I& - I)/I] or the so-called 'log' plots should be linear with intercept E;,2 and slope RT/nF (Section 9.4 in Chapter 2) under steady-state conditions at a microdisc elecments with the slope of the 'log trode. Processes I and exhibit slight variations (apparent plot' giving a value of n n values calculated from the slopes of 'log' plots are 0.83 and 0.87, respectively). The fact that the limiting current of IV is considerably smaller than that expected (ideally the limiting current values for all processes should be identical) may be due to electrode blockage. Complete 'electrode blockage', perhaps due to precipitation or adsorption of [ ~ ~ ~ o (or~ protonated ~ 0 ~ ~ forms) or double-layer effects [33] (some repulsion of anions may occur at the negatively charged electrode), takes place at the plati suriace soon after scanning the potential past process scan rate employed in steady-state rnicrodisc electrode experiments combined with the small surface area always enhances the risk of electrode fouling or blockage relative to that encountered with fast scan rates and transient conditions at macrodisc electrodes. The very short time-scale of the steady-state microdisc electrode and the very large negative charge and negative potential enhances the probability of a double-layer electrode kinetic effect [33]. Clearly, additional studies are required to identify the exact cause of this problem. Hydrodynamic Rotating-Disc Electrode A second series of steady-state voltammograms was recorded under hydrodynamic conditions using a GC rotatingmacrodisc electrode (2.8 mm diameter). It may be anticipated that the use of a macrosized electrode and rotation will minimize electrode fouling or blockage compared to that noted above under microdisc steady-state conditions. The rotated-disc voltammogram in Fig. 3.13(b) shows that, in addition to ~ ~ omo~ ~ ] ~ process V is now also well defined and for the [ s ~ M ~ system, ily interpreted voltammograms are obtained an with the platinum microdisc and use of a rotated GC electechnique. Scanning the potential beyond trode enables further processes to be observed which, on the basis of cyclic ] Electrochemical reduction of a -IS2Mols o62I4- 205 voltammetric data, are attributable to multi-electron reduction of the mixture of potonated and non-protonated, or adsorbed, or precipitated species now present at, or on, the working electrode surface. The first four processes obtained at the rotated electrode exhibit El12 values are essentially independent of the rotation rate. Analysis of linear 'log ersus ln[(Ii,,, - I)/I] for each of the first three processes at a rotation 00 rpm provide estimates of n-values of 0.99, 1.01, and 1.02, respecection 9.4 in Chapter 2). The apparent n-values obtained from the ' for the fourth process is 0.91, suggesting that a minor departure from emins for processes at negati e potentials, even when the electrode is he ideal behaviour of I and allow their total limiting current to be culate the diffusion coeffici D of [ S 2 ~ o 1 8 0 6 2 ]in 4 -CH,CN using equation (Chapter 2, Table 2.3). The value of 6.4 x 10-6cm2s-' at e compared with values of 6.2 lop6cm2 s-' estimated from microelectrode voltammetry and use of process and the equation Ihm = 4nFDr,[Alo ection 10.1 in Chapter 2). The injuence of electrolyte and solvent electron-transfer steps observed in the reduction of [ ~ ~ ~ o ~ ~ 0 ~ l o 4 is used as electrolyte [34,35], mimic those found on addition of d may be accounted for by assuming that ~ i acts + as a moderately is acid [36] (or forms strong ion pairs [16]). For example, in (95/5) / H 2 0 (0.1 M NBu4C104), the voltammetric behaviour obtained on of ~ i can + be simulated [34] according to Scheme 3.6: Scheme 3.6 206 Illustrating basics of voltammetry Fig. 3.14 Solvent dependence in CH3CN and DMF of cyclic voltammograms for reduction of 1 mM [ s ~ M ~ ~ ~ato a~G~C ]electrode ~ (area 0.071 cm2) using a scan rate of 1 0 0 r n V ~ - ~ . Reproduced by courtesy: Chern. Soc. Dalton Tmns. (2001) 1076. Copyright, Royal Society of Chemistry. The reversible potentials E1-E7 (V versus FC+/FC) in this mixed solvent media are estimated to be 0.12, -0.11, -0.73, -0.91, -0.56, -0.67, and -0.60, respectively, and the equilibrium constants Kl - Kg (M-l) to be lo1, 5 x lo2, lo6, lo3, and 8 x lo3, respectively. In view of these results in Scheme 3.6, the role of ~ i ' , frequently contained in the electrolyte, cannot be assumed to be thermodynamically innocent in studies of polyoxometalates [21], nor can the solvent (e.g. CH3CN and in Scheme 3.6), nor, presumably, even the tetraalkylammonium electrolyte cations, as ion pairs are always likely to be significant when highly negative polyoxometalate species are generated at electrode surfaces. Figure 3.14 shows a comparison of the first four reductions steps of [ s ~ M ~ in ~ acetonitrile ~ Q ~ ~ ] ~ and dimethylformamide [37]. Clearly, a very large solvent effect is present in the electrochemistry of polyoxometalates [38], so that interpretation of the thermodynamics at a fundamental level can be very complicated. 4.1.4 Conclusions derivedjom voltammetric studies in acetonitrile The data obtained from voltammetric studies indicate that, after avoidance of any influence from the presence of trace water or acid, the choice of a suitable electrolyte with minimal ion pairing (e.g. Bu4NC1Q4), and the use of transient conditions at a GC macrodisc electrode at low temperature, eight reversible one-electron reductions of [ s ~ M o ~ ~ Q occurring ~ ~ ] ~ - , as four adjacent pairs, are accessible in CH3CN. The difference in potential within each pair is remarkably constant, 0.26 z t 0.02 V, as are the separations between adjacent pairs, 0.60 f 0.06 V (Table 3.2). The (Ei12 EfO) thermodynamic 208 Illustrating basics ofvoltammetry shorter voltammetric time-scale. The observation of well-defined isosbestic points (Fig. 3.15) in electronic spectra generated during the course of these low-temperature reductive electrolysis experiments supports the notion that no decomposition occurs at -45"C, as does the fact that oxidation experiments after reduction, led to the quantitative reappearance ofthe initial [S2M018062]4electronic spectrum. It can be seen from data contained in Table 3.3 that sequential oneelectron reduction to form [ s 2 ~ o 1 062]5-, 8 [ s ~ M 0o6 2~1 6~- , [ S 2 ~ 0 1 8 ~ 6 2 1 7 and [ ~ ~ ~ o generates ~ ~ 0a band ~ ~ in ]the~ red - region of the visible spectrum that is absent in [ ~ ~ ~ o ~Additionally, ~ 0 ~ ~ it ]can ~ be - noted . that this band shifts to higher wave numbers on sequential reduction and the extinction coefficient increases in magnitude. [ ~ ~ ~ o 1has ~ each 0 ~molybdenum ~ ] ~ atom in a do configuration and the only transitions that occur are in the UV or close to this region (c.30 800 cm-l). However, on sequential reduction, electrons occupy the formerly empty d orbitals of the molybdenum atoms in the cluster, permitting d-d transitions to occur in the visible region of the spectrum [5]. The relatively high values for the measured extinction coefficients suggest that the transitions occurring are spin-allowed intra-valence transitions between separate molybdenum nuclei [5,36]. 4.2.2 Electron paramagnetic resonance spectra of veduced species Reduced forms of [ s ~ M o ~ ~ omay ~ ~be ] ~paramagnetic or diamagnetic. If they are paramagnetic, then EPR spectra may be observed, although there are, of course, circumstances when paramagnetic species do not give rise to EPR signals. Thus, lack of detection of an EPR signal cannot be taken as evidence of diamagnetism. As expected, no EPR signal was observed for [ ~ ~ ~ o ~ which is known to be diamagnetic on the basis of NMR and magnetic measurements. The EPR spectra (if any) of species, formed after well-defined and known levels of reduction, may be obtained by measurements on reduced solutions obtained by coulometric titration using large-scale bulk electrolysis cells, of the kind described in Section 15.2.1 in Chapter 2, and controlled potential conditions, at appropriate potentials for each level of reduction. The respective values with applied potentials (versus ~ c / F c + were ) $0.12 V ( 0.02 V), -0.12V (-0.28V), -0.78V (-0.88V) and -1.05 V (- l.lOV), for n = 1-4, respectively. The extent of bulk electrochemical reduction at a platinum gauze basket electrode was monitored by measuring both the charge passed (Faraday9s Law) and the position of zero current in RDE voltammograms. That is, voltammetric confirmation that sequential one-electron reductions had occurred, as predicted theoretically on the basis of the coulometric calculations (Section 15 in Chapter 2) was obtained by measurement of the sign and magnitude of the limiting current for the four voltammetric one-electron waves in the RDE steady-state voltammogram. Application of both of these methods for assigning the level of reduction, therefore, provided conclusive evidence that the species formed had the appropriate number of electrons added and therefore that + ~ 210 Illustrating basics of voltammetry Table 3.3 Summary of absorption maxima," in the visible region (5000-25 000 cm-') for a variety of reduced species of [ s ~ M o ~ ~ o ~ ~ I ~ Reduced species Medium T ("C) Absorption a [ ~ 2 ~ ~ 1 8 ~has 6 2no ] 4absorption maximum in the visible region (5000-25 000 cm-l). b ~ ereferences e [5] and [36]for probable assignment of relevant intra-valence transitions that give rise to the absorption bands. 'In CH3CN (0.1 M Bu4NC104). d ~ a t obtained a by OTTLE experiments at a platinum gauze electrode at -45OC. Well-defined isosbestic points obtained during the course of electrolysis to each redox level confirm the absence of decomposition as do oxidation experiments after reduction, which quantitatively regenerate the initial electronic spectrum of [ s ~ M ~ ~ ~ o ~ ~ ] ~ - . eIn (9515)CH3CN/H20 (0.2 M HC104). *Data obtained at 22°C by sequential (2eP, 2H') reduction to form [ H ~ S ~ M O ~ ~ and O~~]~[ H ~ s ~ M ~ ~demonstrate ~ o ~ ~ ] that ~ - large shifis are observed in absorption band maxima when protonation occurs. a unique reduced polyoxometalate species was formed whose EPR properties could be selectively probed. Figure 3.16 shows EPR spectra recorded on frozen acetonitrile glasses (77 K) formed after addition of a specified number of electron equivalents (n) to a solution of 4 x M [ s ~ M ~ ~ in acetonitrile ~ o ~ ~ (0.1 ] ~M Bu4NC104)at 22°C. At the n = 1 stage of this coulometric titration, the intense, anisotropic EPR spectrum of the frozen solution (Fig. 3.16(a)) was identical to that obtained from an authentic sample of synthesized [Hex4NI5[S2M018062]dissolved in acetonitrile (0.1 M Bu4NC104)solution and then frozen to form a glass under the same conditions. The EPR signal associated with the n = 1 reduced species decayed progressively upon further reduction to the n = 2 level (Fig. 3.16(b)), indicating that the two-electron reduced anion, [ ~ ~ ~ o ~is EPR ~ 0 silent ~ ~ ] ~ or close to EPR silent at 77K. Diamagnetism would need to be established by magnetic measurements. Upon further reduction to the n = 3 stage and freezing of the solution, a new EPR signal was detected which was assigned to the paramagnetic three-electron reduced species [ s ~ M ~ (Fig. ~ ~ 3.16(c)). o ~ ~ ] ~ Electrochemical reduction of a -[S2 Adol80 ~ ~ 1 ~21 -1 DPPH internal reference . 3.16 Ex situ frozen glass EPR spectra (77 K) detected at different stages of a coulometric titration of [ s ~ M ~ ~ ~in oacetonitrile ~ ~ ] ~ (0.1 - M Bu4NC104).Provided by courtesy: T. Vu, Monash University, Victoria, Australia. spectrum is consistent with the presence of a single unpaired electron ion of [ s ~ M ~ to ~ the ~ no =~4 level, ~ ] led ~ to a progressive decrease in the magnitude of the EPR signal assigned to [ s ~ M ~ ~ ~ oHowever, ~ ~ ] ~ - . ty of the species present after the bulk four-electron reduction is as the voltammograms of these solutions are more complicated than edicted, if the only species present was the four-electron reduced species, M O ~ ~ O ~In~all ] ~probability, -. protonation has occurred to give a mixture ted and non-protonated 4e- reduced products. Thus, coulometric titration experiments establish that frozen acetonitrile glasses of the pure oneand three-electron reduced species give intense EPR signals, whereas the pure two- and four-electron reduced forms are EPR silent or EPR insensitive at 77 K. As for the n = 1 reduced species, no hyperfine coupling to the95797~o i in the framework is observed for the n = 3 reduced species in glass phase experiments at 77K. Apparently, the odd electrons are not localized at a single site at this temperature on the EPR time-scale, but rather they are elocalized over all or part of the polyoxometalate structure. .3 Electvochemical synthesis of one- and two-electron reduced fovms o f [ & ~ o ~ ~ ~ ~ ~ ] ~ The voltammetric and spectroelectrochemical data imply that large-scale electrochemical synthesis of at least solid [ s ~ M ~ and ~ ~[ so ~~M~~ ]~ ~~ should o ~ ~ ] ~ - 212 Illustrating basics of voltammetry be possible via electrochemical reduction in aprotic media using large GC or platinum basket bulk electrolysis cells described in Section 15.2 in Chapter 2. However, results also imply that prevention of protonation reactions is likely to be difficult under the long time-scale conditions associated with largescale electrochemical synthesis. Thus, attention in this section is focussed on the electrochemical synthesis and isolation of the non-protonated one- and two-electron reduced species. 4.3.1 Synthesis of [S2Mo 8 0621560 mL of acetonitrile solution containing 2.4 rnM [ B u ~ N ] ~ [ S ~ M andO ~ ~ ~ 0.24 M Bu4NC104 was reduced at 400 mV versus Ag/AgCl. After an hour, the solution had changed colour from transparent yellow to a deep transparent green. Upon completion of electrolysis, the green solution was placed in a refrigerator at 4°C. After several weeks, green crystals of [Bu4N15[S2M~18062] were found to be present. Synthesis of the green [ B U ~ N ] ~ [ S ~ M salt O ~ via ~ Oreduction ~~] of 2 rnM [Bu4N14[S2M018062] in dichloromethane (0.1 M Bu4NC104)is even more efficient as analytically pure product precipitates progressively during the course of electrolysis. 4.3.2 Synthesis of[Pr4N]6[SzMo and [ B U ~ N ] ~ [ H S Z18M0 O s2] A 2.4 rnM solution of [ H ~ x ~ N ] ~ [ Sin ~60M mL~ CH3CN ~ ~ ~ ~ (0.24 ~ ] Bu4NC104) was reduced at -0.45 V versus FC/FC+. Pr4NBr (0.25 g) was added to the deep-blue solution which was stored at -5°C. After one week, analytically pure blue crystals -of [Pr4N]6[S2M018062] were isolated, washed with ethanol, and dried under vacuum. If no Pr4NBr is added and the solution obtained after a two-electron reductive electrolysis is stored at 4"C, then the protonated (2e-, H') product [Bu4N] [HS2Mo180 6 2 ] crystallizes. Thus, even with the two-electron level of reduction, protonation readily occurs. An X-ray structural determination of this protonated polyoxometalate anion [39] confirmed that the a-structural form is retained after addition of two electrons. Salts of non-protonated species were not suitable for X-ray ~ ~ ]not ~ - , structural analysis. Salts of [ s ~ M ~ ~and~ [ os ~~ M~ ~] ~~~ ocould be synthesized by bulk electrolysis. Rather, mixtures of species of different protonation levels were formed, again as predicted on the basis of the voltammetry. 4.4 A systematic approach to chemical synthesis6 of a two-electron vedcrced f o m of [SzMo 8 od214- Figure 3.17 shows voltammograms at a rotated GC disc electrode over a potential range that encompasses the first two reduction waves of [ s ~ M ~ ~ ~ o ~ ~ (E;,, = 165 and -86 mV versus A g / ~ g + )and the one-electron oxidation 6 ~ d a p t e from d reference [39] and S. Juraja, MSc thesis, La Trobe University, 1999 Electvochemical reduction ofa -[S2M0i80621~- -400 -200 0 200 213 400 Potential (mV vs Ag/Ag+) 3.17 Glassy carbon RDE voltammograms for 2rnM (a) decamethylferrocene; and (b) [ s ~ M ~ ~ ~ino acetonitrile ~ ~ ] ~ - (0.1 M Bu4NPF6). The reference electrode is A ~ / A ~ +M AgNO,; 0.1 M Bu4NPF6). decarnethylferrocene ~ e ( q ~jMe5)2 -C (EiI2 = -400 mV versus Ag/Ag') in acetonitrile (0.1 M Bu4NPF6). (The E;12-values were determined by clic voltammetry.) O n the basis of the Ei12 values (m and callations derived from theory in Chapter 1, it can be predicted that reaction of 2 mol of ~ e ( q ~ - C ~ M with e ~1 )mol ~ of [ s ~ M ~ ~ ~in Q acetoni~ ~ ] ~ trile will produce 2 mol of [ ~ e ( q ~ - ~ ~ Mand e ~1)mol ~ ] of + [ s ~ M ~ ~ ~aso ~ ~ ] ~ E~O + eh5-~5Me5)2 [ ~ 2 ~ 0 1 8 ~ 6 + 2 ] ~2Fe(q5-c~MQ)~]' -k [ ~ 2 ~ 0 1 8 0 6 2 ] ~ (3.29) that the reaction will be essentially quantitative. Figure 3.18 shows RDE voltammograms when [ s ~ M ~ ~ is titrated ~ o ~ ~ ] ~ M acetonitrile e~)~ (0.1 M Bu4NPF6).These into a 2 rnM solution of ~ e ( q ~ - C ~ in ata confirm, via noting the position of zero current, that addition of 1rnM 2 ~ 0 1 0621 8 4- is required to fully oxidize all of the 2 rnM decarnethylferrocene. That is, the redox reaction between [ s ~ M ~ and ~ ~decamethylferrocene o ~ ~ ] ~ occurs in the expected 1 : 2 rnol ratio (eqn 3.29). Analogous titration experiments show that when 1 rnM [ s ~ M ~ ~ ~is oadded ~ ~ ]to~a -1 mM solution of two-electron reduced [ s ~ M ~ ~ ~ othat ~ ~[ ]s ~~ - M , ~ ~ ~becomes o ~ ~ ]oxi~ ized by one electron, and the [ s ~ M ~ ~ ~species o ~ ~ reduced ] ~ - by one electron. us, the reaction between the two-electron reduced [ s ~ M ~ ~ ~and o ~ ~ ] ~ 2 ~ 0 1 8 0 6 2 occurs ]4 in the 1 : 1rnol ratio predicted on the basis of reversible otentials as in eqn (3.30). 214 Illustvating basics of voltammetry I -700 I I I -500 I -300 I I -100 I I 100 I I 300 Potential (mV vs A ~ / A ~ + ) I I 500 Potential (mV vs A ~ / A ~ + ) Fig. 3.18 Titration of a 2mM decamethylferrocene solution with [ s ~ M o ~ ~ oas~monitored ~]~by a GC RDE. Approximate mM ratios of decamethylferrocene: [ s ~ M o I ~ o ~are ~ ]given ~ - in parentheses. The reference electrode is as in Fig. 3.17. Adapted from reference 39. This is the reaction that produces the changes in the voltammograms in Fig. 3.18 when the ratio of decarnethylferrocene to [ ~ ~ ~ ois increased ~ ~ 0 from ~ 2~ : 1] ~ to 2 : 2. The experiment shown in Fig. 3.18 also confirms that [ ~ ~ ~ o ~ ~ is stable in 'dry' acetonitrile, since no evidence of processes associated with formation of a protonated polyoxomolybdate is observed. Rotated-disc voltammograms were also used to monitor the course of titration of 2 rnM decamethylferrocene with the one-electron reduced polyoxomolybdate, [ s ~ M ~ ~ ~in oacetonitrile ~ ~ ] ~ -(0.1 M Bu4NPF6).It was expected that since [ ~ ~ ~ ois already ~ ~ one-electron 0 ~ ~ ] reduced, ~ the stoichiometry of Electrochemical reduction ofa -[S2Mo180621~- 215 the reaction between decamethylferrocene and [ ~ ~ ~would o be~ 1 : 1. ~ The occurrence of the reaction in eqn (3.31) was confirmed. 0 ~ n CH3CN solution, it is evident that a very clean reaction occurs between q5-C5Me5)2and [ s 2 ~ o 01682 1 4 - without intervention of protons from adventitious water. However, isolated solid from this reaction mixture, always had the formulation of a solvated [ ~ e ( q ~ - ~ [HS2Mo18062] ~ ~ e ~ ) compound. ~ ] ~ That is, as in the case of direct electrochemical synthesis from CH3CN Bu4NC104) described in Section 4.3.2, the (2e-, H f ) form of the d polyoxomolybdate was isolated. n a typical chemical synthesis of [ F ~ ( ~ ~ - C ~ M ~ ~ ) ~ which ][HS~MO~ contains the two-electron reduced polyoxometalate and a one-electron oxidized decamethylferrocene, 20 mL of an ether (Et20) solution (0.6 mol e(q5-c5Me5)2) was added dropwise to 30 rnL of an acetonitrile solution containing 0.2rnrnol of [ H ~ X ~ N ] [ S ~ M O The ~ ~ Oblue-green ~~]. itate was filtered and recrystallized from N,Nt-dimethylformamide F). Elemental analysis of the solid was consistent with the formuion [ ~ e ( q ~ - ~ 5 M e5 [&H] S ~ M O ~( D ~M OF ~ )~ (~~] t 2 0 ) ~The . 5 : 1 ratio of e(q5-C5~e5)2]+ to [ H S ~ M O I ~ O and ~ ~ ]the ~ - presence , of solvent molecules of crystallization were confirmed by voltammetric and spectroscopic examination of solutions (obtained by dissolution of the solid in DMF) respectively. lioltammetvy o f [ ~ ~ ~ o in~acidic ~ 0(9.54) ~ ~ ] ~ acetonitvile/watev media Voltammetric generation of highly reduced forms of [ s ~ M ~ ~ ~in oacetoni~ ~ ] ~ trile has been shown to be complicated by the presence of adventitious sources of protons. Clearly, an obvious method of deliberately seeking to understand the nature of the interaction of the proton with reduced forms of [ s ~ M ~ ~ ~is o ~ ~ ] ~ to repeat the voltammetric measurements described above in aprotic acetonitrile in the presence of known concentrations of protons. A medium in which the concentration of H+ can be deliberately varied is a (95/5, v/v) acetonitrile/water solvent mixture to which aqueous perchloric acid, of known H+ concentration, can be added. ' 1. Cyclic voltammetry Voltammograms at a 1-mm diameter glassy-carbon working electrode in (95/5)CH3CN/H20 (0.02 M HC104) revealed the presence of at least seven chemically reversible reduction waves in the narrow potential range of 0.3 to -1.0 V versus FC/FC+ (Fig. 3.19). The processes observed in this medium are labelled I, 11, etc., to distinguish them from the one-electron waves 216 illustrating basics of voltammetry t -1 .OO I -0.50 0 Potential (V vs FC/FC+) 0.50 Fig. 3.19 Cyclic voltammograms obtained with a 1-rnrn diameter GC disc electrode for reduction of 1.0 rnM [ s ~ M ~ ~ ~in o(95/5) ~ ~C ]H ~ 3-C N / H 2 0 (0.1 M Bu4NC104;0.02 M HC1O4) at 20°C; scan rate (VS-l): (a) 0.05; (b) 0.50; (c) 10. Reproduced by courtesy: Inorg. Chem. 36 (1997) 2826. Copyright, American Chemical Society. observed in CH3CN which have been labelled I, 11, etc., in earlier discussion. Processes I-IV are particularly well defined in the presence of 0.02 M HC104 (Fig. 3.20). The reversible potentials in this medium are 0.19, 0.08, -0.12, and -0.43 V versus Fc/Fc+. Electrochemical reduction o f ~ ! - [ S ~ M0621~o~~ -0.50 0 217 0.50 Potential (V vs FC/FC+) -20 Cyclic voltammograms obtained with a 1-mm diameter GC disc electrode using a scan in o(95/5) ~ ~ ] ~ 0.5 V s-' for the first four reduction processes observed with 1.0 rnM [ s ~ M ~ ~ ~ CM3CN/H20 (0.1 M Bu4NC104;0.02 M HC104) at 20°C. Reproduced by courtesy: Inorg. Chem. (1997) 2826. Copyright, American Chemical Society. witching the potential after the first process, I, gave I ," /I;~( = 1.0, as uired for a chemically reversible process, and AEp = 0.038 v at a scan rate of 50 mV s-l, consistent with an essentially diffusion-controlled overall twoelectron p r o ~ e s s .Simulations ~ presented in Section 3.1 on the reduction of suggest that process I consists of two unresolved one-electron cesses I and 11) accompanied by proton-transfer reactions, rather than eous transfer of two electrons. Ell2 for process I is 0.19 V versus FC+ and is independent of scan rate over the range 0.05-10 V s-' . This value ositive than those of0.10 and -0.14 V versus FC/FC+for processes I and 3.2), highlighting the postive shift in potential that has occurred due to nce of protonation reactions which accompany the electron-transfer ilar conclusions can be drawn about processes 11-IV, which implies re also overall two-electron, proton coupled processes, although Eliz depend slightly upon scan rate, varying by 0.02 V in the range 0.05-10 V s-'. Thus, eight electrons have now already been added in the first four processes, which is the total that could be added to [ ~ ~ ~overo entire potential range available in 'dry' acetonitrile. rocesses V, VI, and VII (Fig. 3.19) overlap but extrapolation of information available from earlier studies again indicate that they are derived from groups of reversible multi-electron charge-transfer steps coupled to proton-transfer reactions. However, the reversible potentials of the simple one-electron processes, from which these overall multi-electron processes are derived, must be more 7 ~ h nuances e associated with reversible two-electron EE and ECE processes are summarized in references [40-431. ~ ~ 2 18 Illustvating basics of voltammetry Table 3.4 Steady-state voltammetric data for 2 rnM [ S 2 ~ 0 1 8 ~ 6 2in] 4 9515 C H 3 C N / H 2 0 (0.02 M HC104)' Process Platinum microdisc electrodeb GC rotating-disc electrodeb " v = 5 m ~ s - l ;T = 20°C. b~lectrode diameter = 50 pm. 'Electrode diameter = 2.8 mm. d~stimated from plots of E versus h [ ( I L i r n- I ) / I ] . 'Estimated from ILim values. f Estimated from data at 500 rpm. negative than the acetonitrile solvent limit of about -3 V versus FC/FC+and hence unobservable in that solvent (Table 3.2). Thus, protonation of extensively reduced [ ~ ~ ~musto be ~ the cause ~ 0of potential ~ ~ shifts ] well ~ in excess of a volt. Switching at potentials more negative than the seventh wave reveals a further group of reduction processes between -1.0 and - 1.8 V versus Fc/Fc+. The total number of electrons that can be added to [ s ~ M ~ ~ ~ oas~ ~ ] ~ predicted in Section 4, must therefore be exceptionally large. 2. Steady-state voltammetry Figure 3.21(a) shows a near steady-state voltammogram obtained at a 50-pm diameter platinum microdisc electrode over the potential range encompassing waves I-IV. Parameters Ell2, (Ell4 - E314)and hi, are listed in Table 3.4. (Ell4 - E314)is expected to be 0.028 V for a simple reversible two-electron process. The observed values for processes I11 and IV are larger, implying that they do not involve simultaneous transfer of two electrons at the same potential. 'Log' plots of E versus log[& - I)/I] for waves I and I1 provide n-values of 2.1 and 1.9 (h0.I), as expected for reversible two-electron charge-transfer processes. The intercepts provide Ell2 values (Table 3.4) similar to those found in cyclic voltammetry. The same form of analysis of waves I11 and IV gave apparent n-values of 1.6 and 1.5 electrons, respectively, based on the assumption that they are simple reversible processes. Clearly, they are not. However, essentially equivalent limiting currents for each of the four waves confirm that all these processes involve the overall transfer of two electrons. Figure 3.21(b) shows a hydrodynamic steady-state voltammogram at a GC RDE (diameter = 2.8mm) at a rotation rate of 500rpm. Well-defined sigmoidal-shaped steady-state processes are seen out to -1 -5V versus FC/FC+ under these hydrodynamic conditions. Limiting currents for processes I-IV Electrochemical reduction O ~ O ~ - [ S o62I4~ A ~ O ~ ~219 obtained at a rotation rate of 500 rpm are summarized in Table 3.4. Similar conclusions to those drawn from the above mentioned rnicroelectrode steady-state data can be made about processes I-IV via the hydrodynamic RDE method. he minimization of 'surface blockage7again present at very negative potentials with microdisc electrodes, but not under hydrodynamic conditions, means that information on the number of electrons associated with processes V-VII may be gained from data obtained with the RDE technique. Thus, since a limiting current of -21 =t1 pA is associated with the transfer of one electron at a rotation rate of 500 rpm in the absence of acid, the total current associated with processes V, VI, and VII (Fig. 3.21(b)) of -210 f 4pA is equivalent to the total transfer of ten electrons for these three processes. This conclusion is ed for rotation rates in the range 500-3000 rpm. The combined cyclic ady-state voltammetric data indicate that waves V-VII are chemically reversible and involve a total of 10 electrons in the ratios 4 : 4 : 2. Consely, a total of 18 electrons has been added to the [ s ~ M o ~ ~ oanion ~~]~potential where process VII is observed to produce a (protonated) product, which is stable on the time-scale of these voltammetric experiments. The agnitude of the limiting current of wave VIII indicates that at least eight furer electrons can be transferred in a series of unresolved processes, to give a total of 26 added electrons in the presence of acid within the available potential range. I I I I I I I I I -1.50 0 0.50 -1.50 -1.00 -0.50 0 0.50 1.00 Potential (V vs FC/FC+) Potential (V vs FC/FC+) ig. 3 -21 Steady-state voltammograms for reduction of 2.0 rnM [ ~ 2 ~ o l s 0 6 2 ]in ~ - (95/5) C H 3 C N / H 2 0 (0.1M Bu4NC104; 0.02 M HC104) at 20°C; scan rate, 0.005 V s-l. (a) 50-pm diameter platinum microdisc electrode; (b) 2.8-mm diameter GC RDE with a rotation rate of 500 rpm. Reproduced by courtesy: Inorg. Chern. 36 (1997) 2826. Copyright, American Chemical Society. 220 Illustrating basics of voltammetry 4.5.2 Voltammetry as afunction of acid concentration in (95/5/ CH3 CN/H2 0 1. Simulation of the first two processes Simulations analogous to those presented for the [ P ~ w ~ ~ oand ~ ~[ ]H~ -~ w ~ systems ~ ~ ~(Section ~ ] ~3)-at a range of acid concentrations should enable an understanding of how at least the initial oneelectron processes converge into two-electron processes. As shown in Section 3, the interesting regon with respect to acid concentration in unbuffered media actually occurs when the concentrations of acid and polyoxometalate anion are into ~ a 1 m~ solution of [ s ~ M ~ ~ ~in Q ~ ~ similar. Upon titration of H C ~ O (95/5) C H 3 C N / H 2 0 , the first two one-electron waves convert progressively to the first two-electron wave (Fig. 3.22). The processes responsible for the one-electron waves observed prior to addition of acid have been summarized in eqns (3.19) and (3.20). The voltammograms of Fig. 3.23 were simulated assuming Scheme 3.7 applies, which incorporates eqns (3.19) and (3.20), and protonation equilibria between the one- and two-electron reduced species in an analogous fashion to reaction Schemes developed previously for the simulation of the [P2Wls062]6and [ H ~ w ~ ~6- osystems. ~ ~ ] Simulation of Scheme 3.7 evolved from the following considerations: (1) [ s ~ M ~ ~ ~was o ~assumed ~ ] ~ -to be unprotonated. Experimentally, electronic spectra and electrospray mass spectra of solutions of [ s ~ M ~ ~ ~ o ~ in acetonitrile are independent of [Hf] up to 100 mM. (2) Initial estimates of the two E;,, values of the two processes in eqns (3.18) and (3.19) were made voltammetrically (Table 3.5). cm2 s-' was used for the diffusion coefficient of (3) A value of 6.4 x [ s ~ M o ~ ~ The o ~ same ~ ] ~value . was assumed for the reduced anions. The diffusion coefficient for H+ is unknown in C H 3 C N / H 2 0 solutions. While cm2s-', limitations best fits were obtained with a DH+value of 1.8 x arising from input of diffusion coefficients noted in Section 3 need to be kept in mind. (4) The forward rate constants kf of the three protonation equilibria were assumed to be fast (10" M-' s-'). The backward rate constants kb were allowed to vary. (5) The electron-transfer processes were assumed to be reversible, so that values of ko > 1 cm s-' were used in the simulations. (6) Other input parameters such as electrode area, uncompensated resistance, and capacitance were obtained directly by measurement as described in Section 3. Comparisons of experiment and theory are made in Figure 3.23 for [H'] = 0,0.3, and 0.7 mM. Agreement is excellent for all H+ concentrations examined in the range 0-0.7 mM and for scan rates of 20, 50, 100, and 500 mV s-' . This success validates the assumptions that the heterogeneous and homogeneous rates of the redox and protonation processes are very fast relative to the voltammetric Electrochemical reduction of a -[S2M O8 0621~~ 22 1 Potential (V vs FC/FC+) ig. 3.22 Cyclic voltammograms obtained with a 3-mm diameter GC electrode using a scan rate of 0.5V s-I for reduction of [ s ~ M ~ ~ ~ino the ~ ~presence ] ~ - and absence of acid. (a) (-)CH3CN (0.1M Bu4NC104)/(. . . .) (95/5) C H 3 C N / H 2 0 (3 M HC104); (b) (95/5) CH3CN/H20 with indicated amounts of acid. Reproduced by courtesy: Inorg. Chern. 36 (1997) 4227. Copyright, American Chemical Society. time-scale and that the redox processes are diffusion controlled under this range of conditions. It is clear that while the observed waves differ in relative current intensity as [H+] varies (Fig. 3.23), this does not imply irreversibility. Parameter ElI2V (versus Fc/Fc+) and K = kf/kb (M-') values used to simulate voltammograms are listed in Table 3.5. The simulations confirm that two one-electron reversible reduction processes occur in (95/5) C H 3 C N / H 2 0 in the absence of acid. However, in the Potential (V vs FC/FC+) Fig. 3.23 Simulation of cyclic voltammograms for reduction of [ S ~ M O ~ ~ O in ~(95/5) ~]' CH3CN/H20.[HC104],mM: (a) 0; (b) 0.3; (c) 0.7. Experimental conditions are as in Fig. 3.22(b). Reproduced by courtesy: Inorg. Chem. 36 (1997) 4227. Copyright, American Chemical Society. Electrochemical reduction o f ~ ~ - [ s ~06214Mo~~ 223 Scheme 3.7 Table 3.5 Summary of parameters used in the simulation of cyclic voltammograms obtained for reduction of [ s ~ M ~ ~ in~ (95/5) o ~ ~ ] ~ C H 3 C N / H 2 0 (0.1 M Bu4NC104)in the presence of HC104 Charge transfer reactions E1/2 (V) presence of acid, the (one-electron) reduction product [ s ~ M o ~ ~proo ~ ~ ] ~ tonates rapidly and reversibly to form an equilibrium with [ s ~ M ~ ~ ~and o ~ ~ ] ~ [ H S ~ M O ~ ~ (Table O ~ ~ ]3.5). ~- The more basic (two-electron) reduction product [ ~ ~ ~ o forms ~ ~an 0 equilibrium favouring [ H ~ s ~ M ~ ~over ~ o[ ~H~S] ~~ M - ~ ~ in ~ O moderately ~ ~ ] ~ concentrated acid media. ~ ~ ] 224 Illustrating basics ofvoltammetry The (one-electron) reduction product is essentially stable to disproportionation in the absence of added acid, as noted in Section 4.1.4. However, the Ell2 value for reduction of [ S ~ M O ~ ~ isOmuch ~ ~ ]more ~ - negative than that for its protonated form [ H S ~ M ~ ~ ~ (-0.13 O ~ ~ versus ] ~ -0.35 V; Table 3.5 and so, in the presence of acid, the [ S ~ M O ~ ~ isOunstable ~ ~ ] ~to- the disproportionation reactions in eqns (3.36) and (3.37). Clearly, the final state of protonation of the two-electron reduction product will depend on [H+] as quantified by the influence of the equilibria in eqns (3.33) and (3.34). In principle, the coalescence of all the (one-electron) reduction processes into (two-electron) processes could be simulated. However, as the extent of reduction increases the influence of redox cross reactions becomes very complex and so only simulation of the initial processes has been attempted. Nevertheless, qualitatively, certain conclusions may be reached. In (95/5) CH3CN/H20(0.02MHC104), voltammograms exhibit four two-electron, chemically reversible steps. The separations in Ell2 values are -0.1 1, -0.20, and -0.3 1V, that is every two electrons (with accompanying protons) transferred to the [ s ~ M ~ ~ ~anion o ~causes ~ ] ~a -0.1 V stabilization of the molecular framework with respect to further reduction. In the absence of acid, the separation between adjacent pairs of one-electron reductions is constant at about -0.6V (Table 3.2). The high basicity of the unprotonated reduced species is arent and it can e concluded that process I is derived from processes I and IV, process I11 from V and VI and process 1V from VII and VIII. It therefore follows that processes V-VIII must arise from simple electron-transfer processes whose reversible potentials are more negative than the acetonitrile solvent limit. 2. Nernstian behaviour in hiqh acid concentrations For high acid concentrations, it can be assumed that, during the course of the voltammetry, the concentration of Hf at the electrode surface remains constant at its bulk solution value. This simplifying feature means that an analytical theoretical solution is available to The interpret the dependence of Ei12 on [H+] when [H'] >> overall equation for an electrode process for the reduction of a (ne-, y ~ + ) Electrochemical reduction of a -[s2M0i8 0621~- 225 reduced species is thermodynamically equivalent to e Nernst equation relevant to eqn (3.38) indicates that a plot of Ell2 versus ill have a slope of (x - y)RT/nF [33]. As discussed above, the 0 ~ to~be ]zero. ~ umber of protons y associated with [ ~ ~ ~ ocan~ be~assumed r the first reduction process observed in the presence of excess ows that the slope derived from use of the Nernst relationship will ing steady-state voltammetry at the Pt microelectrode, Ell2 values for two-electron processes were estimated as a function of [HC104]in 300 mM. Figure 3.24 shows a plot of E;/, for the first process versus - ln[H+] for reduction of 0.4 mM [ s ~ M o ~ ~ oin~(95/5) ~ ] ~ -C H 3 C N / H 2 0 containing 10 mMBu4NC104.There is a linear dependence, which gives x = 1 m the calculated value of slopes for [HC104] < 100rnM, and x = 2 for C104] > 120 mM, consistent with eqns (3.39) and (3.40). (V vs Ag/AgCl) on [HC104] for the initial two-electron reduction . 3.24 Dependence of (10 rnM Bu4NC104).Reproduced by courtesy: process of [ s ~ M ~ ~ ~ino(95/5) ~ ~ CH3CN/H,0 ] ~ Inog. Chem. 36 (1997) 4227. Copyright, American Chemical Society. 226 Illustrating basics ofvoltammetry A dependence on [H+] corresponding to eqns (3.40)-(3.43) is observed for processes I1 and 111. All the species listed in eqns (3.39)-(3.44) are in equilibrium with other protonated forms, although the form of analysis employed only identifies the major species present at a given proton concentration range. At higher ionic strengths (0.1 MBu4NC104),only eqns (3.40), (3.42), and (3.44) apply, so that medium effects are again detected. - acidic media 4.5.3 Spectroelectvochemical studies on [SZMo 0 6 ~ 1 ~ in Electronic spectra may be obtained for the species predicted to exist in Section 4.5.2 (eqns 3.40, 3.42, and 3.44) by undertaking spectroelectrochemical experiments in an OTTLE cell during the course of the reduction of in (95/5) C H 3 C N / H 2 0 (0.2 M HC1o4). The potentials applied in an OTTLE cell in order to bring about these reductions were 0.27V versus FC/FC+ (Ell2 = 0.31V) and 0.15V versus FC/FC+ (Ell2 = 0.22V). It can be seen from Table 3.3 and Fig. 3.25 that the two-electron reduced, two-proton [ H ~ s ~ M ~ ~and ~ osix-electron ~ ~ ] ~ - reduced, six-proton [ H ~ s ~ M O ~ species ~ O ~ ~have ] ~ three absorption bands in the red-visible region, again probably arising from suspected intervalence transitions, whereas the fourelectron, four-proton reduced [ H ~ s ~ M O ~ ~complex O ~ ~ ]exhibits ~two bands in this region. The data in Table 3.3 demonstrate that large wavelength shifts are observed in the electronic spectra when protonation occurs. Typically, large shifts in Ell2 are associated with large shifts in ,A since both parameters are associated with an electronic transition. 4.5.4 Directed electrochemical syntheses of veducedforms of [SzMo 0 6 ~ 1 ~ in - acidic media Voltammetric studies predict that one-electron and two-electron reduced species, [ s 2 ~ o 10 ~8~ 1 ' - and [ s 2 ~ o 1 8 0 66-,2 ] will be accessible synthetically in the absence of acid and indeed this is shown to be the case in Section 4.3. Equations (3.39) and (3.40) indicate that the (2e-, 1 H+)- and and [ H ~ s ~ M ~ ~ ~might o ~ ~ ] ~ (2e-, 2 H+)-reduced species, be synthetically accessible after a two-electron reduction at low and high [H+], respectively. In contrast, the (le-, 1 H+)-reduced anion [ H S ~ M ~ ~ ~is O ~ ~ known to disproportionate (eqns 3.36 and 3.37) and hence will not be isolatable. Analogous arguments apply to the predicted, possible synthesis of the Electrochemical reduction ~ ~ C Y - [ &o62I4M O ~ ~ 227 (4e-, 2 H') [ H ~ s ~ M ~ and~(4e-, ~ o4 H+) ~ ~ [ ]H~~ s ~ M O after ~ ~ aOfour~ ~ ] ~ electron reduction in high- and low-acid concentrations respectively (eqns 3.41 and 3.42). Definition of the optimum conditions for isolation of pure materials from the solution phase was guided by the above considerations. However, relative solubilities and precipitation rates of the different salts formed on addition of R ~ N +cations can, of course, determine the identity of the isolated solid. Controlled potential electrolysis, coupled with coulometry, and monitoring with steady-state voltammetry, confirmed that each of the first two two-electron rocesses, observed in (95/5) C H 3 C N / H 2 0 , with [HC104] = 1 and 100mM is chemically reversible: reoxidation leads to quantitative regeneration of the original species. Further, salts of the two- and four-electron reduction products may be obtained. The (2e-, 1 H') and (4eP, 2 H') products, [ H S ~ M ~ ~ ~ O ~ ~ ] 5000 10000 15000 25000 20000 30000 35000 Wavenumber (cm-l) I 5000 10000 I I I I 15000 20000 25000 Wavenumber (cm-l) Fig. 3.25 Continued. I I 30000 I 35000 228 Illustrating basics ofvoltammetry I I 5000 10000 15000 25000 20000 30000 35000 Wavenumber (cml) + + Fig. 3.25 Spectroelectrochemical experiments for (a) [ ~ ~ ~ o ~ 2H+ ~ 0 2e~ ~ -+] ~ [ ~ 2 ~ 2 ~ 0 1 8 0 6 2 ] ~(b) -; [ H Z S ~ M O ~ ~ O 2H+ ~ ~ ] ~ 2 e -+ [ H ~ S ~ M O I ~ O ~ and ~]~-; ~ ~ O ~processes ~ ] ~ for the Hex4N+ (c) [ ~ 4 ~ 2 ~ 0 1 8 0 6 2 ] ~2- ~ ' 2e- -+ [ H ~ S ~ M O reduction salt (5 x lo-' M) in (95/5) C H 3 C N / H 2 0 containing 0.2 M HC104 and 0.1 M Hex4NC104 in an OTTLE cell at 22°C. "Detector change. Provided by courtesy: T. Vu, Monash University, Victoria, Australia. + + + + and were obtained when [HC104] = 1 mM while the (2eP9 2 H+) and (4eP, 4 H+) products, [ H ~ s ~ M ~ ~and ~ o[ ~H~ ~ ] ~s - ~ M ~ ~ were obtained when [HC104] = 100rnM. A six-electron reduced form was also produced efficiently in solution and reoxidation produced the oxidized form quantitatively. However, upon standing, the six-electron reduced solution oxidized spontaneously (back to the four-electron level), probably by reduction of H+ to H2, preventing isolation of salts. Similar observations of spontaneous oxidation back to the four-electron level hold for even more highly reduced solutions. 1. Isolation of [ P Y ~ N ] ~ [ H S ~ 0M6O2 ] and related salts A solution consisting of 5 mM [Hex4NI4[S2M~18062] 1 & HC1o4 and 0.2 M Bu4NC104 in (95/5) M e C N / H 2 0 was reduced by exhaustive bulk electrolysis at 0.15 V versus Fc/Fc+. Voltammetric monitoring of the dark blue-green solution with the Pt microelectrode confirmed a two-electron reduction (i.e. the point of zero current was at the plateau between the first and second waves). Pr4NBr was added. Storage at 4°C produced needle-like, dark blue-green crystals after 1h. These were isolated as the solvated salt. E~,+N+ and B U ~ N + salts can be synthesized in a similar manner, and synthesis of [Bu4NI5[HS2M018062] salt as an analytically pure non-solvated salt can also be achieved by isolation after reduction in 'dry9 CH3CN (Section 4.3.2). Chemical synthesis of solvated [ H S ~ M O ~ which ~ O ~ ~also ] includes the [ ~ e (-qc5Me5)2j5 ~ anion is described in Section 4.4. 2. Isolation of [ f i x 4 N ] 4 [ H 2 S z M o 1 8 0 6 2 ] and velated salts A solution of 5.0 mM [Hex4NI4[S2M~18062] and 10 mM HC104 in (95/5) C H 3 C N / H 2 0 ? 229 Electrochemical vedttction ofa -[S2Mo180621~- was reduced by exhaustive bulk electrolysis at 0.14 V versus Fc/Fc+. Voltammetric monitoring confirmed a two-electron reduction. Hex4NBr was added. Storage at 4°C for four weeks produced blue crystals of ~ x ~ N ] ~ [ H ~ Pr4N+ S ~ Mand ~ Bu4N+ ~ ~ ~ salts ~ ~ can ] . be synthesized in a similar manner. 3. Isolation of [Pr4N]6[fiSzhfo180~ This salt was obtained in the form of blue crystals using a procedure equivalent to that for [PrqNI5[HS2M018062] except that the electrolysis potential was set at 0 V versus Fc/Fc+. Voltammetric onitoring of the blue solution confirmed a four-electron reduction. A Bu4Nf salt can be synthesized in a similar manner. ~ salt was obtained in the 4. Isolation of [ H ~ X ~ N ] ~ [ H ~ S ~ M OThis form of deep blue crystals using a procedure equivalent to that for ex4NI4[H2S2MoI8 0 6 2 ]except that the electrolysis potential was set at 0.09 V versus Fc/Fc+. Voltammetric monitoring of the deep blue solution confirmed a four-electron reduction. Pr4N+ and Bu4N+ salts can be synthesized in a similar manner. 5.5 Voltammetric chavacterization of salts and stoichiometry of all isolated salts were determined by elemental s, and by monitoring the point of zero current and wave shapes of steadystate voltammograms of the salts dissolved in the media from which they were isolated. The voltammetric technique allows, for example, the H e x 4 ~ salts + of [ s ~ M ~ ~ ~ o the~ (2e7 ~ ] ~2-H+) , product [ H ~ s ~ M ~ ~ ~and o ~the~ (dew, ] ~ - , 4- to be distinguished. They differ in compo+) product sition by only 2 and 4 hydrogen atoms in a molar mass of 4204 Da. The I -0.50 I 0 Potential (V vs FC/FC') I I I I 0.50 -0.50 0 Potential (V vs FC/FC+) 0.50 ig. 3.26 Near steady-state voltarnmograrns of 1rnM solutions of ~ e x ~ Nsalts + of polyoxornolybdates at a 100-prn diameter Pt microelectrode in (95/5) C H 3 C N / H 2 0 (0.2 M Bu4NC104: 0.1 M HC104): (a) [ H ~ s ~ M ~ ~ ~(b) o ~[ H ~ ]~ ~s -~; M ~ ~ ~Reproduced o ~ ~ ] ~ -by. courtesy: Inorg. Chem. 36 (1997) 4227. Copyright, American Chemical Society. 230 Illustrating basics of voltammetry (a) I I I -0.50 0 Potential (V vs FC/FC+) 0.50 Fig. 3.27 Near steady-state voltammograms at a 100-pm diameter Pt microelectrode of 2.3 mM [(Pr4N)I6[S2M018062](a) in CH3CN (0.23 M Bu4NC104);(b) after addition of 3.8 rnM HC104. Reproduced by courtesy: Inorg. Chem. 36 (1997) 4227. Copyright, American Chemical Society. positions of the zero current in Fig. 3.26 confirm that [ H ~ x ~ N ] ~ [ H ~ S ~ M is two-electron reduced and that [ H ~ x ~ N ] ~ [ H ~ is four-electron S ~ M ~ ~ ~ ~ ~ ~ reduced. As noted in Section 4.5.1, the addition of acid to the one-electron reduced anion [s2Mol80 ~ ~ 1causes disproportionation as evidenced by monitoring of the position of zero current in steady-state voltammograms. The oxidation level of the two-electron reduced anion [ ~ ~ ~ ois confirmed ~ ~ 0 ~ ~ ] by its steady-state voltammogram (Fig. 3.27(a)). Addition of acid leads to the (2e-, 2 H') behaviour characteristic of [ H ~ s ~ M ~ ~in~acidified o ~ ~ CH3CN ] ~ (Fig. 3.27(b)). The position of zero current is at the plateau between the first two two-electron waves (Fig. 3.27(b)) and shows that [ s ~ M ~ has ~ ~been o ~ ~ ] protonated but does not disproportionate in the presence of acid. The studies on the voltammetry of [ ~ ~ ~ oreveal ~ ~that0directed ~ ~ elec] ~ trochemical synthesis is possible for inherently complex systems, if adequate voltammetric data are available. 4.6 Photoelectrochemical studies of [ S ~ M1O8 ~ 6 2 / 4 - using a hydrodynamic channel electrode8 Since their discovery more than 100 years ago, many examples ofphotochemical reactions involving polyoxometalate compounds have been identified. In the case of [ ~ ~ ~ o ~exposure ~ 0 ~of ~ the]solid ~ -to ,sunlight for a period of time, causes a colour change from yellow to green to blue to occur progressively. Since [ s ~ M ~ is ~ green ~ o and ~ ~[ s] ~~ M ~ ~ ~is oblue, ~ ~these ] ~ -observations are consistent with photoactivity involving reduction of the [ s ~ M ~ ~ ~ando ~ ~ ] ~ presumably oxidation of water, since photoactivity is not detected when light is shone on samples contained in a vacuum. ' ~ d a ~ t ewith d permission from Inovg. Chem. 34 (1995) 3378. Copyright, American Chemical Society. Electrochemical reduction of a -[&Mol O62I4- 23 1 In order to study the photoelectrochemistry of (and M ~ ~ which ~ ois also ~ photoactive) ~ ] ~ a channel electrode (Section 9.2 in apter 2) made of optical quality synthetic silica was employed with acetonitrile (0.1 M Bu4NC104)and solvent flow rates in the range 10-~-10-'cm3 s-' . se of this flow-type cell makes it easy to shine light of the required wavelength onto the electrode surface. Since the solution is flowing, heat is rapidly dissipated so that thermal effects from the light source can be neglected. Finally, as noted in Section 9.2 in Chapter 2, the hydrodynamics of the channel electrode may be readily modelled so that the quantitative effect of the contribution of the light to the reduction process can be calculated. The working electrodes were fabricated from thin platinum foil (thickness 0.025 mm), of dimension 4 x 4 mm, and were periodically irradiated with a He-Cd laser light source having a maximum irradiant power output of 40 f 5 mW cmW2.A silver wire pseudo-reference or saturated calomel reference electrode was located upstream and a platinum foil counter electrode downstream with respect to the channel electrode. .6.1 Photoelectrochemical experiments in the presence of toluene and tetrahydrojuran As expected, on the basis of studies described in Section 4.1, hydrodynamic channel electrode voltammograms at platinum electrodes for reduction of ~ ~ ~ exhibit o four~ reversible ~ reduction 0 ~ processes ~ over ] the ~ potential range +0.7 to -1.3 V versus SCE in acetonitrile, which correspond to the formation of [ s ~ M o ~ ~ o ~[ ~s ]~~ M - , ~ ~ ~ o[S2M01 ~ ~ ] 8~~ -6 2, ] 7 -and , [ s ~ M ~ ~ ~ oThe ~ ~Ell2 ] ~ -values . are -I-0.49, +0.19, -0.46, and -1.20 V versus SCE. 0621 5-, and As will emerge, only the yellow [ s ~ M o ~ ~ o ~ green ~ ] ~[s2Mo18 -, blue [ s ~ M o ~ ~areo relevant ~ ~ ] ~to the photochemistry so that the processes relating to the formation of the 7- and 8- anions are not considered further in Section 4.6. From the voltammetric data, it can be deduced that if the potential of a channel electrode is held at a value which is more positive than the first reduction step, zero current (relative to the background) should be observed. However, if [ s ~ M o ~ ~ oor~ ~ [ ]s ~~ - M ~ ~ ~areo generated ~ ~ ] ~ -photochemically, then an oxidation current will be detected at these positive potentials. Use of the platinum channel electrode, acetonitrile (0.1 M Bu4NC104)con~ irradiation ~ ] ~ - , with laser light of wavelength taining 1op3M [ s ~ M ~ ~ ~ oand 325 nm, introduced no new features into the hydrodynamic voltammetry over the potential range +0.9 to +0.2 V versus SCE. However, on irradiation of in the presence of 0.6M toluene or tetrahydrofuran (THF), steady-state oxidative currents were observed in this potential range. These mass-transport limited currents are consistent with photochemical generation of reduced forms of [ ~ ~ ~which o are ~ then ~ detected 0 ~ by ~their ] transport-limited oxidation. Equations (3.45) and (3.46) summarize likely photochemically induced processes, where ED = the electron donor ~ 232 Illustrating basics of voltammetry (toluene or THF): The 'photocurrent' is much larger in the presence of THF than toluene, suggesting that the kinetics of the reaction of the photoexcited state molecule(s) with THF must be faster than with toluene. In initial experiments, electrode passivation at the platinum electrode (see also Section 4.1.2) was substantial in the presence of light and toluene or THF and the photocurrent decayed steadily with time. However, this problem was minimized by the use of a 'sacrificial electrode' which was irradiated upstream of the channel detector electrode. The sacrificial electrode consisted of a platinum foil (4 x 5 mm) located in the irradiation zone, immediately upstream of the working electrode but insulated from it. Its purpose was to act as an adsorptive surface for any surface-active minority species, either initially present or photogenerated in solution, thus, preventing them from reaching and contaminating the working electrode surface. The latter electrode was screened from the light source using o ~ ~upstream ] ~ masking tape. In this way, [ s ~ M ~ ~ ~oro[ ~s ~ ]M~ ~- ~ ~formed were swept to the working electrode for voltammetric interrogation while the majority of the passivatingspecies were removed. Using the above protocol, solutions containing known concentrations of [ ~ ~ ~ ando toluene ~ ~or THF 0 were ~ ~flowed ] through ~ the channel electrode and the working electrode held at f0.8V versus SCE, correspond0621 0 682 1 6 - to ing to transport-limited oxidation of [ s 2 ~ o 1 8 5- and [ s 2 ~ o 1 [ s ~ M ~ ~ ~ oLaser ~ ~ ]light ~ - .of wavelength 325 nm and intensity of 40 f 5 mW cmW2was periodically used to irradiate the area immediately upstream of the working electrode. The resulting total steady-state transport-limited current (Fig. 3.28) was measured under irradiative conditions (A = 325 nm) as a function of flow rate of solution over the electrode. After each measurement, the potential was switched to reducing potentials of -2.00 V versus SCE for a period of time (about 1min) in order to clean the electrode. The photocurrents at 0.8 V versus SCE were measured over a wide range of flow rates (6 x low4cm3 s-'-5 x 1oe2 cm3 s-') and concentrations (0.05-0.2 rnM), and at two light intensities (Io) of 40 and 18 mW ~ m - In ~ .the absence of light there was negligible oxidative current. [ s ~ M o ~ ~ oabsorbs ~ ~ ] ~light - strongly at 325 nm9 (E = 3.2 x l o 4 M-' cm-I). It was also considered likely that a second electron transfer could occur between photoexcited ( [ S ~ M O ~ ~ O ~ and ~ ]the ~ - electron )* donor, since [ s ~ M ~ ~ ~ o ~ ~ ' ~ o t ethat the units of wavelength employed in Fig 3.15 are cm-' rather than nm. Electrochemical reduction ofa-[S2Mol8o62I4- 233 LIGHT OFF (b) I LIGHT OFF ~~=8.10~10-~cm~s-~ LIGHT ON ---+ time 1 minute LIGHT ON I Itime I 1 minute ocurrent obtained in a channel electrode in acetonitrile (0.1M Bu4NC104) for 0 ~ ~ 0in ~ the~ presence 1 ~ -of (a) toluene; and (b) THF. Reproduced by courtesy: Inorg. Chem. also exhibits strong absorption at 325 nm (E = 3.3 x lo4M-' cm-I). A theoretical CECEC model observed for photocurrents at potentials corresponding to the transport-limited oxidation of [ ~ ~ ~ o and ~ [S2Mo ~ 0 8 ~0 ~ ~ ]- ~ ~ 1 ~ was therefore developed as in eqns (3.47-3.51). - Since the donor concentration was in considerable excess, it was postulated at photoreduction reactions occur to form [ s ~ M ~ ~ ~ and o [~s ~~ ]M~ ~- ~ ~ o ~ ~ ] ~ (eqns 3.47 and 3.49) via a pseudo-first-order process which is followed by their detection by electrochemical oxidation (eqns 3.48 and 3.50). The final step postulated, involves decomposition of the donor (ED) cations, [toluene]+ and [THF]+. It was assumed that these cations decompose instantaneously on the time-scale of the experiments and that this rapid decomposition therefore recludes the occurrence of any back-electron-transfer reaction. Possible protonation of the polyoxometalate [ s ~ M o ~ by ~ oH+, ~ formed ~ ] ~ by decomposition of ED', was also neglected because these voltammetrically distinguishable forms 234 Illustvating basics ofvoltammetvy of the polyoxometalate were not detected under these conditions. The genera0 68 2 1 8 - or even more highly reduced species tion of [ s 2 ~ o 01682 1 7 - and [ s 2 ~ o 1 was also not included in the model as the much higher energes required for their formation made this a less likely event than the generation of [ S 2 ~ o 1 8 0 6 2 ] 5 and [ s ~ M o ~ ~ o ~NO ~ ]account ~ - . was taken, in the modelling, of the disproportionation step shown in eqn (3.28), since this reaction occurs to less than 1 per cent. The experimental results were compared with the theoretical model for CECE process derived from the solution of the relevant convective-diffusion equations. [ s ~ M ~ ~ ~[ os ~~ ~M~ 5-, ~ -and ~ , ~[ so ~~M~~ ~~ ~were o ~assumed ~ ] ~ to have equal diffusion coefficients of magnitude equal to that deduced for cm2 s-' from rotating-platinum-disc [ s ~ M ~ which ~ ~ was o ~5.0~f]0.5~x electrode voltammetry. Additional modelling work was carried out to check if alternative mechanisms could give agreement with the experimental data for the photocurrent variation with flow rate observed. The alternative mechanisms postulated all had reversible chemical steps in which ED+ reacted with [ ~ ~ ~ o or~ ~ [ s ~ M ~ ~ ~toore-form ~ ~ ] [~ s- ~ M ~ ~ ~oro[ ~s ~ M ] ~~ - ~ ~ respectively, o ~ ~ ] ~ - so , that the step for the decomposition of the donor cation became kinetically significant. The experimental fits for the CECE mechanism for both the toluene and THF cases are shown in Fig. 3.29. The high correlation between theory and experiment is indicative of the fact that the CECE mechanism provides an accurate representation of the reaction. The rate obtained for steps kl and k2 are summarized in Table 3.6. The best fit values of kl and k2 were found to be independent of [ s ~ M ~ ~ ~concentration, o ~ ~ ] ~ - in the range 0.05-0.2 &, (studies using higher concentrations were precluded due to electrode passivation, notwithstanding the sacrificial electrode approach), and as expected theoretically, the rate constants were found to have a linear dependence on light intensity. A detailed knowledge of the voltammetry of [ ~ ~ ~ o has ~ enabled ~ 0 ~ directed synthesis of reduced forms of this polyoxomolybdate. This knowledge also enables the course of redox reactions with other compounds to be understood. In particular, when acid-base reactions accompany electron-transfer reactions, nuances such as why different types of products are formed when [ ~ ~ ~reacts o with ~ Ph3P ~ and 0 Bu3P ~ can ~ be] established ~ by voltammetric monitoring of the reaction pathway. 1°~daptedwith permission from Inorg. Chem. 37 (1998) 2366. Copyright, American Chemical Society. ~ Use ofvoltammetric techniques 235 (a) 0.40 - 2. 0.30 w 4 2 2 9 0.20 ; -c0 0.10 0 0.010 0.020 0.030 0.040 Volume flow rate (cm3 sf1) (b) 0.40 2* 0.30 w 5 g 0.20 ; 0 2 0.10 0 0.01 0.02 0.03 0.04 0.05 Volume flow rate (cm3 S-l) . 3.29 CECE mechanism, experiment and theory comparison for photocurrents obtained in a o ~ (a) ~ ]toluene ~ - and (b) THF channel electrode for (a) 0.2 mM; and (b) 0.1 mM [ s ~ M ~ ~ ~when are the electron donors and the light intensity is (40 f5) m W crnp2. Reproduced by courtesy: Inorg. Chern. 34 (1995) 3378. Copyright, American Chemical Society. Table 3.6 Kinetic data obtained from photoelectro~ o ~ ~ ] ~ chemical measurements on [ s ~ M ~ in~ acetonitrile (0.1 MBu4NC104)in the presence of toluene and THF using a platinum channel electrode. Experimental details are available in Inorg. Chem. 34 (1995) 3378 Rate constant (s-l) Value of k Value of k (Io= 55 m w ~ m - ~ ) (Io= 25 r n w kl (toluene) k2(toluene) kl (THF) k2 (THF) 0.0085 (*0.0005) 0.0047 ( f 0.0002) 0.0410 (A0.0050) 0.0370 ( f 0.0030) 0.0041 (f0.0005) 0.0020 (f0.0003) 0.0190 (f0.0060) 0.0150 ( f 0.0050) 236 Illustrating basics of voltammetry 5.1 Reaction of [&MOl 8 0 6 2 1 4 - with Ph3P in (95/5) C H 3C N / H 20 Figure 3.30 shows cyclic voltammograms obtained over the potential range 2] -0.30 to +1.10V versus FC/FC+ for 1mM [ ( H e ~ ) ~ N ] ~ [ S ~ M o l 8in0 6(95/5) C H 3 C N / H 2 0 (0.1 M Bu4NC104)in the absence and presence of 1 rnM Ph,p at a GC macrodisc-electrode. This mixed solvent medium is the same as that in which the simulations presented in Section 4.5.2 were undertaken, so that quantitative details of the [ s ~ M o ~ ~redox o ~ chemistry ~ ] ~ are available. In the absence of Ph3P, and as seen previously, two reversible one-electron waves are observed over the potential range considered in Fig. 3.30 with reversible El,, values of 0.12 and -0.13 V versus Fc/Fc+. Clearly, in the presence of Ph3P, the nature of the cyclic voltammograms and the values change slowly with time. Ph3P itself is irreversibly oxidized at f0.70 V under the conditions shown in Fig. 3.30, in agreement with other studies in different media [44-481. In the presence of Ph3P, the most positive process associated with the polyoxomolybdate system increases with respect to current magnitude and shifts to a more positive potential, whereas the current for the second polyoxomolybdate reduction wave decreases, as does that for the Ph3P oxidation wave (Fig. 3.30). Steady-state voltammetry at a microdisc-electrode (Fig. 3.31, note position of zero current) reveals that the [ s ~ M o ~ ~ osystem ~ ~ ] is~ extensively reduced after 1 h of reaction time. After 48 h, only two processes can be detected (Fig. 3.30); the new oxidation wave and the remaining reduction wave (Fig. 3.31) corresponding to reversible two-electron charge-transfer processes. Further, the voltammetric feature associated with oxidation of Ph3P has completely vanished (Fig. 3.30). -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Potential (V vs FC+/FC) Fig. 3.30 Voltammograms of 1mM [ ~ ~ ~ o in ~(95/5) ~ C 0 H ~3 C N ~ / H] 2 0~(0.1 - M Bu4NC104) before and after addition of Ph3P (1 mM): (a) cyclic voltammograms at a G C disc electrode (diameter = 3.0 mm; v = 100 mV s-l. (-, no Ph3P; - - - , 1 mM Ph3P, 1 h; . . . , 1mM Ph3P, 48 h.) Reproduced by courtesy: Inorg. Chem. 347(1998) 2366. Copyright, American Chemical Society. Use Ofvoltammetn'c techniques 237 2.>-After addition of Ph3P Potential (V vs FC/FC+) . 3.31 Steady-state voltammograms at a GC microdisc electrode (diameter = 10pm; v = 10 mV s-') for the experiment described in Fig. 3.30. Reproduced by courtesy: Inorg. Chem. (1998) 2366. Copyright, American Chemical Society. -0.4 -0.2 -0.0 0.2 0.4 Potential (V) vs FC+/FC 0.6 ig. 3.32 Simulation of cyclic voltammograms of 1 m M [ S ~ M O ~ ~in O (9515) ~ ~ ] ~ CH3CN/H20; (0.1 M Bu4NC104)in the presence of differing concentrations of acid using the parameters and mechanistic scheme described in the text. (-) [H'] = 0 mM; (- - -) [H'] = 0.3 mM; ( . . . ) [H+] = 0.7 mM). The changes in voltammetric peak heights and potentials of the polyoxomolybdate processes as a function of time of reaction with Ph3P suggests that an increase in proton concentration may be occurring during the course of the reaction. Figure 3.32 shows simulated cyclic voltammograms using the parameters derived in Section 4.5.2 and the experimental conditions shown in Fig. 3.30 in the absence and presence of varying proton concentrations. The theoretical voltammograms obtained in the presence of varying amounts of acid (Fig. 3.32) clearly resemble, very closely, those obtained experimentally (Fig. 3.30) if loss 238 Illustrating basics ofvoltammetvy of one mole of Ph3P is accompanied by generation of 2 mol of H+. To test was examined experhenthis hypothesis, the voltammetry of tally in the presence of 2 mol eq. HC104 and shown to be virtually identical with that of the reaction solution after 48 h. The only difference is that the first two-electron wave of the completely reacted solution is an oxidation rather than a reduction process. O n the basis of the simulated and experimental data, it is apparent that the final product in this reaction is the two-electron reduced species, [ H S ~ M O ~ ~ Ogenerated ~ ~ ] ~ - ,by the initial one-electron reduction of [ s ~ M ~ ~ ~too[ ~s ~ ~] ~ M - ~ by ~ Ph3P ~ o followed ~ ~ ] by ~ its disproportionation in the presence of the protons released during the Ph3P oxidation process. and Ph3P by 3 1 NMR ~ Monitoring the reaction between spectroscopy in (95/5) C H 3 C N / H 2 0 both in the presence and absence of electrolyte, showed that Ph3P (6 = -4.4ppm) is oxidized to P h 3 P 0 (6 = 30.1 ppm). However, the rate of reaction was found to be much faster in the absence of electrolyte, presumably because of ion pairing (relatively weak) of the very negatively charged polyoxomolybdate species with BU~N' that occurs when 0.1 M Bu4NC104is present. 1 7 0 N M R experiments on solutions enriched in H ~ (50 ~ O per cent 1 7 0 ) confirmed that the source of the oxygen Electron atom in the product P h 3 P 0 was solvent water and not impact mass spectra on solids obtained from this 170-enriched reaction solution exhibited peaks at m / z = 278 and 279 in the intensity ratios expected for ~ per O cent l 7 0 ) . ph3p160and ph3p170produced from the presence of H ~ (50 The combination of voltammetric and N M R data therefore indicate that [ S 2 ~ o l s ~ 6 2 undergoes ]4an overall two-electron reduction reaction to form [ H S ~ M O ~ ~ while O ~ ~ oxidizing ]~Ph3P to Ph3P0. O n the basis of the above results, the reaction scheme is given in eqns (3.52) and (3.53) with the overall reaction being represented by eqn (3.54). Overall Ph3P undergoes an irreversible one-electron oxidation at platinum electrodes in acetonitrile solution and the initial product of this reaction is believed to be the phosphonium radical cation (Ph3P+)[44-481. Hence, it is postulated that in the C H 3 C N / H 2 0medium, Ph3P initially transfers one electron to [ s ~ M ~ ~ ~ o ~ ~ ] Use of ooltammetn'c techniques 239 The Ph3P+ cation radical is proposed to react rapidly with water present in the mixed solvent used, possibly forming a phosphine oxide precursor (such as the radical Ph3POH) and protons [49]. This generation of protons will lead to protonation of [ s ~ M o ~ ~ o ~ ~ ] ~ and subsequent disproportionation to [ s ~ M ~ ~ ~and o ~[ H ~ ]S ~ M - O ~5-~ O ~ ~ ] ection 4.5.2). The phosphine oxide precursor could react rapidly with 2 ~ 0 1 8 ~ 6 2 to ] 4form the oxide and (eqn 3.57), which would again disproportionate. n the basis of the above data, it can now be assumed that after addiof Ph3P to the solution of [ s ~ M ~ ~ ~ othe ~ ~ oxidative ] ~ - , component of the current detected in voltammograms obtained under steady-state conns is predominantly due to the overall two-electron oxidation of the final product back to [ s ~ M ~ ~ ~ Under o ~ ~ such ] ~ -con. ditions, an estimate of the concentration of [ H S ~ M ~ ~ ~formed O ~ ~may ] ~ be obtained from the equation (Section 10.1 in Chapter 2) for the lirniting current at a microdisc electrode, Ili, = 4nFDr,[Alo, where in this case it is assumed that n=2, D = 6.4 x cm2s-l for and [Ale is the concentration of [ H S ~ M O ~ ~ O ~ ~ ] ~ Other -(~O ~ symbols have their usual significance. Knowledge of the initial concentrations of Ph3P and ~ 0 ~ ~in 0solution ~ ~and1 the ~ concentration of the reaction product, s ~ M ~ ~ ~ as o a~function ~ ] ~ -of, time (as determined from rnicrodisc voltamtry) enables a second-order kinetic analysis to be developed which may then utilized to estimate the rate constant, kl = 0.06 k 0 . 0 4 ~ - ' s - ' , for the reaction between Ph3P and [ s ~ M ~ ~ ~(eqn o ~3.54) ~ ] under ~ - non-irradiative conditions. -2 Reaction of [ S ~ M Ooh214with Ph3P under irradiative conditions The photochemical reaction between [ ~ ~ ~ o and ~ Ph3P ~ 0 was ~ exam~ ] ~ ined in the presence of filtered light (300-400 nm, 10 mW ~ m - ~ )Irra. o ~ in ~ (9515) ] ~ diation of an equimolar solution of [ s ~ M ~ ~and~ Ph3P C H 3 C N / H 2 0 (0.1 M Bu4NC104)with this light source resulted in a colour change from yellow to blue-green, and an overall voltammetric change identical - 240 illustuating basics of voltammetry to that shown in Fig. 3.30 for equivalent non-irradiated solutions. 3 1 NMR ~ confirmed P h 3 P 0 as the sole phosphorus-containing product of the photoreaction. It is therefore concluded that the overall reaction in the presence of light is identical to that observed in its absence, the light merely accelerating the rate-determining electron-transfer reaction between Ph3P and [S2M018062]4-. The effect of irradiation on the kinetics of the reaction was quantified by channel electrode experiments (Section 4.6) conducted as rapidly as possible ( < l h) in order to minimize the effects of the 'dark' reaction (see above). An equimolar solution of Ph3P and [ ~ 2 ~ o l s 0 6 2in] ~(95/5) C H 3 C N / H 2 0 (0.1 M Bu4NC104) was irradiated by light filtered down to 300-400 nm which represents the wavelength corresponding to the lowest ~ 0 ~ The ~ plat] ~ energy electronic absorption band of [ ~ ~ ~ o in ~acetonitrile. inum channel electrode was held at a potential of +0.30 V, which will oxidize photo-reduced forms of [ ~ ~ ~ o ~thus, ~ 0permitting ~ ~ ] rapid ~ - detection , of such species. Neither Ph3P nor P h 3 P 0 undergo redox processes at +0.30 V in acetonitrile. Light (300-400 nm; intensity -10 mW ~ m - periodically ~ ) irradiated the platinum working electrode sudace, providing a phototransient response, similar to o toluene ~ ~ ] ~or-T that observed on irradiation of solutions of [ s ~ M ~ ~ ~and (Section 4.6.1). The resultant photocurrent generated at the working electrode was measured as a function of the flow rate (Vf = l0-~-10-' cm3 s-') of the reaction solution over the electrode sudace. It was postulated above that the rate limiting step in the dark reaction ~ one-electron-transfer ~ ] ~ process given between Ph3P and [ s ~ M ~ ~ ~is othe in eqn (3.55). It is now proposed that this step may be photo-accelerated by a positive shift in redox potential in the photoexcited state: 5 [ s ~ M o ~ ~ o ~ ~ (] [~S- ~ M O ~ ~ O ~ ~ ] ~ - * ) accelerated rate ([s~Mo~~o~~ f ]Ph3P ~ - * )-----+ Product(s) (3.58) (3.59) The final product, [ H S ~ M O ~ ~ Ois ~again ~ ] ~detected -, at the electrode surface by its two-electron oxidation back to the original [ ~ ~ ~ oanion. ~ ~Therefore, 0 ~ ~ the reaction mechanism measured photoelectrochemically is postulated to be a photo C2E reaction, where C2 represents the second-order reaction between Ph3P and [S2Mo18 0G214-* (eqn 3.60) and E represents the electro-oxidation of o ~3.61) ~ ]: ~ back to [ s ~ M ~ ~ ~(eqn the reduced species ] Use of voltammetric techniques 24 1 t is assumed that water is in a large concentration excess and plays no part in the rate determining step. kr reflects the second-order rate constant for eqn 3.60 in the presence of light and is analogous to the rate constant kl obtained in the absence of light. A theoretical model for a C2Eprocess can be derived by solving the relevant convective-diffusion equations, of each species, to the channel electrode surface [50]. While considerable uncertainty exists because of the contribution from the dark reaction, k; values obtained by comparison of theory and experiment are in the range 0 . 6 - 3 . 0 ~ - l s-I for a variety of equimolar concentrations of Ph3P and [S2Mo18062]4(0.4-1.0 mM), and water contents (0-5 per cent v/v added H 2 0 ) . Comparison of these values with that for the equivalent dark reaction in the presence of 5 per cent water (0.06 M-'s-') shows that the redox reaction associated with eqn (3.55) when modified to give eqn (3.59) is accelerated by up to two orders of magnitude in the presence of light. This substantial acceleration in rate is again consistent with a significant 0 ~ ~ ] ~ positive shift in the excited state redox potential of the [ ~ ~ ~ o ~ ~and couples over those of the ground state. ed with Ph3P can be compared with the studies (Section 4.6) acts ] " )as* a powerful oxidizing agent ted ( [ S ~ M O ~ ~ O ~ ~ oluene and THF. Whereas toluene and THF have formal reversible potentials greater than 1.1 V versus Fc/Fc+) and require photoexcitation of the polyoxo-cluster to undergo oxidation, the peak potential (and, hence, the formal reversible potential) of Ph3P is lower and it is oxidized slowly by [ s ~ M ~ ~ ~even o ~in~the ] ~ absence of light. + Reaction of [ S ~ M O ob214~ with "Bu3P in (95/5) of dgerences relative to reaction with PPh3 3 C N / H 20:an explanation A colour change from yellow to green occurs upon mixing equimolar solutions of [ s ~ M ~ and ~ ~"Bu3P o ~in ~ (95/5) ] ~C H 3 C N / H 2 0 . However, the basic features of cyclic voltammograms obtained at a macrodisc-electrode are virtually independent of time in the sense that two reversible one-electron processes are served irrespective of the colour of the solution. This behaviour is very difent from that obtained in the presence of Ph3P where changes in wave height otential occur. However, while the first two one-electron charge-transfer ~ ~ o the ~ position ~ ] ~ of zero current sses associated with [ s ~ M ~ remain, ed in steady-state voltammograms at a microdisc-electrode has shihed and the initial one-electron reduction process has now become a one-electron oxidation process (Fig. 3.33). The one-electron reduction, one-electron oxiation end point achieved with a [ ~ ~ ~ o to~nBu3P ~ 0molar ~ ~ratio ] of ~ 1 : 1.5. The voltammetric oxidation of "Bu3Poccurs [48] at about +0.5 V versus ~ c / F c + ,and the peak height for this process is observed to decrease with time, using cyclic voltammetry, with 1.5 mM being required to convert 1 rnM [ s ~ M ~ ~ ~to o1 rnM ~ ~ [] s~~- M ~ ~ ~ This o ~ ~ result ] ~ is- consistent . with chemical 242 Illustrating basics ofvoltammetr, After addition of 'Bu3p . 1n o "Bu3P s2 - V 2 _____------- 0 -1 2 - , 0 -2 - -4 -0.4 -0.2 0.0 0.2 Potential (V vs FC/FC+) 0.4 Fig. 3.33 Steady-state voltammograms of 1 mM [ S ~ M O ~ in ~ O(9515) ~ ~ ]CH3CN/H20; ~ (0.1M Bu4NC104)before and after addition of 1.5rnM nBu3Pat a 10-pm diameter GC microdisc electrode. Reproduced by courtesy: Inez. Chem. 347(1998) 2366. Copyright, American Chemical Society. production of one-electron reduced [ S ~ M O ~5-,~ O rather ~ ~ than ] a protonated form of the two-electron reduced species, 3 1 N ~ M R spectra for a 5 mM equimolar reaction solution revealed the generation of a mixture of "Bu3P0 (6 = 57.6ppm) and "BU~PH' (6 = 13.7 ppm; J(31 P H) = 480 Hz). Equivalent experiments in C H C~ N / ~ H 0~ showed that the source of hydrogen in "Bu3P2H+ was water, via observation of a triplet ( J ( 3 1 ~- 2 ~ = ) 74Hz) in place of the doublet observed in ' ~ 2 0solutions. In summary, the nature of both the polyoxometalate anion and phosphorus-containing products are different to those formed when [ s ~ M o ~ ~ ois~reacted ~ ] ~ - with Ph3P. This difference may be rationalized by proposing that, [ ~ ~ ~ reacts o again ~ with ~ "Bu3P 0 ~ in ~ an initial ] ~ one-electron-transfer step (compare with eqn 3.55). -' The "Bu3P+ cation radical, also reacts with water in a manner analogous to that of Ph3P (compare with eqn 3.56) However, "Bu3P is a much stronger base than Ph3P ( " B u 3 p ~ + , p K a= 8.43; ph3PH+,pKa = 2.73 [51]) so it reacts with the protons generated in A n ovewiew of results 243 q n (3.63) to form "BU~PH+: is leaves [ S ~ M O 062] I~ as the finally observed polyoxomolybdate s. The removal of protons by "Bu3P prevents the disproportionation of 1 8 0 6 2 1 5 - from occurring and, as a result, [ s ~ M ~ ~ ~ is othe~ product ~ ] ~ ofthe redox reaction between "Bu3P and [ ~ ~ ~ o ~The ~ overall 0 ~ reaction ~ ] ~ - . in this case is n summary, [S2Mo18 0 ~ ~ has 1 been shown to oxidize phosphine molecules, oxidation processes being greatly accelerated by irradiation with light in the 300-400 nm range (corresponds to an absorption band of the polyoxometalate ies). It is proposed that in (95/5) C H 3 C N / H 2 0 solutions, [ s ~ M ~ ~ ~ o ~ ~ ] ~ rgoes an initial one-electron-transfer process with both aryl and alkyl phosphines to form [ ~ ~ ~ o ~Concurrently, ~ 0 ~ ~ the ] phosphine ~ - . is oxidized in the presence of water to its phosphine oxide with generation of protons. If the prodisproportionation of [ s ~ M ~ then ~ ~theo final ~ polyoxometalate ~ ] ~ ected is [ H S ~ M O ~ ~InOcontrast, ~ ~ ] ~the . more basic "Bu3Premoves solution, forming "BU~PH+. In this situation, the final polyoxroduct is [ s ~ M o ~ ~ ~ ~ ] is stable to disproportionation 5-, o which solutions and the phosphine products are a mixture of "Bu3P0 . The advantages of voltammetric monitoring of the course of reactions can be appreciated by considering the data presented in Section 5. ovewiew of results o metric, simulation, ues to polyoxometalate reduction studies A detailed understanding of the redox chemistry of polyoxometalates in the presence and absence of light has required the combined use of voltammetric, ulation, spectroelectrochemical, and conventional spectroscopic techniques. portantly, data presented in Chapter 3 should convince the reader that once the nuances of the voltammetry have been understood, then this class of electrochemical techniques can be employed as a powerful analytical tool for monitoring reaction pathways. T o conclude Chapter 3, a summary of the application of different techniques, and the knowledge gained from the studies, is resented, with respect to unravelling the redox chemistry of polyoxometalate complexes. 244 6.1 Illustrating basics of voltammetry Cyclic voltammetry (1) Rapidly enabled the broad picture related to the number of reduction processes as well as the extent of their chemical and electrochemical reversibility to be established over a wide time domain. (2) Enabled the reversible potential of some processes to be measured. (3) Provided a quantitative understanding of the acid-base equilibria accompanying electron-transfer processes by comparison of simulated and experimental cyclic voltammograms. 6.2 Rotated-disc electrode voltammetry (1) Frequently gave an excellent estimate of the relative numbers of electrons involved in the numerous reduction processes by measurement of limiting current values. (2) Enabled the extent of reduction, and sometimes the identity of products, to be readily determined as a function of time by measurement of voltammograms relative to the position of zero current during the course of bulk-electrolysis experiments as well as during the course of chemical reaction of [ s ~ M o ~ ~ owith ~ ~F ] ~~ -( V ~ - C ~Ph3P, M ~ and ~ ) "Bu3P. ~ , (3) Enabled n-values to be determined by analysis of waveshapes for reversible processes. (4) Enabled the reversible potential of many processes to be established. (5) Enabled diffusion coefficients to be measured, using the Levich Equation. 6.3 Channel-electvode voltammetry (1) Enabled photochemical effects to be measured in the absence of significant thermal effects, since heat is dissipated by solution flow. (2) Enabled a quantitative understanding of photochemical reactions to be achieved by simulations of channel electrode voltammetry. 6.4 Microdisc-electrode voltammetry (1) Frequently provided equivalent data to the RDE experiments, but with minimal ohmic drop so that accurate values of reversible potentials could be established. Electrode blockage problems were more severe with the smallsurface-area microdisc-electrodes, than with macrodisc-electrodes used in rotated-disc and cyclic voltammetry. (2) Enabled diffusion coefficients to be determined from measurement of ILim and use of a very simple equation. References 245 Spectroelectrochemistry (1) The technique of UV-visible spectroelectrochemistryhas demonstrated that [ s ~ M ~ ~[S2M018062]~-, ~ ~ ~ ~ I [ ~~2 ~ - 0,1 8 0 6 2 1 and ~ - , even [ ~ 2 ~ o ~ ~ 0 ~ ~ can be generated quantitatively by electrolysis in a thin-layer OTTLE cell in acetonitrile at low temperature. (2) UV-visible spectroelectrochernical experiments enabled electronic spectra of reduced non-protonated and protonated forms of the polyoxometalate species to be obtained. (3) EPR experiments after bulk electrolysis demonstrated that one- and three-electron reduced forms of [ s ~ M ~ ~ ~are o paramagnetic, ~ ~ ] ~ while two- and four-electron reduced species are EPR silent. Bulk electrolysis (1) Enabled n-values to be determined via coulometry. (2) Enabled directed electrochemical synthesis of reduced forms of the polyoxometalates to be achieved when used in combination with the results of voltammetric experiments. (3) Provided bulk quantities of material that could then be characterized by spectroscopic techniques. -7 Combinations of techniques The knowledge gained by application of voltammetric, chemical, theoretical, simulation, NMR, mass spectrometric, EPR, electronic spectra, X-ray diffraction, and other methods of measurement of the physicochernical properties of 2 ~ 0 1 8 ~ 6 2and ] 4 -its reduced forms, has been used to establish qualitative and quantitative details of the redox chemistry of this polyoxometalate system. The use of a wide range of physicochemical and other techniques in combination with the voltammetric methods supports the protocol recommended in Chapter 2. eferences M.T. Pope, Comprehensive Coordination Chemistry, (ed. G. Wilkinson, R.D. Gillard, and J.A. McClevert~), Pergamon Press, New York, 1987, vol. 3, ch. 38. J.T. Rule, C.L. Hill, D.A. Judd, and R.F. Schinazi, Chem. Rev. 98 (1998) 327. D.E. Katsoulis, Chem. Rev. 98 (1998) 359. M.T. Pope and A. Muller, Angew. Chem., Int. Ed. Engl. 30 (1991) 34. M.T. Pope, Heteropoly and Isopoly Oxometalates, Springer-Verlag, Berlin, 1983. M. Sadakane and E. Steckhan, Chern. Rev. 98 (1998) 219. F. Couto, A. Cavaleiro, and J. Simao, Inorg. Chim. Acta 281 (1998) 225. I.A. Weinstock, Chem. Rev. 98 (1998) 113. M.T. Pope and B.W. Dale, Quarterly Rev. Chern. Soc. 22 (1968) 527. Illustrating basics of voltammetry E. Papaconstantinou, Chem. Soc. Rev. 18 (1989) 1. M.T. Pope and A. Miiller (ed.), Polyoxometalates: From Platonic Solids to Anti-Retrovira1 Activity, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994. H.T. Evans, Jr., Perspectives in Structural Chem. 4 (1971) 1. P.D. Prenzler, C. Boskovic, A.M. Bond, and A.G. Wedd, Anal. Chem. 71 (1999) 3650. M.T. Pope and E. Papaconstantinou, Inorg. Chem. 6 (1967) 1147. B, Keita and L. Nadjo, J. Electroanal. Chem. 227 (1987) 77. V. Grigoriev, C. Hill, and I. Weinstock, J. Am. Chem. Soc. 122 (2000) 3544. P.W. Atkins, Physical Chemistry, 5th edn, Oxford University Press, New York, 1994. pp. 975, 822, C28. L.A. Woolf, J. Phys. Chem. 64 (1960) 481. J. Alden, M.A. ~eldman,E. Hill, F. Prieto, M. Oyarna, B.A. Coles, et al., Anal. Chem. 70 (1998) 1707. M.T. Pope and G.M. Varga, Inorg. Chem. 5 (1966) 1249. C. Tourn&,Bull. Soc. Chim. Fr. (1967) 3196, 3199, 3214. J.P. Launay, Compt. Rend. 269C (1969) 971. J.P. Launay, P. Souchay, and M. Boyer, Collect. Czech. Chem. Commun. 36 (1971) 741. J.P. Launay, Inorg. Nucl. Chem. 38 (1976) 807. M. Rudolph, D.P. Reddy, and S.W. Feldberg, Anal. Chem. 66 (1994) 58912. L. Barcza and M.T. Pope, J. Phys. Chem. 77 (1973) 1795. L.C.W. Baker and D.C. Glick, Chem. Rev. 98 (1998) 3. T. Hori and S. Himeno, Chem. Lett. (1987) 53. B. Carti&,J. Chem. Res. Synop. (1988) 290. S. Himeno, T. Hori, and A. Saito, Bull. Chem. Soc. Jpn. 62 (1989) 2184. T. Hori, 0 . Tarnada, and S. Himeno, J. Chem. Soc., Dalton Trans. (1989) 1491. K. Piepgrass and M.T. Pope, J. Am. Chem. Sac. 111 (1989) 753. J. Heyrovsky and J. Kuta, Principles of Polarography, Academic Press, New York, 1966. A.M. Bond, T. Vu, and A.G. Wedd, J. Electroanal. Chem. 494 (2000) 96. B. Keita and L. Nadjo, J. Electroanal. Chem. 217 (1987) 287; 227 (1987) 77; 230 (1987) 267. P.W. Atkins, D.F. Shriver, and C.H. Langford, Inorganic Chemistry, Oxford University Press, Oxford, 1990. V.M. Hultgren, A.M. Bond, and A.G. Wedd, J. Chem. Soc. Dalton Trans. (2001) 1076. B. Keita, D. Bouazi, and L. Nadjo, J. Electrochem. Soc. 135 (1988) 87. S. Juraja, T. Vu, P.J.S. Rickhardt, A.M. Bond, TJ. Cardwell, J.D. Cashion, et al., Inorg. Chem. 41 (2002) 1072. W.E. Geiger, InorganicReactions and Methods, (ed.JJ. Zuckerman), VCH, Weinheim, 1986, vol. 15. A.E. Kaifer and M. Gornez-Kaifer, Supramolecular Electrochemistry, Wiley-VCH, New York, 1999. AJ. Bard and L.R. Faulkner, Electrochemical Methods, Fundamentals and Applications, Wiley, New York, 1st edn, 1980. 2nd edn, 2001. P.H. Rieger, Electrochemistry, 2nd edn, Chapman and Hall, New York, 1994. G. Schiavon, S. Zecchin, and G. Bontempelli, J. Electroanal. Chem. 48 (1973) 425. A.M. Leiva, L. Rivera, and B. Loeb, Polyhedron 10 (1991) 347. S.G. Davies, M.R. Metzler, W.C. Watkins, R.G. Cornpton, J. Booth, and J.C. Eklund, J. Chem. Soc., Perkin Trans. 2 (1993) 1603. References 247 1471 F. Pragst and M. Niazymbetov, J. Electroanal. Chem. 197 (1986) 245. [48] A.P. Tomilov and N.E. Chomutov, Encyclopedia of Electrochemistry of the Elements, (ed. A.J. Bard), Marcel Dekker, New York, 1975, vol. 3, ch. 1. [qq] CJ. R h o d a and C.R. Symons, J. Chem. Soc., Dalton Trans. 2 (1989) 1393. 1501 R.G. Compton, R A W . Dryfe, and J.C. Eklund, Res. Chem. Kinet. 1 (1993) 239. [51] C.A. Streuli, Anal. Chem. 32 (1960) 985. e processes that illustrate the uence of irreversi ogeneous reactions an etition between s that occur in the so ution phas e electro e surface: fu tovoltaic dye-sensitizers, se biosensors 1 Introduction In Chapter 3, the solution-phase voltammetric theory presented in Chapter 2 was applied to the electrochemically and chemically reversible electrode processes associated with some polyoxometalate compounds. However, examples of this relatively straightforward reversible class of processes are not too common and the influence of complexities that may arise in a voltamrnetric study are now illustrated in the examples of voltammetric studies in this chapter. Initially, the results of a fundamental study on the electrochemical oxidation of the compound cis, r n e r - ~ n ( ~ o( )g, 1 - ~ h 2 ~ ~ (~g22~- ~~ hh22) ~ ~ ~ 2 ~ ~ in an organic solvent is presented to give an example of an electrode process where a wide range of homogeneous processes accompany the charge-transfer process. This is followed by a second fundamental study of the [v(co),]/O system in water, where one-half of the redox couple, [V(CO),]-, is soluble in the solvent, whereas the V(CO), half is insoluble, so that both surface and solutionphase reactions are evident in the voltammetry. The chapter then concludes with examples of electrode processes that are used in significant applications of electrochemistry and also where careful control of different combinations of homogeneous and heterogeneous processes is essential to the success of the application. The initial example relevant to applied applications of voltammetry is the one-electron oxidation of Ru(2,2'-bipyridine-4,4'-dicarboxylicacid),(NCS),, which is widely used in dye-sensitized photovoltaic cells (Section 6.2 in Chapter 1). Since this compound has been designed specifically to be attached Introduction 249 to a surface in the photovoltaic cell application, it is not surprising that adsorption of material accompanies this oxidation process. However, it will be shown that despite the propensity of this system to interact with the surface, it is still possible to obtain conditions that enable the reversible potentials, required in the thermodynamic description of photovoltaic cells, to be calculated. Almost since the invention of the electrochemical method over two hundred years ago, this technique has been widely used in analytical chemistry (Chapter 1, Table 1.1).In the case of voltammetry and related I-E-t-type techniques, the most widely used analytical applications at the start of the twenty-first century are probably associated with trace analysis by stripping voltammetry and monitoring of glucose in blood by diabetic patients using an electrochemical biosensor. These two techniques of stripping voltammetry and electrochemiiosensors also utilize an inherently complex sequence of reaction pathways that are described in the concluding section of this chapter. All the studies in this chapter illustrate a wide range of the features that need to be addressed in studies of complex electrochemical processes involving I-E-t principles, irrespective of whether they are being applied to problems associated with fuel photovoltaic cells, or electroanalysis, or to fundamental studies associated reactions involving inorganic, organometallic, organic, or biologically rtant molecules. 4.1 IR and 3 1 ~NMR spectroscopic data obtained for the associated with the electrochemical oxidation of cis, mern ( ~ 0(q~l-dpm) ) ~ ( q ~ ~ - d ~ rinn dichloromethanea )~r c i s , r n c r - [ ~ n ( ~ ~ ) ~ ( ~ ' - d1866 ~m) 1936 50.3 35.0 0.3 -28.1 53.2 49.3 19.0 -31.8 (v2-dpm)~rl c i s f a c - [ ~ n ( ~ ~ ) ~ ( ~ ' - d ~ r1878 n) 1945 (v2-dpm)~rI * c i s , r n e r - [ ~ n ( ~ ~ ) ~ ( ~ ' - d1950 ~m) (02-dpm)~r]+ * cisfac- [M~(co), (v l-dpm) 1960 (02-dpm)~r]+ (v '-dpm) tvans-[Mn(~O)~ (v2-dprn)W trans-[Mn(~~)~(~~-dprn) (02-dpm)~r]+ trans-[Mn(C0)2(112-dpm)2]+ 2022 203 1 1891 1971 1916 35.3 "Data taken from reference [lo]. "educed by reference to v ( C 0 ) data obtained for the isostructural neutral analogues. 250 Electrode processes 2 Elucidation o f the homogeneous reaction pathways that accompany the electrochemical oxidation o f cis,mer-Mn(CO),(ql-dpm)( q 2 - d p m ) ~(dpm r = PhzPC in dichloromethanel The electrochemical oxidation of stable, so-called 18-electron2 transition metal organometallic complexes containing combinations of carbon monoxide, phosphine and other ligands has received much attention in the recent literature 11-31. Upon one-electron oxidation, a number of reaction routes for the resulting 17-electron product may be possible [3]: (1) If the resulting 17-electron species is stable, a chemically reversible oneelectron oxidation process is observed. This occurs in the case of oxidation of mer-c~(co), (r$dprn) (r12-dpm)[4,5] (dprn = Ph2PCH2PPh2) and cis, rne~-Mn(CO)~ (Ph2P(CH2)2P(Ph)(CH2)2PPh2)Br [6] which are reversibly oxidized to the isostructural 17-electron cations on the voltammetric time-scale. (2) The product may isomerize. A classic example involves the oxidation of fac-~n(~0),(~~-d~m)~1[7,8] (see Section 8.1.4 in Chapter 2). In this case, the initially generated 17-electron cationic fat' isomer, isomerizes to the 17-electron mer' cationic form. In turn, this species may be reduced to the neutral 18-electron mer form at less positive potentials than those associated with thefac/'ac+ couple. Overall, this sequence of reductions gives the wellknown square reaction scheme [3,7,8], summarized in eqn (4.1), which describes a sequence of reactions, such as isomerization and cross redox reactions that may accompany the electron-transfer step. (3) The oxidized species may react to form a new product [3,8]. Oxidation of mer- or ~ ~ c - M o ( c o (.rll-dpe) ), (.r12-dpe)(dpe = PhzP(CH2)2PPh2results in the formation of the 17-electron cationic species which may disproportionate into the starting material and dicationic [MO(CO),(11'-dpe) (q2-dpe)]2+[9]. ~ d a ~ t ewith d permission from Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. 2 ~ h 18-electron e rule refers to a highly stable bonding arrangement in organometallic chemistry. Details of the concept are contained in many Inorganic Chemistry textbooks. See for example, J.E. Huheey, Inorganic Chemistry, 3rd edn, Harper International SI edition, Cambridge, 1983, pp. 590-5. In contrast, 17-electron oxidized or 19-electron species generated electrochemically (or chemically) tend to be far more reactive. 1 1I i 1 ! [ ! i I D Elucidation of honzogeneous reaction pathways 7 2 n 7 CO - I-' 25 1 ' P Structural representation of organometallic compounds associated with Section 2 where dpm = Ph2CHzPPh2 and X = Br. Adapted from Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. his 16-electron product may then undergo internal nucleophilic attack by the pendant phosphorus of the ql-dpe ligand to form the seven coordinate (~~-dpe)~]~+. 18-electron species [MO(co), In the study described in Section 2, the electrochemical oxidation of cis, mer-[Mn(C0), (ql-dpm) (q2-dpm)Br] (Fig. 4.1 (a)) in dichloromethane by voltammetric, bulk electrolysis, and spectroelectrochemical techniques is described [lo]. In principle, on oxidation of the 18-electron cis, m e r - [ ~ n ( C 0(ql ) ~-dpm) (q2-dpm)Br], the resulting isostructural cis, mer+ cation may isomerize to give the 17-electron cis,fac+, and transf cationic versions of compounds whose structures are contained in Fig. 4.1 (b) and (c), or eject d and/or undergo internal attack by the pendant phosphorus atom assowith the q1-dpm ligand to give the compound illustrated in Fig. 4.1 (d). stem also is considered in Chapter 2, Section 8.1.4. Voltarnmetvicstudies in dichloromethane Figure 4.2(a) depicts a cyclic voltammogram obtained at a scan rate of 200 mV s-' and at 20°C for oxidation of cis, mer-[M~(co), (ql-dpm) (q2-dpm) r] in dichloromethane (0.1 M Bu4NPF6). Over the potential range -0.60 to 0.40 v3versus FC/FC+ and in the first cycle, a chemically irreversible 3 ~ potentials 1 in Section 4.2 are versus the FC'"(see Chapter 2, Section 2.3.2). couple, where Fc denotes ferrocene 252 Electrode processes (a) -2nd scan t--, !A '. Potential (V vs FC"') Fig. 4.2 Cyclic voltammograms obtained at a scan rate of 200 mV s-' for the oxidation of 1.0 mM cis, m e ~ - [ M n ( C 0(rll-dpm) )~ (r12-dprn)~r] in dichloromethane (0.1 M Bu4NPF6)at a 1-mm diameter Pt disc electrode; (a) 20°C; (b) -40°C. Reproduced by courtesy: hog. Chem. 38 (1999) 2005. Copyright, American Chemical Society. response is observed (process 1) with an oxidative peak potential (EF) of f0.20 V. In addition, a reductive feature (process 2') is evident at E:~, -0.44 V with its corresponding oxidation peak (process 2) being detected in second and subsequent cycles at E F , -0.36V. As the scan rate increases, a reduction peak associated with process 1' is detected (Fig. 4.3). Concurrently, the current magnitude of process 2' decreases relative to that of process 1. The scan rate dependence suggests that the product of process 1 seen at slow scan rates reacts to form a new species that in turn undergoes a chemically reversible redox couple at less positive potentials (i.e. to generate processes 2 and 2' on second and subsequent cycles). If the temperature is decreased to -40°C, redox couple 1 becomes chemically reversible (see Fig. 4.2(b)), while processes 2 and 2' disappear, indicating that the rate of the homogeneous chemical reaction following the initial charge-transfer process is slowed upon lowering the temperature. Process 1 was further studied using rotating-disc electrode which showed that this oxidation exhibits Levich behaviour in the lirniting current region (Section 9.1 in Chapter 2) over the rotation speed range of 500-3000 rpm. Analysis of this lirniting current-mass-transport behaviour (Section 9.4 in Chapter 2 and Table 2.3) gives a diffusion coefficient of 7 x 10-~cm' s-' and suggests that process 1 involves a one-electron charge-transfer process at all rotation rates exarnined. Fast scan rate voltammetry using a 25-pm diameter platinum microdisc electrode (Section 10.1 in Chapter 2) achieves chemically reversible voltammograms which enables the reversible half-wave potential (Ei12) to be Elucidation of homogeneous reaction pathways 8 1OOmV s-l 500mVs-1 +..* ; ; 253 ; '. %! , ?. . . . ", ' Potential (V vs ~c"') -3 Cyclic voltammograms obtained at 20°C for the oxidation of 0.92mM cis,mer-[~n(~0)2(q~-d~m)(q~-d~m)~r] in dichloromethane (0.1 M Bu4NPF6) at a 1-mm diameter Pt disc electrode using scan rates in the range 100-2000 rnV s-I . Reproduced by courtesy: h o q . Chem. 38 (1999) 2005. Copyright, American Chemical Society. E~O determined for process 1 (equivalent to the reversible formal potential assuming equal diffusion coefficients for reactant and product) from the average of the oxidation and reduction peak potentials (Section 8.1 in Chapter 2). In the scan rate range of 2000-5000 mV s-', the E;,,-value measured in this manner is ependent of scan rate, as expected when the homogeneous reactions followthe one-electron transfer process are out-run. Thus, an E;,2 value for the reversible potential of 0.16 V is obtained at 20°C. The same reversible potential was obtained under near steady-state conditions at platinum or GC microdisc electrodes. These microdisc data also imply that homogeneous reactions may also be out-run under these short time domain near steady-state conditions ection 10.1 in Chapter 2). B u l k electrolysis and spectvoelectvochemical expeviments ulk oxidative electrolyses experiments on solutions of cis,mer-[Mn(CO), l-dpm) (72-dpm)~r] in dichloromethane (0.1 M Bu4NPF6)were conducted 2OoC and -40°C using both a conventional bulk electrolysis cell with a platinum basket working electrode and a thin-layer IRRAS cell (Section 16.2 in Chapter 2) contained within the sample compartment of an I R spectrometer enabling in situ reflective I R spectroelectrochemical experiments to be conducted. Unless otherwise stated, the potential of the platinum working elece was held at f0.25 V which is sufficiently positive to achieve oxidation ess 1. At both 20°C and -40°C, process 1 was determined by couloetry (exhaustive electrolysis conditions at a platinum basket electrode) to be a one-electron process, as was also concluded to be the case in voltammetric time-scale. The product(s) formed was examined by ex situ EPR measurements and found to contain six lines of equal intensity indicative of a Mn(I1) product ( 5 5 ~ In = , 512). 254 Electrode processes In situ IR spectral monitoring the course of electrolysis experiments at -40°C results in the two cis, m e r - [ ~ n ( c ~(ql-dpm) ), (q2-dpm)~r]carbonyl bands at 1936 and 1866cm-' (see Fig. 4.4(a)) decreasing in intensity while unresolved pairs of bands initially grow at approximately 2031, 2022, 1960, and 1950 cm-'. These new carborlyl bands are attributed to the generation of two cationic cis isomeric forms of oxi) ~-dpm) (q2-dpm)~r]since the difference in fiedized cis, m e v - [ M n ( ~ 0\ql quency of about 80 cm- relative to cis, m e v - [ M n ( ~ 0($-dpm) )~ (q2-dprn)~d is consistent with this interpretation. The two cis cation isomers possible (a) 0.06 1 I I 2100 I 1 2000 1900 Wavenumber ( c w 1 ) 1 J 1800 Fig. 4.4 In situ I R spectra obtained in the carbonyl stretching range during electrolysis experiments in an IRRAS cell commencing with 1.0 mM cii,rner-[Mn(~0)~ (ql-dpm) ( q 2 - d p m ) ~ rin ] dichloromethane (0.1 M Bu4NPF6) at -40°C. (a) Change in I R absorbance, relative to that of the initial I R spectrum of cis, m e r - [ M n ( ~ o(ql ) ~-dpm) (q2-dpm)Br] during oxidative electrolysis at +0.25V versus Fco/+ (the t,j, arrows signify that the I R intensity initially increases and then decreases); (b) change in I R absorbance relative to that of the I R spectrum of trans-[Mn(~~)~(q~-d~m)(q~-dpm)~r]+ formed in (a) during reductive electrolysis at -0.55 V versus Fco/+. Reproduced by courtesy: Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. Elucidation of homogeneous veaction pathways 255 dpm) (1950 and 2022 cm-') and are the c i r , m e v - [ ~ n ( ~ 0 ) ~ ( q ~ - (q2-dpm)Br]+ i i s , - f a c - [ ~ n ( ~(ql ~ -dpm) )2 (q2-dpm)Brlt (1960 and 203 1 cm-') species (see Figs 4.1(a) and (b)). After initially increasing with time (seconds) the intensity the overlapping v (CO) bands from compounds cis, mer- [Mn ( ~ (ql 0 -dpm) ) ~ (112-dpm)Br]+and cis,fac- [ M ~ ( c o ) (q ~ -dpm) (q2-dpm)Br] eventually decay. The intense single carbonyl band observed to grow at 1971 cm-' is assigned to the formation of the trans- [Mn(C0), (q -dpm) (q2-dpm)Br]+ isomeric form ig. 4.1(c)).An additional minor product with carbonyl bands at 1878 and 1945 cm-l detected as an intermediate also disappeared upon complete electrolysis. Since cis, m e r - [ M n ( ~ 0(0' ) ~-dpm) (q2-dpm)Br] has I R bands at 1866 and 1936 cm-l, the transient species with a similar I R spectrum is attributed to the generation of a small amount of cis,fac-[Mn(C0), (ql-dpm) (l12-dpm)~r]. 1f only partial rather than exhaustive electrolysis is undertaken at -40°C, then the I R spectrum shown in Fig. 4.5 is observed. This spectrum implies that catalytic isomeric conversion of cis, mer- [Mn(Co), (ql-dpm)( q 2 - d p m ) ~ r ] to cis,fac-[~n(C~)~(q'-dpm)(q~-dprn)Br] occurs in good yields in the presence of only trace amounts of the cis, m e r - [ ~ n ( ~ ~ ) ~ ( q ' - d(q2-dprn)Br]+ pm) catlon. pm) redox couple has resumably the c i s , f a c - [ ~ n ( ~ ~ ) ~ ( q ' - d(r12-dpm)~r]+/0 a similar reversible potential to that of the cis, mer-[M~(co), (0' -dpm) (q2-dpm) ~ r ] + / process ' so that cis,fac-[Mn(C~)~ (0 -dpm) (q2-dpm)Br] formed in a bulk trolysis experiment is oxidized to cis,fac-[M~(co), (ql-dprn) (r,~~-dprn)Br]+, ch like the cis,mer cation form is also isomerized to the trans cationic isomer (see above), as shown by the detection of the carbonyl band at 1971 cm-' 4 . 4 ) . However, after only a small amount of electrolysis, all species required for catalytic isomeric conversion of cis, rner-[M~(co), (0' -dpm) (l12-dpm)~r] + Wavenumber (cml) . 4.5 In situ absolute I R spectrum obtained in the carbonyl stretching range during the early stages of oxidative electrolysis at +0.25V versus FC'~' in an IRRAS cell of l.OrnM cis, m e r - [ M n ( ~(ql ~ )-dpm) ~ (q2-dpm)~r]in dichloromethane (0.1 M Bu4NPF6) at -40°C. Note ( q ' (q2-dpm)~r] at I878 and 1945 cm-' are marked with that the bands for cis,f a c - [ M n ( ~ ~ ) ~-dpm) an asterisk. Reproduced by courtesy: Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. 256 Electrode processes to cis,fac-[M~(co), (ql-dpm) (q2-dpm)Br] are present in bulk solution. The reactions summarizing the catalytic generation of cis,fac- [Mn(CO), (q -dpm) (q2-dpm)Br] after formation of small amounts of cis, mer-[Mn(CO), (ql-dpm) (q2-dpm)Br]+ from cis, m e r - [ M n ( ~ 0(ql ) ~-dpm) (q2-dpm)~r]in bulk solution at early stages in the low temperature oxidation in the thin-layer IR spectroelectrochemical cell are ' -+ cis,fac-[~n(CO)~(q'-dpm) (q2-dpm)~r]+ (4.2) --+cis,fac - [ ~ n ( ~ ~ ) ~ ( q ' - (q2-dpm)Br] dpm) + cis, mer- [M~(co), (q'-dpm) (02-dpm)~r]+ (4.3) Under the conditions of electrolysis at -40°C in a conventional cell, only reductive process 2' was observed in the cyclic and steady-state microdisc voltammetry after exhaustive electrolysis, and there was no spectroscopic or voltammetric evidence of liberated Br-, C O , or dpm. From steady-state microdisc electrode voltammetry, the magnitude of the reductive current associated with process 2' is the same as the oxidative current associated with process 1 before bulk electrolysis (compare Fig. 4.6(a) and (b)). Thus, all bulk electrolysis data are consistent with the formation of essentially a 100 per cent yield of trans-[M~(co), (ql-dpm) (q2-dpm)~r]+ 1 Process 2' Process 2 / Potential (V vs FC"') Fig. 4.6 Microdisc near steady-state voltammograms obtained at -4OoC with a 25-pm diameter Pt macrodisc electrode (scan rate 10 mV s-l) from an initial 1.0 rnM solution of cis,mer-[~n(~o),(q'-d~m)(q~-dpm)~r] in dichloromethane (0.1 M BurNPF6) (a) before electrolysis, (b) after electrolysis at 4-0.25 V versus FC'/+, and (c) afier reduction of the solution formed in (b) at -0.55 V versus FC'/+. Reproduced by courtesy: Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. Elucidation of homogeneous reaction pathways 257 m) and c i s , f a c - [ ~ n ( C 0 ) ~ ( q ' - d ~ ~ ) with c i s , m e r - [ ~ n ( ~ ~ ) , ( q ' - d p(q2-dpm)Br]+ ($-dpm)Br]+ cations, and cis,fac-[M~(co), (ql-dpm) (q2-dpm)Br] species being generated at earlier stages of the experiment. n re-reduction in the IRRAS cell at -0.55 V and -40°C, the IR signal at 1971 crn-l for trans-[M~(co), (ql-dpm) (q2-dpm)Br]+ decays with timeand is replaced by a single carbonyl band at 1891 cm-' (Fig. 4.4(b))which is assigned to the formation of the neutral 18-electron t r a n s - [ ~ n ( ~ ~ ) , ( q ~ (q2-dpm)Br] -d~m) species (Fig. 4.1 (c)). e 3 1 N ~ M R spectrum of the product formed by the bulk oxidativetive electrolysis sequence obtained in a conventional cell was recorded at -40°C with Bu4NC1O4being used instead of Bu4NPF6as the supporting electrolyte. Four lines of equal intensity were observed as expected for formation of trans- [M~(co), (q -dpm) (q2-dpm)13r](Table 4.1). The 31P N M R signal at -3 1.8 ppm (trans-[M~(co), (ql-dpm)(q2-dpm)Br]) is consistent with retention of the pendant phosphorus. In addition, steady-state microdisc voltammetry after this electrolysis sequence produced only one wave with an identical halfe potential and limiting current (now for process 2) to that observed prior to ction. However, importantly the position of zero current indicates that the species in solution is now in the reduced form (Fig. 4.6(c)). When this reduced solution was warmed to 20°C, steady-state voltammograms indicate that concomitantly the limiting current for process 2 decreases and that for process 1 grows until process 2 finally disappears. In addition the v ( C 0 ) infra-red band at 1891 cm-' , assigned to trans-[M~(co), (ql-dpm)(q2-dpm)Br], decreases and two new bands grow at 1936 and 1866cm-l as expected for formation of cis,mer-[Mn(~~)~(~'-d~m) (q2-dpm)Br],which must therefore be the thermoically favoured 18-electron form of [M~(co), (ql-dpm) (0,-dpm)Br]. en bulk electrolysis experiments were conducted at 20°C in the conventional cell, the pink colour associated with the formation of trans- [M~(co), (v' -dpm) ($-dpm)Br]+ gradually disappeared when the oxiized solution was left to stand (no applied potential) and the solution became ale yellow. Cyclic voltammetric monitoring of this experiment towards comletion of the electrolysis reveals (compare Fig. 4.7(a) and (b)) that process 1 has almost vanished and that a response detected is associated with redox uple 2. However, a previously undetected reversible process (couple 3) is o observed with a half-wave potential of 0.37V. Further monitoring by cyclic voltammetry after electrolysis is completed shows that couple 3 conhues to grow until 30min post-bulk electrolysis, redox couple 2 is not etected while couple 3 is extremely well defined (Fig. 4.7(c)). The 3 1 ~ R spectrum from bulk electrolysis in dichloromethane (0.1 M Bu4NC104) obtained at this time shows a single resonance having a chemical shift of 35.3 ppm. In situ I R spectroelectrochemical oxidation experiments in the RAS cell at room temperature lead to a decrease in the intensity of the cis,mer-[M~(co),(~'-dpm) (q2-dpm)Br]carbonyl bands at 1937 and 1866 cm-l and concomitant growth of a single sharp band at 1971 cm-' due to formation of trans-[M~(co), (ql-dpm) (q2-dpm)Br]+,whereas after 30 min standing, ' 25 8 Electrode processes Potential (V vs FC"') Fig. 4.7 Cyclic voltammograms obtained at a 1-mm diameter GC macrodisc electrode with a scan rate of 16OmVs-' during the course of monitoring electrolysis ex eriments at 20°C in a conventional cell (a) before electrolysis of cis,mer-[~n(~~)~(q'-d~m)(q -dpm)Br] (1.0 mM) in dichloromethane (0.1 M Bu4NPF6), (b) after completion of bulk electrolysis at +0.25 V versus FC'/+, and (c) 30 rnin after completion of bulk electrolysis. Reproduced by courtesy: Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. f the I R spectrum of the solution oxidized in a conventional cell, exhibits a single carbonyl stretch at 1916 cm-'. The I R and NMR data of this latter species are similar to that reported [ l l ] for the tvans-[~n(~~),(q~-d~m)~l+ cation (1916 cm-' and 33 ppm respectively) which suggests that it is this com~ -dpm) (q2-dpm)~r]'. pound which is formed slowly from trans- [ M ~ ( c o )(q This assignment is supported by the positive-ion electrospray mass spectrum obtained from the bulk electrolysed solution which produced a strong signal at cation. ) ~ ] ' Further879 (m/e), as expected for the t r a n s - [ ~ n ( ~ ~ ) , ( u ~ - d ~ m more, the simulated and experimental mass spectra for this formulation of the cation are in excellent agreement. O n the basis of all the above evidence, it is therefore postulated that redox couple 3 corresponds to the reaction Analysis of the rate of increase in intensity of the carbonyl IR band at 1916 cm-' and decrease at 1971 cm-' , using the IRRAS cell, by a first-order Elucidation of homogeneous reaction pathways 259 law gave a rate constant of 1.6 x s-l at 20°C for the conversion of ( ~ o ) , ( v ' - d p m (q2-dpm)Brlt ) to t r a n s - [ ~ n ( ~ ~ ) , ( q ~ - d ~ r n ) ~ ] + . the evidences obtained imply that process 1, at short voltamdomains, must correspond to the oxidation of the 18-electron ( ~ (ql 0 -dpm) ) ~ (q2-dpm)Br] to the isostructural 17-electron and nganese(II) species cis,mer-[~n(~~),(q~-d~rn)(q~-d~m)~r]+ hat process 1' is the corresponding reduction process, so that couple 1 is the reaction However, c i s , m e r - [ ~ n ( C(ql ~ )-dpm) ~ (q2-dpm)Br]+ apparently is unstable on longer time-scales so that under slow scan rate cyclic voltammetric conditions, cis,mer-[~n(~0)~(q~-dpm)(~~-dprn)~r]+ isomerizes to (CO),(ql-dpm)(q2-dpm)Br]+. Thus, if processes 2 and 2' are associthe redox couple then it follows that the slow scan rate voltammetric oxidation of cis,mer- [M~(co), (ql-dpm) (q2-dpm)Br] occurs in dichloromethane via an C scheme is EC reaction scheme assumes that the catalytic process which gencis,fac- [Mn(C0), (ql-dpm) (q2-dpm)Br] under bulk electrolysis conons is too slow to be significant on the voltammetric time-scale. Additionally, the reaction cis,mer-[M~(co), (ql-dpm) (q2-dpm)Br]+ -+ cis,fac-[~n(~~),(q~-dprn)(q~-d~m)~r]+may occur more rapidly than reaction (4.7) and hence not be detected under these conditions (not rate determining) or else it may not be detectable because of lack of resolution of the cis,mer-[M~(co)~(O'-dpm) (r12-dpm)~r]+lo and cis,fac-[M~(co), (ql-dpm) (q2-dpm)Br]+/Oprocesses. Since the 18-electron trans- [M~(co), ( ~ ~ - d p m ) ~compound ]+ is the final stable product of bulk electrolysis, it can be concluded that the 260 Electrode processes ' 17-electron trans- [M~(co), (11 -dpm) (11,-dpm)Br]+ slowly releases bromide to give trans-[M~(co), (r12-dp111)2]2+. However, this trans di-cation is a strong oxidant and can oxidize bromide to bromine, SO that steps (4.5-4.7) may be followed by ---+ t r a n s - [ ~ n ( ~ O ) , ( ~ ~ - d p r n )+z Br]~+ k2 (slow) ks (fast) ----+ trans-[~n(~~),(~~-f d ~,$rm 2 )~]+ where the reaction in eqn (4.8) is the rate-determining step and the value of k2 s-l at 20°C as noted above. associated with this reaction is 1.6 x Thus, at 20" C the overall oxidation of cis,mer-[Mn(cO), (11' -dpm) ( r , ~ ~ - d ~ munder ) ~ r ] the time-scale of bulk electrolysis is represented by the reaction 2.3 Simulation of the voltammetry The cyclic voltammetric response obtained at 20°C was simulated using the DigiSim software package [12] according to a form of the square reaction scheme (eqn 4.1), which in this particular case can be described by eqns (4.5)-(4.7) in combination with the slow bromide expulsion step described by eqn (4.8). The reversible potentials for the redox processes 111' (0.16 V) and 212' (-0.40 V) were obtained as described above. Double-layer capacitance values of 25 pF cm-2 and uncompensated resistances of 2000 C2 were used in the simulations, which are typical of a dichloromethane electrolyte system. The isomerization process (eqn 4.7) was assumed to be completely irreversible. Thus, solely for the purposes of the simulation, a very high (lo1'), but chemically insignificant value of the equilibrium constant was used to model eqn (4.7). The rate constant (k2) used for the debromination of trans-[M~(co), (ql-dpm) (11,-dpm)Br]' (eqn 4.8) was the value obtained from IR experiments, although it eventuated that this rate constant is too slow to be significant at the scan rates employed in voltammetric studies. The diffusion coefficients of all the species in the cm2 s-' (the value deterelectrode-reaction mechanism were set to 7 x m) using microdisc mined for compound c i s , m e r - [ M n ( ~ ~ ) ~ ( q ' - d p(q2-dpm)Br] and rotating-disc voltammetry). As can be seen in Fig. 4.8 excellent agreement is obtained between experiment and theory at scan rates of 100 and 1000 m~ s-' for the proposed Elucidation of homogeneous reaction pathways 26 1 Theory -0.6 -0.4 -0.2 0.0 0.2 Potential (V vs Fc'/O) -0.6 -0.4 -0.2 0.0 0.2 Potential (V vs Fc+/O) 0.4 Comparison of experimental and simulated (according to the mechanism described by eqns (4.4)-(4.7) and the parameters given in the text) voltammograms obtained at a 1-mm diameter Pt disc electrode for the oxidation of 0.92mM c i s , r n e r - [ ~ n ( ~ ~ ) ~ ( ~ ~ - d ~ r n ) ( ~ ~at- d20°C ~rn)~r] in dichloromethane (0.1 M Bu4NPF6). (a) Scan rate, 100 mV s-I (kl = 2.9 s-I), (b) scan rate, 1000m~ s-I (kl = 3.4 sP1). Reproduced by courtesy: Inorg. Chem. 38 (1999) 2005. Copyright, American Chemical Society. anism in dichloromethane when the heterogeneous charge-transfer rate nts for electron transfer in steps (4.5) and (4.6) were both set at 0.06 s-' en a kl value of (3.1 dz 0.3) s-' is used. Similarly good fits were obtained for other scan rates in the range of 100-20001nVs-~ and concentrations of cis,mev-[~n(~~)~(y~-dpm)(y~-d~m)~r] (0.2-1.0 mM). Conclusions derivedfvom electvochemical studies on cis, m e r - M n ( C O ) z ( q*-dpm)(q2-dpm) BY e electrochemistry of cis,mer- [M~(co), (yl -dpm) (y2-dpm)~r]in organic solvents, even though inherently complex, can be completely explained by a combination of heterogeneous electron-transfer reactions and coupled solutionphase homogeneous chemical reactions. While there are many examples of complex reaction schemes involving solely solution-phase processes coupled to 262 Electrode processes electron transfer, frequently even greater complexity is associated with reactant or product interaction with the electrode su*ace. In the remainder of this chapter, examples of nuances introduced by different forms of surface activity will be considered, as will strategies for minimizing the extent of surface interaction in cases where this is an undesirable phenomenon. 3 Electrochemical studies on the [v(co),]-lo aqueous media4 process in The vanadium hexacarbon~lanion [V(CO),]- is another example of a redox active organometallic system. By analogy with data presented in Section 2, the stable 18-electron [ V ( C O ) , ] would be expected to be oxidized to the neutral but inherently more reactive 17-electron V(CO),. In the study described below, the reaction of water with V(CO), electrochemically generated from oxidation of the sodium diglyme (diglyme = 2-methoxyethyl ether, , is { C H 3 0 C H 2 C H 2 J 2 0stabilized ) [V(CO),]- salt, [ N a ( d i g l ~ m e[V(CO)6] )~ considered as are nuances associated with the fact that V(CO), is only sparingly soluble in water. 3.1 Voltammetric oxidation of [ V (CO)6]- in acetone solutions containing water In the absence of oxygen and water, the voltammetry obtained from dissolution of [Na(diglyme)2[V(CO)6] in acetone (0.1 M Bu4NPF6)solutions is extremely well defined (Fig. 4.9(a)). Under conditions of cyclic voltammetry (scan rates between 10 and 1000 mV s-'), a reversible one-electron process (eqn 4.11) is observed at platinum, gold, and GC electrodes with the reversible half-wave potential for the [v(co),]'/process being -0.35V versus FC+/FC in pure acetone. Further details of the voltammetry in organic solvents are available in reference [I 31. (4.11) [ ~ ( c o ) ~ ] v(co), e + + Figure 4.9 shows the voltammetry of [V(CO),]- in acetone as a function of added water concentration. Clearly, the addition of water introduces chemical irreversibility into the [v(co),]'/ couple, implying that dissolved V(CO), rapidly reacts with water. Figure 4.10 shows the scan rate dependence of voltammograms obtained from a solution of [V(CO),]- in acetone with 10 per cent added water. The couple is chemically reversible only at scan rates >I000 mV s-'. Since the rate of reaction of V(CO), with water also is dependent on the water concentration (Fig. 4.9), the system was simulated [12] as a pseudo-first-order EC reaction, according to the reactions given 4 ~ d a p t e with d permission from J. Phys. Chem. B 102 (1998) 1229. Copyright, American Chemical Society. Electvochemical studies o n the [ v ( c o ) ~ ] - ~ O -0.6 -0.4 process 263 -0.2 Potential (V vs FC+/FC) .9 Cyclic voltammograms obtained at 20°C at a scan rate of 1 0 0 m ~ s -and ~ with a Pt macrodisc electrode showing the effect of addition of water (a) 0 per cent, (b) 3 per cent, (c) 5 per cent, and (d) 10 per cent (v/v) to an acetone (0.1M Et4NPF6)solution containing 2 mM [Na(diglyme)2][V(C0)6].Reproduced by courtesy: J. Phys. Chem. B 102 (1998) 1229. Copyright, American Chemical Society. in eqns (4.12) and (4.13): e value of the pseudo-first-order rate constant, k[H20] was calculated at a range of water concentrations by comparison of experimental and simulated data. The second-order rate constant, k' was then calculated from a knowledge of the known water concentrations to give a constant value of 0.3 M-' s-' for the water concentration range 3-10 per cent. According to this model, the chemical reversibility of cyclic voltammograms should be dependent on both the scan rate and the concentration of water. Comparison of Fig. 4.9(d) with Figs 4.9(b) and 4.10 shows that decreasing the water concentration by a factor of 1013 is equivalent to an increase in the scan rate by (1013)~ or 10, as required if the postulated mechanism is correct. 264 Electrode processes -0.6 -0.4 -0.2 Potential (V vs FC+/FC) Fig. 4.10 Cyclic voltammograms obtained at 20°C with a Pt macrodisc electrode showing the effect ofscan rate on an acetone (0.1 M Et4NPF6)solution containing 2 rnM [Na(diglyme)z][V(CO)6]an: 10 per cent (v/v) added water. (a) 100 mV sV1, (b) 200 mV sV1,(c) 500 mV sP1, (d) 1000 mV s- . Reproduced by courtesy: J. Phys. Chem. B 102 (1998) 1229. Copyright, American Chemical Society. The overall reaction of V(CO), with a coordinating solvent such as water (on the synthetic time-scale) has been described as a disproportionation reaction [I41 where two-thirds of the vanadium is retained as [V(CO),]-, and carbon monoxide gas is released However, the pseudo-first-order kinetics observed on the voltammetric timescale indicate that the initial step in the decomposition ofV(CO), in the presence of water probably occurs via a rate-determining substitution reaction with subsequent reactions leading to the overall stoichiometry shown in eqn (4.14) where V(I1) is the [ v ( H ~ o ) ~ ] ~ di-cation, + when the coordinating solvent is water. 3.2 Voltammetric, EQCIZI, and chronocoulornetric studies on the oxidation of[V(CO)& in water Figure 4.11 shows multiple cyclic voltammetric scans obtained for oxidation of 2 rnM[Na(digl~me)~] [V(CO),](solution) in water (0.05 M CsC104) at Pt, Au, and basal-plane pyrolytic graphite macrodisc electrode^.^ In each case, a welldefined oxidation process, with a shape associated with diffusion control is seen when the potential is scanned in the positive direction. A significantly 5 ~ these n studies in purely aqueous media, the reference electrode potential was calibrated versus that of [ F ~ ( c N ) ~ ] ~ -process, /~whereas in studies in acetone, the FC+/' scale was used (see Figs. 4.9 and 4.10). Electrochemical studies on the [v(co)~]-/' process 265 Potential (V) vs [F~(cN),]~-'~-(1M KC1) .I1 Ten voltammetric cycles obtained at 20°C for oxidation of [V(C0)6]- from an aqueous [V(CO)6] at (a) platinum, (b) gold, (0.05 M CsC104) solution containing 2 rnM [Na(digl~me)~] and (c) pyrolytic graphite macrodisc electrodes. Reproduced by courtesy: J. Phys. Chem. B 102 (1998) 1229. Copyright, American Chemical Society. larger reduction response (non-diffusion-controlled) is observed on the reverse or negative potential scan. The symmetrical nature of the reduction response indicates that the product of oxidation is insoluble in water and adsorbs or precipitates onto the electrode surface. The overall process is consistent with eqn (4.16) [ v ( c o ) , ] (solution) 4 V ( C 0 ) 6(surface) -I- e- (4.16) Apparently, surface confinement prevents the oxidized V(CO)6(surface)species from reacting with the water on the voltammetric time-scale so that in urely aqueous media the voltammetry is described by eqn (4.16) rather than eqns (4.12) and (4.13). Confirmatory evidence for a surface-deposition process was obtained by simultaneous cyclic voltammetry and electrochemical quartz crystal microbalance (EQCM) experiments (Section 19.2 in Chapter 2). A cyclic voltammogram (one cycle only) was recorded for 2 mM[Na(diglyme)2][V(CO),] in water 266 Electvode processes (0.1 M NaC1) at a scan rate of 100 mV s-' over a potential range6 from -0.83 to -0.23 V versus [ F ~ ( c N ) ~ ] ~ using - / ~ - a Q C gold electrode. Upon oxidation, the electrode mass increased as expected if deposition of the insoluble neutral species V(CO),(solid) occurred. The mass deposited in this experiment was (28 f3 ng). Assuming that the Sauerbrey equation (Section 19.2.1 in Chapter 2) is valid, upon reduction, the mass decreased by almost the same amount (26 f 3 ng), corresponding to reduction of V(CO),(solid) to a soluble [ V ( C O ) 6 ]salt. Using the crystallographic data [15] for V(CO),, the radius of the molecule was calculated to be 0.39 nm, and assuming a packing factor of 0.91 for a hexagonally close-packed flat layer, the mass increase corresponds to a final surface coverage of approximately two layers on the electrode. This result suggests that V(CO), is not simply adsorbed onto the electrode surface, but is deposited as solid V(CO), under conditions where the concentration of the neutral molecule exceeds the solubility limit in water and precipitates onto the electrode surface. [V(CO)6]in Chronocoulometric experiments on 2.25 rnM [Na(digl~rne)~] water (0.1 MNaC1) at Pt, Au, and GC macrodisc electrodes provide addii~n) tional evidence for deposition of V(CO), when [ V ( C O ) 6 ] ( ~ ~ l ~ist oxidized in aqueous media. These double-step chronocoulometric experiments consist of an initial potential step from -0.76 to -0.26 V versus [ F ~ ( c N ) ~ ] ~ -and / ~ -a reverse step from -0.26 to -0.76 V versus [ F ~ ( c N ) ~ ] ~ - 'Figure ~ - . 4.12 shows an Anson plot [16] that confirms that the oxidation of [V(CO),]- to V(CO), at an Au electrode is an uncomplicated diffusion-controlled process (upper straight line). However, during the reduction of V(CO), (lower curve), there is an initially rapid increase in charge as a function of time, corresponding to the reduction of the majority of the surface-confined V(CO),, and dissolution of I 0 10 Square root of time (rns') 20 Fig. 4.12 Anson plot obtained from double-potential step chronocoulometric data (gold electrode, step width = 500 ms derived from an aqueous (0.1 M NaC1) solution containing 2 mM [Na(digl~me)~] [V(co)(j].See reference [13] for further details. Reproduced by courtesy: J. Phys. Chem. B 102 (1998) 1229. Copyright, American Chemical Society. 6 ~ e n. e 5. Electrochemical studies on the [v(co),]-lo process in aqueous media 267 the resultant [V(CO),]-. The plot then becomes horizontal when the reduction is completed. alculation of the surface coverage from the chronocoulometric data [16] and using the same packing factor assumptions as before showed that the quantity .fV(CO), deposited is much greater than a monolayer and also dependent on the step time. At a 500 ms step time, the chronocoulometric data corresponds to 5.7 f0.2 (Pt), 5.5 f0.2 (Au) and 3 . 0 k 0 . 2 (GC) layers ofV(CO),, assuming the deposition is in the form of uniform flat layers. At 1500 ms step time, deposition on Pt was 9.6 f 0.4 layers, on Au was 7.8 k 0.8, but on GC was highly variable. Both the simultaneous cyclic voltammetry/EQCM and chronocoulometric experiments are consistent with precipitation of solid V(CO), onto the e large apparent surface coverage suggests that V(CO), may be precipitated as arrays of microcrystals (microparticles) on the electrode surface, rather than as a thin film. Electron micrographs of V(CO), deposited from aqueous solution after oxidation of [Na(diglyme)2][V(CO),] showed the presence of only a partially covered surface and the attached solid consists of lumps of approximate diameter of 0.1 pm separated by distances of up to 1pm. Thus, it is apparent that the solid is not in fact deposited as a uniform film (also see Chapter 5), and hence, calculated surface coverage represents only average values of solid per unit electrode area, rather than the extent of coverage in terms of monolayers as is frequently assumed when using theoretical models of the kind described above. Conclusions devivedjom voltammetvic studies on [ I / ( C O ) & in aqueous media e solution-phase voltammetry of [ V ( C O ) , ] in organic solvents exhibits an V(CO), extremely well-defined, reversible, one-electron [V(CO),]e- process with an E;,,- value of -0.35 V versus FC+/FC.Addition of water to the organic solvent causes the response to become chemically irreversible, ut in this mixed solvent media all components remain soluble. Simulations of e solution-phase voltammetry in acetone/water mixtures are consistent with H 2 0 +-V(CO),(H20) C O being rate deterrnine reaction V(CO), ing. The sodium diglyme stabilized [V(CO),]- salt ([Na(digl~me)~] [V(CO),]), is slightly soluble, but does not react with water. In contrast, solid V(CO), is insoluble in water, but reacts so slowly that chemically reversible voltametry of the [V(CO),] - (solution)/V(CO), (solid) system is observed in aqueous media. Consequently, oxidation of [Na(diglyrne)2][V(CO),] dissolved in water (electrolyte)medium gives insoluble V(CO),, which precipitates onto the electrode surface. Cyclic voltammetry, EQCM, chronocoulometric, and electron microscopy studies show that V(CO), is precipitated as lumps of solid rather than as uniform layers. It is therefore concluded that the [V(CO)~]~'-process provides an example of a reaction where competition between solution-phase homogeneous reactions and surface-based processes occur. + - I + + + 268 Electrode processes Voltammetric studies on the oxidation of the highly surface-active polypyridyl ruthenium sitizer cis-Ru(11)(dcbpy)z(NCS)z(dcbpy = photovoltaic 2,2'-bipyridin ,4'-dicarboxylic acid7 The electron transfer and photochemical properties of ruthenium polypyridyl compounds have been studied extensively for many years (see references [l7-26] for example) with voltammetric techniques being used to characterize their redox properties and to determine their reversible potentials. In terms of development of photovoltaic cells based on ruthenium sensitizers (Section 6 in Chapter 1) it needs to be noted that after substitution of the bipyridine ligands in the 4,4' position with carboxylate groups, it is possible to attach ruthenium polypyridyl compounds to Ti02 semiconductor surfaces via ester linkages. The combination of the light absorptive properties of the chemically attached ruthenium sensitizers and the charge separation properties of the semiconductor electrode enable photo electrochemical cells to be constructed [27-321 with energy conversion efficiencies of greater than 10 per cent (also see Section 6 in Chapter 1). The most common sensitizer used [27,32-351 in ruthenium-titania photovoltaic systems is cis-Ru(d~bpy)~(NCS)~(dcbpy= 2,2'-bipyridine-4,4'dicarboxylic acid). This sensitizer (Fig. 4.13) provides excellent absorption of light in the visible region of the spectrum, a high electron injection rate, high turnover rates and high stability in photoelectrochemical cells. O n the basis of electrochemical studies on simple ruthenium bipyridyl complexes [17], it would be expected that conventional cyclic voltammetric techniques at macrodisc electrodes could be used in a straightforward manner to measure the reversible potential of the metal-based ground state [ ~ u ( d c b ~ y ) ~ ( ~ redox ~ S cou) ~ ] + ~ ~ ple, which is an essential component in the thermodyn.amics of the photovoltaic cell that are summarized by eqns (4.17)-(4.20) .8 + Dye regeneration: [ ~ u ( d c b ~(NCS)~]+ y)~ El- + -+ R ~ ( d c b p y ) ~ ( N C SEl )~ Electrolyte regeneration: El + e- El- Excitation: ~ u ( d c b ~( yN) ~C S )[Ru(dcbpye-) ~ ~ (dcbpy)(NCS)2]* (4.18) (4.19) + e- Injection: [ ~ u ( d c b ~ y '(dcbpy) -) ( N C S ) ~ ][ *~ ~u ( d c b ~ y ) ~ ( ~ ~e-S ) ~ ] + (4.20) 7 ~ d a p t e dwith permission from J. Electrochem. SOL. 146 (1999) 648. Copysight, The Electrochemical Society. 8 ~ hreation e scheme summarized by eqns (4.17)-(4.20) provides a schematic representation of reactions that occur in a photoelectrochemical cell and demonstrate that both the ground and excited state redox potentials of the c i i - [ ~ u ( d c b p ~ ) ~ ( ~couple ~ ~ ) ~are] + important. '~ El and El- are the oxidized and reduced forms of the electrolyte (commonly I; and I-, respectively). Fig. 4.13 Structural representation of cis-R~(dcbpy)~ (NCS)2. However, since cis-Ru(dcbpy)2(NCS)2 (Fig. 4.13) has been designed to be to electrode surfaces, the likelihood of surface activity being associated with the Ru(II)/Ru(III)oxidation process is substantial. Importantly, if surfacebased reactions are coupled with the charge-transfer process then the application of techniques such as cyclic voltammetry and diffusion-controlled theory may not readily provide the values of the reversible potential (see Section 18.4 in ion it is demonstrated that the combined use of a range of electrode ectrochernical techniques (cyclic, rotating disc, and microelectrode ), and chemical modification of the electrode surface is required to ensure that the effects of surface and other reactions present with the photovoltaic sensitizer are minimized so that the required reversible potential of the mass-transport-controlled solution-phase process is correctly measured. Again, ection 3, the extent ofthe surface activity will be shown to be conveniently monitored by the EQCM method. ejerence studies o n model mass-transport-controlled processes The subtleties of the c i s - [ ~ u ( d c b ~ ~ ) ~ electrode ( ~ ~ ~ ) ~process ] + / ~associated interactions with the surface are conveniently demonstrated by comparwith data obtained with model systems that are mass-transport controlled ~ ] ~ -in/ ~ (Section 7 in Chapter 2). For example, the [ s ~ M ~ ~ ~ o ~process acetonitrile is essentially ideally behaved (Chapter 3) and classically the oxidation of Ferrocene (Fc) to the Ferricenium cation (Fc+) in many organic solvents 4.21) is assumed to be reversible and mass-transport controlled. e close to ideal nature of this process is one of the reasons why the voltamtric oxidation of ferrocene is used as a reference potential scale (Section 3.2 PY)2]2+complex (bpy = 2,2'-bipyridyl) of which the photovoltaic sensitizer cis-Ru(dcbpy), (NCS)2 is a derivative, also exhibits ideal Electrode processes Table 4.2 Cyclic voltammetric data at 20°C for the oxidation of 0.5 rnM [ ~ u ( b ~ y )in~ acetonitrile ]~+ (0.1 M Bu4NPF6)at a 2-mm diameter GC disc electrodea aData taken from reference [22].Symbols are defined in Chapter 2. b~otentialsare reported versus the FC/FC' redox couple. 'The dependence of AEp on scan rate implies that the process is quasireversible. d ~ lvalues p calculated as ( E r E F ~ ) / ~ . + mass-transport-controlled voltammetry under conditions of cyclic voltammetry at platinum or GC macrodisc electrodes. [ ~ u ( b ~ ~exhibits ) ~ ] ~one + chemically reversible metal-based oxidation (Fig. 4.14(a), eqn 4.22) and three chemically reversible ligand-based reductions (Fig. 4.14(a), eqn 4.23). Since the Ru(II)/Ru(III) oxidation process is of interest in this study, only data relevant to eqn (4.22) are presented.9 The reversible E;,, value for the Ru(II)/Ru(III)process in acetonitrile, derived from the average of the oxidation and reduction peak potentials, is located at (888 4 4) mV versus FC/FC+ and is independent ofscan rate (Table 4.2). The E;,, value in acetone was (882415) mV versus FC/FC+.The peak current for the oxidation process in both, acetonitrile and acetone, was found to be proportional to the square root of scan rate, ~ , 1 : 1.00( & 0.05). The diffusion and the ratio of peak currents, 1 ~ / $ ewas coefficient for [ ~ u ( b ~ y )in ~ ]acetone, ~+ calculated from the Randles-Sevzik equation (eqn 2.34) was (2.2 & 0.5) x lov5cm2s-' . Under steady-state conditions at a 6 pm radius GC microdisc electrode, one oxidative and three reductive processes also were observed in acetonitrile and '!See Chapter 2 for definition of the symbols and equations used to calculate parameters reported in this section. Voltammetric studies on polypyridyl ruthenium 271 2.0 (a) 1.o -3 - 0.0 U 6 5:: -1.0 -2.0 -3.0 Potential (V vs FC/FC+) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Potential (V vs FC/FC+) .14 Voltammetry of 1 mM [ ~ u ( b ~ ~ ) at, ]20°C ~ + (a) cyclic voltammetry with a scan rate mV s-' at a 1 mm diameter Pt electrode over the potential range encompassing the single oxidation and three reduction processes in acetonitrile (0.1 M Bu4NPF6),(b) RDE voltammogram of the oxidation rocess in acetone (0.1 M Bu4NPF6),using a rotation rate of 1000 min-' , and a scan rate of 10 mV s-', with a 3 mm diameter Pt disc electrode. Reproduced by courtesy: J. Electroihem. 46 (1999) 648. Copyright, The Electrochemical Society. acetone. The Eil, value of the oxidation process in acetone was found to be 0.89(&0.01)V versus FC/FC+. he RDE experiments on [ ~ u ( b ~ ~in) acetone ~ ] ~ + also produced wellefined oxidative (Fig. 4.13(b)) and three reductive processes (not shown). e average value of E314 - Ell4 of 6 0 ( f 3) mV compares well with the eoretical expected value of 56 mV (for T = 20°C) for a reversible oneelectron process (Section 9.4 in Chapter 2). Ell2 was found to be O.W(f 0.02) V versus Fc/Fc+ for the oxidation process at the RDE. In summary, the 272 Electrode processes [ R ~ ( ~ P 2+/3+ Y ) J process like that for FC/FC+ is essentially an ideal chemically reversible mass-transport-controlled one-electron oxidation process. 4.2 Electrochemical studies o n c i s - R u (dcbpy)2 (NCS)2i n acetone Comparison of the structures of cis-R~(dcbpy)~(NCS)z and [Ru(bpy)J2+ suggests that cis-R~(dcbpy),(NCS)~ would also exhibit one reversible or close to reversible metal-based oxidation process. Irreversible processes due to oxidation of the thiocyanate ligand also could be expected [36]. Simple inspection of cyclic voltammograms for oxidation of the photovoltaic dye-sensitizer in acetone (Fig. 4.15) shows that two oxidation processes are present, but that neither corresponds to the expected simple diffusion-controlled process. The even more complex series of reduction processes for Ru(dcbp~),(NCS)~ and related photovoltaic sensitizers are described in references [23-26,371. 4.2.1 Cyclic voltammetry at macrodisc electrodes O n the basis of analysis of cyclic voltammograms of the kind as shown in Fig. 4.15 and more extensive data contained in reference [22], the mechanism for the oxidation of cis-R~(dcbpy),(NCS)~ may be postulated to involve the expected solution-phase one-electron charge-transfer process coupled with surface-based processes that occur prior to and after oxidation as well as oxidation of surface-modified species at positive potentials. Equations (4.24)-(4.28) Potential (V vs F C / F C + ) -0.2 0.0 0.2 0.4 0.6 0.8 Potential (V vs F C / F C + ) 1.0 Fig. 4.15 Cyclic voltammograms of cis-R~(dcbpy)~(NCS)~ at 2OoC in acetone (0.1 M Bu4NPF6) obtained at different electrode materials diameter, (d), concentrations (c) and scan rates (v). (a) c = 0.5 mM, v = 50 mV s-', GC electrode, d = 2rnrn; (b) c = 0.5 mM, v = 2000 mV s-', GC electrode, d = 2 mm; (c) c = 0.2 mM, v = 50 m~ s-', Pt electrode, d = 1 mm; (d) c = 0.5 mM, v = 1000 mV s-', GC electrode, d = 2 mm; (e) i = 0.5 mM, v = 100mV S-l, GC electrode, d = 2 mm. Reproduced by courtesy: J. Electrockem Soc. 146 (1999) 648. Copyright, The Electrochemical Society. Voltammetric studies on polypyn'dyl ruthenium 273 the basic features of the postulated mechanism Dsol A Dsurf and Dsudrepresent the dye molecule, cis-R~(dcbpy),(NCS)~ in the and surface-confined states respectively, and Xsud or Ysudrepresent surface-attached forms of the dye, whose identities are unknown. As theoretically predicted (Section 18.4 in Chapter 2), and as shown in Fig. 4.15, when surface-based phenomena are coupled to the electron-transfer the shape and nature of voltammograms are strongly affected by the nature e working electrode, the scan rate, the switching potential, the extent of potential cycling and the concentration. In this particular case, the extent of material attached to the surface is related to the current magnitude of the processes at positive potentials, and is less on platinum than on GC or gold electrodes [22]. The scan rate, the electrode material and concenratio of the first influence both the tration of R~(dcbpy),(NCS)~ oxidation process and the prominence of the second oxidation peak (compare Figs 4.15(a)-(c)). The scan rate relationship is expected, since the primary solution-phase oxidation process (eqn 4.26) becomes closer to diffusion cond at fast scan rates when it would be predicted that the extent or formation was never unity and hence YSudis minimized. The ratio of I,""/IF~ as required for a completely diffusion-controlled process (Section 8.1.1 in Chapter 2), but at fast scan rates and when the potential is switched prior to the onset of the second phase, it approaches 2 : 1 (see e.g. the cyclic voltammogram obtained at moderately fast scan rates of 1000 mV s-' in Fig. 4.15(d)). A ratio greater than unity is expected (Section 18.4 in Chapter 2) when reactant adsorption occurs [38]. Also noteworthy is the significant decrease in the peak heights detected in the first and subsequent cycles of the potential (Fig. 4.15 (e)). Apparently, during the course of sweeping the potential, surface-attached material is removed from the surface. Thus, when the potential is returned to the initial value prior to commencing the second cycle, less time is available for the reactant to become attracted to the electrode surface than is the case with the initial cycle, where the electrode is held at the initial potential value for a significantly longer period of time. 1,""/yd 274 Electrode processes Table 4.3 Cyclic voltammetric data obtained for the oxidation of c i ~ - R u ( d c b p ~ ) ~ ( N in C Sacetone )~ (0.1 M Bu4NPF6)at 1-mm diameter platinum and 2-mm diameter GC macrodisc electrodes as a function of scan rate (v) and concentrationa aData taken from reference [22]. Symbols are defined in Chapter 2. Potentials are reported versus Fc/Fc+. E 1 p values calculated as (EpO" E F ~ ) / ~ . b ~ odetected. t + For a simple diffusion-controlled process, the reversible Eil, potential is E r d )121 expected to be approximated as the average value of E,O" and EFd[(E; as is the case for the ideal FC'/+ and [ ~ u ( b ~ y ) ,13+ ] ~processes + considered above. The data in Table 4.3 actually indicate that the potential of the first oxidation process calculated in this manner is remarkably insensitive to the experimental conditions, unlike other features of the voltammetry. The (E,O" EFd)/2 + + Voltammetric studies on polypyvidyl ruthenium 275 listed in Table 4.3 were all calculated from the third cycle of the potential, but no significant difference was found in values obtained from other cycles. The peak-to-peak separations are clearly larger than those obtained for oxidation of [ ~ u ( b ~ ~ ) (see , ] ~Table + 4.2) at the same scan rate, and part of this feature may be attributed to the surface effects.'' However, the calculated (E,O" Erd)/2 value of (0.41 f 0.01) V versus FC/FC+ for the c b p y ) 2 ( ~ ~ ~ ) 2 ]couple, 0 i + was found to be independent of concentration (0.05-0.5 M ) , scan rate (50-2000 mV s-l), and electrode (platinum, GC, old) at the 10 mV uncertainty level, which implies that this is a good approximation of the reversible potential (Ei12 value) for the solution-phase diffusion-controlled process. Therefore, it is concluded that the influence of the surface-based reactions does not appear to be significant in the thermodynamic sense, with respect to the first oxidation process. + Microelectrode voltammetry ar steady-state voltammetry of cis-R~(dcbpy)~(NCS)~ (0.05-0.5 M) tinum microdisc electrode in acetone shows no evidence of a second n process. In contrast, at a GC microdisc electrode there is a small xidation response, detected as a slightly rising limiting current region (a)),and which is enhanced as the concentration is increased. As noted 10 of Chapter 2, radial, rather than linear, diffusion is dominant under -state conditiok, so it would appear that the greater flux of material away microelectrode, that is associated with radial relative to linear diffusion, has removed the majority of the oxidized material away from the electrode ce before significant interaction occurs with the surface. The E;12 value ned from microdisc-electrode experiments was found to be (0.40 f0.01) V Potential (V vs FC/FC+) Potential (V vs FC/FC+) -16 Steady-state voltammograms of 1.1 mM cis-Ru(dcbpy)2(NCS)2 in acetone (0.1 M Bu4NPF6)at 20°C, (a) GC microdisc electrode, d = 1 2 p n , c = 1.1mM, v = 10mVs-I, (b) GC RDE, d = 3 mm, w = 500,1000,1500,2000,2500, and 3000 min-I , v = 10 mV s-I . Reproduced by courtesy: J. Electrochem. Soc. 146 (1999) 648. Copyright, The Electrochemical Society. 10 he [ ~ ~ ( b 2+/3f ~ y ) and ~ ] [ ~ u ( d c b ~(NCS)~]'/+ y)~ processes are also probably both quasi-reversible rather than reversible with respect to the electron-transfer process (Section 8.1.3 in Chapter 2) with the electron-transfer rate being faster for the [ ~ u ( b ~ y ) ~ ] ~ + ' ~ + process. 276 Electrode processes versus Fc/Fc+, which is in good agreement with the value obtained under conditions of transient cyclic voltammetry at macrodisc electrodes. Assuming that the limiting current is diffusion controlled under these near steady-state conditions and use of eqn (2.48), gives a calculated diffusion coefficient of (9.5 0.5) x 1o - cm2 ~ s-' , which is slightly smaller than the diffusion coefficient calculated for [ ~ u ( b ~ ~in)acetone ~ ] ~ +(Section 4.1). + 4.2.3 Rotating-disc electrode voltammetry The RDE voltammetry of cis-Ru(d~bpy)~(NCS)~ in acetone is consistent with the suggestion that the second oxidation process is due to oxidation of surface-attached material. At the lower rotation rates and at a concentration of 1.1 x lov3M, the second process is of almost the same size as the first, but as the rotation rate is increased, the relative size of the second process decreases, until at sufficiently high rotation rates it eventually disappears (Fig. 4.16(b)). Again, the second process is less evident in platinum than GC or gold electrodes. Presumably, at high rotation rates, products are swept away from the electrode suriace so rapidly that not enough time is available for interaction with the electrode surface. This feature of the RDE experiment results in the elimination of the second peak as is the case when products are removed by radial diffusion at a microdisc electrode. As expected for a mass-transport-controlled process, a plot of limiting current is dependent on the square root of the rotation frequency at a platinum electrode over the range of 500-3000 min-' and passes through the origin (Section 9.4 in Chapter 2). The value of (E314- EIl41for the first oxidation process is (66 f 3) mV at a rotation frequency of 3000 min-', and (68 rt 3) mV at a rotation frequency of 500 min-' relative to a value of 56 mV expected for a reversible process (Section 9.4 in Chapter 2). Furthermore, the Ell2 value is independent of rotation rate and electrode material and is located at (0.409 4~ 0.002) V versus Fc/Fc+, which is in agreement with values calculated from cyclic voltammetric and microdisc-electrode voltammograms. Consequently, both the microdisc steady-state and rotating-disc techniques give almost ideal voltammetric behaviour for a chemically reversible mass-transport-controlled one-electron oxidation process. 4.2.4 Studies with an electrochemical quartz crystal microbalance T o confirm the presence ofthe surface-based processes, studies were carried out on gold electrodes using the EQCM technique, where small mass changes on surfaces occurring during voltammetric experiments can be detected, assuming that the Sauerbrey equation is valid (Section 19.2 in Chapter 2). Figure 4.17 shows the EQCM response at the open-circuit potential for an acetone solution (0.1 mM Bu4NPF6) before and after the solution is spiked with 0.6 mM cis-Ru(dcbpy)2(NCS)Z.Apparently, a large amount of material becomes attached to the gold electrode under open-circuit conditions at a stationary electrode. Under the conditions of Fig. 4.17, a rapid mass increase of 410 ng occurred onto the surface of the 5 mm gold electrode, which, assuming Voltammetn'c studies on polypyridyl ruthenium 277 u 200 300 Time (s) -17 EQCM experiments at 20°C in an acetone (0.1 M Bu4NPF6)solution which is spiked with 0.6 mM ci~-Ru(dcbpy)2(NCS)~ at the time indicated. Open-circuit potential, 5-mm diameter gold Q C electrode. Reproduced by courtesy: J. Electrochem. Soc. 146 (1999) 648. Copyright, The ~lectrochernicalSociety. a flat surface and that the material is adsorbed in an unreacted form, corresponds to a surface coverage of l-' = 3 x lop9mol ~ m - The ~ . surface coverage was calculated assuming a flat electrode surface and that the cis-R~(dcbpy)~(NCS)~ molecules were spheres having a diameter of 1 4 k This diameter was estimated from X-ray structural data [39,40]. If cubic packing for the molecule is assumed, a surface coverage corresponding to 30 monolayers is calculated at the open-circuit potential. e EQCM experiments during a cyclic voltammetric experiment in acetone on a gold electrode give the results shown in Fig. 4.18(a). Results from this experiment show that holding the potential at the initial value of -450 mV versus Fc/Fc+ for 120 s and then scanning until a potential of about 200 mV versus Fc/Fc+ is reached leads to only a small decrease of material initially attached to the gold electrode. However, at about 200 mV versus FC/FC+which corresponds to the onset of the oxidation process (eqn 4.26), a large amount of material is rapidly removed from the electrode surface. The amount lost of about 350 ng is almost equal to the amount originally adhered onto the surface under open-circuit conditions. When the potential is scanned to values slightly beyond the half-wave potential, a very abrupt mass increase occurs, but as more positive potentials are reached, the mass of material attached to the electrode decreases to a value which is similar to that at the start of the experiment. Incorporation F,, the electrolyte anion, into solid attached to the electrode surface may occur after oxidation in order to achieve charge neutralization. Figure 4.18(b) shows that the mass fluctuations became much smaller on repetitive cycling of the potential until an almost constant mass situation is reached, with respect to the potential cycle number. The EQCM data are consistent with the mechanism proposed in eqns (4.24)-(4.28). The identities of the species attached to the electrode surface and associated with the second oxidation process at more positive potentials are unknown. 278 Electrode processes (4 Potential (V vs FC/FC') Time (s) Potential (V vs FC/FC+) I 0 I I 200 . I ' I 400 600 Time (s) ' I 800 Fig. 4.18 Simultaneous voltammetric-EQCM experiments cis-Ru(d~bpy)~ (NCS)2 in acetone (0.1 M Bu4NPF6). 5-mm diameter Q C gold electrode, v = 20 mV s-' , vertical dashed line indicates start of potential scan. (a) One scan, (b) successive ) mass, (- - -) current. Reproduced by courtesy: J. Electrochem. Soc. 146 (1999) 648. scans. ( Copyright, The Electrochemical Society. Bron and Hoke [41] investigated the adsorption of free thiocyanate onto gold electrodes. They found a strong affinity of thiocyanate towards gold electrodes over a very wide potential range. The thiocyanate ions are adsorbed mainly through the sulfur atom, although an observed potential dependence was related to whether the adsorption occurred via the nitrogen or the sulfur. In case of cis-R~(dcbpy)~ (NCS)2,the thiocyanate ligands are coordinated via the nitrogen, which means that the sulfur atom is available for surface interactions. Alternatively, electrode-surface attachment via the carboxylate group could occur as is oostulated at semiconductor titania electrodes [34,42,43]. . O n 'soft' metal electrodes, sulfur-metal interactions probably are more dommant. I Voltammetric studies on polypyn'dyl ruthenium I -0.2 0.0 I I I I I I 0.2 0.4 0.6 Potential (V vs FC/FC+) I I 0.8 I 279 I 1.0 9 Effect of addition of SS-bpy at 20°C on the voltammetry of 1.5mM cis-R~(d~bpy)2(NCS)2 in acetone (0.1M Bu4NPF6) at a 1-mm diameter pt macrodisc electrode, scan rate of 100 mV s-l. (- - -) without electrode modifier, (-) after addition of 2 rnM SS-bpy. ~eproducedby courtesy: J. Electrochem. Soi 146 (1999) 648. Copyright, The Electrochemical Society. Free S C N added as Bu4NSCN was found to be irreversibly oxidized at a potential of 0.18V, 0.12V, and 0.23V versus Fc/Fc+ under conditions of cyclic voltammetry (scan rate 100mVs-') in acetone (0.1 M Bu4NPF6) at platinum, GC, and gold macrodisc electrodes, respectively. Thus, the second oxidation process is not associable with oxidation of SCN- released after oxidation of cis-Ru(dcb~y)~(NCS)~, although it could be attributable to oxidation of coordinated thiocyanate associated with surface-attached form of the dye. owever, the process is not associated with oxidation of the thiocyanate ligand coordinated to solution-soluble [ R ~ ( d c b p ~ ) ~ ( ~generated C S ) ~ l ~via oxidation of cis-Ru(dcb~y)~(NCS)~, since the second process is absent when the u(d~bpy)~(~~ process ~ ) ~ is ] ~reversible /' and diffusion controlled. Cyclic voltammetry in the presence ofsurfdce-activeSS-bpy postulated mechanism is correct, then adding an electroinactive surfactant solution may suppress surface attachment of cis-R~(dcbpy)~(NCS)~ and thereby minimize the magnitude of the second oxidation process. Figure 4.19 s the effect on a voltammogram at a gold macrodisc electrode of adding the electrode surface-active substance, 4,4'-bipyridyl disulfide (SS-bpy) [44] in acetone. At equal or higher to a 1.5 mM solution of cis-R~(dcbpy),(NCS)~ centrations of SS-bpy, the processes at positive potentials are eliminated, ch implies that a rather high SS-bpy electrode modifier concentration is necessary to compete for the adsorption sites." l l ~ ~ - b palso y modifies the response in an analogous manner at platinum electrodes, but presumably because SS-bpy does not adsorb strongly on GC, the oxidation processes at positive potentials remained when equivalent experiments were undertaken at this electrode surface. 280 Electrode processes )~ 4.3 Voltammetvy of c i s - R ~ ( d c b p y ) ~ ( N CinS tetvahydvofcrvan, acetonitvile, and dimethyljovmamide Voltammetry in tetrahydrofuran was similar to that in acetone. However, due to the limited positive potential range available in this solvent, detection of the second oxidation process was difficult. Under conditions of cyclic voltammetry at macrodisc electrodes in tetrahydrofuran, chemical reversibility was evident at lower scan rates and higher cis-Ru(dcb~y)~(NCS)~ concentrations than in acetone, presumably due to reduced surface effects. Determining the reversible half-wave potential of 0.32 V versus FC/FC+ by steady-state voltammetry at microdisc electrodes was straightforward, with a reversible, one one-electron process being observed without evidence of adsorption. Half-wave potentials determined by the RDE method gave slightly more positive values, which is attributed to the presence of IR, (ohmic) drop resulting from the high resistance of tetrahydrofuran. The dye is not very soluble in acetonitrile, but even at low concentrations in the loe5 M range evidence of surface activity is found under condition of cyclic voltammetry at a macrodisc electrode (Fig. 4.20). Steady-state voltammograms exhibit less evidence of surface interaction and give an E;,, value of 0.45 V versus Fc/Fc+ in acetonitrile. In dimethylformamide, transient cyclic voltammograms for oxidation of cis-R~(dcbpy)~(NCS)~ require the use of very fast scan rates at platinum microdisc electrodes (c.200 V s-l) before the onset of chemical reversibility becomes evident (Fig. 4.21(a)). Increasing the scan rate beyond 200Vs-', improved the chemical reversibility, but as in acetone, a peak current ratio (1~11:~) of unity was never achieved in this solvent. 0.0 0.5 Potential (V vs FC/FC+) Fig. 4.20 Background subtracted cyclic voltammogram obtained at 20°C with a scan rate of M cis-R~(dcbpy)~(NCS)~ in acetonitrile (0.1 M Bu4NPF6), using a 5 0 0 m V ~ -for ~ 3.5 x 2-mm diameter Pt macrodisc electrode. Reproduced by courtesy: J. Electrochem. Soc. 146 (1999) 648. Copyright, The Electrochemical Society. Voltammetric studies on polypyvidyl ruthenium -0.5 0.0 0.5 Potential (V vs FC/FC+) 281 1.O .21 Fast scan cyclic voltammetry of cis-R~(dcbpy)~(NCS)~ in DMF (0.1 M Bu4NPF6) (a) 2.5mM cis-Ru(d~bpy)~(NCS)~; (b) 4.0 mM c i i - R ~ ( d c b p y ) ~ ( N C with S ) ~ 30 mM SS-bpy. 70-pm diameter Pt microdisc electrode, background subtracted, v = 1000 V s-l. Reproduced by courtesy: J. Electrochem. Soc. 146 (1999) 648. Copyright, The Electrochemical Society. Addition of SS-bpy simplified the voltammograms obtained in dimethylformamide. In the presence of a sufficient concentration of this surface modifier, a close to chemically and electrochemicallyreversible response was observed at a scan rate at 100 V s-' (Fig. 4.21 (b)). Thus, provided a 10-fold excess of SS-bpy was present, the (I:/I,'ed) ratio was close to unity over the scan rate range of 100-4000 V s-'. From these fast scan rate cyclic voltammograms obtained in the presence of a 10-fold concentration from 2.5 mM cis-R~(dcbpy)~(NCS)~ excess of SS-bpy, the reversible half-wave potential for the oxidation process in dimethylformamide was found to be 0.39 V versus Fc/Fc+. L L .4 Conclusions related to the voltammetry ofsuface-active u (d~bpy)( N C S ) reversible potential of the c i s - [ ~ u ( d c b ~ ~ redox ) ~ ( ~couple ~ ~ )may ~ ] ~ etermined in a variety of solvents using different electrochemical techniques and electrode materials provided care is taken to minimize the interaction of is system with the electrode surface. Reactant and product interaction with e electrode surface cause departures from the mass-transport-controlled oxidation process for this compound under commonly used conditions of cyclic voltammetry at a macrodisc electrode. Surface effects are stronger on GC and gold than on platinum electrodes. Steady-state microdisc electrode and RDE experiments provide close to chemically and electrochemically reversible masstransport-controlled voltammograms in acetone and low concentrations of the dye and fast scan rates minimize the influence of the surface-based effects under 282 Electrode processes the transient conditions of cyclic voltammetry. In dimethylformamide, scan rates greater than 100 V s-I are needed to observe a significant level of chemical reversibility, whereas only moderate scan rates were required in other solvents. Addition of the electroinactive surfactant, SS-bpy, may also minimize surfacebased effects. The studies presented on the [ R U ( ~ C ~ ~ ~ ) ~ ( N Cprocess S)~]~+'~+ have been included in this chapter to further emphasize the fact that use of a wide range of techniques is generally needed to unravel mechanistic complexities frequently associated with electrode processes. 5 Stripping voltammetry Stripping voltammetry constitutes a class of techniques where electroactive material is deliberately accumulated from the solution phase onto a solid electrode or into a liquid mercury electrode. After this pre-concentration stage, the material is stripped back into the solution phase. Very low concentrations of electroactive compounds may be determined via this method [45-501. Essentially, all stripping techniques possess three main steps viz. deposition, equilibration, and stripping. 1. Deposition ov accumulation step The deposition step usually involves the electrolytic or adsorptive deposition of a chemical species onto an electrode surface at a constant D C potential. When metal ions are determined by anodic stripping voltammetry [45-471 at a hanging mercury drop electrode, a sufficiently negative potential is applied to the working electrode to cause the metal ion of interest to be reduced to the metal, which, in many cases, forms an amalgam with the mercury electrode (e.g. Cd, Pb, T1 and Sb). In adsorptive stripping voltammetry [45,46], a metal complex is accumulated at the electrode surface by adsorption (e.g. Ni, Co, Sb, Ge). In stripping analysis, the deposition step is usually facilitated by convective transport of the analyte to the surface of the working electrode. This can be achieved by rotation of the electrode, by stirring the solution or by flowing the solution over the electrode (Section 9 in Chapter 2). 2. Equilibration step When the deposition step occurs under convective conditions, a quiet time usually follows this step in order to enable the electrode to return to a quiescent state. This period is usually in the range of 10-30 s and is called the equilibration step. 3. Stripping step In anodic stripping voltammetry, the stripping step is achieved by the application of a voltage applied in the direction of positive potential which, therefore, causes the metal or metal in the amalgam to be oxidized back to the solution-soluble metal-ion state. During the potential scan, the accumulated metal is stripped from the surface, yielding a peak height for each analyte, which is proportional to concentration. Ideally, the peak current is linearly proportional to the concentration of the analyte in the bulk solution and to the deposition time. The different stages associated with D C stripping voltammetry in the linear potential sweep form are described in Fig. 4.22. In Stripping voltammetry 283 3 g 0 Pi Initial or deposition potential *- 4 Deposition time Quiet time 2 Schematic diagram of the waveform used in DC linear potential sweep stripping voltammetry. adsorptive stripping voltammetry, the stripping step generally involves reduction of the adsorbed metal complex by applying a negative direction potential scan. g voltammetry represents one of the most widely used voltammetques for the determination of trace metal concentrations. However, related to the analytical methodology [45-511 are not the focus of . Rather, only the nuances of the electrode processes used in two voltammetric methods are considered, to highlight how the same established in other contexts also are valid in this important field of ical endeavour. As conveyed by the description of the technique ous paragraph, stripping voltammetry represents a combination hase processes and processes where material to be determined is then stripped from an electrode suliace. The first example to be in Section 5.1 represents the electrochemical accumulation of metamalgams with thin films or droplets of mercury plated onto an ce in a technique referred to as thin-film anodic stripping voltamsecond example, accumulation of material occurs by adsorption lex onto a hanging mercury drop electrode which is followed tated by electrochemical reduction in a technique referred to ripping voltammetry. There are almost an infinite number of trochemical stripping techniques [511, but the major features electrode processes utilized in this field is conveyed by consideration of two very widely used forms of stripping voltammetry. .I Anodic stripping voltammetry with thin-jilm mercury electrodes12 n the anodic stripping voltammetric method for determining a metal ion Mn+ in aqueous solution, reduction at a mercury electrode for a carefully timed 12~daptedwith permission from Anal. Chem. 69 (1997) 2673. Copyright, American Chemical Society. 284 Electrode processes Table 4.4 Assignment of subscripts used in the theory presented for anodic stripping voltammetry - Subscript Solute Solvent period, Atred,produces a metal that amalgamates If the volume, V, of the mercury electrode is small, the average concentration of the metal in the mercury phase soon exceeds manyfold the bulk concentration cp of metal ions in the aqueous phase.13 It is this initial pre-concentration or plating stage (see Fig. 4.22) that is responsible for the extreme sensitivity of stripping voltammetry. As noted above, to foster a rapid transfer of metal into the mercury phase, convection is sometimes applied during the pre-concentration stage of stripping voltammetry, either by stirring the solution or rotating the electrode [52]. However, convection is not needed when the electrode is a mercuryplated microdisc [53], or as in an array of such discs, as considered below, because the efficiency of convergent diffusive transport to small inlaid discs [54] is great enough to rival convective transport (also see Section 14 in Chapter 2). The second of the three stages in traditional stripping voltammetry, the equilibration stage (see Fig. 4.22), occurs after the period, Atred,of reduction. This stage, of duration Atwait,allows any convection to subside. If the thickness, 1, of the mercury layer is small (compared with ( & ~ t , , ~ , ) ' / ~where , D2 is the diffusion coefficient of the metal in mercury), as is the case with thin-film mercury electrodes, the pre-equilibrium or inactive stage14 also allows total homogenization of the amalgam to a uniform concentration c;. In the stripping stage of anodic stripping voltammetry, the metal is electrochemically removed from the amalgam often by applying a positive-going potential ramp of scan rate v to the electrode (Fig. 4.22). Thus, (4.31) E = Einit v t + 1 3 ~ o tthat e the use of numerical subscripts to designate various solute species used in this discussion is in accord with Table 4.4. '"here was no deliberate equilibration stage in the experiments considered in Section 5.1, but the initial portion of the anodic scan provides the required brief period of inactivity. Striping voltammetry 285 e potential, El,,, is the initial potential, and t represents time. As a a time-dependent current, I, flows which, when plotted against E or t, of M in the lays a peak. The peak height I, is proportional to the amount VC,~ lgam phase at the beginning of the stripping phase and hence to cp. When *-film mercury electrodes are used, but not necessarily otherwise [55-571, is total, and as an alternative to measuring and interpreting the the total content of metal M can be found by applying Faraday's grating the voltammogram 00 I dt = QL = nFVc2b notes the limiting voltammetric charge. e recognized that, conceptually, carrying out chemical analysis via dic stripping voltammetry involves two distinct steps: 1) determining the amount VC: of amalgamated metal from the voltammo2) relating VC; to the analyte concentration, c:, in the aqueous solution. In practical chemical analysis, steps (1) and (2) are seldom disentangled; instead, calibration or standard addition experiments are employed and the overall proportionality IpO( C: is assumed and exploited. u ' preparation of mercury thin-film electrodes 'in situ technique' of preparing a thin mercury film for anodic mmetry, and the method used in data presented below, is available ng liquid mercury ~ ~ : ( a q u e o u s ) f 2e- -+ mHg(1iquid) m = 1 or 2 (4.33) the pre-concentration phase. This is achieved by adding a soluble ic (m = 2) or mercurous (m = 1) salt to the analyte solution to achieve a concentration ck that is much greater than c,b. If the reduction potential is action (4.29) proceeds where mass transport by diffusion is solely ning (Section 7.1.1 in Chapter 2), then the deposited amount is expected to be proportional to the bulk concentration c,b of the Mn+ ion, to the charge n+ on the cation, and to some power p of its diffusion coefficient. Accordingly vc,"O( n@cp (4.34) VG with no other M-specific terms being expected to enter this relationship. As shown in Section 10.1 in Chapter 2, the power p equals uniq for microdisc electrodes employed in experimental studies presented below, whereas p = 112 (Section 8.1 in Chapter 2) when co-deposition occurs by planar diffusion onto 286 Electrode processes a macrodisc electrode, while p = 213 for hydrodynamic systems under laminar flow conditions (Chapter 2, Table 2.3). Of course, similar proportionalities apply to the ion co-depositing according to reaction (4.33), but the lefthand term in eqn (4.34) is not then appropriate because mercury serves as the solvent (Table 4.4). Instead, if the reasonable assumption that the atomic volume of mercury in a dilute amalgam differs negligbly from that in the pure liquid state is made, then the proportionalities ~~2 may be expected, where P H and ~ MHg are the density and atomic mass of mercury respectively (PHg/hlHg= 67471 mol m-3 at 25°C). Note that the concentration c,b of amalgamated metal depends on the ratio (c,b/c,b) of aqueous concentrations and is unaffected by plating duration.15 A complication that attends the metal-mercury co-deposition technique is that, because most metals M of interest are considerably less noble than mercury, the deposition of mercury continues unabated during the stripping stage. Thus (as is apparent in figures shown later) the baseline of the stripping peak is not zero, but occurs as a negative (i.e. reduction) current. When the electrode is a single inlaid microdisc of radius re and H ~ (n~= + 2) is employed, this baseline current is given (Section 10.1 in Chapter 2) by the relationship Of course this constant baseline current must be subtracted from the measured total current, I,,,,, to evaluate, I, the stripping current. For example the I term in eqn (4.32) should be replaced by I,,,, - Ibase. 5.1.2 Comparison of macro- and microdisc mercury thinjilm electrodes Individual or, even better, arrays of inlaid discs of carbon (Fig. 4.23) provide convenient substrates for co-deposition of thin layers of mercury suitable for use in anodic stripping voltammetry. The size of a disc is characterized by its radius r, or sudace area A = m e 2 . As described in Chapter 2, large inlaid discs (macroelectrodes) may behave differently from small discs (microelectrodes). The distinction arises because diffusion to a 'large' disc electrode is primarily linear (planar), whereas diffusion to a 'small' disc rapidly becomes radial. Again, as noted in Chapter 2, the classification into 'large' or 'small' electrodes is based on whether the disc radius is larger or smaller than the 'distance scale of the experiment'. The experimental distance scale during the pre-concentration stage of anodic stripping voltammetry is (Dl A tred)'I2which is much larger than the 3.5 pm radius of the inlaid discs considered experimentally below, so that these discs are clearly 'small7 during this stage. However, 1 5 ~ hconcentration e ratio applicable to experimental data reported below was chosen so that the amalgam concentration never exceeds 0.3 atom per cent. Stripping voltammetry Current collector Carbon fibres 287 Epoxy resin . 4.23 The random assembly of carbon microdisc electrode or RAM@concept used in anodic stripping voltammetric studies: (a) section view, (b) plan view. Provided by courtesy of Stephen Fletcher, CSIRO Division of Minerals, Clayton, Victoria, Australia. the situation is much more equivocal in the case of the stripping stage of the experiments. Then, the experimental distance scale during the transit of the stripping peak can be considered to be ( 2 . 9 4 ~ ~ ~ ~ l n n For ~ v the ) " values ~. T = 298K, Dl = 8 x 1 0 - ' ~ m ~ s - ln, = 2, and v = 0.5Vs-', which correspond closely to the stripping conditions employed in experiments described below, the experimental distance scale evaluates to 4 pm. Coincidentally, this is very close to the 3.5 pm radius of experimentally used microdisc electrodes. n a typical voltammetric experiment, hybrid behaviour midway between that expected for macro- and microelectrodes [58] could therefore be expected (also see Section 10 in Chapter 2). However, very atypical circumstances apply in stripping from a thin film. During radial (quasi-spherical) diffusion to a small inlaid disc, the current density is markedly non-uniform, most of the current t strippingfrom a flowing through the perimetric region of the disc. ~ u during thin mercury layer, the uniform distribution of the metal M solute will enforce an almost uniform current density, as is the rule at 'large' discs. Enhanced current density at the electrode edge is impossible in thin-film stripping. Accordingly, the theoretical treatment can be based on linear (planar) diffusion. Treatment of the mercury film as 'thin', as is the case in the present consideration, means that the thickness, 1, of the mercury layer is small in comparison with the experimental distance scale associated with stripping metal M out of the film. Thus where the 6-pm length given in relationship (4.37) is based on D2 = 1.5 x m2 ssl in addition to the parameter values cited above. The mercury volume deposited on a disc of radius r = 3.5 pm in experiments to be considered below was calculated on the basis of expression (4.35) to be about 1.3x 10-l7 m3, 288 Electrode processes which leads to a calculated average thickness 1 = v / n r e 2 = 3 x m, so that inequality (4.37) is amply satisfied. In the interest of realism, V I A instead of 1 is used as a measure of the mercury thickness, because [56,57] electrodeposited mercury does not form a uniform thin layer, some bare carbon remaining long after a uniform laver might be exoected. Even after pre-concentration, the Faradaic currents derived from an electrode of 3.5 pm radius in micromolar to nanomolar or even lower analyte concentration are very small and not easily measured with accuracy. To remedy this, arrays of identical inlaid disc electrodes (Fig. 4.23) rather than a single disc can be employed [59]. In analysing the results of array experiments (see below), all the discs are regarded as functioning identically and independently, without mutual interference by overlap of depletion zones. Consequently, the symbols A, V , and I are used indiscriminately, to refer either to the area of a single disc, the volume of mercury deposited on it, and the stripping current from that disc, or to the total area, total mercury volume, and total stripping current of all discs. J I U 5.2 Theory for a reversible process As in solution phase and studies with thin films described in Chapter 2, electrode processes associated with stripping voltammetry may be classified as reversible, quasi-reversible, or irreversible. Only the reversible case is considered in this book. The theory of thin-layer anodic stripping voltammetry for a reversible reaction was first developed by De Vries and Van Dalen [60] some thirty five years ago. They adopted a model based on principles similar to those described above, derived an appropriate integral equation, solved it numerically, and reported expressions for the peak current for the peak potential in terms of the half-wave potential and for the width of the peak at half-height The development of an equation that can be used to describe the shape of the entire stripping voltammogram and which necessarily leads to these relationships is taken from reference [61] and utilizes a range of concepts introduced in Chapter 2. The thinness of the mercury film implies that the concentration c2 of the metal in the amalgam is effectively uniform at any instant during the stripping. I I Stripping voltammetry 289 araday's law applied to the reaction in eqn (4.30) relates the amount of metal removed from the amalgam at any time t to the integral of the stripping current up to that instant: It nF(~c;-Vc~)= Idt=Q (4.41) and when this result is combined with eqn (4.32), the expression Idt VC2 = is derived and relates the amount of metal at time t to the difference between the limiting charge and the stripping charge up to time t. With respect to the solution phase, there is a time-dependent concentration c; of Mn+ ions at the electrode surface. This may be related to the bulk concentration of this ion by the equation [62] when transport is solely by linear diffusion. Here, M is the semi-integral of the current I over the time interval from zero to t (Section 11 in Chapter 2). When stripping voltammetry is being used for trace analysis, with massive preconcentration, cp is very small compared with and is therefore generally insignificant in comparison with ci . Accordingly, ci is a valid replacement for eqn (4.43). In terms of its formal potential E ~ O , the Nernst equation for eqn (4.29) (assumed reversible under the linear-scan stripping regime) is After substitution from eqns (4.42) and (4.45), eqn (4.46) may be rearranged to which shows that a graph of the logarithm of M I ( & - Q) versus potential should give a straight line of slope n F I R T and an intercept potential of 290 Electvode processes Fig. 4.24 'Log plot' analysis of mercury thin-film stripping voltammograms based on eqn (4.47). Reproduced by courtesy: Anal. Chem. 69 (1997) 2673. Copyright, American Chemical Society. v2] E: - (RT/2nF) ln ( A ~ D ~ / or EO f - (RTInF) l n { ~ ~ : V} ' ~ /as illustrated in Fig. 4.24. Such a linear construction to give a 'log-plot' is analogous to the analysis of reversible steady-state or other forms of sigmoidal-shaped voltammograms by graphing the logarithm of (Ili, - I ) / I versus potential (Section 9.4 in Chapter 2). Note that neither the bulk amalgam concentration c,b nor the scan rate v appears in eqn (4.47), so that plotted data derived from experiments at several scan rates or analyte concentrations should overlie each other. It is convenient to define a reference potential for each stripping voltammogram by (4.48) It will transpire that the peak of the stripping voltammogram generally lies within 1mV of this new parameter. The Nernst relationship [63] may be reformulated as in terms of this reference potential. Note that, unlike the intercept potential shown in Fig. 4.24, E* does depend on the scan rate V . Before constructing an equation for the stripping voltammogram shown in Fig. 4.25, it is advantageous to adopt dimensionless variables. In linear sweep anodic stripping voltammetry there is a linear relationship, namely eqn (4.31), between potential E and time t . Both of these variables will be replaced by a dimensionless counterpart L Stripping voltammetry 291 . 4.25 Predicted features of a thin-film anodic stripping voltammogram. The ordinate is the nor~ V~C ~ Vand the abscissa is an undirnensionalized potential scale malized stripping current L = R T I / F~ f = ( n F / R T ) ( E- E*), where E* is defined in eqn (4.48).The peak occurs at ( = -0.05545. The area beneath the curve is unity. Reproduced by courtesy: Anal. Chem. 69 (1997) 2673. Copyright, American Chemical Society. where nF co = -ERT - (4.51) lnlt e 6 variable is an undimensionalized potential scale with its zero at the refnce potential. The Eo term is a negative constant, equal to the value of 6 at the instant when the stripping scan started. The current I can also be replaced y a normalized dimensionless counterpart ubstituting this definition into eqns (4.42) and (4.45), and simultaneously replacing the time variable in those equations by 6, gives and respectively. Finally, eqns (4.53), (4.54), and (4.50) are inserted into the Nernst relationship (4.49). The simple result 292 Electrode processes emerges. In dimensionless form, this is the equation that describes the shape of the stripping peak. The next step in order to obtain an analytical expression to describe the stripping voltammogram in Fig. 4.25 is to replace the lower limit toin eqn (4.55) by -w. This is equivalent to asserting that there would be no important change in the voltammogram if the scan had started at any potential more negative than the actual initial potential; experimental initial potentials are, of course, always selected on such a basis. The valuable property [63] that semi-integration of exp{bx} with respect to x, with a lower limit of -w, gives (114) exp{bx) for any constant positive value of b, and the known limit now permit the summation to be recognized. The coordinates of the peak in the Fig. 4.25 curve are (c,, ip) = (-0.0555, 0.29697) (4.59) while the coordinates of the half-peak points are (cp12, lpI2) = (- 1.6416,O.14848) and (1.2990,O.14848) (4.60) That the area under this peaked curve in Fig. 4.25 is exactly unity is guaranteed by the eqn (4.57) limit as well as by purely chemical arguments. O n returning to experimental variables, the equation of the stripping voltammogram is seen to be peak potential (Ep),and peak half-width ( Wl12)being with the peak current (Ip), Stripping voltammetry 293 and RT Wl12 = 2.9407nF Observe that I, and E, depend on V , but Wl12does not. Furthermore, these values are in excellent agreement with those of De Vries and Van Dalen, reported in eqns (4.38)-(4.40). Notice that the appearance of different diffusion coefficient~in eqns (4.63) and (4.39) arises because the Dutch workers chose to report [ho]the peak potential relative to the polarographic half-wave potential,16equal (RTI2nF) ln{D1/ D2}, instead of relative to the formal potential E ~ O as to, E! is the case in eqn (4.63). For a divalent analyte ion at 25"C, the voltammetric peak is predicted to lie 0.71 mV negative of the reference potential E* and the peak width at halft should be 37.78 mV. Observe the absence of diffusion coefficients from eqn (4.62), unlike the case with solution-phase voltammetry, and note the v re dictions that the peak current is proportional to the square of the electron er and to scan rate v. Analysts tend to prefer measurements of peak height eak area, but there is much to be said in favour of calculating C$ from QLvia .32), rather than via the proportionality in eqn (4.62), because the charge is more fundamentally related to the amalgam content and because integration nishes effects of random noise. Obedience of experimental results to the cted relationship + between peak area and peak height provides a powerful test of the applicability or otherwise of the theoretical model to an experimental system being studied. henever an electrode process involves interaction with the surface, the itional inherent complexity relative to completely solution-phase studalways leads to the likelihood of poorer agreement between theory and ment (see Chapter 5). In the case of thin-film stripping voltammetry, a comparison of data obtained in reference [61] with the theory presented above gives an idea of the level of agreement that is achievable in this area of voltammetry. Comparison of experimental results and theory e thin mercury films for experimental studies were prepared by in situ deposition at - 1.100 V versus Ag/AgCl for 100 s onto an assembly of carbon discs randomly inlaid into the end face of a 10-mm diameter cylinder of epoxy resin olarography is the technique ofvoltammetry at a dropping mercury electrode developed by the Nobel prize winner Heyrovsky. The theory of this technique is described in the book Princbles of Polarography by J . Heyrovsky and J. Kuta, Academic Press, New York, 1966. Also see Table 1.1, of Chapter 1 and references [46,47] of this chapter for more details on the history and practice of the polarographic method. 294 Electrode processes using a RAM@electrode (Fig. 4.23), the carbon discs being the sectioned ends of parallel 7-pm diameter pyrolytic graphite fibres. Based on calibration tests, there were believed to be 653 separate inlaid carbon discs, electrically commoned, in the electrode used. Thus the total electrode area was A = 2.5 x lov8m2. At the end of the 100 s of plating, the electrode potential was immediately ramped positively from the initial potential of - 1.100 V versus Ag/AgCl at a rate of either 0.2, 0.4, 0.6, 0.8, or 1 V s-' until a final potential of 0 V versus Ag/AgCl was attained. At the lowest scan rate, there would have been an additional 3 or 4 s of plating time early in the stripping stage, but no correction was made for the consequential enhancement of c:. All experiments were conducted at 21°C in aqueous solutions containing 100 mM K N 0 3 (pH 1.7). Analyte solutions were 0.38 mM H ~ ~ + , 1.OO pM pb2+, and 1.OO pM cd2+ and tp = 100 s (data obtained under other conditions are available in reference [61]). A typical set of voltammograms obtained under these conditions for the processes in eqns (4.66) and (4.67) is shown in Fig. 4.26. Fig. 4.26 Typical stripping voltammograms of Cd (first peak) and Pb (second peak) from thin amalgam films on an array of microdisc electrodes. Scan rates: (lower curves) 0.4, (upper curves) 0.8 V s-l. The films were prepared by plating for 100 s from a solution containing 1.OO pM each of Cd2+ and pb2+ with 0.38 m~ H ~ ~ Reproduced + . by courtesy: Anal. Chew. 69 (1997) 2673. Copyright, American Chemical Society. Table 4.5 Width of experimental stripping peaks at half-heighta from thin amalgam films Cd (amalgam) Pb (amalgam) 0.20 0.40 0.60 0.80 1.OO 46.8 47.2 47.2 47.7 47.8 43.7 43.3 41.4 39.3 41.7 Ave f SD 47.3 r f 0.4 41.9 f 1.7 'The theoretically predicted width is 37.3 mV; data taken from reference [61]; 0.38 m~ H~"+, 1.OO pm pb2+, 1.00 pm cd2+. For each metal at each scan rate, the stripping current I versus potential E data was analysed in the following ways: peak half-width was measured and compared with the theoretical value 7.3 mV given by eqn (4.64) for n = 2, T = 294 K. The experimental are assembled in Table 4.5. current data were semi-integrated with respect to time, so generating current data were integrated with respect to time, producing a file of a1 entries in the latter file, a value of & was identified. These ta are presented in Table 4.6, together with $ values from item 6. Also ~stedin this tabulation are values of the quantity QLv/Ipwhich, according eqn (4.65) should adopt the value 42.7 mV at 21°C when n = 2. weighted linear regression corresponding to a log plot rating three distinct pieces of information: (a) the slope, to be compared with the predicted value nF/RT which equals 7 8 . 9 ~ - I for n = 2, T = 294K; (b) the intercept potential; and (c) the correlation coefficient, which provides a measure of the linearity of the ln{M/(QL- Q)} ersus E relationship. Examples of experimental 'log plots7 are shown in ig. 4.27 and the entire regression results are compiled in Table 4.7. (6) The peak current and peak potential were identified. The former values, after baseline correction, are reported in Table 4.6. The Epdata are listed in Table 4.8 and compared with the reference potential E*, which is calculated from the intercept potential, described in (5b), by the addition of the quantity 296 Electrode processes Table 4.6 Limiting charge and peak current stripping dataafrom thin amalgam films tn (3 100 100 100 100 100 v (vs-') 0.20 0.40 0.60 0.80 1.00 Ave f SD C d (amal) Pb (amal) Q Ip Ip (PA) (&vIIP) (mV) Q (nC) (nc) (PA) (QdIp) (mV) 117 111 127 144 140 0.455 0.854 1.476 2.199 2.657 51.4 52.0 51.6 52.4 52.7 206 201 191 198 204 0.85 1.671 2.511 3.601 4.394 48.5 48.1 45.6 44.0 46.4 52.0 f 0.5 46.5 f 1.8 "Theoretical value of Qcv/Ip according to the model should equal 42.7 mV; data .OO, pm pb2+, 1.00 pm c d 2 + . taken from reference [61]; 0.38 mM H ~ ~1+ Fig. 4.27 'Log plots' for the Cd and Pb stripping peaks from thin amalgam films with scan rates of 0.40 V s-' (o) and 0.80 V s-' (A). The lines are the linear regression lines, determined from the points shown. Other conditions as for Fig. 4.26. Reproduced by courtesy: Anal, Chern. 69 (1997) 2673. Copyright, American Chemical Society. Since the theoretical difference between these potentials is < l mV, close agreement is expected. (7) The molar amount of analyte metal in the amalgam, VC;, was measured by three methods; (a) from Ip, via eqn (4.62); (b) from &, via eqn (4.32); and (c) from the equation Stripping voltammetry 297 le 4.7 Results of 'log plot' linear regression analysisa of anodic stripping voltammetric data from thin amalgam films (eqn 4.47) v (V sf1) Cd (amal) slope intercept - 9 (V) Pb (amal) con. coef slope - 9 intercept (V) corr. coef 'Theoretically predicted slope is 7 8 . 9 ~ - l ; data taken from reference [61]; 0.38 mM H ~ ~1.O +O,pm pb2+, 1.OO pm ~ d " . Table 4.8 Measured peak potentials, Ep, compared with reference potentials, E*' obtained from stripping voltammograms of thin-film amalgams 'Calculated from the intercept potentials of the 'log plots' (eqn 4.47); data taken from reference [61]; 0.38 mM H ~ 1.O~O pm + pb2+, ~ 1-00prn cd2+. which arises by combination of eqns (4.32), (4.64), and (4.65). The results of these alternative determinations are assembled in Table 4.9. Reasonable agreement is achieved. However, the correct value of vC,~ is unknown and therefore the accuracy of the determinations of the amount of metal by the rival methods cannot be assessed. Table 4.5 shows that the stripping peaks are significantly wider than theory redicts, the width at half-height exceeding prediction by (27 f 1) per cent for cadmium (amalgam) and (12 f 5) per cent for lead (amalgam).It is commonly found that voltammetric stripping peaks from thin amalgams of various varieties exceed in width the value that theory predicts, though the excess peak width for the cadmium case suggests that the model is imperfectly obeyed. 298 Electrode processes Table 4.9 Comparison of three methods of calculating the amount of amalgamated metal (pmol)" associated with stripping voltammetry from thin amalgam films v (V S - I ) Cd(ama1) Pb (amal) from Ip from & from eqn (4.66) from Ip from C& from eqn (4.66) 0.20 0.40 0.60 0.80 1-00 0.503 0.472 0.544 0.608 0.587 0.606 0.575 0.658 0.746 0.725 0.632 0.598 0.689 0.778 0.754 0.940 0.924 0.925 0.995 0.972 1.067 1.042 0.990 1.026 1.057 1.100 1.073 1.028 1.050 1.087 Av f SD 0.543f 0.057 0.662f 0.074 0.690f 0.077 0.951 f 0.031 1.036& 0.030 1.068f 0.029 'Data taken from reference [61]; 0.38 mM H ~ ~1.+ OO,ym pb2+, 1.OO ym cd2+. Fig. 4.28 Dependence of peak current on scan rate for the stripping of cadmium and lead from thin-film amalgams. Reproduced by courtesy: Anal. Chem. 69 (1997) 2673. Copyright, American Chemical Society. Figure 4.28 demonstrates the expected linear dependence of peak height Ip on scan rate v, for both amalgams. However, if eqn (4.62) is to be believed, this diagram implies that the concentration of cadmium in the amalgam is only 60 per cent of the lead concentration. Table 4.6 reveals that both peak areas & are essentially independent of v, as expected, and again the implication is that, in the amalgam, the cadmium concentration is markedly lower than the lead concentration, this time by a factor of 0.64. Values of (&v/I,), which average (52.0 f.0.5) mV for cadmium amalgam and (46.5 & 1.9)mV for lead amalgam, Stripping voltammetry 299 + also are listed in this tabulation. (Here and elsewhere a number preceded by is a standard deviation, SD.) Departure from the theoretical value of 42.7 mV is modest for lead, suggesting that the model is acceptable for this metal, but the cent disagreement for cadmium suggests that this process has additional xity. Nevertheless note that, as for peak widths, the reproducibility of the results is markedly better than for Pb. linearity of the 'log plots' is excellent, as evidenced by Fig. 4.27 and orrelation coefficients in Table 4.7. As is commonplace in other varieties of reversible 'log plot7analysis [64,65], the slopes of the ln{M/(QL - Q)} versus E plots, which average (67.1 f0.8) V-' for cadmium amalgam and (72.7 rt 1.4) V-' for lead amalgam, are smaller than the predicted Nernstian of 78.9 V-'. The intercept potentials are predicted to be independent of rate, but Fig. 4.27 suggests that this prediction is not realized in practice. owever, the data in Table 4.7 reveal no discernable trend with scan rate in the intercept potential. Rather, it appears that the potential scale is not reproducible experiment to experiment to better than a few millivolts. n contrast to the intercept potential, the potential of the stripping peak is icted to depend on the scan rate, shifting positively with increasing v. There convincing evidence of such a trend in Table 4.8. However, the theoretical for the five-fold range of scan rates encompassed by these experiments is 10 mV and this small trend has probably become 'buried7 in the scatter. n specific potentials are compared within a single experiment, the scatter is ess intrusive. Recall that theory predicts that the (Ep- E*)potential difference d be only -0.7 mV. The measured differences are (+4.0 0.9) mV for + . 4.29 Comparison of the theoretical shape of a linear-scan stripping voltammogram (full line) and the experimental current-voltage curve for stripping of lead from thin amalgam films at a sweep rate of 0.800V s-l. Other conditions as for Fig. 4.26. Reproduced by courtesy: Anal. Chem. 69 (1997) 2673. Copyright, American Chemical Society. 300 Electrode processes Cd(ama1gam)and (-2.0 i3.7) mV for Pb(ama1garn).Once more, the lead data fir, the model better than is the case with cadmium, but is less reproducible. Figure 4.29 contains a comparison of the theoretical shape of a stripping voltammogram, as predicted by eqn (4.61), with an experimentally obtained lead amalgam curve. The curves have not been explicitly fitted at any point. Instead, the VC;parameter, needed for eqn (4.61), was calculated via eqn (4.32) from the experimentally measured value of &. Similarly, the needed E* reference potential was calculated by adding the quantity in eqn (4.66) to the measured intercept potential of a graph ofln{M/(& - Q)}versus E (Table 4.8). For the stripping of cadmium amalgam, agreement is significantly worse. The stripping peak for Cd(amalgam)is lower and wider than expected on the basis of the theory for a reversible process. If de-amalgamation reaction is not therrnodynamically reversible, it can be predicted that an irreversible or quasi-reversible stripping peak would have a lower peak and a broader half-peak. Thus, it is tempting to attribute the non-conformity of the cadmium peak to irreversible stripping behaviour. However, this cannot be the whole story, because the stripped charge for cadmium is only 64 per cent of the corresponding QL for lead stripped from amalgam under similar conditions. The magnitude of the stripped charge is not affected by the degree of reversibility of the electrode reaction. There are at least four conceivable explanations for the lower recovery of cadmium than lead. First, despite their equal concentrations in the bulk aqueous solution, less cadmium might have been plated than lead. T o some extent, this explanation is credible, because cd2+(aqueous)has a smaller diffusion coefficient [66] than pb2+(aqueous). However, DCp+/DPb2+has a value of about 0.83 and so, in light of the discussion surrounding eqn (4.34), this cannot explain more than a minor portion of the observed magnitude of the effect. A second possibility is that an intermetallic compound (examples of which are well known [45] in the case of some pairs of metals, such as Cu/Zn) might be formed within the amalgam between Cd and Pb, and stripped with the lead. In that eventuality, some of the & that has been attributed to lead should be ascribed to cadmium. However, experimental lead stripping peaks were found to be independent of whether or not the cadmium was co-deposited, lending no support to the possibility of intermetallic interference. Third, as postulated by Batley and Florence [55], metals may plate on islands of bare carbon, from which it may not readily be stripped. For the carbon-fibre-array electrode used in these studies, no cadmium peak was observed when mercury was absent, either because cadmium was never plated onto the carbon substrate or because the plated cadmium could not be stripped, whereas lead stripping peaks were observed in the absence of mercury. A fourth possibility is that the solubility of cadmium in mercury may have been exceeded in the surface layers during plating, resulting in a smaller cadmium content than the more soluble lead. However, if this were the case, the problem would be alleviated by using lower concentrations of c d 2 + in the plating solution. There is no evidence of such an effect as graphs of I, and QI, are linearly related to the aqueous concentration for both c d 2 + and pb2+. Stripping vo~tammetry 30 1 1n summary, there are several ways in which the model of linear scan stripping of &&-mercury films appears to be deficient. However, agreement between the theoretical predictions of the model and the experimental results for lead is regarded as being satisfactory and consistent with the level expected when surface-basedprocesses form an integral component of an electrode process. chanism associated with the adsoytive stripping voltammetry of cobalt (and nickel) dimethylglyoxime complexes at mercury electrode^'^ 5. More than fifty years ago, Stromberg and Zelyanskaya [67] observed a large increase in the polarographic18limiting current for the reduction of cobalt ions ropping mercury electrode in an ammonia buffer solution when dimethylime was added to the solution. Furthermore, the unusually large adsorptive ing current observed for reduction of cobalt in the presence of dimethylglyoxime at hanging mercury drop and mercury thin-film electrodes is now widely utilized for the determination of trace concentrations of this element by the adsorptive stripping voltammetric methods19 [45,46,68]. ecently, two papers have been published [69,70] which suggest that ligand etal-based reduction occurs in an overall ten-electron reduction process cobalt dimethylglyoxime complexes are reduced at mercury electrodes and that it is this feature that gves rise to enhanced currents relative to a twoelectron reduction of cobalt ion to the metal that occurs in most other media. Prior to that, considerable controversy existed concerning the nature of the mechanism associated with reduction of the cobalt dimethylglyoxime complex. ven though a consensus is now being reached [69,70] on many of the details, it is useful to review the wide range of schemes proposed for this very important analvtical mechanism over the Dast fiftv or so vears to illustrate how difficult a task it is to even qualitatively establish the overall reaction process, let alone quantitative details when a series of solution phase and surface processes are esent. For convenience in writing the various reaction schemes, the symbol o(II)(dmgH), will be used to denote the complexes (Fig. 4.30(a)), M = Co(I1) formed by coordination of two deprotonated molecules of dimethylglyoxime dmgH,). Brief mention of the closely related nickel analogue referred to as i(dmgH,), (Fig. 4.30(a), M = Ni(I1)) also will be made. J L J J l7Lidapted with permission from Anal. Chem. 70 (1998) 1312. Copyright, American Chemical Society. 18See footnote 16 where the term polarography or voltammetry at a dropping mercury electrode is defined. 191n the cobalt adsorptive stripping method at the hanging mercury drop electrode, dimethylglyoxime is present in a significant concentration excess over cobalt and a C ~ ( d r n g Hcomplex )~ is formed in the solution phase. At the initial potential adsorption of the cobalt dimethylglyoxime complex then occurs on the electrode surface during the accumulation stage. Finally, the complex is reduced during the stripping component of the experiment. 302 Electrode processes Fig. 4.30 Structural representation of: (a) cobalt and nickel dimethylglyoxime complexes M(drngH)2; (b) cobalt and nickel dimethylglyoximate analogues, M(CsdoH)2, where M is Co(11) or Ni(1I). Many of the various mechanisms involved in explaining the voltammetry associated with the reduction of cobalt in the presence of dimethylglyoxime have been summarized in reference [70]. According to the exclusively adsorptive mechanism favoured at one stage, the reaction scheme may be summarized as follows: c o 2 +(solution) + 2dmgH2(solution) --+[Co(11)(dmgH)2](solution) + 2 ~ + ( s o l u t i o n ) (4.70) [CO(11)(dmgH)2](solution) --+ [CO(11)(dmgH)2] (adsorbed) [Co(II)(dmgH)2](adsorbed) -I- 2e- -k 2 ~ + + Co (0) (metal) (4.71) + [dmgH2](desorbed) (4.72) According to this scheme, when the mercury electrode reaches the required potential, the cobalt dimethylgloxime complex is reduced in the adsorbed state and dmgH2 is released after reduction of the absorbed complex. In other studies, a slightly different mechanism was proposed in which a reactive cobalt(1) intermediate is generated. [C0 (1I)(dmgH)2] (solution) --+ [Co (II) (dmgH)2] (adsorbed) [Co(II)(dmgH)2](adsorbed)+e--?\[Co(I)(dmgH)2]-(ad~~rbed) [Co(I)(dmgH)2]- (adsorbed) f H+ (4.73) (4.74) + e- --+ CO(O)(metal) + [dmgH2](desorbed) 1-(desorbed) (4.75) 303 Stripping voltammetry Compound X (identity unknown) was said to be produced via a chemical decomposition reaction. In other mechanisms proposed, reduction of both the central Co(I1) ion and the ligand [dmgH]- occurs as in eqn (4.76) [Co(II)(dmgH)2](adsorbed) + x e + yH+ --+ Co (0)(metal) + [dmglred (4.76) where: x = (10-18) electrons and [dmglredis the product(s) of reduction of dimethylglyoxime. According to this mechanism, the coordinated ligand may be partially reduced to 2,3-di(hydroxy1amino)butane H ~ c / ~N-OH \ or totally to 2,3-diaminobutane + 8 ~ +' Be- I +yC\ N-OH I + 2H20 H ~ c / ~ ~ L NH2 (4.78) A range of catalytic schemes were also postulated. The cyclic catalytic reduction mechanism may be summarized as follows co2+(solution) + 2dmgH2(solution) --+ [Co(dmgH)2](solution) + 2~+(solution) (4.79) [CO(11)( d ~ x g H )(solution) ~] -+ [CO(11)(dmgH)2](adsorbed) [Co(II) (adsorbed) (4.80) + xe- + YH+(solution) --+ co2+(solution) +2[dmg]red (4.81) If this mechanism is correct, the Co2+ ions released after the reduction rocess should then react with bulk dmgH2 and the coordination-reductioncoordination process proceed in cycles until all of the dmgH2 becomes reduced. The reduction of cobalt as well as nickel dimethylglyoxime complexes was also suggested in a number of studies to involve catalytic hydrogen evolution, 304 Electvodepvocesses according to the following kind of scheme (metal) -I- [dmgH,] (adsorbed) ---+ c o (0) [C o (0) (dmgH)]- (adsorbed) + H+(solution) [CO(0) (dmgH)]- (adsorbed) (4.83) + BH+ (solution) { [CO(0) (dmgH)]- (adsorbed)HC + e -+ H, (gas) where BH' is the source of the donor proton, for example, NH;. As recommended in Chapter 2, establishment of the details of the cobalt (and nickel) dimethylglyoxime reduction process at mercury electrodes requires the use of a wide range of techniques and strategies with spectroscopic characterization of reaction pathways being mandatory. The inherent difficulty associated with establishing mechanisms associated with surface-based processes is illustrated by the discrepancies and controversies surrounding the nature of an electrode process that is widely employed in trace analysis [69,70]. 5.4.1 Voltammetric reduction ofthe cobalt dimethylglyoxime system at mercury electrodes in aqueous media Studies on solutions containing only non-coordinated dimethylglyoxime (added as dmgH,) provide useful reference data for the studies on the reduction of the cobalt dimethylglyoxime complex. D C polarograms of a solution containing 1x M free ligand in an aqueous 0.1 M ammonia buffer medium,,' show one reduction wave with an El/, value of - 1.55 V versus Ag/AgCl when the drop time is 0.6 s. Figure 4.3 1(a) shows a polarogram in 0.1 M ammonia for reduction of dmgH, compared to that of the well-documented two-electron cadmium reduction cd2+(solution) 2e- + Cd(ama1garn) at the same concentration of 1 x M and with all other experimentally controlled parameters being kept constant. From the data it is evident from the ratio of the diffusioncontrolled limiting currents, id(dmgH,)/ id(cd2+),that the number of electrons (n) transferred during the course of reduction of dmgH, is significantly greater than the known value of n = 2 for the cadmium ion, assuming - that the diffusion coefficients (D) of the cadmium ion and dmgH, are similar.21 Cyclic voltammetric experiments at a hanging mercury drop electrode show that the reduction wave of the free ligand is situated on the shoulder of the + 200.1M ammonium chloride/O. 1M ammonia solution. 2 1 ~ hdiffusion-controlled e limiting current, Id, in a DC polarogram is given by the Ilkovic equation, which means Id oc n ~ ' / See ~ . references [46-481 and Section 7.1 in Chapter 2 for details. Stripping voltarnrnetvy 305 M c d 2 + with . 4.31 (a) D C polarogram for the reduction of 1 x lop3 M dmgH2 and 1 x a drop time of 0.6 s. (b) Cyclic voltammograms of 1 x loF3M dmgH2 at a hanging mercury drop electrode with a scan rate of 200 mV s-l, (i) first scan; (ii) second scan. The temperature was 20°C and 0.1 M ammonia buffer was the electrolyte. Adapted from: Anal. Chem. 70 (1998) 1312. rocess giving rise to the aqueous solvent limit (Fig. 4.31 (b)) at the mercury electrode. However, on the reverse scan, a new oxidation wave at about -0.50 V versus Ag/AgCl is observed. This wave is only present after the free ligand has been reduced and therefore represents an oxidation process associated with the generation of a reduced form of the ligand. In the second and subsequent cycles, a new reduction wave is evident at about -0.60 V versus Ag/AgCl as shown in Fig. 4.31 (b(ii)). This reduction process is present only subsequent to the oxidation process at -0.50 V versus Ag/AgCl, and this chemically reversible 306 Electrode processes redox coude is therefore the result of an initial reduction of the free ligand. The reduction'of d m g ~ has , been proposed to lead to the formation (eqn 4.77) of 2,3-di(hydroxylamino)butane (DHAB). If this is correct, the reversible redox couple observed on the second and the subsequent cycles is likely to be the result of the formation of a mercury complex with DHAB at the electrode surface. The following scheme for the voltammetry of dmgH2 at a mercury electrode therefore is proposed: 2DHAB (solution) + Hg(e1ectrode) +Hg (DHAB)2(solution) + 2e- (-0.55 V) (4.87) Importantly, the reversible redox couple observed on second and subsequent cycles can be used as an indicator to determine whether the reduction of the ligand is involved in the reduction process observed in the presence of cobalt (and nickel). Figure 4.32 shows D C polarograms obtained for c o 2 + ions (Fig. 4.32(a)) and then with increasing additions of dmgH2 to the 0.1 M ammonia buffer solution (Figs 4.32(b-d)). The polarographic reduction of co2+in the absence of dmgH2 has a limiting current value which is the result of a diffusion-controlled Fig. 4.32 DC polarograms in 0.1 M ammonia buffer at 2OoC of. (a) 1 x lop3M co2+; (b) with addition of 2 x lo-' M dmgH2; (c) with addition of 5 x lo-' M dmgH2; and (d) with addition of 1 x lop3 M dmgH2. Adapted from: Anal. Chew. 70 (1998) 1312. Copyright, American Chemical Society. Stripping voltammetry 307 3 3 Linear sweep voltammogram at a scan rate of 1000 mV s-' for the reduction of adsorbed Co(dmgH)2 and Ni(dmgH)2 complexes at a 0.24 cm2 hangin mercury drop electrode. Experimental conditions: 4 M NH3/NHrC1 buffer (pH 8.8); 10 pg L-'CO and ~ i ~ 20°C; ' ; 2x MdqH2 ligand; accumulation potential -300 mV versus Ag/AgCl; accumulation time 60 s. Provided by courtesy: R.W. Knight, Deakin University, Victoria, Australia. 5' two-electron reduction to C o ( 0 )(metal) under the conditions of Fig. 4.32. The initial addition of dmgH2 to the solution results in an increase in the limiting current as well as the appearance of a maximum.22With a considerable excess of dmgH2, the limiting current attains a constant value which is about four times greater [70] than the limiting current for the reduction of noncomplexed co2+. This result again indicates that a multi-electron reduction process occurs at negative potentials where the number of electrons partaking in the reduction reaction in the diffusion-controlled region is about eight electrons, assuming equal diffusion coefficients for complexed and non-complexed forms of cobalt(I1). This increase in the polarographic limiting current is similar to at reported by Stromberg almost sixty years ago 1671. Linear sweep voltammograms of solutions containing c o 2 + and ~ i and ~ excess dmgH2 at a hanging mercury drop electrode reveal large peaks attributable to reduction of adsorbed cobalt or nickel complex (Fig. 4.33). The orptive stripping peak currents [72] are linearly proportional to scan rate -1000 mV s-l), which is characteristic ofthe reduction of an adsorbed species ,48,49,72] in the 'thin film' configuration (Section 18 in Chapter 2). The symmetrical shape of the process is also consistent with reduction of a surfaceconfined species (Section 18 in Chapter 2). At more negative potentials, the reduction of the free ligand is encountered due to an excess being present in the solution. Reduction of this excess ligand under conditions of cyclic voltammetry (nickel case only shown in Fig. 4.34) gives rise to the observation of a chemically reversible process on the second cycle as expected when the ligand is reduced (compare Figs 4.31(b) and 4.34). However, even when the switching potential was - 1-20V versus Ag/AgCl, thus eliminating the possibility of reducing the free ligand, the same chemically reversible redox couple is still evident (Fig. 4.34). This redox couple present on second and subsequent cycles results from the formation of reduced dmgH,, and therefore the reduction of 22~olarographic maxima are attributed to differences in interfacial tension around the mercury drop causing solution streaming (see reference [711 for details). + 308 Electrode processes (4 Fig. 4.34 Cyclic voltammograms at a scan rate of 100 mV s-I and 20°C for the Ni(dmgH)2 cornplex generated in situ with excess dimethylglyoxime at a hanging mercury drop electrode in 0.1 M ammonia buffer: (a) first scan and (b) second scan, (c) second scan, but after switching the potential at -1.2 V versus Ag/AgCl. Adapted from: Anal. Chem. 70 (1998) 1312. Copyright, American Chemical Society. the Co (dmgH), and Ni (dmgH), complexes also must involve ligand reduction. Analogous cyclic voltammetric results were observed for both the nickel and cobalt dimethylglyoxime systems. The voltammetric data therefore imply that the electrochemistry of cobalt and nickel complexes in the presence of excess ligand involves strong adsorption at a hanging mercury drop electrode and that reduction of the adsorbed complex in a thin film format and also from bulk solution represents a multi-electron system at both the dropping and hanging mercury drop electrodes. 5.4.2 Bulk electrolysis and coulometn'c experiments i n aqueous media at dropping mercury and mercury pool electrodes For microelectrolysis experiments, a cell was designed which enabled a small volume of the C ~ ( d m g Hsolution )~ (1-2 mL) to be exhaustively reduced over a 10-h period of time with a dropping mercury electrode (DME) having a drop life of 0.5 s [70]. Since the limiting current in D C polarograms was reached over the range from - 1.2 to -1.4 V versus Ag/AgCl (Fig. 4.32), the electrolysis was carried out at constant potential in this region, with stirring provided by a stream of nitrogen or argon gas which also removed oxygen. During the course of electrolysis, D C polarograms were periodically recorded. From the plot ofthe polarographic limiting current versus microelectrolysis time, the charge needed for complete reduction was calculated by extrapolating to the time predicted Stripping voltammetry 309 for completion of the electrolysis. The number of electrons taking part in the reduction process at the DME was subsequently calculated from the derived value of the total charge for exhaustive electrolysis. The determination of the number of the electrons transferred as described gave an n-value of 10.2 k 0.9 for 11 experiments [70]. The value was endent of the ligand concentration when the dmgH, to Co(I1) concentration ratio was in excess of 2 : 1. This independence on the determined number of electrons on the dmgH, excess, provides strong evidence that no cyclic catalytic electrode reaction occurs at the dropping mercury electrode under diffusion-controlled conditions. To confirm the microcoulometric results at a dropping mercury electrode are valid at stationary mercury electrodes, larger scale bulk-CPE (controlled potential electrolysis) experiments were performed at a mercury pool electrode. he results for the exhaustive electrolysis (coulometry) with different ratios of gH2 and Co(I1) are summarized in Table 4.10. The Co(I1) concentration m these experiments was constant at either 3.4 x lop5 or 5 x lop5M while dmgH, concentration varied and it was found that the number of electrons sferred (n) increases with increasing concentration of dmgH,, from the value n % 2 for Co(I1) reduction in the absence of dmgH,, reaching n 10 for mgH, concentrations higher than the stoichiometric 2 : 1 concentration ratio. Table 4.10 The number of electrons (n) determined via coulometry (bulk-CPE at a mercury pool electrode at 20°C) for the Co(dmgH)2 reduction process in 0.1 M ammonia buffer for different concentration ratios of dmgH2 to C0(11)~ - Coniposition of electrolysed solution - Concentration ratio [dmgH,] / [Co(11)] 3.4 x M Co(11) 0 3.4 x ~ O - ~ M C O ( I I ) 1.18 4x M dmgH, 5.0 x MCo(11) 2 1.0 x lop4M dmgH, 2.94 3.4 x loM5M Co(11) M dmgH, 1.0 x 1o - ~ 5.0 x low5M Co(11) 10 ~ d m ~ ~ , 5.0 x M Co(11) 29.41 3.4 x 1.0 x 1o - ~M dmgH, M CO(II) 100 5.0 x 5.0 x lop3 MdmgH, - Calculated number of electrons, n 2.3 5.18 11.6 (1.5) 9.43 10.2 (1.7) 10.39 9.0 (2.3) 'Values in parenthesis are standard deviations from triplicate experiments; data taken from reference [70]. 3 10 Electrode processes These results imply that the reduction of the Co(dmgH)2 complex, whether present in bulk solution or adsorbed onto a mercury surface, still represents a 10-electron reduction process per molecule of Co(dmgH)2 complex. During the reductive electrolysis at a mercury pool electrode, the solution changed from a deep brown colour to clear, indicating complete loss of complex. Very little Co(dmgH)2 could be voltammetrically detected in the colourless solution. Voltammetric monitoring at very negative potentials also revealed that the excess dmgH, is not consumed during the reduction. This result indicates that free Co(I1) ions are not a product of electrolysis as they would immediately react with the excess of dmgH2 in the solution and the brown colour would persist. That is, the overall process does not involve pure ligand reduction of the kind Co (dmgH)2--+ Co (11) reduced ligand giving rise to a cyclic catalytic reduction process as represented in eqns (4.79)-(4.81). Evidence to support reduction to cobalt metal was obtained via analysis of the mercury pool electrode. After exhaustive electrolysis experiments, the mercury pool electrode was dissolved in nitric acid and the resulting solution examined by the cobalt dimethylglyoxime adsorptive stripping method. The expected amount of cobalt was detected after cobalt metal present in or on the mercury surface has oxidized to Co(I1) by nitric acid. A CPE experiment also was performed at the mercury pool electrode on a solution made from a sample of synthesized Co(dmgH)2. Coulometry showed that the number of electrons transferred in the exhaustive reduction process was 9.5 k 0.5 [70]. All coulometric evidence therefore suggests that both the Co(I1) metal centre and the ligand are reduced when C ~ ( d m g His) ~ reduced at a mercury electrode. + 5.4.3 Constant current reductive coulometrlc stripping at mercury thinrfilm electrodes Ma et al., [69] have described a coulometric method for the determination of the number of electrons involved in the reduction of Co(dmgH)2 and Ni(dmgH)2 which is based on the analysis of chronopotentiometric (E - t ) data.23In this method, cobalt and nickel as their dimethylglyoxime complexes are first quantitatively accumulated onto a mercury thin-film electrode as in adsorptive stripping voltammetry, but they are then exhaustively stripped by means of a controlled current rather than by sweeping the potential. The plot of E versus t (Fig. 4.35) or, more usefully in the analytical sense, E versus dt/E (Fig. 4.36 (a)), produces the adsorptive stripping chronopotentiogram in the technique of chronopotentiometric adsorptive stripping analysis. Figure 4.36(b) illustrates the addition of cobalt and nickel standard solutions to dimethylglyoxime when the derivative form of readout is used. Reductive coulometric stripping chronopotentiometry, using adsorptive accumulation of metal complexes, M,L,, (Co(dmgH)2 and Ni(dmgH)2 are 3 detailed ~ description of the techniques of chronopotentiometry and constant current chronopotentiometric stripping analysis is contained in reference [46]. 2 Stripping voltarnrnetr, 311 Time ig. 4.35 Chronopotentiometric (potential-time) curve. t represents the transition time [46] or ts,,p in the coulometric stripping method [69]. Fig. 4.36 (a) Chronopotentiometric stripping analysis showing transformation of E versus t into dt/dE versus E profile; (b) dt/dE versus E form of chronopotentiometric stripping curves obtained after 180 s of accumulation followed by reduction with a constant current of 50pA in 24.8 pL volumes of samples containing 0.10mM dimethylglyoxime (pH 9.2) and to which 0, 1, 2, 4, and ~ (ii)+co2+ have been added. Adapted from Anal. Chem. 69 (1997) 1782. 8 pg L-' (i) ~ i and 3 12 Electrode processes the cases of interest in this book) is based on the quantitative adsorption of the complexes onto a mercury drop or film electrode from very small solution volumes, typically [69] 10-30 pL, samples. Thus the initial stage of the electrode process is MmLp(solution)--+ MmLP(adsorbed) (4.88) After adsorption, the metal complex is reduced by means of an applied constant current, Istrip, according to the reaction scheme in which the metal ion(s), the ligand(s), or both are reduced. From known values for the sample volume, V, the number of electrons involved in the reduction, n, and the time needed for quantitative reduction of the adsorbed complex, tstfiP, the sample concentration of complex CcompIex, can be calculated from Faraday's law as (4.90) Ccomplex = tstrip Istrip / n F v However, any other reducible species present in the sample will also diffuse to the electrode during reduction in quiescent conditions. This, as well as the double-layer current requirements will lead to a fraction of the applied current being consumed by alternative pathways [69]. Denoting this 'chemical current7, ichem, allows eqn (4.90) to be modified to The chemical current, Ichem,which is normally at least one order of magnican be determined by repeating the adsorption/stripping tude smaller than Istrip, process under identical conditions, with the exception that different constant are applied during reductive stripping. By plotting l/tstn, versus values of Istrip I,,,, a straight line is obtained, the intercept on the current axis24being equal to Ichem. Using this value of Ichem,the concentration of the complex in the sample can be determined from eqn (4.91) and, obviously, vice versa, if the sample concentration is known, the number of electrons, n, can be determined. In the experimental studies described in reference [69] exhaustive adsorption of Ni(I1) or Co(I1) complexes, in the 0-4 pg L-I concentration range, was achieved by vibrationally promoted adsorptive accumulation of complex for 3 min at -0.30 V for Ni(dmgH)2 and -0.75 V versus Ag/AgCl for Co (dmgH)z using E25 pL volume samples, hanging in drop form under a 3-mm diameter GC mercury thin-plated working electrode [69] in a nitrogen atmosphere. The adsorbed complexes were reduced by means of a constant current. Additional details of the use of these very small volumes of solution and the enhanced mass 24~amples containing either 1pg L-' Ni(I1) or 1 pg L-' Co(I1)were analysed using constant reductive currents equal to 10, 30, and 50 pA. By plotting the inverse of the stripping times versus the stripping currents, chemical currents equal to 3.1 pA for nickel and 3.4 pA for cobalt were obtained by linear extrapolation. Stripping voltammetry 313 ig. 4.37 Values of tSmp obtained by chronopotentiometric stripping voltammetry after 180s of accumulation followed by reduction with a constant current of 50pA on samples containing 0-400 pg L-' nickel(I1). Reproduced by courtesy: Anal. Chem. 69 (1997) 1782. Copyright, American Chemical Society. transport achieved by vibration of the small volume are available in references [69,73,74]. The coulometric form of analysis requires quantitative adsorption of the complex and a linear relationship between metal complex concentration and stripping signals, or stripping signals and electrolysis time. For a surface-based process of the kind utilized in adsorptive stripping voltammetry, these linear relationship conditions can be expected only at relatively low electrode surface loadings, (typically less than 5 per cent). The required linear relationship is obtained in the 0-4 pg L-' concentration range for both nickel and cobalt (see Fig. 4.37 for the nickel case). By repetitive analysis of samples containing 1, 2, or 4 pg L-' Ni(I1) or Co(I1) the number of electrons, n , involved in the reduction of Ni(dmgH)2 and Co(dmgH)2 could be determined using eqn (4.91). The results are summarized in Table 4.11. The mean n values, 10.1 for Ni(I1) and 9.9 for Co(II), with an estimated standard deviation of 0.2, clearly show that there are 10 electrons involved in the reduction at thin-film electrodes also as deduced above by coulometry and CPE at dropping mercury and mercury pool electrodes. This combination of coulometric studies almost certainly established that an overall 10-electron process involving both metal and ligand reduction occurs in the reduction of Co(dmgH)2 and Ni(dmgH)z complexes at mercury electrodes. Examination of electrolysis products generated by exhaustive electrolysis at a mercury pool electrode Infired spectroscopic study 5.4.4 Examination of products formed after large-scale reductive electrolysis at a mercury pool electrode is difficult with conventional infrared spectroscopic techniques due to the presence of strong absorption from the aqueous solvent. 3 14 Electrode processes Table 4.11 Number of electrons involved in the reduction of Ni(dmgH)2 and C ~ ( d m g H calculated )~ according to eqn (4.91) and use of the technique of coulometric stripping chronopo tentiometrya 'Potentiostatic adsorption from a 24.8 pL sample drop in a nitrogen atmosphere for 180s prior to reductive stripping with a constant current of 50 pA; data taken from reference [69]. b~oncentration. However, it is possible to examine these solutions by Fourier Transform Attenuated Total Reflectance Infra-red (ATR) Spectroscopy using a water insoluble zinc selenide crystal cell for the measurements. In order to obtain any information relevant to the electrolysis products, background subtraction was required. Thus, negative bands are associated with consumption of the starting material and positive bands correspond to formation of new products. The major new bands are located at 1630 cm-' and a group of peaks in the region around 3300 cm-l. These data are now considered with respect to each of the products considered likely to be formed after an eight-electron ligand reduction process. 1. Reduction ofthe carbon-nitrogen double bonds ofthe ligand according to eqn (4.77) A total of four electrons per ligand and a total of eight electrons for the two ligands in the complex are expected according to the interpretation given by eqn (4.77). I R evidence for 2,3-di(hydroxy1amino)butane being a product of electrolysis is provided by the occurrence of new I R bands attributable to N H groups in the 3300 cmwlregion and at about 1630 cm-l. The shape ofthe bands in the 3200-3500 cm-' range suggests that hydrogen intramolecular bands, such as N-H . . - 0or N-H . N may be present in the spectrum. A negative I R peak would be expected for the consumption of the double bond at approximately 1600 cm-l. Unfortunately, this is difficult to detect in the 1R spectrum because it is masked by the large positive peak at about 1630 cm-l, which is assigned to the formation of an NH group as expected according to eqn (4.77). The Stn'pping voltammetry 3 15 negative band located in the 1400 cm-' region may be assigned to the loss of the symmetric C = N stretching band [75]. 2. Reduction of the oxime group on the ligand Equation (4.92) involving of both ligands would give rise to an overall eight-electron ligand-based reduction process. owever, this seems unlikely to be the major pathway because there is no evidence of hydroxyl reduction in the I R spectrum. 3. Complete reduction of only one of the ligands in the complex to form the amine according to eqn (4.78) In the scheme given in eqn (4.78), one ligand (eight electrons) and the metal centre would be completely reduced leaving one unreduced oxime group. However, again no IR evidence to support this proposal was found, since if the oxime groups were to be reduced to amine or imine groups, the decay of their bands appearing above 3000 cm-' would have been expected. The great similarity between the I R spectra of the products resulting from the reduction of Co (dmgH)2(electrolysispotential = - 1.25 V versus Ag/AgCl) and reduction of free dmgH2 ligand (electrolysis potential = - 1.8 V versus Ag/AgCl) provides evidence to support the proposal that the ligand undergoes reduction in the complex, and that in both cases the same product(s) is (are) obtained. After eliminating 2,3-diiminobutane and 2,3-diaminobutane as major products, it can be proposed that 2,3-di(hydroxy1amino)butane is a major roduct of reductive electrolysis of the C ~ ( d m g Hcomplex )~ in ammonia buffer. ss spectromehy study In the mass spectra of both dmgH2 and C ~ ( d m g H )the ~ , parent peak corresonding to dmgH2 ( m / z = 116, % Int = loo), as well as peaks corresponding to fragments of the decomposition of dmgH2 ( m l z = 99, % Int = 69, C 4 H 7 N 2 0m ; / z = 84, % Int = 9, C4H6NO;m / r = 68, % Int = 21, C4H6N; m / z = 58, % Int = 24, C2H4NO; m / z = 42, % Int = 28,CNO) were identified [70]. In the mass spectra of the electrolysis product(s), the five most intensive peaks have the following characteristics: m / z = 87, % Int = 27, C3H7N20; m / z = 85, % Int = 6, C3H5N20; m / z = 73, % Int = 81, C 3 H 7 N 0 or C2H50N2;m / z = 60, %C2H6NO; m / z = 45, % Int = 13, C H 3 N 0 . Thus, they contain in their composition the hydroxylamine (-CH-NHOH) groups. The peak ( m l z = 60, % Int = 100, C2H6NO),which is consistent with half of the 2,3-di(hydroxy1amino)butane molecule, provided the highest intensity in the mass spectrum. The fact that the peak is not observed in the dmgH2 nor in the Co(dmgH)2 mass spectra implies that a major product of 3 16 Electrode processes bulk electrolysis is 2,3-di(hydroxylamino)butane.The absence of a parent peak for 2,3-di(hydroxy1amino)butane ( m / z = 120, C4HI2N202)in the spectrum of the electrolysis product is attributed to the ready and symmetrical splitting of the parent molecule under the conditions of mass spectrometry employed in these studies [70]. It can also be noted that the mass spectrum of the electrolysis product does not fit that expected for other hypothesized products of electrolysis such as 2,3-diaminobutane or oxygen free 2,3-diiminobutane, which might have been formed as a result of eqns (4.78) and (4.92). The results of the mass spectrometric analysis of solid dmgH2, Co(dmgH)2, and the product of electrolysis therefore also supports the conclusion that a major reduction product is 2,3-di(hydroxy1amino)butane. 5-4.5 Detection of one-electron reduced intermediates via electrochemical studies i n aprotic organic solvents The electrode process assigned to reduction of C ~ ( d r n g Hand ) ~ the nickel analogue has been concluded to involve an overall 10-electron reduction process. The role of water and pH is always likely to be significant in complex reaction schemes of this kind, so that studies in aprotic organic solvents may reveal intermediates in the reaction scheme. To overcome solubility problems associated with Co(dmgH)2 and Ni(dmgH)2 in aprotic organic solvents, a dimethylglyoxime analogue was examined in which a six-carbon backbone chain replaced the two methyl groups. The basic structure of the cobalt and nickel complexes of 1,2-cyclooctanedione dioxime is shown in Fig. 4.30(b). These derivatives may be referred to as carbocyclic bis-dioxime complexes25and are abbreviated as C ~ ( c g d o Hand ) ~ Ni(C8doH)2. Co (dmgH)2 The sparing solubility of C ~ ( d m g Hin ) ~dichloromethane allows a comparative electrochemical investigation to be undertaken in this solvent in order to veri@ that it is valid to extrapolate data obtained from the C O ( C ~ ~ Oanalogue. H)~ The initial reduction of the Co(dmgH)2 complex at a hanging mercury drop electrode in dichloromethane (0.1M Bu4NPF6)which occurs at about -2.3 V versus FC/FC+is barely resolved from the solvent limit at 20°C. However, when the temperature is lowered to -50°C, when the mercury electrode is solid rather than liquid, two redox processes having some degree of chemical reversibility are observed (Fig. 4.38(a)), although the second reduction process is not resolved from the solvent limit. At -70°C, both reduction processes are extremely well defined (Fig. 4.38(b)). The reversible EIl2 values are -2.25 V for the first process and -2.40V versus ~ c / F c +for the second process. Similar potentials were obtained when acetone (0.1 MBu4NPF6)was used as the solvent. 2 5 ~ h ecomplexes are actually isolated as their dihydrates C O ( C ~ ~ O H ) ~ and -~H~O N i ( c , d ~ H -)2~H 2 0 , so on dissolution in an organic solvent neither completely anhydrous or aprotic conditons are achieved. The presence of the waters of solvation is neglected in subsequent discussion. Stripping voltammetry . 4.38 Cyclic voltammograms for reduction of 1 x loW3M C ~ ( d m g H in ) ~ dichlorornethane (0.1M Bu4NPF6)at a hanging mercury drop electrode and using a scan rate of 1V s-' at (a) -50°C and (b) -70°C. Adaptedfrom: Anal. Chem. 70 (1998) 1312. Copyright, American Chemical Society. Voltammetric studies of the reduction of Co(dmgH)2 at mercury electrodes in aprotic solvents therefore indicate that two primary one-electron transfers, which could be metal or ligand based, are available: Co (dmgH)2(solution) f e[Co(dm@) 21 - (solution) +e [Co(dmgH)21 - (solution) (4.93) [CO( d m g ~21)2- (solution) vidence for a one-electron reduced nickel dimethylglyoxime complex was also obtained in dichloromethane by cyclic voltammetry and also simultaneous electrochemical-ESR experiments [70]. Consequently, one-electron and two-electron reduced intermediates probably do exist in the overall-electron reduction process. CO(C~~OH)~ The reduction of C O ( C ~ ~ Oin H )dichloromethane, ~ as is the case with C ~ ( d m g H )also ~ , occurs close to the solvent limit and again is only well defined at low temperatures at a solid frozen mercury electrode. In dichloromethane, at a hanging mercury drop electrode at -40°C, two reduction waves are again observed, with the second not being fully resolved from the solvent limit. The reversible Elj2 value for the first reduction process is -2.35 V versus ~ c / F c + which is 100 mV more negative than for reduction of Co(dmgH)2. However, clearly the voltammetry of the two complexes is closely related. An investigation of the effect of water addition on the reduction process was undertaken in acetone 20°C. Unlike the case with dichloromethane, water is very soluble in acetone so the water addition experiments are readily undertaken in this solvent. Voltammograms obtained at a scan rate of 500mVs-' 3 18 Electrode processes M C ~ ( c ~ d o at H a) hanging ~ mercury drop electrode for reduction of 1 x in acetone, in the absence of deliberately added water, and with 2 per cent water added, showed that the peak potential shifts reduction by about 300 m ~ , from -2.45 to -2.15 V versus FC/FC+, and the peak height increases by a factor of three. Furthermore, in the presence of water, a new oxidation peak is generated on the reverse scan (-0.8 V versus FC/FC+ in presence of 1 per cent water) which has an oxidation potential which is dependent on the amount of water added and has similar characteristics to the oxidation peak observed after reduction of dimethylglyoxime in water. Similar results were obtained when a pH 9 ammonia buffer solution was added instead of pure aqueous solvent. The voltammogram for reduction of C O ( C ~ ~ OinHa) 100 ~ per cent water solution containing 0.1 M ammonia buffer at pH 9 exhibits only one large reduction peak and has most of the features observed for reduction of C ~ ( d m g H in ) ~aqueous media. The peak potential for the reduction process is shifted by about 600mV to less negative potentials in changing from pure organic to pure aqueous solvent. Analogous experiments based on addition of 0.2, 0.6, and 1 per cent water to acetone solutions were undertaken under polarographic conditions with a drop time of 0.5 s. With increasing water content, not only was there a shift in the half-wave potential towards less negative potentials (-2.40 to -2.20 V versus FC/FC+ on addition of 1 per cent water) and an increase in the limiting current (50 per cent increase on addition of 1 per cent water), but the formation of a polarographic maximum (see Fig. 4.32) was also observed. Polarograms in acetone with addition of small amounts of added water therefore have most of the characteristics observed for reduction of C ~ ( d m g Hin )~ aqueous media. Clearly water and acid-base reactions play an important role in the reduction of C ~ ( d m g Hand ) ~ presumably they are also critical in reactions with the previously identified one- and two-electron reduced forms of the complex. Conclusions related to the reduction ofcobalt (and nickel) i n the presence of dimethylglyoxime 5.4.6 The results described above, taken from references [69,70] suggest that the electrochemical reduction of cobalt and nickel dimethylglyoxime complexes in aqueous media involves the overall reduction ofboth the central metal atom and the surrounding ligands in an overall 10-electron reduction process. In aprotic solvents, both the cobalt and nickel complexes undergo an initial one-electron probably followed by a second reduction one-electron step. However, in water, electron transfer is coupled with proton transfer giving rise to a stable electrolysis product, 2,3-di(hydroxy1amino)butane. In the case of the cobalt complexes this is evidenced by the number of electrons obtained during coulometric and microcoulometric experiments, identification of electrolysis products by I spectroscopy and mass spectrometry, as well as the voltammetric observation of a reduced ligand-based process after reduction. Apparently, reduction and subsequent disruption of the ligand liberates c o 2 + , which must then lead to Glucose biosensovs 3 19 formation of C o ( 0 ) at the prevailing potential. Hence, during the determination of cobalt by adsorptive stripping voltammetry, the predominant overall process that occurs at the mercury electrode surface is believed to be as follows: c o 2 +(solution) + 2dmgH2(solution)-+ [Co(11)(dmgH)J (solution) + 2 ~ (solution) ' (4.95) o (11)(dm@) (solution) + Hg(1iquid electrode) --+[CO(11)(dmgH)2]Hg(a&orbed) (4.96) + 1 0 e + 1OH' (solution) +CO(Hg)(amalgam or metal) + 2DHAB (solution) [Co(II)(dmgH),]Hg(adsorbed) (4.97) In summary, there is no detailed theory-experiment comparison available with the adsorptive stripping method, unlike the case with anodic stripping voltammetry. It has in fact taken about fifty years of study on the cobalt dimethylglyoxime system to achieve consensus on the nature of the overall rocess. Indeed, even after employment of many modern voltammetric and spectroelectrochemical studies, significant gaps in our knowledge of the details of all steps associated with the mechanism still exist. Again the conclusion is reached that the difficulty involved in establishing the details ofprocesses involving a complex mixture of solution phase and surface-based processes should never be underestimated. Voltammetric techniques frequently do not have adequate resolution for direct application in biologically important fluids such as blood or urine. The problem is that literally hundreds of electroactive species encompassing a wide concentration range may be present, which almost guarantees that overlap of processes will occur within the small 2-3 V potential range available under ideal conditions in aqueous media. However, electrochemical detection of the reactions between an enzyme and its biological partner, whose concentration needs to be known, provides a powerful approach to selective and sensitive determination of some biologically important compounds. The sensors prepared in this manner constitute the electrochemical class of the biosensor field of analysis, and the series of reactions utilized illustrate the need to understand the details of a complex series of reactions that enable these devices to operate. The voltammetric principles are in fact no different from those described above for carbonyl complexes, photovoltaic dye-sensitizers, or stripping voltammetry, with a combination of homogeneous and heterogeneous processes being involved in all of the mechanisms. In 1962, the working principle of an electrochemically based biosensor was demonstrated by Clark and Lyons [76]. In these pioneering studies [77], glucose oxidase (GOD) was fixed to a dialysis membrane which was then placed 320 Electrode processes , over the measuring section of an oxygen electrode. The device constructed ; this manner may be termed a glucose biosensor and its use for the determination of glucose relied on the reaction in eqn (4.98) and measurement of the consumption of oxygen via the oxygen e l e ~ t r o d e . ~ ~ glucose + oxygen +gluconolactone + hydrogen peroxide GOD The diagnosis and effective management of diabetes requires the convenient, rapid, and precise determination of blood glucose. Consequently, the search to fabricate commercially viable glucose biosensors has been the focus of intensive research during the last twenty years [78-811. While the initial protocols for development of electrochemically based glucose biosensors employed eqn (4.98) and measurement of oxygen consumption [75,82] or hydrogen peroxide formation [83], in commonly available hand-held devices, the chemical redox reaction of glucose with oxygen is replaced by the reaction of GOD with so-called electrochemically detectable mediators such as ferrocene and its derivatives [79], ferricyanide [ F ~ ( c N ) ~ ] [84] ~ - or other suitable redox reagents [85,86]. The mediated enzymatic reaction sequence utilized with an oxido-reductase such as GOD which contains a flavin adenine dinucleotide (FAD) coenzyme centre can be represented [78] by the reaction sequence I + Substrate -%Enzyme - FADH2 + Product (4.99) Enzyme - FADHz + 2Med,, ----+ Enzyme - FAD + 2MedXd+ 2 ~ ' Enzyme - FAD I k2 I (4.100) I with the reaction detected at an electrode by a mediator M being associated with the process In the reaction process given by the equation sequence (4.99-4.101), Medred and Med,, represent the reduced and oxidized form of the mediator respectively and the current associated with catalysed process (4.101) is related to the concentration of Medredwhich is in turn proportional to the substrate concentration which is glucose in the case of the glucose biosensor (Fig. 4.39). In terms of the notation given in Section 7.3 in Chapter 2, the reaction sequence, when all chemical species are water soluble, is represented by two chemical ( C )steps (eqns 4.99 and 4.100) having homogeneous rate constants kl and k2 respectively, and an electron-transfer (E) step having a formal potential, E!, a heterogeneous I II I 11 I 8 I 2 6 ~ hoxygen e electrode, often known as the Clark electrode, is another example of an important electrochemically based sensor. The principles of this device are available in most textbooks on analytical chemistry. See for example, D.A. Skoog, E.J. Holler, and T.A. Nieman, Princ@les of Instrumental Analysis, 5th edn, Saunders College Publishing, Philadelphia, 1998. I 1 1I i Glucose biosensors 32 1 Electrode surface . 4.39 Reaction scheme applicable to an electrochemical biosensor which depicts the role of the mediator in the enzyme-catalysed reaction, where E is the enzyme and Med the mediator and the subscripts ox and red represent their oxidized and reduced forms respectively. charge-transfer rate constant k0 and charge-transfer coefficient a. The voltammetric theory associated with this sequence of reactions will be considered ater. Oxygen consumption can be monitored using a Clark oxygen electrode which consists of a platinum working electrode, covered with an oxygenermeable membrane (e.g. Teflon), held at a potential of about -0.8 V versus Ag/AgCl [76]. The current that flows under these conditions is associated with the reaction 0 2 + 4 ~ +' 4e- Pt P 2H20 -0.8 V versus Ag/AgCl (4.102) and the measurement of the reduction current as a function of time monitors the depletion of oxygen. Monitoring of H 2 0 2 generated by eqn (4.98) can be made by poising a platinum electrode at +0.7 V versus Ag/AgC1 [78] and measurement of the oxidation current derived from the reaction H202 Pt f0.7 V versus Ag/AgCl + + 2e- 2 ~ ' O2 (4.103) as a function of time. Figure 4.40 summarizes the principles of the two main classes of electrochemical glucose biosensors which utilize either oxygen as the electron acceptor or an artificial electron acceptor. Numerous biosensors based on O2 consumption or H 2 0 2 generation have been reported. However, a potential difficulty in using oxido-reductase-oxygen reactions is the stoichiometric limitation which arises under circumstances where the oxygen concentration is lower than that of the analyte (e.g. glucose) concentration [78]. The now highly popular mediator-based biosensors eliminate the oxygen dependency and also minimize interferences from ascorbic and uric acid [79-81,84471. Clearly the mediator should react rapidly with the enzyme, exhibit reversible heterogeneous charge-transfer electrode kinetics (large value of k0 in eqn (4.99)) and be stable with respect to pH, temperature, redox state, and 0 2 . 322 Electrode processes + Glucose + Electron acceptor Glucose oxidase '---r-J I Electron acceptor = Oxygen Artificial electron acceptor 1 Electrochemical transducer (i.e. electrode) Fig. 4.40 Schematic representation on the two methods available for development of an electrochemical glucose biosensor utilizing enzymatic oxidation of glucose by GOD. According to the biennial reviews published in Analytical Chemistry, the number ofpapers and patents based on electrochemical methods represent about three-quarters of the total literature on chemical biosensors [88]. Thus, electrochemical biosensors hold a leading position in this area of research activity. In the commercial sense, there are several forms of biosensors used in medicinal chemistry [78,89-971. A remarkable feature of the commercial market is that 85 per cent of biosensor sales are for a single analyte-glucose biosensor [98]. The success ofthis market predominantly can be attributed to the introduction of the ExacTech system27(Fig. 4.41) which is a disposable glucose biosensor produced by a combination of microelectric and screen printing techniques [81,99,100] and which uses a ferrocene-mediated system. In practice, a single drop of blood obtained by a pin prick from a finger is placed onto a sensor (Fig. 4.42) and afier a few seconds the diabetic sufferer has access to their required glucose concentration level. Presently, more than a billion of these disposable single use sensors are mass produced annually so this is a major success story of electroanalytical chemist*. The principles and applications of biosensors have been described in numerous books and reviews (see references [88,101-1111 for example). However, the dominance of the ferrocene-mediated glucose sensor in the market place and the elegance of the chemistry provide a compelling reason for choosing to assess this device in terms of the principles established in Chapter 2. Ferrocene (Fc) voltammetry presented in other parts of this book has been shown to present an almost ideal example of a chemically and electrochemically 27~anufactured by MediSense Inc., Abingdon, England and Cambridge, Mass., USA. 28~dapted in part with permission from H.A.O. Hill and G.S. Sanghera, Biosensovs-A Practical Approach (ed. A.E.G. Cass), Oxford University Press, Oxford, 1990, pp. 19-46. Glucose biosenson -41 The MediSense range of blood glucose electrochemical biosensors. Provided by courtesy of MediSense, Abingdon, England and Cambridge, Mass., USA. 4.42 Measurement of glucose concentration by placement of a drop of blood onto a strip sensing electrode which is coupled to a battery-operated hand-held instrument [81,98]. Provided by courtesy of MediSense, Abingdon, England and Cambridge, Mass., USA. Electrode processes Fig. 4.43 Structure of ferrocene derivatives (FcR) and representation of the ferrocene electrode process employed in ferrocene-mediated glucose electrochemical biosensors. le 4.12 Reversible potential and second-order rate constants for the oxidation of glucose oxidase by the ferricinium derivative of the various ferrocenes as measured at pH 7.0 and 25"Ca " Ferrocene desivative E: (mv) loP5k , , , ( ~ - ' sec-') 1,1'-dimethyl Ferrocene Vinyl Carboxy 1,lr-dicarboxy (Dimethylamino)methyl 100 165 250 289 403 3 86 0.77 0.26 0.30 2.01 0.26 5.26 "Data taken from references [79, 811. b ~ e l a t i vto e a SCE. + + reversible Fc FC+ e- process (e.g. Section 3.2 in Chapter 2). In this sense, it is not surprising that electrochemical investigations using cyclic voltammetry also have shown [79,81,112-1 151 ferrocene, (bis(~5-cyclopentadienyl) iron) to be an excellent mediator for use in electrochemical biosensors. Ferrocene itself [79,81] exhibits a reversible value of 165 mV versus a SCE and with the added advantage that the many derivatives (FcR) are available if fine tuning of properties is required (Fig. 4.43, Table 4.12). In this form of glucose biosensor, the ferrocene mediator replaces dioxygen as the cofactor for GOD (Fig. 4.40). Thus, at a suitable electrode, held at a potential where FcR is oxidized to FCR', the following reaction scheme occurs [79,81] + + 2FcR + 2H' k Glucose + GOD,, ---+ GODred+ gluconolactone GODred 2FcRf k'"' GOD,, (4.105) (4.106) in which catalytic oxidation of the ferrocene derivative occurs to give very large and easily measured currents that are proportional to the glucose concentration. Glucose biosensors 325 The design and response optimization of a ferrocene-based biosensor for glucose escribed in the following section. Optimization of the pe f o formance $ a solution-phase electvochemical glucose biosensor Voltammetric studies on water-soluble forms of ferrocene can be employed to demonstrate the interaction of ferrocene and the GOD-glucose system29. errocene and its derivatives exhibit a reversible one-electron charge-transfer rocess under conditions of cyclic voltammetry. Figure 4.44 shows a typical cyclic voltammogram at a pyrolytic graphite electrode for 0.5 rnM water-soluble ferrocene monocarboxylic acid (FMCA) in the presence of glucose. As required for a diffusion-controlled reversible process (Section 8.1 in Chapter 2), the peak~ / ~(Ipis to-peak separation, AEp is close to 60 mV at 25°C and ~ ~ / is vconstant peak current and v the scan rate) over the scan rate of 1-100 mV s-'. From ot of the peak current values against the square root of scan rate and use of 0.0 0.1 0.2 0.3 0.4 Potential, (V) vs SCE 0.5 Fig. 4.44 (a) Cyclic voltammograms at a scan rate of 1 mV sec-' for oxidation of 0.5 mM FMCA in the presence of 50 rnM glucose; (b) as for (a) with the addition of 10.9 pM GOD. Reproduced by courtesy: Anal. Chern. 56 (1984) 667. Copyright, American Chemical Society. "' he commercially available systems shown in Fig. 4.41 utilize principles related to those described in Section 6.2, but are based on electrode immobilized (rather than solutionsoluble ferrocene) and GOD reagents in contact with both the worhng electrode and the drop of blood to be determined for its glucose concentration (Fig. 4.42). 326 Electrode processes the Randles-Sevzik equation (Section 8.1 in Chapter 2), where [FMCA] is the concentration ofthe ferrocene monocarboxylic acid in the bulk solution and the other symbols are as defined in Section 8.1 in Chapter 2, the diffusion coefficient of FMCA can be determined to be 3 x cm2 sec-I. The change in shape of the voltammogran~upon the addition of 10.9 pM GOD can be clearly seen by examination of Fig. 4.44. Thus, the peaks evident with the reversible voltammetry of FMCA completely disappear on addition of GOD and instead a large catalytic current flows at positive potentials, due to the regeneration of ferrocene according to the equation sequence (4.108)-(4.110) MEd(solution) , e M,, (solution) Ered(solution) + M,, (solution) kcat i E,, (solution) + e- + Mred(solution) (4.108) (4.109) A reversible electron-transfer process, which is followed by a catalytic reaction, as occurs in redox mediation by a mediator M with an enzyme E, such as GOD, can be modelled by a reaction scheme of the kind shown in eqns (4.108) to (4.110). The theoretical treatment of this reaction mechanism has been reviewed extensively by Bartlett et al. [I 151. Under conditions where eqn (4.109) represents the rate-determining step (k fast relative to kc,,), the reaction schemes can be treated as a simple catalytic process represented as in Chapter 2 by the notation where Z is a component which regenerates A. The theoretical analysis for such a system has been provided by Nicholson and Shain [I161 for the case where the concentration of Z > A. From their treatment, different values for k:,,/a, where a = nFv/RT and kLat is the pseudo-first-order rate constant, may be obtained. If kLat/a, termed the kinetic parameter is small, then the cyclic voltammogram will approximate that obtained for a simple reversible electron transfer as depicted in Fig. 4.44(a). Conversely, if kL,/a is large and the reduced A (FcR) species is continually replenished at the electrode, then a limiting or plateau current (him) is observed as in Fig. 4.44(b). Consequently, no reduction peak is observed since the concentration of species B (FCR') in the region close to the electrode surface will be negligible. An analytical solution to the equation describing the process under these pseudo-first-order conditions and assuming equal diffusion Glucose biosensors 327 coefficients, D, for all species is given by where [Ale is the concentration of A in the bulk solution (Section 8.2 in Chapter 2) and Ell2 is the half-wave potential. At very negative potentials where I = him, eqn (4.113) reduces to which means that the limiting current is independent of scan rate for large values of kLat/a. This is the reason why 4i, is referred to as a steady-state limiting current. Alternatively, quantitative kinetic information may be obtained by making use of the working curve provided in reference [I 161 which relates Ic/Idto the kinetic parameter k:,,/a, where Idis the diffusion current calculated as the average of IP/v1l2(constant for a reversible system) and I,, the catalytic current, is calculated from the increase in current upon the addition of enzyme. From a set of Ic/Iddata points, values of k:, /a may be determined for several scan rates. he calculated values of kLa,/a are then replotted against the inverse of scan rate (v-I), for a series of GOD concentrations as depicted in Fig. 4.45(a). From the slope of each curve, a good estimate of k:, for each GOD concentration is obtained. A plot of k:, as a function of GOD concentration will have a slope equal to the second-order homogeneous rate constant (kc,,) for the reaction etween FMCA and GOD (in this example kc,, = 2.01 x lo5M-I sec-l) . This inetic analysis provides an excellent method for choosing a good mediator for a given enzyme system. A range of ferrocene derivatives and the rate of GOD oxidation determined by this method are given in Table 4.12. Obviously, a full simulation of the reaction scheme could be generated and kc,, calculated by comparison of simulated and experimental voltammograms as described in ection 12 in Chapter 2. In glucose electrochemical biosensors, the limiting current value is measured at a constant potential, e.g. 0.5 V versus SCE, based on the FMCA case given in Fig. 4.44. Thus, the sensing is really of the amperometric (current at constant otential) rather than voltammetric kind. In a practical enzyme electrode, where rrocene is immobilized on the electrode surface rather than being present in the solution phase as in the above discussion, other criteria must also be considered. ost importantly, the solubility of the reduced form of the ferrocene derivative must be low in aqueous solutions to aid entrapment within the electrode. In this context 1, 1'-dimethylferrocene is an excellent mediator in terms of rate of oxidation of the enzyme and desirable physical characteristics for immobilization. 1, 1'-dimethylferrocene has an ~ F ~ v a l uofe 100mV versus SCE (Table 4.12) and consequently for amperometric experiments the electrode may be poised at 160mV versus SCE. The enzyme electrode is calibrated over the range 1-30 mM glucose (stirred solutions). Figure 4.45(b) depicts a typical calibration curve with the background current (-- 1.5 PA) subtracted and demonstrates 328 Electvode pvocesres l/(Scan rate mVs-l) 0 5 10 15 20 25 30 35 Glucose (mM) Fig. 4.45 (a) The kinetic parameter, kL,,/a, as a function of the inverse scan rate (mV s-I) for GOD concentrations of ( ID ) 10.9, ( ) 20.6, ( ) 29.3, ( o ) 37.2 pM; (b) calibration curve for the glucose electrode in (*) argon-, (0)air- and (+) dioqgen-saturated buffer. Reproduced by courtesy: Anal. Chem. 56 (1984) 667. Copyright, American Chemical Society. + * that a linear current versus concentration response is obtained in the range of 0-30 mM glucose. Above this concentration range the response is non-linear, becoming insensitive to additional amounts of glucose above 70 rnM. An important application of a glucose biosensor is in the clinical assay of whole blood. In order to confirm that no problem arises from the presence of oxygen dissolved in blood, the performance of the sensor has been tested in air, argon, and oxygen-saturated buffer (Fig. 4.4507)). While there is very little difference between the response in air and under argon, under pure oxygen, there is a significant difference. However, since whole blood contains less than 200 pM dioxygen, this is not a significant problem. Analysis ofbuffered solutions containing 7 rnM glucose and a range of metabolites commonly found in blood shows that only ascorbic acid at 0.13 mM gives any increase in current [811. Glucose biosensors 329 .3 Fabvication of a glucose bioelectvochernical sensor employing glucose ~ x i d a s eimmobilized onto a n electvode suvface hile the details of commercially available glucose biosensors are propriety nowledge, a laboratory bench-based experiment suitable for a student practical exercise or evaluation experiments based on the following enzyme immobilization method has been described in reference [$I]. A brief outline ofthis method rovides the concepts needed to produce a practical sensor. (1) Graphite electrodes onto which GOD can be immobilized are constructed by cutting a 4-mm diameter disc from a rod. The disc is then sealed into a glass tube with epoxy resin, with a connection to the external circuit being made by a wire, bonded with silver araldite, which is attached to the back of the electrode. After electrode pre-conditioning at 100°C for 40 h, and cooling in air, the enzyme, and ferrocene mediator may be immobilized by the following steps. ) Deposit 15 pL of a 0.1 M ferrocene solution (1,1'-dimethylferrocene dissolved in toluene) on to the electrode surface and allow it to air dry. (3) Place the electrode in 1 mL of a 0.15 M solution of l-cyclohexyl-3(2-morpholinoethyl) carbodiimide-p-methyltoluenesulphonate in 0.1 M acetate buffer (pH 4.5) and incubate for $0 min at 20°C. ) Thoroughly rinse the electrode in water and then place it in a stirred 0.1 M acetate pH 4.5 buffer solution containing 12.5 mg m ~ - 'GOD. Incubate at 20°C for 90 min. ) Rinse the electrode with the same acetate buffer, cover it with 0.03 pm polycarbonate membrane (Nucleopore) and store in buffer containing 1 rnM glucose. (6) Prior to use, condition the electrode to give a stable current. This is achieved by maintaining the electrode potential at 160 mV versus SCE for 10 h in a 7 mM glucose solution. 4 Glucose analysis ofwhole blood with a cornrnercially available ucose bioelectvochernical sensor The transformation of the ferrocene-based glucose enzyme electrode from a laboratory bench version to a hand-held commercial device has been achieved in the instrument marketed worldwide as the ExacTech glucose meter (Figs 4.41 and 4.42). The meter, in one form, comprises a pen-sized potentiostat (length 136 mm), weighing less than 30 g, with an LCD display for the glucose reading ig. 4.42). The electrode, disposable test strip, incorporates an immobied layer of GOD and l ,lr-dimethyl-3-(1-hydroxy-2-aminoethyl)ferrocene, ated with a hydrophilic membrane to attract the blood sample (one drop). ch strip also contains its own reference electrode. The ExacTech blood glucose meter kit includes an automatic lancing device and glucose control solutions for testing the meter, in an easy to carry travel case. The test strips are calibrated on the ExacTech system with fresh whole capillary blood and the meter is able 330 Electrodeprocesses to operate between 18°C and 30°C and 20-80 per cent humidity, producing- a glucose reading in mg L-' in 30 s. Assays of blood plasma samples with the enzyme electrode have been compared with results obtained with a Yellow Springs Instrument glucose analyser routinely used in hospitals [81]. The latter device also incorporates the use of GOD but is based on the detection of hydrogen peroxide in pre-diluted plasma. Results for a sample size (n) of 23 gives a correlation coefficient between the two assays of 0.98. 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Smyth, Voltammetric Determination of Molecules of Biological Signijicance, John Wiley, Chichester, 1992. A.P.F. Turner (ed.), Advances in Biosensors, 111, JAI Press, London, 1995. R . Rollema, B. Watering, and B. Drijfhout (ed.), Monitoring Molecules in Neuroscience, Groningen University Centre, Groningen, 1991. J. Wang, Anal. Chem. 65 (1993) 450R. A.E.G. Cass, G. Davis, M.J. Green, and H.A.O. Hill, J . Electroanal. Chem. 190 (1985) 117. J.E. Frew and H.A.O. Hill, Phil. Trans. R. Soc. Lond. 316 (1987) 95. J.E. Frew and H.A.O. Hill, Anal. Chem. 59 (1987) 933. P.N. Bartlett, P. Tebult, and R.G. Whitaker, Prog. React. Kin. 16 (1991) 57. R.S. Nicholson and I. Shain, Anal. Chem. 36 (1964) 706. In Chapter 2, the basic theory describing the voltammetry associated with oxidation or reduction of an ideal thin layer was considered. Unfortunately, such ideally behaved thin films are rarely encountered in practice and cannot even be prepared for many redox active systems. Thus, concepts based on these principles have limited applicability. As an alternative to preparation of film modified electrodes, a general form of attachment of solids to electrode surfaces has arisen from the work of Scholz et al. [I-41. In the common form of this attachment method, the face of a disc electrode is placed in contact with crushed or powdered microparticles and on pressing the electrode against the solid, mechanical transfer of small quantities of material occurs. Other methods of transferring microparticles to electrode surfaces, and which achieve the same end result, have been employed in more recent studies [4]. In this chapter devoted to electrochemical studies of solids, the electrode onto which has been placed an array of microparticles is transferred to a solution (electrolyte) in which the solid is insoluble (sparingly soluble). An attractive feature of this method is that the voltammetry of almost any redox active solid can be studied, irrespective of whether the oxidized or reduced forms of the solid are conducting or nonconducting, or whether 'thin film' or 'thick film', or other forms of adhered solid conditions are achieved in the theoretical sense. Furthermore, and just as importantly in the educational sense, almost all the basic features relevant to all forms of solid-state electrochemistry, including those relevant to the thin film case can be illustrated via a detailed description of a few carefully selected examples of voltammetric studies of redox active solids adhered to electrode surfaces as arrays of microparticles. Under the conditions relevant to studies on microparticles considered in this chapter, the interfaces formed by an individual solid particle present on an electrode surface (as a hemisphere) can be described by the diagram in Fig. 5.1. As revealed by casual inspection of this schematic diagram, an electrochemical solid-state redox reaction, in even its simplest form, represents an inherently complex multiphase problem. However, the processes that must occur are not too difficult to envisage in a conceptual manner. For example, assuming both Introduction 335 Phase 4 Electrode . 5.1 Schematic representation of an example of (a) a three-phase system initially present prior to commencement of electrolysis and (b) a four-phase interface system generated when a (hemispherical) solid particle is oxidized or reduced after being adhered to an electrode surface which is then placed in contact with solution (electrolyte). Phases 1 and 2 are the oxidized and reduced forms of the solid. Phase 3 is the solution (electrolyte). Phase 4 is the electrode surface. the oxidized and reduced forms of a species adhered to an electrode surface are insoluble in the solution (electrolyte) phase, the oxidation process, when neutral species A(so1id) is attached to the electrode surface and oxidized in a one-electron process to [A+][X-] (solid), can often be described by eqn. (5.1) + + [A+][X-] (solid) eA(so1id) f X- (solution) (5.1) X- is the anion from the electrolyte that must be transported across the n-solid interface and then within the solid, as a means of achieving charge neutralization as the electron is transported from the solid to the electrode. n order to understand the processes that occur when A(so1id) is converted to [A'] [x-](solid) at an electrode surface, as for example in eqn. (5.1), many of the spectroscopic techniques used to elucidate features of the solution-phase voltammetry (Section 16 in Chapter 2) will need to be applied in their solid-state relevant formats. Additionally, surface analysis techniques that enable changes in chemical composition of a solid to be detected, X-ray diffraction techniques t allow the phases of A(so1id) and [A+][X-](solid) to be characterized, and situ and ex situ forms of microscopy (electron scanning, atomic force, etc. as scribed in Section 19.1 in Chapter 2) will emerge as important techniques t need to be used to understand the important morphological changes that take place when A(so1id)is converted to [A'] [X-] (solid).Additionally, since mass changes almost invariably accompany a solid-state electrochemical process, the use ofthe EQCM technique (Section 18.2 in Chapter 2) becomes very valuable. A long list of variables have already been identified as being present in the solid-state voltammetry of a process as simple as that given in eqn (5.1). However, to understand the full level of complexity, it needs to be recognized that solids may be attached to electrode surfaces in numerous ways and that it is not always obvious whether the attached solid exists as a thin film, a thick film, an array of microcrystalline or amorphous solid particles, or combinations of these morphologies. Essentially, it must be recognized that the nature of the surfaceattached solid does matter and that even the voltammetry itself may induce a otential dependent change in the nature of the adhered solid. Instead of having a film or an array of microparticles on an electrode surface, a solid-electrode interface also may be established by mixing solid sample with, say, carbon paste and making a composite electrode or by incorporating the redox solid into a conducting polymer electrode system. However, in essence, in all forms of solid-state electrochemistry, a complex interfacial, multi-phase system is inherently always present, irrespective of the format in which the solid is adhered to an electrode surface. Consequently, since the charge and ion-transport processes and morphological changes also are likely to be cornplicated, it is not surprising that the time (scan rate) dependence of solid-state voltammograms is enormously variable, and far more difficult to quantify than when the oxidized and reduced forms of an electrode process are both soluble in the solution phase. It follows from the above discussion that matters to be addressed in electrochemical studies of solid microparticles adhered to an electrode surface, and illustrated in the examples provided in this chapter, must include the following: (1) What is the mechanism of the electron-transfer process? (2) How is the charge neutralization achieved to counterbalance the charge associated with the transport of the electrons? (3) IS the size (thickness, length, width, volume) and morphology of the microparticles important? (4) What is the reversible potential of the process described in eqn (5.1) and how should the activities of species involved in the reaction and the nature of the different phases formed huring the course of a voltammetric experiment be defined? (5) What is the relationship of the voltammetry of an array of microparticles to that of an ideal thin film considered in Section 17 in Chapter 2? (6) What is the relationship to the voltammetry of microp&-ticles to that of redox active centres incorporated into conducting polymers grown onto electrode surfaces and to solids mixed with carbon paste to make modified carbon paste electrodes? (7) Are dissolution processes inherently likely to be associated with the voltammetry of solids attached to electrode surfaces? This point needs to be considered since neither A(so1id) nor [A+][X-](solid) are truly insoluble in the solvent (electrolyte) of interest and it also needs to be noted that during the initial stages, [A+][X-] (solid), generated by oxidation of A(solid), must be present in quantities below the solubility level. In view of their inherent complexity, a fully comprehensive account of the subject of solid-state voltammetry (electrochemistry)is beyond the scope of this Mechanistic aspects of transport processes 337 book. For a more detailed account on the subject of solid-state electrochemistry, the reader is referred to references [4-81. Results obtained for the redox active solid systems presented in this chapter illustrate only the common features that are associated with voltammetric studies of solids. Importantly, the coupling of spectroscopic, microscopic, surface science, and microgravimetric techniques with electrochemical measurements is highlighted to emphasize that voltammetric data alone are even less likely to be adequate to characterize a redox response that occurs at an electrode surface, than is the case when redox active species are solution soluble. A major problem in solid-state studies is that the measured current may only reflect the 'average' of many non-time-resolved events rather than the microscopic details that are required to provide a detailed en arrays of nonorder to introduce the concept of voltammetry of non-conducting croparticles attached to electrode surfaces in contact with solution (electrolyte), the oxidation of decamethylferrocene, ~ e ( q ~ - ~ ~ ~ e ~ ) ~to( s o l i d ) , its cationic, [ ~ e ( q ~ - ~ ~ ~ salt e ~ and ) ~ ]the + , oxidation of tranr- and ~i+Cr(CQ),(dpe)~(solid) and reduction of the tranr-[Cr(CQ)2(dpe)2]X salt e = Ph3PCH2CH2PPh2,X- = anion) are considered as typical examples of this form of solid-state voltammetry. T h e oxidation of decamethylfewocenel As noted in Section 3.2 in Chapter 2, the organic solvent solution-phase ~ Hfor ~ reference ) ~ voltammetry for the oxidation of ferrocene, F ~ ( ~ ~ - isc used ectrode calibration because it represents an example of an almost ideal model of an electrochemically and chemically reversible process. In Section 3.1, the voltammetry of the related decamethylferrocene compound, Fe(q5-C5Me5)2, is shown to represent an ideal process to illustrate many of the principles of the voltammetry of adhered microparticles. 3.1.1 Voltammetry of decamethyljirrocene dissolved in dichloromethane The voltammetry of F e ( q ' - ~ ~ M ewhen ~ ) ~ dissolved in organic solvents corresponds to an essentially reversible one-electron charge-transfer process 19,101. + [ ~ e ( ~ ~ - ~ ~ M e ~ ) ~ ] + ( s+o le-u t i o n )(5.2) ' ~ d a ~ t with e d permission from r. Electroanal. Chem. 372 (1994) 125. Copyright, Elsevier. 5 Fe(q -C5Me5)2(solution) 0.5 E (V) vs Ag/AgCI Fig. 5.2 Cyclic voltammograms obtained at 22°C with a basal-plane pyrolytic y p h i t e electrode at scan rates of 20 (smallest current), 50, 100, and 200 (largest current) mVs- for oxidation of 1 x 1oP3 M decamethylferrocene dissolved in dichloromethane (0.1 M Bu4NPF6).Adapted from: J. Electroanal. Chem. 372 (1994) 125. M decamethylferrocene disA cyclic voltammogram for oxidation of 1x solved in dichloromethane (0.1 M Bu4NPF6)using a basal-plane graphite electrode is shown in Fig. 5.2. The voltammetric response is chemically reversible and corresponds to a reversible one-electron diffusion-controlled process. Ideally, the cyclic voltammetric peak potentials for both oxidation and reduction for a reversible process should be independent of scan rate (Chapter 2), and the slight dependence of peak potentials on scan rate observed in Fig. 5.2 is attributable to a small amount of uncompensated resistance (Section 6 in Chapter 2). General considerations related to the voltammetry of microcrystals of decamethyljifewocene attached to a n electrode surface 3.1-2 Since decamethylferrocene is insoluble and does not react with water, the voltammetry of this compound when attached to an electrode surface in contact with aqueous (electrolyte) media, could be expected to provide a simple system to explore some of the factors that govern the charge-transport process and the incorporation of electrolyte anion (X-) when water insoluble [ F ~ ( $ - c ~ M ~[XI ~ )(solid) ~ ] is formed via the process described in eqn (5.3). A major difficulty that normally arises in voltammetric studies of surfaceconfined non-conducting solids like decamethylferrocene is associated with the large IRu (ohmic) drop and the associated large value of the R,C time constant (R, = uncompensated resistance, C = capacitance), which makes it difficult to couple electron transfer and ion transport in a sufficiently fast manner to achieve measurable currents within the available potential range. However, when the solid is attached to the electrode as an array of microparticles, a relatively large surface area of sample is exposed to the electrolyte solution at the Mechanisticaspectsoftransportprocesses 339 electrode-solution interface. This solid-electrode-solvent (electrolyte)interface generated during a voltarnrnetric experiment (Fig. 5.1) plays an important role in achieving well-defined voltammograms with non-conducting solid compounds by minimizing the IR, drop and time constant, allowing rapid coupling of electron and ion-transport processes within the solid and allowing rapid transport of ions across the solid-solvent (electrolyte) boundary. 3.1.3 Method of attachment of decamethyyeferrocene to the electrode suface working electrode used to describe the solid-state voltammetry of methylferrocene at aqueous (electrolyte)interfaces in this chapter was made from basal-plane pyrolytic graphite (5-mm diameter). In order to transfer solid to the surface of the carbon electrode, 1-3 mg amounts of crystalline decamethylferrocene complex were placed on a filter paper. After grinding the sample to microcrystalline size using the flat side of a spatula, the carbon electrode was pressed onto and rubbed over the crushed decamethylferrocene, thereby causing some of the compound to adhere to the electrode surface as an array of microcrystalline particles. For electrochemical measurements, the electrode was transferred into a conventional electrochemical cell which contained the aqueous (electrolyte) solution of interest. The electrode surface was renewed after each measurement by dipping into dichloromethane and allowing the comund to dissolve in the organic solvent or alternatively, a clean surface was tained by cutting the soft graphite electrode surface with a razor blade. 3.1.4 Generalfeatures of the voltammetry of solid decamethyyefenocene attached to a graphite electrode which is placed i n contact with aqueous electrolyte A voltammogram for the oxidation of solid microcrystalline decamethylferrocene attached to a basal-plane graphite electrode and then subsequently immersed in aqueous 0.1 M NaC104 electrolyte solution is shown in Fig. 5.3 as a function of scan rate.2 The symmetrical responses are clearly different in shape to those obtained in solution-phase voltammetry (Fig. 5.2). The areas under reduction and oxidation signals are similar and for the voltammograms shown in Fig. 5.3 the charge corresponds to 96 pC at a scan rate of 10 mV s-'. Scanning electron microscopy (SEM) data reveals the presence of microcrystalline material on the surface with a particle size range for the majority of particles eing 0.3-2 pm (Fig. 5.4). Using a very crude estimate of the electrode surface coverage of approximately 1 per cent for 1 pm particles (200 ng decamethylferrocene over the 0.5 cm electrode diameter), the magnitude of the current for exhaustive electrolysis should produce about 60 pC of charge. This calculation suggests that the compound is significantly electrolysed during the course of the slow scan rate voltammetric experiment. However, the appearance of the microcrystalline compound after oxidation, as established by SEM, reveals no 'under some circumstances, particularly at very high scan rates or with very high surface coverage, peak splitting, and additional processes may be detected. This more complex situation is only briefly considered in this book. The interested reader should consult references [I 1,121 for a more detailed discussion of these phenomena. E (v)'vs Ag/AgCl E (V) vs Ag/AgC1 Fig. 5.3 Cyclic voltammograms obtained at 22'C with scan rates of 10, 20, 50, and 100 mV s-I for oxidation of microcrystalline decamethylferrocene attached to a basal-plane pyrolytic graphite electrode placed in contact with aqueous 0.1 M NaCIOi electrolyte. Adapted from: J. Electroanal. Chem. 372 (1994) 125. Fig. 5.4 Scanning electron micrograph of microcrystalline decamethylferrocene attached to a basal-plane pyrolytic graphite electrode. Reproduced by courtesy: J. Electroanal. Chem. 372 (1994) 125. Copyright, Elsevier. dramatic changes in the number of particles and their sizes. In contrast, it will emerge in other systems considered later in this chapter, that significant changes in particle shapes and sizes may occur, and in other cases only a small fractions of the solid are oxidized or reduced during the course of a voltammetric experiment. Varying the scan rate in NaC104 electrolyte leads to a marked change in both peak width and peak separation. At higher scan rates, the signals broaden Mechanistic aspects of transport processes 34 1 5.1 Cyclic voltammetric data obtained as a function of scan rate at 22°C fir oxidation of microcrystalline decarnethylferrocene attached to a basal-plane py~olyticgraphite electrode which is in contact with aqueous (0.1 M NaC104) electr~l~te"~~ 7 Scan rate (mV s-l) EpO" (mVc) I3rd(mVc) AEp (mV) WP;2 (mV) W$ (rnv) -- a l l a h taken from J. Electroanal. Chern. 372 (1994) 125. h ~ , " " represents the oxidation peak potential; E F ~the , reduction peak potential; AEP = E r - Ered; P W G , the peak width at half-height for the oxidation process; w$, the peak width at half-height for the reduction process. ?nmV versus Ag/AgCl. considerably (Fig. 5.3, Table 5.1). At a scan rate of 10 mV s-l, the peak width at half-height of about 30mV is clearly much lower than the value of about 90 mV predicted for the ideal thin film case (Section 18 in Chapter 2). The agnitude of peak currents decreases slightly after the first cycle. However, the rocess remains visible over prolonged periods of cycling of the potential. Voltammograms obtained with a rotating disc electrode in the presence of 0.1 M NaC104 electrolyte (Fig. 5.5) show the same general characteristics as with a stationary electrode, although the small change in wave shape of the reduction process and decrease of the current with repetitive cycling suggest that minor loss of material may be occurring into the solution phase by product dissol~tion.~ Comparison of results at stationary and rotated electrodes leads to the conclusion that the influence of mass transport as a rate-determining step is confined predominantly to the solid phase or the solid-solvent (electrolyte) interface. 3.1.5 Analysis of composition o f solid before and after oxidative electrolysis lectron probe analyses of samples of adhered decamethylferrocene electrolysed in the presence of 0.1 M KC104 electrolyte at different potentials enables the 3~oltamrnograms obtained with 0.1 M KPF6 as the electrolyte show no wave shape change and no loss of oxidation or reduction current within experimental error irrespective of whether the electrode is rotated or stationary. The almost indefinitely stable response leads to the conclusion that no loss of oxidized or reduced decamethylferrocene compound occurs by dissolution into aqueous 0.1 M KPF6 electrolyte. E (V) vs Ag/AgCl Fig. 5.5 Voltammetry (three consecutive potential cycles) at 22O C of microcrystalline decamethylferrocene adhered to a rotated basal-plane pyrolytic graphite electrode placed in contact with aqueous 0.1 M NaC104 electrolyte. Scan rate = 100 mV s-' . Rotation rate = 1000 rpm. Adapted from: J . Electroanal. Chem. 372 (1994) 125. change in elemental composition of the solid to be m ~ n i t o r e d Prior . ~ to electrolysis, the carbon background is clean with respect to both iron, chlorine, and potassium (Fig. 5.6(a)). In the case of decamethylferrocene attached to a basalplane graphite disc electrode, oxidation for 2 min at 500 mV versus Ag/AgCl in the presence of 0.1 M KC104 as the electrolyte leads to the smaller particles on the electrode surface having close to a 1 : 1 iron to chlorine composition (Fig. 5.6(b)), as required for formation of [ ~ e ( q ~ - ~ ~[C104] M e ~(solid). ) ~ ]This suggests that surface oxidation occurs with uptake of one perchlorate anion for each electron transferred. Larger particles in the order of 10 prn show a reduced chlorine signal implying that oxidation is favoured at the surface or edge of the crystals and that unoxidized material remains at the centre of the larger crystals on the time-scale of this experiment. A sample oxidized first at +500 mV and then reduced at -500 rnV versus Ag/AgCl shows only iron to be present (Fig. 5.6(c))as expected when [ ~ e ( q ~ - ~ ~(solid) M eis~reformed ) ~ ] after expulsion of C l o y incorporated during the initial oxidation step. The use of a wide range of electrolytes in the aqueous solution phase was found to produce drastic changes in the voltammetric behaviour which, as might be expected if eqn (5.3) is correct, are almost exclusively anion related. Figure 5.7 shows the voltammetry of decamethylferrocene when the electrode to which it is attached is placed in contact with HC104, NaC104, and KC104 electrolyte solution. No major change is found when C l o y remains as the anion and only "he NaC104 electrolyte was replaced by KC104 in these experiments because of the easier detection of potassium, instead of sodium, by the electron probe analysis technique. In principle, K+ cations could become incorporated into the solid during the course of potential cycling experiments so the failure to detect the element potassium eliminates this possible mechanism. Mechanistic aspects of transport processes 343 . 5.6 Electron probe X-ray microanalysis of decamethylferrocene attached to a basal-plane pyrolytic graphite electrode placed in contact with aqueous 0.1 M KC104 electrolyte. (a) Electrode background; (b) after oxidative electrolysis at +500 mV; (c) after oxidative electrolysis at +500 mV and then reductive electrolysis at -500 mV versus Ag/AgCl. Reproduced by courtesy: J. Electroanal. Chern. 372 (1994) 125. Copyright, Elsevier. the cation is varied. Thus, changes in the cation are concluded to be of minor importance. In Fig. 5.8, voltammograms obtained in different electrolyte media are comared when the electrolyte anions are varied. A very wide range of potentials observed as the identity of the anion is changed. Other differences are so present. The distinctively different voltammetric data obtained when the drophobic tetraphenylborate anion (BPhJ (Fig. 5.8 (a)) and the carboborane anion ([CB1I Hlz]-) (Fig. 5.8(b)) relative to hydrophilic PF, (Fig. 5.8(c)) and C l o y (Fig. 5.8(d)) support the concept that hydrophobicity is important, although the size ofthe anion also may be relevant. With BPh, and [CBIIHl2]the current magnitude decreases relative to the C104 case and there is a negative shift in potential of more than 400mV. In perchlorate electrolyte, both oxidation and reduction peak potentials have their most positive values. The relationship of the voltammetry in C10, media to that observed in the presence of the slightly more hydrophobic anion PF, is interesting. The oxidation process shows a similar symmetrical response at low scan rates in both cases, whereas the reduction process in PF, electrolyte is broader and less symmetric (compare Fig. 5.8(c) and (d)). When fluoride (Fig. 5.8(e)) or chloride (Fig. 5.8(f)) are present in the electrolyte, the response rapidly decreases in current magnitude and almost disappears after 10-20 cycles indicating dissolution of oxidized product. Peak splitting is sometimes observed under higher coverage conditions than those used to obtain the voltammogram shown in Fig. 5.7. Hence, in 344 Solid-electvode-solvent intefaces NaC104 (a) -0 E (V) vs Ag/AgCl Fig. 5.7 Cyclic voltammograms obtained at 22°C and with a scan rate of 100 mV s-' for microcrystalline decamethylferrocene attached to a basal-plane pyrolytic graphite electrode and then placed in contact with aqueous media containing (a) 0.1 M NaC104, (b) 0.1 M KC1O4, and (c) 0.1 M HC104 electrolyte. Adapted from: J. Electroanal. Chem. 372 (1994) 125. NaClO E (V) vs Ag/AgCl E (V) vs Ag/AgCl Fig. 5.8 Cyclic voltammograms obtained at 22°C and with a scan rate of 100 mV s-' (except for (f) at 200 mV s-') for microcrystalline decamethylferrocene attached to a basal-plane pyrolytic graphite electrode and placed in contact with aqueous (0.1M) electrolyte (a) NaBPh4, (b) CsCBl1Hl2, (c) KPF6, (d) NaC104, (e) NaF, and (f) NaC1. Adapted from: J. Electroanal. Chem. 372 (1994) 125. Mechanisticaspectsoftransportprocesses 345 E (V) vs Ag/AgCl . 5.9 Cyclic voltammograms obtained at a scan rate of 10 mV s-' for oxidation ofmicrocrystallir~e decamethylferrocene attached mechanically to a basal-plane pyrolytic graphite electrode and placed in contact with aqueous 0.1 M KPF6 electrolyte at temperatures of (a) 22" C, (b) 52" C, and (c) 82" C. Adapted from: J. Electroanal. Chem. 372 (1994) 125. summary, the identity of the anions as well as particle size, electrode coverage, and scan rate all clearly influence the voltammetry. 3.1.7 Efect of temperature th a kinetically controlled process, the rate usually increases with temature. The voltammetric response of decamethylferrocene attached to a basal-plane graphite electrode immersed in 0.1 M aqueous KPF6 electrolyte Is (Fig. 5.9) that a step of 30°C to higher temperature results in an ximately three-fold increase of peak current. The current increase with temperature is much more pronounced than in solution-phase voltammetry and comparable to data reported in electrochemical studies with polymer films [13]. Electrochemistry of microparticles of r a n ~ - C r ( C O ) ~ ( d p ter) a~ n, ~ - [ C r ( C O ) ~ ( d p[XI e ) ~salts, ] and C ~ ( C o ) ~ ( d p (dpe e ) ~= , bidentate P h 2 P C H 2 CH2PPh2, X - = anion) attached to a n electvode surface5 th trans- and ~ i s - C r ( C O ) ~ ( d p esolids ) ~ are non-conducting and insolue in water, so that studies analogous to those on decamethylferrocene possible. However, significant additional information is available with t r a n s - [ ~ r ( ~ ~ ) ~ ( d ~reaction e ) ~ ] ~ /via + use of the EQCM and other methods [I 2,141, while structural changes accompanying oxidation of solid ~ i s - C r ( C O ) ~ ( d pto e ) ~the trans-[Cr(C0)2(dpe)2][X] salt can be probed by a combination of voltammetry and specular reflectance IR spectroscopy [15]. ' ~ d a ~ t ewith d permission from J. Amer. Chem. Soc. 115 (1993) 9556; Organometallics,13 (1994) 5 122; J.Electvoanal. Chem. 404 (1996) 227. Copyright,American Chemical Society and Elsevier. 346 Solid-electrode-solvent intefaces Fig. 5 -10 Structural representation of (a) cis- and (b) trans-Cr(CO)z ( d ~ e ) ~ . 3.2.1 Structural aspects and solution-phase voltammetry Cr(CO)2(dpe)2,unlike decamethylferrocene, has cis and trans isomeric structural forms (Fig. 5.10). After chemical or electrochemical oxidation, a wide range of stable trans-[C~-(Co)~(dpe)~] [XI (X- = anion) salts may be isolated, but the cis analogue of the oxidized form is unknown as a solid. Each and trans-[Cr(C0)2(dpe)2][X] are soluble in of cis- and tran~-Cr(CO)~(dpe)~ non-polar organic solvents and the organic solution-phase voltammetry of this chromium carbonyl system has been studied in considerable detail [16-181. If t r a n s - [ ~ r ( ~ ~ ) ~ ( d pise present ) ~ ] + in bulk solution, then the one-electron reversible reduction process + e- +trans-Cr(C0)2(d~e)~(solution) ($91 trans-[~r( ~ (dpe)2]' 0 ) ~(solution) (5.4) is observed. As expected, if tran~-Cr(CO)~(dpe)~ is in bulk solution, then the reverse of eqn (5.4) occurs: 1 tran~-Cr(C0)~(dpe)~(solutiotl) , &t r a n s - [ C r ( ~(dpe)2]+ ~ ) ~ (solution) + e(5.5) However, if ~ i s - - C r ( C O ) ~ ( d is p ein) ~bulk solution, the more complex reaction scheme given in eqn (5.6) is operative on the voltammetric time-scale. +c i s - [ ~ r ( ~ ~ ) ~ ( d ~ e ) ~ ] ~ ( s+o le-u t i o n ) ( ~ 3 2 cis-Cr(CO)2(dpe)2(solution) J, fast (q') 1 + trans-Cr(C0j2(dpe)2(solution) Ff trans-[~r( ~ (dpe)2]+(sol~ti~n) 0 ) ~ e(5.6) 3.2.2 Voltammetry of solid trans- Cr(CO)z(dpe)z attached to a graphite electrode Since many aspects of the solid-state t r a n s - [ ~ r ( ~ ~ ) ~ ( d p e )process ~]~"[12,14,15] are closely related to those of the [ F ~ ( ~ I ~ - C ~ M ~couple ~)]O/' [I 11, only facets of the voltammetry of solid trans-Cr(C0)2 (dpe)z and Mechanistic aspects of transport processes 347 t~ans-[Cr(CO), (dpe)2][XI adhered to a graphite electrode that require amplification or have not been featured in Section 3.1 need to be presented in any detail. Electrolyte concentration dependence ~oltatnmo~ram obtained s with rnicroparticles of trans-Cr-(C0)2(dpe)2attached to a basal-plane graphite electrode and placed in aqueous NaCl solution at 30°C are shown as a function of electrolyte concentration over the range of 0.1-3.5 M in Fig. 5.11. This series of experiments leads to the conclusion that the anion concentration, while not strongly influencing the current magnitude, does have a small influence on the peak potentials, which approximates a Nernstian shift of 2.303RTIF volt per decade change in concentration. If the value of (E,"" ~ ; ~ ) /is2 assumed to be the reversible potential, then this result is as ected6 for an equation of the kind given in eqn (5.7, assuming the activity + E (V) vs Ag/AgCl E (V) vs Ag/AgCl 5.11 Cyclic voltammograms obtained at 30° C and with a scan rate of 200 mV s-' for oxidation of trans-Cr(CO)z(dpe)z adhered to a basal-plane pyrolytic graphite electrode and then placed in contact with (a) 0.1 M, (b) 0.3 M, (c) 1.0 M, and (d) 3.5 M aqueous NaCl electrolyte. Reproduced by courtesy: Organometallics 13 (1994) 5 122. Copyright, American Chemical Society. Nernstian form of dependence of potential on electrolyte concentration has been detected with a range of solid-state systems, but exceptions to this result are also commonly observed, so that even the thermodynamics of the processes are not always well established 141. 6~ Table 5.2 Cyclic voltammetric dataa obtained at 50°C for oxidation of microcrystalline trans-Cr(CO)z(dpe) adhered to a basal pyrolytic graphite electrode placed in contact with aqueous (electrolyte) media as a function of electrolyte anion. OHF- sotc1BrNO, IClO, ~ 1 0 , ~ ~r~ "Data taken from Organornetalliis 13 (1994) 5122. Symbols E r and with units of mV versus Ag/AgCl, and AEp are as defined in Table 5.1. Ep values are obtained by extrapolation to zero current of data obtained at low scan rates. b ~ h aqueous e electrolytes used were 0.1 M NaOH, NaF, NaC1, KBr, KI, Na2S04,NaN03, and NaC104. ' A G p = Gibbs energy of partition of anions for a water-1,2-dichloroethane interface [191. 20 cycles by oxidation of cis-Cr(CO)z(dpe)a. d ~ e n e r a t e after d of the solids is unity, which of course need not be the case (see later). trans-Cr(C0)2( d ~ e(solid) )~ - A + C1- (solution) trans-[Cr (C0)z( d ~ e )[Cl] ~ ](solid) + e- (5-7) Electrolyte anion and cation dependence The oxidation of solid trans-Cr(CO)z(dpe)2as a function of different electrolyte anions has been studied in detail at 50°C by cyclic voltammetry at a range of scan rates [12]. Under these conditions, changing the anion from perchlorate to hydroxide produces a potential shift7 of almost 500 mV (Table 5.2). A large 7 ~20-30°C, t as used for most studies, currents are difficult to detect above the background value with some electrolytes. At 50°C used for these comparative studies, voltammetric responses are always very well defined. An additional process also may be detected at elevated temperature, at high surface coverages and fast scan rates. When peak splitting occurs, or more than one process is detected, the peak potentials cited correspond to the dominant signal pair. The influence of different electrode coverage and particle sizes in these anion and cation dependence studies was addressed by extrapolation of peak potential data obtained as a function of scan rate to zero current and using these zero current potentials as the basis of comparison [15]. Mechanistic aspects oftransport processes 349 electrolyte anion effect was also observed for oxidation of decamethylferrocene. The comparison ofpeak potentials with the Gibbs energies for partition of anions [I 91 at a 1,2-dichloromethane-waterinterface (Table 5.2), suggests that the free energy of transfer of the particular anion from solution into the solid phase is an ortant term in determining the peak potential. The influence of cations on ~otentialof voltammetric response for oxidation of microparticles of solid t~ans-Cr(CO)~(dpe)~ attached to graphite electrodes, as was the case with the decamethylferrocene system, was not significant [12]. Electvochemical quartz cryrtal microbalance studies The EQCM technique has been highly useful in the investigation of surlacebased electrode processes associated, for example, with monolayers [20], multilayer deposition and dissolution [21], mass transport in polymer films [22], corrosion processes [23], and electroless deposition and mass changes caused by adsorption [24] (see Section 19 in Chapter 2 for details). Not sur~]+'~ prisingly, important mechanistic aspects of the t v a n ~ - [ C r ( C O ) ~ ( d ~ e )redox reaction related to the charge neutralization process also can be probed conveniently via studies of the oxidation of tran~-Cr(CO)~(dpe)~ and reduction of t~ans-[Cr(CO)~(dpe)~] [XI microparticles attached to a gold Q C electrode and use of the EQCM method [12]. icrocrystalline tran~-Cr(CO)~(dpe)~ was attached to the Q C electrode by ng a cotton bud containing a small amount of the solid onto the gold electrode. The trans-[Cr(C0)2(dpe)2][X] salts were not mechanically ached to the gold Q C in this manner because of a tendency of the gold er to be scratched from the Q C during the rubbing process. Thus, the tvan~-[Cr(CO)~(dpe)~] [XI salts were attached to the electrode by dissolving the solid in acetone and then placing a drop of this solution onto the electrode. Arrays of microcrystalline deposits of trans- [Cr (C0)2(dpe)2][XI were formed gold electrode after the solvent was evaporated. n order to obtain well-defined voltammograms, an adequate coverage rocrystalline particles must be achieved. A scanning electron microobtained for solid t~ans-Cr(CO)~(dpe)~ attached to a gold Q C electrode ns crystalline particles of approximately 20 pm in length (Fig. 5.12). ough trans-[Cr(CO)2(dpe)2][Cl] attached to a gold Q C produced microtals which, on average, had a smaller surface area relative to those for attached tral compound (compare Fig. 5.12(a) and (b)),particles were detected with lengths ranging from 0.1 to 20 pm. CM studies ofsolid tran~-Cr(CO)~(dpe)~ attached to a gold electrode igure 5.13(a) shows a cyclic voltarnrnogram obtained at a scan rate of 50 mV s-' for the oxidation of microcrystalline particles of t~ans-Cr(CO)~(dpe)~ mechanically attached to a gold Q C electrode over a potential range of -800-600 mV versus Ag/AgCl in 0.1 M KC1 electrolyte. A well-defined process was observed which will be shown to correspond to the general process given in eqn (5.8), Fig. 5.12 Scanning electron micrographs of (a) tran~-Cr(CO)~(dpe)~and (b) trans-[Cr(CO)z(dpe)2]Cl attached to a gold QC. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 227. Copyright, Elsevier. but where X - , the electrolyte anion, is Cltrans-Cr (CO), (dpe), (solid)+X- (solution) Figure 5.13(b) shows the relative mass change that accompanies the oxidation and reduction processes at the gold-coated Q C electrode as a function of potential. The mass change data indicate that the oxidation of solid tran~-Cr(CO)~(dpe)~ is accompanied by an increase in mass which is consistent with incorporation of chloride ions from the 0.1 M KC1 electrolyte. However, the mass continues to increase even on the reverse scan of the cyclic voltammogram, until the potential is reached where solid trans-[Cr ( C 0 ) 2(dpe)z]Cl (formed via oxidation in the first half-cycle) is reduced. Thus, oxidation of microcrystalline trans-Cr(CO), (dpe)? in 0.1 M KC1 solution, which requires incorporation of C1- into the lattice, is found to be a very slow process. In Mechanistic aspects of tvanspovt processes -800 -600 -400 -200 0 200 Potential (mV) vs Ag/AgCl 400 35 1 600 Potential (mV) vs Ag/AgCl -13 (a) Cyclic voltammogram (scan rate 50 rnV s-') and (b) the corresponding mass change diagram for oxidation of microcrystalline particles of t r a n ~ - C r ( C O ) ~ ( d p eattached )~ to a gold Q C which has been placed in contact with aqueous 0.1 MKC1 electrolyte. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 227. Copyright, Elsevier. contrast, the expulsion of chloride ions, which accompanies the reduction rocess on the reverse scan of a cyclic voltammogram, is associated with both a sharp peak and a rapid decrease in mass. The EQCM diagrams therefore imply that the rate-determining step in the oxidation of solid t~ans-Cr(CO)~(dpe)~ in contact with 0.1 M KC1 electrolyte is the very slow reaction involving incorporation of anion into the solid. This explains why the oxidation peak current is relatively small and the oxidation current fails to decay to zero on the time-scale of the cyclic voltammetric measurements. Figure 5.13(b) also shows that an overall increase in mass is evident after completion of each potential cycle involving the oxidation of trans-Cr(CO)2(dpe)2 and then its reformation by reduction. This result implies that some chloride ions inserted via oxidation remain inside the solid on this time-scale even after the reductive electrochemical treatment. Presumably, the reverse reductive scan leads to rapid expulsion only of those chloride ions that are incorporated at or 352 Solid-electrode-solvent intefaces Table 5.3 Theoretical and experimentally determined molar masses (M) obtained from EQCM experiments when solid tran~-Cr(CO)~(dpe)~ is adhered to a gold electrode which is placed in contact with different electrolytesa Electrolyte (0.1 M) Experimental (M/g mol-') heo ore tical ( M / mol-')c ~ aData taken from J. Electroanal. Chew. 404 (1996) 227; scan rate = 50 mVsC1. b ~ r r oisr standard deviation (10 experiments using three different gold QC electrodes). Calculations are based on the reduction process observed during the reverse scan of cyclic voltammograms. Talues are calculated assuming that only the non-solvated electrolyte anion is associated with the charge neutralization process. near the surface of the solid on the time-scale of cyclic voltammetric experiments. With continuous cycling of the potential, the mass changes associated with oxidation and reduction processes become constant. Quantitative analysis of the microbalance data in terms of charge and mass change relationships enables the molar mass of the anion expelled from the solid to be calculated. Since it is very difficult to calculate accurately the mass change from the oxidation reaction, because the process occurs over a wide potential range, all molar mass data have been calculated from the better defined and sharper reduction process. Table 5.3 contains the experimental and theoretical molar masses of the species being expelled from trans- [Cr (CO)z( d ~ e )[XI ~ ](solid) formed by oxidation of trans-Cr(CO)2(dpe)2(~olid) when the electrode is in contact with a variety of electrolytes. Clearly, the species being expelled in all experiments corresponds to the electrolyte anion. Electron microprobe X-ray analysis experiments analogous to those shown in Fig. 5.6 for decamethylferrocene also support the hypothesis that the oxidation of tran~-Cr(CO)~(dpe)~ involves the uptake of the anion from electrolyte solution, and the expulsion of the anion during reduction. Figure 5.14 shows the result of a double-potential step experiment in which (dpe)2 attached to a gold electrode microcrystalline particles of tran~-Cr(CO)~ were alternatively oxidized and then reduced in the presence of 0.1 M KC1 solution. The potential was initially held at -600 mV versus Ag/AgCl. After 1000 s, the potential was stepped from -600 to 0 mV (Fig. 5.14(a)),and this resulted in to trans-[Cr(C0)2 (dpe)d [Cl](solid). the oxidation of trans-Cr(C0)2(dpe)2(~~lid) Figure 5.14(b) shows the very rapid development of an oxidation current which subsequently decayed rapidly and then slowly as a function of time. Figure 5.14(c) shows that there was also an increase in mass for about 6000s, after which time there was no further mass change (or apparent further oxidation of the neutral compound). Time (s) 0 5000 10000 Time (s) 15000 20000 Time (s) ig. 5.14 A double-potential step experiment for microcrystalline particles of trans-Cr(CO)a(dpe)a attached to a gold Q C which was then placed in contact with aqueous 0.1 MKC1 electrolyte. (a) potential-time sequence; (b) current-time data; (c) relative mass change as a function of time. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 227. Copyright, Elsevier. After 10 000 s, the potential was stepped back to -600 mV versus Ag/Agcl, in order to reform neutral tvans-Cr(C0)2(dpe)2(solid).The mass decrease was indicative of the expulsion of chloride ions from the crystal lattice. However, even on this time-scale, not all of the chloride ions incorporated into the microcrystalline particles of tvan~-Cr(CO)~(dpe)~ during oxidation appear to have been expelled from the solid during the reverse process. The double-potential step data again suggest that, while the slow oxidation process involves the conversion of trans-Cr(C0)2 (dpe)2(solid) to trans- [Cr (CO)2(dpe)2][XI (solid), not all the neutral tvans complex is recovered during the relatively rapid component of the reverse reduction process. [XI salts attached to a gold electvode EQCM studies of solid tran~-[Cv(CO)~(dpe)~] Figure 5.15(a) shows a cyclic voltammogram over the potential range 400 to -900 mV versus Ag/AgCl for the reduction of solid tvans-[Cr(CO)2(dpe)2][Cl] Potential (mV) vs /AgC1 -1000 -800 -600 -400 -200 0 200 400 Potential (mV) vs Ag /AgCl Fig. 5.15 (a) Cyclic voltammogram (scan rate 50 mV s-l) and (b) the corresponding mass change diagram for microcrystalline particles of trans-[Cr(C0)2(dpe)z][Cl] attached to a gold QC which was then placed in contact with 0.1 M KC1 aqueous electrolyte. Reproduced by courtesy: J Electroanal. Chew. 404 (1996) 227. Copyright, Elsevier. Mechanistic aspects of transport processes 355 in 0.1 M KC1 solution at a scan rate of 50 mV s-' . In this particular experiment, the compound and electrolyte anions are the same, although this of course need not be the case. The well-defined reduction response at -400 mV versus A g / ~ g l is due to the reduction of tran~-[Cr(CO)~ (dpe)2][Cl](solid) to neutral tmns-Cr(C0)2 (dpe)2(solid). The plot of relative mass as a function of potential (Fig. 5.15(b))indicates that no mass change occurs until reduction current is observed. The mass decrease at potentials more negative than -400 mV versus A ~ / A is ~ due C ~to the reduction of trans-[Cr (C0)2(dpe)2][Cl](solid) to neutral trans-Cr(C0)2(dpe)2(solid)with C1- ions being expelled from the crystal lattice. n the reverse scan, the oxidation peak for trans-Cr(C0)2(dpe), at -100 m~ versus Ag/AgCl also is smaller than the reduction peak (as previously obsemed 13) when using solid trans-Cr(C0)2(dpe)2. a potential of -300 mV is reached on the reverse scan, there is a conincrease in mass due to the reformation of the chloride salt. The mass ontinues to increase until a potential of 400 mV versus Ag/AgCl is reached, and resumably would continue to increase at more positive potentials. However, in order to prevent gold electrode oxidation, the potential range was limited the to 400 mV. As was the case when starting with trans-Cr(CO)2(dpe)2(~ahd), oxidation process was found to be very slow compared with the reduction of trans-[Cr(CO)2( d ~ e )[Cl] ~ ] (solid). Other trans-[Cr(CO)2(dpe),] [XI salts were also investigated in a variety of electrolytes and under circumstances where the solid anion may or may not be the same as the electrolyte anion. The molar masses of the ions expelled from the salts during the reduction process were calculated and the values are listed in Table 5.4. The results suggest that, in cases where the salt anion is different from the electrolyte anion, that an ion-exchange .4 Theoretical and experimentally determined molar masses (M) obtained by EQCM experiments when solid trans-[Cr(CO)2(dpe)2][X] is attached to a gold electrode which is placed in contact with different electrolytesa X in trans-[Cr(CO)2 (dpehl [XI Electrolyte (0.1 M) Experimental (M/g rnol-) Theoretical ( M / mol-I)' ~ 'Data taken from J. Electroanal. Chem. 404 (1996) 227; scan rate 50 nlV s-' . ' ~ r r o ris standard deviation (six experiments using three different gold Q C electrodes). Calculations are based on the reduction process observed in cyclic voltammetric experiments. 'Values are calculated assuming that only the non-solvated electrolyte anion is associated with the charge neutralization process. 356 Solid-electuode-solvent intefaces reaction takes place prior to the reduction of tuan~-[Cr(CO)~(dpe)~] [XI. That is, in these cases, the molar mass for the reduction of trans-[Cr(CO)2(dpe)2][XI to tuan~-Cr(CO)~(dpe)~ is not equivalent to the molar mass of the anion in the salt. Rather, the experimentally determined molar mass approximates that of the anion in the electrolyte. For example, reduction of trans-[Cr(C0)2(dpe),1[Br] in 0.1 M KBr has an experimental molar mass of 73.1 g mol-' , which correlates with the expulsion of bromide ions from the crystal lattice. However, reduction of initially tuans-[Cr(C0)2(dpe)2][Br](solid) in contact with 0.1 M KC1 electrolyte produces an experimental molar mass of 27.8 g mol-I, instead of 79.9 gmol-l which implies that tuans-[Cr(C0)2(dpe)z][Cl](solid)was formed rapidly by an ion-exchange process and that the chloride ion and not the bromide ion was expelled from the solid during the reduction step. Results obtained from electron microprobe X-ray analysis experiments also indicate that an ion exchange reaction occurs prior to electrolysis. Figure 5.16(a) represents the electron microprobe analysis of trans-[Cr(C0)2(dpe)~[Cl](solid)and the expected P, Cr, and C1 peaks are Fig. 5.16 Electron microprobe X-ray analysis of (a) solid trans-[C~(CO)~(dpe)~][cl] attached to a graphite electrode, (b) solid trans-[Cr(CO)2(dpe)2][C1] attached to a graphite electrode which was held at 200 mV versus Ag/AgCl for 2 min in 0.1 M KBr aqueous electrolyte. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 227. evident. trans-[Cr (CO)2(dpe)2][Cl](solid) was then attached to a graphite electrode which was then dipped into a 0.1 M KBr electrolyte for 2 min with the electrode being held at 200 mV versus Ag/AgCl to prevent any redox processes horn occurring. The electron microprobe analysis shows the disappearance of C 1 ions from the solid and the incorporation ofBr- ions (Fig. 5.16(b)).These results are consistent with the occurrence of an ion-exchange process. However, it was also observed that larger particles of trans-[Cr(CO)2(dpe)2][Cl] (above 5 pm) are not completely converted to trans-[Cr(C0)2(dpe)2][Br]. quation (5.9) summarizes the ion-exchange process that is believed to occur at the electrode surface at open-circuit potential: tm~s[Cr(CO)2 (dpe)21 [Cl](solid) + Br (solution) - A double-potential step experiment in 0.1 MKC1 solution is shown for reduction of trans-[Cr (CO), (dpe)2][Cl](solid) in Fig. 5.17. The potential was initially held at -20mV versus Ag/AgCl for 300 s. At this potential, trans- [Cr(C0)2(dpe)2][Cl] is stable in the redox sense. The absence of any mass change confirms that there was no Faradaic process during the course of this part of the experiment (see Fig. 5.17(c)).After 300 s, the potential was stepped from -20 to -600 mV versus Ag/AgCl and held at the latter potential for 2000 s. At -600 mV versus Ag/AgCl, the salt was reduced to the neutral compound and the charge-transfer process was accompanied by a very rapid mass decrease due to the expulsion of chloride ions from the salt, as shown in Fig. 5.17(c). A constant mass was achieved after 60 s and no further detectable mass change occurred during the remainder of the experiment. The current response shows analogous behaviour to the mass change (Fig. 5.17(b)). After a total time of 2300 s had elapsed, the potential was then stepped back to -20 mV versus Ag/AgCl for 2000 s which produced an oxidation current that decayed rapidly as a function of time, and an increase in mass due to the reincorporation of chloride ions into the solid. The oxidation of trans-Cr(C0)2(dpe)2(so~id)to achieve the starting mass condition for trans-[Cr(CO)2(dpe),] [Cl](solid) took approximately 1300 s. This experiment again confirms that the incorporation of chloride ions is slower than the expulsion process. The major difference with the potential step experiments for trans-[Cr (CO), (dpe)2][Cl](solid) and trans-Cr(C0)2(dpe)2(solid) was that C1- ion expulsion and uptake proceed to the same extent in the former case. The fact that reduction of tran~-[Cr(CO)~(dpe)~] [Cl], which is attached to the electrode by evaporation of a sample dissolved in a drop of organic solvent, seems to lead to a more extensive level of electrolysis than when this compound is may formed in situ by oxidation of mechanically attached t~ans-Cr(CO)~(dpe)~, be attributed to the fact that the particle size of solid attached to the electrode using a solvent evaporation technique is smaller than is achieved with direct attachment of solid trans-Cr(C0)2(dpe),. Time (s) Fig. 5.17 A double-potential step experiment for solid trans-[Cr(C0)2(dpe)2][C1]attached to a gold electrode which was then placed in contact with 0.1 M KC1 aqueous electrolyte. (a) Potential, (b) current, and (c) relative mass change as a function oftime. Reproduced by courtesy: J. Electvoanal. Chem. 404 (1996) 227. Copyright, Elsevier. Mechanistic aspects of transport processes 359 3.2.3 Voltammetric and FTIR studies on solid cis-Cr(C0)2(dpe)2 attached to a graphite electrode The eighteen electron c i ~ - C r ( C O ) ~ ( d p is e ) ~known to be the thermodynamically favoured isomer. In contrast, observation of isomerization of the transiently formed ci~-[Cr(CO)~(dpe)~]+ reveals that the seventeen electron tran~-[Cr(CO)~(dpe)~]+ cation is strongly favoured in both thermoynamic and kinetic senses [16]. Accordingly, the solution phase voltammetry of c i ~ - C r ( C O ) ~ ( d pis e ) governed ~ by eqn (5.6) with the short lived c i s - [ ~ r ( C O ) ~ ( d p e )cation ~ ] + being difficult to detect spectroscopically (Table .5). For convenience, the solid-state voltammetry may be written in shorthand form as cisO(solid)4 cis+(solid) I trans+(solid) where ciso = solid c i ~ - C r ( C O ) ~ ( d pcis' e ) ~ ,= solid c i s - [ C r ( C ~ ) ~ ( d p e )and ~]+ and the electrolyte anion required for trans' = solid tran~-[Cr(CO)~(dpe)~]+ charge neutralization has been omitted. In Fig. 5.18, and in accordance with eqn (5.lo), the voltammetric response obtained at 50°C when cis-Cr(C0)2(dpe)2(solid)attached to a graphite electrode ? Cvcle 3-1 0 J. E (V) vs Ag/AgCl Fig. 5.18 Cyclic voltammograms obtained at 50°C with a scan rate of 200 mV s-' over 10 potential cycles for oxidation of solid cis-Cr(CO)2(dpe)2, mechanically attached to a basal-plane pyrolytic graphite electrode and then placed in contact with aqueous 0.1 M NaCl electrolyte. Reproduced by courtesy: Organornetallics 13 (1994) 5122. Copyright, American Chemical Society. 360 Solid-electrode-solvent intefaces is in contact with aqueous 0.1 M NaCl can be seen to change from an initial response associated with the oxidation of the cis isomer, to that for the solidstate t r a n s - [ ~ r ( ~ ~ ) ~ ( d ~redox e ) ~ ]couple ~ / + described in Section 3.2.2. The voltammogram of the solid-state trans+I0 process is in fact clearly evident after 2 cycles (Fig. 5.18). With 0.1 M NaC104 electrolyte, the data obtained after 10 cycles when commencing with solid ~ i s - C r ( C O ) ~ ( d pise )indistinguishable ~ from that obtained with solid trans-Cr(C0)2 (dpe)2 (Table 5.2). A useful technique to monitor the course of processes that take place on an electrode surface is specular reflectance FTIR spectroscopy. Good FTIR signal-to-noise ratios are possible after about 5-40 scans of the I R spectrum when solids are attached as arrays of microcrystals to basal-plane graphite electrodes because the modified graphite surface still reflects sufficient light intensity. Effective background subtraction is possible by measuring the initial response prior to the start of electrolysis and then plotting only the relative change in intensity of the I R absorbance during the course of electrolysis. An I R spectrum obtained after electrochemical oxidation of solid trans-Cr(CO)2(dpe), to solid trans-[~r(CO)~(dpe)~]+ cation at a graphite electrode in contact with aqueous 0.1 M NaCl is shown in Fig. 5.19(a). In this experiment, the tran~-Cr(CO)~(dpe)~ isomer with an I R band at 1796 cm-* (compare diffuse reflectance KBr powder I R spectrum 1783 cm-') is converted into the trans+ cation form which has an I R band at 1846 cm-' (compare diffuse reflectance KBr powder I R spectrum 1845 cm-') when oxidation is undertaken at 500 mV versus Ag/AgCl. The spectroscopic identification of the electrochemical generation of solid cis-[Cr(C0)2 (dpe)21f via oxidation of solid cis-Cr(C0)2 (dpe)2 and proof of the subsequent isomerization step which generates trans-[Cr (CO)2(dpe)2]+also is achieved by use of in situ specular reflectance FTIR spectroelectrochemical experiments (Fig. 5.19(b) and (c)). After oxidation of solid cis-Cr(CO)2(dpe)2 attached to an electrode at 500 mV versus Ag/AgCl, the detection of new I bands at 1846 and 1933 cm-' shows that some ofthe ciso starting material (diffuse reflectance I R bands for cis-Cr(C0)2(dpe)2(solid)occur at 1780 and 1844 cm-') has been oxidized. The I R band at 1844 cm-' corresponds predominantly to formation ofthe transf isomer. The I R band at 1933 cm-I (Table 5.5) is attributable to the formation of the oxidized cis+ isomer, which is too unstable to be detected in solution-phase spectroelectrochemical studies. The second I R band expected for cis' is unresolved from the trans+ band (Table 5.5). The shift of 89 cm-' for comparable I R bands of the cisf species relative to the cis species (Table 5.5) is of the order expected for the formation of cis+ and is associated with the increased positive charge on the metal centre. The I R band at 1933 cm-' shown in Fig. 5.19(b) decays slowly (50 per cent after 60 rnin) when monitored at room temperature. Evidently, constraints posed by the solid matrix allow the achievement of kinetic stabilization of a thermodynamically unstable isomer. The I R detection of the trans+ isomer after a potential of 500 mV versus Ag/AgCl is applied for 2 min is achieved with considerably decreased spectral overlap with the cis+ isomer (Fig. 5.19(c)).Thus, while the processes leading to generation of cisf and subsequent isomerization to transf may be complex, it is - Mechanistic aspects of transport processes 36 1 trans . 5.19 Specular reflectance FTIR spectra obtained for cis- and trans-Cr(C0)a ( d ~ emechanically )~ attached to a basal-plane pyrolytic graphite electrode, after being placed in contact with aqueous 0.1 M NaCl electrolyte, electrochemically oxidized at ambient temperature, and then dried in air after removal of the electrolyte solution: (a) trans-Cr(CO)a(dpe)a afier the potential was held at 500 mV versus Ag/AgCl for 2rnin; (b) c i ~ - C r ( C O ) ~ ( d p eafier ) ~ the potential was held at 500mV versus Ag/AgCl for 5 s; (c) the same system as in (b) after 2 min. The spectra were background-corrected by subtraction of the response prior to electrolysis. Reproduced by courtesy: Oqanornetallics 13 (1994) 5 122. Copyright, American Chemical Society. clear that the basic mechanism has a solid-state parallel to that identified in the solution-phase voltammetry. A summary of surface attached and other forms of spectra is contained in Table 5.5. 3.3 Overview offactors that influence the voltammetry of decamethylferrocene and trans-Cr ( C O ) 2 attached to an electrode suface The data obtained for the voltammetry of solid decamethylferrocene and trans-Cr(CO)z(dpe)2, which both involve an overall one-electron oxidation process to generate a close to isostructural cation, show that: (a) a wide range of responses can be observed from microcrystalline samples of the non-conducting solid which depend on the crystal size and surface coverage, and also the medium in contact with the solid; (b) voltammetric wave shapes may have Table 5.5 I R data obtained in the carbonyl region (V (CO))for cisand tvans-[cr ( ~ (dpe)2]o/+ 0 ) ~ species in solution (CH2C12),in the solid state by the diffuse reflectance method (KBr powder) and by the specular reflectance method before and after electrolysis when solid is adhered to a basal-plane pyrolytic graphite electrode Technique (medium) v (CO) (cm-') trans trans+ cis Solution-phase (CH2C12) 1792 1850 Diffuse reflectance (KBr powder) 1783 1845 Specular reflectance (graphite electrode) 1796 I846 1846 1772 1830 1764 1844 1780 cisS 1933 "Data taken from Organometallics 13 (1994) 5122. b~somerizationto transsi to rapid for detection. 'Second band not resolved from trans' band. different characteristics, depending on the electrolyte, solvent, and scan rate; (c) a large separation between oxidation and reduction peak potentials may occur; (d) oxidation and reduction components of the processes associated with cyclic voltammograms may exhibit different characteristics; (e) anions may be incorporated from the electrolyte into the solid during oxidation and expelled during reduction. The primary questions to resolve are how the electron-transfer step occurs in the oxidation of these non-conducting solids and how the mass-transport mechanism of anions occurs to achieve charge neutrality. The microcrystalline material has small areas where simultaneous contact with both the electrode and solution occurs. Starting from the three-phase boundary contact position (Fig. 5. I), it is proposed that a current flow occurs via a coupled electron-transfer self-exchange and ion-exchange charge neutralization mechanism within the solid or along the solid-solution boundary. Figure 5.20 gives a schematic form of the mechanism that may apply for the t v a n s - [ ~ r ( ~ ~ ) ~ ( d ~couple. e ) ~ ] ~The /+ mechanism of surface conduction, which is accompanied by transport of ions across a solid-solution interface would, as observed, be expected to depend very much on electrolyte, temperature, and solvent. In the case of oxidation of decamethylferrocene, a flow of charges up to the order of millicoulombs is observed, which requires that oxidation of more than just the surface of 8 0 n some occasions a counter intuitive charge neutralization process may occur. For example, in the oxidation of the [BU~N]+salt of [ C r ( C 0 ) 5 1 ] to give Cr(CO)51(solid), when the modified electrode is in contact with perchlorate containing electrolytes, charge neutralization may occur by C10& uptake into the solid phase rather than the expected expulsion of Bu4N+ into the solution phase [25]. Mechanistic aspects of transport processes 363 Solution C1- K+ Electrode Neutral trans-Cr (CO)2(dpe), Oxidation of trans-Cr (CO)2(dpe), [Cr (CO), (dpe),l C1 ' \ I I Reduction of ig. 5.20 A schematic representation of the redox chemistry of solid particles of trans-Cr(C0)2(d~e)~ and trans-[Cr(CO)2(dpe)2][C1] attached to a gold electrode which has been placed in contact with 0.1 MKCI aqueous electrolyte. Reproduced by courtesy: J. Electroanal. Chem. 404 (1996) 227. Copyright, Elsevier. the rnicrocrystals occurs. This postulate is supported by electron probe X-ray analysis experiments, which demonstrate that a substantial part of the surfaceattached decamethylferrocene is oxidized at positive potentials and reduced at negative potentials. Of particular significance is the observation that the cation in the electrolyte is not crucial to the voltammetry of solid decamethylferrocene or t~ans-Cr(CO)~(dpe)~ whereas a wide range of voltammetric behaviour can be found by varying the electrolyte anion. In these cases, this sensitivity to the anion would appear to be associated with the fact that oxidation takes place with anion uptake and reduction occurs with anion expulsion. The transport of ions between two immiscible (solid-solution) phases is clearly a complex process, but could be expected to depend on the free energy of anion exchange, that is on the anion distribution between the two phases. Solid-solution interaction t ........ Solid dissolves ....................... in electrolyte Surface conduction '..'...-:... ... ... . ..'.. . ..... ,. . . ". . .a. . . . 2 dim. 1 d m . '"...... 3 dim?. ..... ":. .....Intercalation'.. .... b Temperature Fig. 5.21 Schematic representation of some of the different phenomena related to ion transport that may take place in the solid-state voltammetry of microparticles attached to an electrode and placed in contact with a solvent (electrolyte) medium. Reproduced by courtesy: J. Electroanal. Chem. 372 (1994) 125. Copyright, Elsevier. The peak splittings most commonly observed under conditions of high surface coverage and fast scan rate suggest that at least two processes may exist which have different scan rate and temperature dependencies. Figure 5.21 schematically illustrates some oithe phenomena that are believed to occur with the ion transport part of the mechanism associated with the redox chemistry of microcrystalline solids. However, clearly there are many features not predicted on the basis of a thin film model considered in Section 18 in Chapter 2. In the case of oxidation of microcrystalline trans-Cr(CO)z(dpe)2 to trans-[Cr(CO)2(dpe)2]+, a variation of potential of more than 400mV is observed when 0.1 M NaF is used instead of 0.1 M NaC104 as the electrolyte (Table 5.2). A similarly large anion dependence is found for oxidation of decarnethylferrocene (Fig. 5.8). The correlation of these reversible potential data with free energies of partition for anion transport across a water-dichloromethane interface (Table 5.2), coupled with voltammetric and spectroscopic data indicate that the overall oxidation reaction for the oxidation of trans-Cr(CO)z(dpe)z(solid) may be summarized by eqns (5.1I)-@. 13) trans0(solid) trans+ (solid) -k e- X- (solution) +X- (solid) trans' (solid) + X- (solid) ---\ (trans' - X- (solid)) (5.11) (5.13) where X- denotes the electrolyte anion, and the trans0/+ nomenclature represents the trans isomer of the [ ~ r ( ~ ~ ) ~ ( d couple ~ e ) ] in ~ the / + appropriate oxidation state, and where an analogous set of equations also probably applies for oxidation of decamethylferrocene. T o achieve the oxidation of the solid, both electron and ion transport are necessary and the ions have to be transported to sites within the solid. This may occur via diffusion of the ions within the solid, which is coupled Mechanistic aspects of transport processes 365 with an electron-transport process involving electron hopping. Additionally, a nucleation-growth mechanism may be needed to convert one solid phase to another and this step or the coupled electron-transport-ion-transport process may be rate determining. Simultaneous electrochemical and Q C microbalance studies at the solidelectrode-aqueous solution (electrolyte) interface confirm that oxidation of microcrystalline t~ans-Cr(CO)~(dpe)~ mechanically attached to a gold electrode involves the formation of a t r a n s - [ C r ( ~ ~ ) ~ ( d ~salt e ) via ~ ] +incorporation of anions from the supporting electrolyte in order to maintain charge neutrality. O n the reverse scans of cyclic voltammograms and in the several stages of double-potential step experiments, reduction occurs and anions are expelled. owever, not all of the anions incorporated during the oxidation step are necessarily expelled from the crystal lattice on the time-scale of fast sweep cyclic voltammetric experiments. This result suggests that the reduction reaction at short time domains predominantly occurs in a spatial region relatively close to the surface of the solid. Evidence also has been provided for a slower process, which probably occurs at greater depths within the microcrystal. .4 Problems with a theovetical descviption o f the voltammetry of non-conducting microcr$als - The vast majority of solution-phase voltammetric experiments utilize conditions with a well-defined electrode-solution interface consisting of just two phases. n the solid-state electrochemical reactions considered so far, the process always involves a multiphase system. In the most likely case, there will be four phases. ne phase is the electrode, serving both as the electrical conductor and also as a surface on which the solid sample particles are immobilized. The second and third solid phases are the oxidized and reduced forms of the solid, although this can be considered as a single phase if the oxidized and reduced forms of the solid can exist as a continuous phase. The fourth phase is the solution (electrolyte). The electronic conductivity of the sample phase will determine the potential difference between the sample phase and the electrolyte solution. If this conductivity is very high, the potential difference will be equal to that existing between the electrode and the solution. In this case, the electrode process can, if not otherwise inhibited, proceed on the entire surface of the solid and within the bulk solid. Metal electrodes and adhered alloy rnicroparticles will most likely react in this way [4]. However, when the conductivity of the sample is low, one may wonder how an electrochemical reaction can proceed at all. Experimental evidence and available for oxidation of decamethylferrocene and tr~ns-Cr(CO)~(dpe)~ other systems (41 would indicate that the only possible initial reaction place is the three-phase boundary between the electrode, the sample, and the solution (electrolyte) (Fig. 5: 1(b)). At this three-phase bound&y, electrons can be exchanged between the electrode and the sample, and ions between the sample and the solution (Fig. 5.22). In recent theoretical studies [26-281, the Electrolyte solution Insulator Ion exchange Electron exchange h Electrode Fig. 5.22 Schematic representation of a simple three-phase electrochemical system supporting both ion transfer between the solid compound and the solvent (electrolyte), and electron transfer between the solid and the electrode. Adapted from: Electroanal. Chem. 20 (1998) 1. propagation of an electrochemical reaction through a solid (the single phase simplification) was considered for a case involving both electronic and ionic conductivity of the solid. In this theoretical description, coupled diffusion of electrons and ions within the crystal lattice was assumed and the redox reaction was initiated at the three-phase boundary, where the solid was in contact with both the electrode and the solution. From this contact point, the redox reaction advances either along the surface of the solid or into the body of the solid by diffusion of ions and the transport of electrons. This theoretical treatment of a very simple model when a microparticle is attached to a solid electrode surface, produced the following conclusions: (1) The three-phase boundary is always the starting point for the reaction front, independent of the geometry of the particle and its conductivity. (2) The reaction will be surface confined if the diffusion of ions into the bulk of the crystal is impossible or very slow. (3) Generally, the net current is the sum of the current from the surface and bulk processes. (4) If both the surface and the bulk reactions proceed at comparable rates, the reaction front expands in three dimensions from the three-phase boundary. (5) The surface current will be negligible in cases where the bulk reaction is dominating. The voltammetric behaviour of azobenzene microcrystals is considered to be an example where the electrode reaction is confined to the surface of the solid materials [29], whereas the oxidation of decamethylferrocene and tv~ns-Cr(CO)~(dpe)~ is clearly more complex and may occur via a range of mechanisms. A major problem to be encountered in a realistic theoretical description of a solid-state electrochemical process is that the morphology of the sample distributed on the electrode surface contributes to the voltammetry and is often complex. For example, microcrystals of the sample are often scattered on a solid Voltammetuy of TCNQ 367 electrode and may have a certain size distribution as well as a preferential orientation due to the immobilization procedures. The microcrystals will expose their different faces to the solution and also to the solid support so that in principle the polyciystallinity can decisively influence the electrochemical properties. urthermore, the morphology can be potential dependent. A major difficulty in providing a theoretical description also arises if the generation of an additional solid phase occurs with the direct conversion of one solid phase into another, as will commonly be the case (see Section 4 below). n this case, the number of phases varies during the course of an electrochenileal reaction, and the interfacial areas are no longer independent of time. The transformation of one solid phase into another cannot always proceed along a continuous series of mixed crystal phases as assumed in the simple theory considered above. A new phase is generated when the starting and the product ses are unable to form mixed crystals at all potentials in the voltammetric eriment. This situation can lead to a considerable splitting of the oxidation reduction peaks in cyclic voltammetry (see reference [30] and the T C N Q case considered below). However, it is also possible that a continuous transformation from one phase to the other occurs through mixed-phase formation I], so that numerous possible scenarios are available in attempting to develop eoretical models. The examples of voltammetry presented in the remainder f this chapter represent cases where the rate-determining steps are nucleationrowth processes (Section 4) or coupled electron and ion transport within the microparticle to give thin film or diffusion-like (Section 5) behaviour. 7,7,8,8 tetracyanoquinodimethane, (Fig. 5.23) usually designated as T C N -, is well known as an more particularly its one-electron reduced salt, T C whereas pure T example of an organic semiconductor [32,33]. Th ssesses a rather low conductivity of 3 x 10-l2 S cm-I [34], the potassium S cm-' [35], which is typ] has a conductivity of 2 x nductor. Consequently, unlike the case with non-conducting ) ~ ] ~ /transport + of ions required [ ~ e ( q ~ - ~ ~ ~ e ~ ) ~ ~] )~~"( -d ~ e systems, (solid) process should be able to occur rapidly to accompany the [ in three dimensions within the solid adhered to an electrode surface, even with thick microparticles or films. Therefore, surface diffusion should not play a major role in the voltammetry, and exhaustive electrolysis of all adhered solid T C N Q should be rapidly achieved on the voltammetric time-scale. Not surprisingly, because of the semiconducting properties of TCNQ- salts, the 368 Solid-electrode-solvent intefaces Fig. 5.23 Structure of 7,7,8,8 tetracyanoquinodimethane (TCNQ). Process I1 I I -1.0 -0.5 I I I 0.0 0.5 1.O E (V) vs Ag (s)1 AgCl (s)lKC1 (aq), 3 M Fig. 5.24 Voltarnmograms for reduction of a 1 x lop3 M solution of T C N Q in acetonitrile (0.1 M Bu4NPF6).(a) Steady-state voltamniograrn at a 10-pm diameter Pt microdisc electrode (scan rate 10mVs-l). (b) Transient cyclic voltammogram at a 1-mrn diameter Pt macrodisc electrode (scan rate 200 r n s-l). ~ Reproduced by courtesy: J. Chem. Soc., Faraday. Trans. 92 (1996) 3925. Copyright, Royal Society of Chemistry. [ T C N Q ] ~ /reaction is one of the most widely studied electrochemical systems in both solution and solid-state phases. The wide variety of data available can therefore be scrutinized to illustrate how numerous surface science and electrochemical techniques may be coupled with the electrochemistry in order to identify the nuances that accompany the voltammetry of T C N Q in particular, and probably the voltammetry of many other solid-state systems. 4.1 Solution-phase voltammetry of TCNQ Typical solution-phase voltammograms obtained when T C N Q is dissolved in an organic solvent such as acetonitrile are shown in Fig. 5.24. That is, two chemically and electrochemically reversible one-electron reductions are observed under both transient (cyclic voltammetry) and steady-state (microdisc electrode) conditions [36] and they correspond to the reduction processes given in eqns (5.14) and (5.15). + e- 4 TCNQ-(solution) Process 11 TCNQ- (solution) + e- + TCNQ~-(solution) Process I TCNQ(so1ution) (5.14) (5.15) Further reduction processes are also possible, but are not of interest in this discussion. r (dpe)2]0/+solidIn studies on the [ F ~ ( T , I ~ - c ~ M ~and ~ ) ~trans] O / +[ ~(co), state redox reactions, the electrochemical responses have been attributed to Voltammetry of TCNQ 369 reactions that occur rapidly on the surface of the non-conducting microcrystals and more slowly within the bulk solid. However, an obviously distinguishing feature of T C N Q is the conducting nature of the one-electron reduced salts which should drastically aid the transport of ions required to achieve charge neutralization within the bulk solid. Voltamwzetvic studies o n micvocvystals of TCNQ adheved to electrode su faces i n contact with N a + , K+, RD', and CS+containing electrolytes9 Q has been adhered to electrodes in a variety of ways. Initially, studng arrays of microcrystals are described [37,38] which are analogous to eported above with ~ e ( q ~ - C ~ M ande C ~ r)( ~ c O ) , ( d ~ e )Subsequently, ~. voltammetric studies on other forms of adhered T C N Q will be considered. n the studies described in 4.2, microcrystals of T C N Q were adhered to the electrode surface as follows. First a sample of 1-3 mg of crystalline TCNQ owder was placed on a coarse-grade filter paper. The electrode was then gently rubbed into the powder until it became thoroughly coated with TCNQ. uccessful coating was-evidenced by observing the shiny blue colour present when the electrode was observed at a low angle. A cyclic voltammogram of surface-immobilized microcrystals of T C N Q on a basal-plane pyrolytic graphite electrode immersed in aqueous 0.1 M KC1 solution is shown in Fig. 5.25. As for the voltammetry of ~ e ( q ~ - ~ and ~ Mtran~-Cr(CO)~(dpe)~, e ~ ) ~ the nature of the solid-state voltammograms differs considerably from those observed in the solution phase (Fig. 5.24). In particular, an 'inert zone' appears between the principal peaks. Figure 5.26 is a schematic form of representation of the first reduction process in which the principal peaks (I,, and Ired) are equal I -1 .O I I I -0.5 0.0 0.5 E (V) vs Ag(s)IAgCl(s)II<Cl(aq),3 M I 1.O ig. 5.25 Cyclic voltammograms obtained at a scan rate of 100 mV s-* for microcrystals of TCNQ immobilized on a basal-plane pyrolytic graphite electrode placed in contact with aqueous 0.1 M KC1 electrolyte (dashed: potential scanned only over region of process I). Reproduced by courtesy: J. Chem. Soc., Faraday. Trans. 92 (1996) 3925. Copyright, Royal Society of Chemistry. ' ~ d a ~ t ewith d permission from A.M. Bond, S. Fletcher, F. Marken, SJ. Shaw, and P.G. Symons, J. Chem. Soc. Faraday Trans. 92 (1996) 3925 and A.M. Bond, S. Fletcher, and P.G. Symons, Analyst 123 (1998). Copyright, Royal Society of Chemistry. Fig. 5.26 Schematic representation ofprocess I (eqn 5.15) for reduction of microcrystals of TCNQ adhered to an electrode. as required for a chemically reversible reaction. The reduction process will be shown below to be accompanied by insertion of cations from the electrolyte solution, [M+][X-] (solution), into the solid material to maintain charge neutrality, implying an overall general reaction for process I of the form xTCNQ(so1id) + ye- + y ~ + ( s o l u t i o n ) The second signal pair in Fig. 5.25 (process 11) corresponds to the further reaction Significant chemical irreversibility is evident in process 11, which is partially dianion dissolution. Consequently, because of this accounted for by T C N Q ~ and other complications only process I is considered in the discussion that follows. The oxidation level of the T C N Q solid before and after the first reduction process at a basal-plane pyrolytic graphite electrode in contact with 0.1 M KC1 can be quantitatively determined using the microelectrode method illustrated in Fig. 5.27. In this experiment, the potential of the electrode containing adhered solid T C N Q was held at either +0.50 or -0.10 V versus Ag/AgCl for 5 min. The resulting material was then dissolved in a minimum amount of acetonitrile containing 0.1 M Bu4NPF6as supporting electrolyte, and the steady-state voltammogram was recorded at a 10-pm diameter platinum microdisc electrode. From analysis of the results presented in Fig. 5.27, with respect to the position of zero current, it immediately becomes clear that the solid material present when the potential is maintained at f0.50 V versus Ag/AgCl contains predominantly neutral TCNQ, whereas the solid material present when the electrode potential is changed to -0.10 V versus Ag/AgCl contains predominantly an anionic TCNQ- salt. Voltammetry of TCNQ 371 F l v e d TCNQ- I -0.7 I I -0.1 I I 0.5 E (V) vs Ag (s) I AgC1 (s)I KC1 (aq), 3 M ig. 5.27 Steady-state voltammograms (obtained at a scan rate of 10 mV s-' using a 10-pm diameter Pt microdisc electrode) of solid dissolved into minimal volumes of acetonitrile (0.1 M Bu4NPF6)after holding the potential of a T C N Q coated basal-plane pyrolytic graphite electrode in contact with 0.1 MKCl for 5 min at different potentials. Top curve: TCNQ- generated in the solid state at -0.10V versus Ag/AgCl. Bottom curve: T C N Q regenerated in the solid state at f O.5OV versus Ag/AgCl. Reproduced by courtesy: J. Chern. Soc., Faraday. Tmns. 92 (1996) 3925. Copyright, Royal Society of Chemistry. -100 100 300 500 E (mV) vs Ag(s)l AgCl(s)l KC1 (aq), 3 M Fig. 5.28 Test of the effect of the electrode material. Cyclic voltammograms obtained at a scan rate of 100 mV s-' for T C N Q microcrystals immobilized on a 1-mm carbon electrode, a 0.5-mm platinum electrode, a 0.4-mm gold electrode, and a RAMTMelectrode in contact with aqueous 0.1 M KC1 electrolyte. The currents are normalized to compensate for the different reacting masses. It is evident that, within experimental error, the normalized responses are essentially independent of electrode material. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. T o test if the underlying electrode material had any effect on the voltammetry of the T C N Q microcrystals, 1 mm GC, 0.5 m platinum, 0.4 mm radius gold macrodisc electrodes and a RAMTMmicroarray electrodelo were used as substrates. In all cases the normalized responses (Fig. 5.28) were virtually identical, ' O ~ h eRAM^^ array electrode had a working surface of 28 mm2 and was inlaid with about 3200 carbon microdiscs (7 ym diameter) embedded in epoxy resin. About one-third of the microdiscs were electrically connected, so the nearest-neighbour distance of active microdiscs was approximately 70 ym. See references [39,40] for further details. 372 Solid-electvode-solvent intefaces Table 5.6 Comparison of charge densities, critical potentials, inert zone widths (qi) and peak shape parameters obtained at a scan rate of 100 mV s-' froln cyclic voltammetric experiments with T C N Q microcrystals adhered to different electrode materials in contact with 0.1 M KCla Electrodes GC Parameter measuredb 500 Platinum 250 Gold 200 1000 microdiscY. 5 2600 10000 5500 6 900 224.5 215.5 228 228 24 24.5 27 29.5 200.5 191 210 198.5 33 35 31 23 27 42.5 27 24 RAM'" "Data taken from reference [37]. ' r is the electrode radius, q,d, charge density associated with reduction process, E$: and E:$, the critical potential associated with the onset of oxidation and reduction processes, respectively, qi, the width of inert zone between oxidation and reduction processes, AEiT4 and A E G ~are the widths at three-quarters of wave height for oxidation and reduction processes respectively. 5 e e footnote 10 on previous page. with voltammetric steady states achieved after 10 cycles being used as the basis of comparison. It is therefore concluded that the underlying electrode materials exert no significant effect on the voltammetry of the microcrystals. Table 5.6 summarizes numerical data derived from Fig. 5.28. For all four electrode materials, the charges passed in redox cycling experiments are considerably larger than those expected from purely surface reactions, confirming that a significant component of the redox reactions occurs inside bulk TCNQ(so1id) material. Moreover, within experimental error, the critical potentials for the onset of the redox reactions are also independent of the underlying electrode materials, so this parameter also must be associated with phenomena occurring inside the bulk of the solid TCNQ. In order to undertake comprehensive studies on the influence of the electrolyte, studies at a RAM^^ electrode can be undertaken in a flowing solution using the cell illustrated in Fig. 5.29. The major advantage of using a flowing solution is that different electrolyte solutions can be rapidly exchanged and the effects on the voltammetry at a given electrode noted under conditions where the nature of the electrode-TCNQ(so1id) interface remains constant. It can be noted that some T C N Q salts have a small degree of solubility in water and that this may lead to a time-dependent voltammetric response. The problems of the small solubility of T C N Q salts and mechanical stability of adhered crystals in flowing solution may be overcome by applying a thin overcoat of sparsely cross-linked ~ a f i o n @ over the array of microcrystals adhered to the electrode surface. The ~ a f i o n ' coating is thin, ionomeric, and not highly cross-linked and as a result, it swells. An important consequence of Voltammetry of TCNQ Solut~onoutlet 373 - RAM^^ working electrode Solution inlet / / Stainless steel counter electrode Teflon spacer \ EPOXY resin block 2 9 Schematic representation of a thin-layer flow cell used to study the electrolyte dependence ofthe voltammetry of microcrystals of T C N Q adhered to a RAMTMelectrode. The stainless steel cell body forms the counter electrode, while the RAMTMelectrode forms the working electrode. The reference electrode is located downstream. This apparatus permits the rapid exchange of electrolyte solutions without disturbing the electrode surface. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. ese characteristics is that the NafionB coating does not act as a microporous (electrolyte-excluding) ion-selective membrane, but instead acts as a macroporous (electrolyte-including) gel, preventing convection in the immediate vicinity of the TCNQ(solid), but not preventing the solid from experiencing e bulk concentration of cations. This means that the T C N Q microcrystals neath the ~ a f i o n @ coating are bathed in the same concentration of KC1 as t found in the bulk of solution, as required if the electrolyte dependence is to be assessed. Figure 5.30 shows voltammograms of T C N Q microcrystals immobilized on afion-coated RAM^^ electrode in contact with 0.1 M aqueous solutions of KCl, K N 0 3 , KBr, KF, and KI. There is very little effect of changing the identity of the anion. Within experimental error, the critical potentials for oxidation and reduction are independent of the identity of the anion. These results powerfully suggest that the anions play no role in the electrochemical reaction, and justify their omission from eqn 5.16. By contrast, the identity of the cation and its concentration is crucial. If the concentration of potassium chloride in the bulk of solution is increased in decade increments from 0.001 M to 1 M, then the entire voltammetric response shifts by about 60 mV decade-' (Fig. 5.31). Figure 5.32 shows the voltammetric ' hi his result should be contrasted with the conclusion reached in studies on the oxidation of decamethylferrocene and trans-Cr(C0)2( d ~ ewhere ) ~ the voltammetry is independent of the identity of the cation, but depends on the nature and concentration of the anion. 374 Solid-electrode-solvent intefaces I I I I I 0 200 400 600 E (mV) vs Ag (s)1 AgCl (s)I KC1 (aq), 3 M Fig. 5.30 Cyclic voltammograms of T C N Q microcrystals adhered to a ~afion@-coated RAMTM electrode (scan rate 1 0 0 m ~ s - ' )in contact with aqueous 0.1 MKCI, K N 0 3 , KBr, KF, and KI electrolytes. The responses are similar because the anions do not take part in the charge neutralization process. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. I -0.3 I I -0.1 I I 0.1 I I I 0.3 I 0.5 E (V) vs Ag (s)/AgCl (s)I KC1 (aq), 4 M Fig. 5.31 The dependence of cyclic voltammograms (scan rate 100 mV s-l) for T C N Q microcrystals immobilized on a ~afion@-coated RAMTMelectrode in contact with aqueous KC1 electrolyte of different concentrations confirms the dependence of the cation on the charge neutralization process. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. responses of T C N Q microcrystals in 0.1 M NaC1, 0.1 M KC1, 0.1 M RbNQ3, and 0.1 M CsC1, all recorded on the same electrode. It is clear that the critical potentials, the widths of the inert zones and the peak widths all depend upon the identity of the cation. Numerical data are collected in Table 5.7. These data confirm that the cation plays an important role in the charge neutralization process and shows why the cation is included in eqn 5.16. Voltammetry of TCNQ 375 0 200 400 E (mV) vs Ag (s) l AgCl (s) I KC1 (aq), 3 M . 5.32 Cyclic voltammograms (scan rate 50mVs-l) obtained for T C N Q immobilized on a RAMTMelectrode in contact with aqueous 0.1 M NaCl, 0.1 M KC1,O. 1M R b N 0 3 , ~afion@-coated and 0.1 M CsCl electrolytes demonstrate the different widths of inert zones for different cations and confirm that the cation is associated with the charge neutralization process. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. .7 Effect of changing the cation on the critical oxidation and reduction potentials, inert zone widths (vi), and peak shape parameters of cyclic voltammograms of T C N Q microcrystals on a NafionB-coated RAMTM electrodea 0.1 M NaCl 0.1 M KC1 0.1MRbN03 0.1 M CsCl 244 212 154 240 24 32 14 4 220 180 140 236 20 20 21 28 20 23 27 17 "Data from Fig. 5.32 (reference [38]). Clearly the cations have a significant effect on the kinetics of the phase transformations. 4.2.1 Voltammetn'c evidencefor a nucleation-growth mechanism e effect of scan rate on the reduction T C N Q microcrystals on a lXllMTM trode placed in contact with 0.1 M NaCl, 0.1 M KCl, 0.1 M R b N 0 3 , and 0.1 M CsCl is shown in Fig. 5.33, where the peaks at lower scan rates can be seen to emerge from the rising portions of the voltammograms at higher scan rates. This is a tell-tale sign of a rate-determining nucleation and growth mechanism [41]. The effect occurs because of the special mathematical relationship which couples nucleation to growth, which causes current-voltage curves to have steeper gradients at low scan rates than at high scan rates. Further evidence of nucleation is provided by Fig. 5.34, in which the scan directions are reversed in the foot of each peak. Current maxima occur on the reverse scans, which Solid-electvode-solvent intefaces TCNQ -+(N~+)(TCNQ-) Fig. 5.33 Effect of scan rate ( m ~ s - I )on the reduction of T C N Q microcrystals adhered to a ~afion@-coatedRAMTM electrode in contact with aqueous 0.1 M NaC1, 0.1 M KC1, 0.1 M R b N 0 3 , and 0.1 M CsCl electrolytes. The emergence of the voltammetric peaks at low scan rates from the voltammetric peaks at high scan rates is characteristic of a nucleation-growth mechanism. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. are diagnostic of rate-determining nucleation and growth kinetics. The 'triggering' of nucleation at high overpotentials results in an enhanced current at low overpotentials when the scan direction is reversed as in Fig. 5.34. This is in stark contrast to diffusion-controlled processes, which inevitably show lower currents on reverse scans due to the depletion of reactant. Diffusion control can also be excluded because of the absence of a 'tail' in the voltammograrns caused by the necessary waiting for the reactant to arrive (or depart) from the reaction site. Thus, nucleation is implicated in both the reduction (Fig. 5.34(a)) and the oxidation processes (Fig. 5.34(b)),indicating a reversible solidsolid phase transformation. Definitive evidence for nucleation-growth kinetics also is provided by chronoamperometric (double-potential step) experiments [41]. In Fig. 5.35, the results of two successive potential steps experiments are shown for 0.1 M aqueous solutions of NaC1, KC1, R b N O z , and CsCl: the first one reductive and the second one oxidative. The step durations are 10 s each, except in the case of CsC1, where 20 s is used. Note that the current-time transients exhibit well-defined peaks (not to be confused with the vertical spikes, which are caused by the rapid onset and decay of the capacitance charging currents at short times). The existence ofwell-defined peaks in response to potential steps is the standard 'text-book' test for the existence of nucleation-growth kinetics. The presence Voltammetry of T C N Q -0.1 0.15 377 0.40 E (V) vs Ag (s)IAgCl (s)I KC1 (aq), 3 M Fig. 5.34 Cyclic voltammograms (scan rate 100mVs-')of T C N Q microcrystals adhered to a ~afion'-coated RAMTMelectrode in contact with aqueous 0.1 MNaC1 electrolyte. Two cycles are shown in which the scan directions are reversed at potentials corresponding to the foot of (a) the reduction and (b) the oxidation process. Current maxima observed on scan reversal are diagnostic of nucleation-growth and are observed in both directions. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. of nucleation and growth now explains the phenomenon of the 'inert zone' shown in the cyclic voltammogram in Fig. 5.26. If every reduction and oxidation event is driven to 100 per cent completion, then a nucleation overpotential must be supplied on each subsequent scan to restart the phase transformation process. In summary, electrochemical experiments reveal that T C N Q microcrystals immobilized on the surface of an electrode and then placed in an aqueous solution containing a Group I cation exhibit responses which are consistent with chemically reversible solid-solid phase transformations occurring via nucleationgrowth mechanisms. The electrochemical responses are essentially independent of the identity of the anions but strongly dependent on the identity and concentration of the cations. This is because the cations rather than the anions are intercalated and de-intercalated within solid TCNQ. 4.2.2 Theoretical thewnodynamic considerations velevant to a nucleation-growth model A model of the form shown in Fig. 5.1(b) can be used to explain the principal experimental features of the solidsolid transformations in T C N Q [37]. In this model, a T C N Q nanocrystal (phase 1) is assumed to be a hemisphere whose volume does not change during the phase transformation to its cation 400 (N~+)(TCNQ-)-----> TCNQ (K+)(TCNQ-) ---) TCNQ I TCNQ d (R~+)(TCNQ) Fig. 5.35 Double-potential-step chronoamperograms for T C N Q microcrystals adhered to a ~afion@-coated RAMTMelectrode in contact with aqueous 0.1 M NaC1, KC1, R b N 0 3 , and CsCl electrolytes. Potentials are cited in mV versus Ag/AgCl. The existence of peaks in the current-time transients is further confirmation of a nucleation-growth mechanism. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. salt (phase 2). The aqueous solution and the electrode constitute phases 3 and 4, respectively. Though geometrically idealized, the assumption of hemispherical geometry actually does not greatly affect the conclusions, but it does fix some geometric constants at certain values. The reversible work required for formation of unit area of interface between two phases p and q is called the specific interfacial free energy y,, . This parameter will be shown to play a controlling role in the solidsolid transformation. From the theory of the thermodynamics of solids [42], it is expected that the specific interfacial free energy y12between the solid phases 1and 2 will be high (hundreds of mJ mp2)owing to lattice mismatch. However, no such mismatch should exist at the interfaces (1,3) and (2,3) due to the liquid nature of phase 3. In the case of T C N Q , there is probably significant lattice mismatch at the interface (1,2) due to the different arrangements of the T C N Q stacks in the anionic and neutral forms. In principle, the first nucleus of the new phase 2 arising from reduction of phase 1 could appear at four different locations: inside phase 1, at the two-phase boundaries (1,3) or (1,4), or at the three-phase boundary (1,3,4). In an obvious notation, the total work done to form a small crystal of the new phase 2 in each Voltanlnzetry of TCNQ 1 symmetry): locations C1 = - In these equations, AG, is the change in volume free energy per unit volume of reactant and is given by AG, = nFp,,,q, where p,, is the molar density of and q is the overpotential. However, since the terms in parentheses tend to be self-cancelling, while yl2 is large, it is expected that ~t therefore follows that nucleation is most likely to occur at the three-phase ary (1,3,4)since this is the location that minimizes the emergent area of the nergy (1,2) interface in the critical nucleus. Furthermore, consideration of conductivity and transport pathways also suggests the three-phase boundary e region in which an electrochemical reaction is most likely to occur. after, attention is restricted to this case. y a standard argument of nucleation theory [43] it can be noted that A G1z,4 passes through a maximum A GT3,4at a value of r denoted r*, known as the critical radius. Evidently A G[3,4is the energy barrier to nucleation. Differentiating eqn (5.20) and setting the result equal to zero yields ince the nucleation rate is of the form [43] a = a0 exp -4" Yf2 3kT(nF~mr)~ This formula clearly reveals the relationship between the nucleation rate a , the overpotential q, and the specific interfacial fiee energy y12 of the twophase boundary between TCNQ and its cation salt during the transformation. However, what is less clear is how a critical overpotential qcn, arises, below 380 Solid-electrode-solvent intefaces which the system is inert and above which the phase transformation occurrapidly (Fig. 5.26). To understand this feature, it may be first of all supposed that the minimum detectable rate of nucleation in a statistically large field of independent nanocrystals is x nuclei cm-2 s-'. (Note: although this rate is obviously dependent on system size, it will conveniently emerge that the critical overpotential is only a very weak function of x .) Next, it is necessary to explore conditions for which a=x (5.27) because this equality is first satisfied at q = qcn, Finally, substituting for a from eqn (5.26) and inverting the expression yields which is the required result. Equation 5.28 demonstrates that the greater the specific interfacial free energy ylz of the two-phase boundary in the critical nucleus, the greater the critical overpotential for the nucleation process. Moreover, for x << ao, which corresponds to the case in which the minimum observable rate is much less than the maximum possible rate (the usual case), the system size dependence of x has only a small influence on qcrit.For example, for a0 = 102' and x = 10, 100, and 1000, the term in brackets in eqn 5.28 has the values 0.151 [ 4 n / 3 k ~ ] ' / ~0.155[4n/3kt]'/~, , and 0.160[4n/3k~] 'I2, respectively, which is a constant within 6 per cent. Note, also, that for large values of y12 there exists a large range of q values (up to qcrit)where the rate of reaction is vanishingly small, that is, the system is inert. The origin of this phenomenon clearly lies in the non-linear dependence of a on q given by eqn 5.26, and it is this which causes the 'inert zones7in the voltammograms. The above model also explains why, in the absence of mass-transport or ohmic control, the peak widths in voltammograms are narrow: the growth rate of phase 2 at the expense of phase 1 is expected to increase exponentially (or greater) with overpotential. Hence, the interface (1,2) is predicted to sweep through phase 1 at a very high rate after it has been nucleated, which is precisely what is observed. It has been shown above that the voltammetry of nanocrystals of T C N immobilized on an electrode surface exhibits the response expected for a compound undergoing a solid-solid phase transformation under rate control by nucleation and growth. Characteristic features of this transformation are (a) the existence of an inert zone between large reduction and oxidation peaks, (b) narrow peak widths, (c) peaked current-time transients in response to large amplitude potential steps, and (d) loops in cyclic voltammograms. Although the theoretical model is successful in explaining the principal experimental features of the voltammograms, full quantitative application of the model must be approached with caution. The reasons are two-fold. First, the model makes no provision for the development of strain at sites of lattice mismatch. Second, the model assumes an insignificant change in volume Voltammetry of TCNQ 381 during uptake and expulsion of cations, and this is strictly true only12 in the case n general, the occurrence of strain at sites of lattice mismatch depends on whether the interface is coherent or incoherent, and in the experiments described above, this has not been ascertained. If an interface were coherent, large strains might develop and then it would be necessary to modify the theory (or, at least, the interpretation of yI2)because of the additional work needed to form the interface. Alternatively, if an interface were incoherent, which is ht to be the case in most reconstructive first-order phase transformations ere would be no crystallographic continuity and hence no strain. he effect of a small change in volume during uptake and expulsion of cations ess worrisome, because the resulting stress can be relieved by plastic flow or motion of lattice defects. Moreover, the use of widely spaced nanocrystals in the present work also prevents the pile-up of large-scale stresses such as one see in densely packed metallurgical specimens. O n the other hand, large es in volume (say, >10 per cent) may be problematic, and in such cases some modification of the theory might be needed. 2 . 3 Exploration of the nucleation-growthprocess and her mechanistic details by ancillary techniques voltammetry of surface-immobilized T C N Q provides evidence of solidphase transformations controlled by nucleation and growth mechanism. ta obtained by ancillary techniques such as in situ optical microscopy, ex situ scanning electron microscopy (SEM) and X-ray diffractometry help to further elucidate the details of [ T C N Q ] ~ ' process. Optical microscopy n order to monitor colour changes that occur during potential cycling experiments on solid TCNQ, an electrochemical cell was fitted with a quartz-window ase, and the working electrode was attached to a screw thread which allowed t to be positioned in the focal plane of an inverted metallurgical microscope 371. Optical data were then recorded as video images or stored as single frames in a computer [37]. Using this approach, a colour change from yellow to bluegreen was observed upon electrochemical reduction of T C N Q microcrystals adhered to an electrode in contact with 0.1 M KC1. Interestingly, the colour change occurred on the time-scale of seconds for small crystals (< 1ym) but on the time-scale of minutes for larger crystals. This observation suggests that the voltammetric responses recorded on short time-scales are primarily associated with crystals in the nanometer size range. 1 2 ~ h eunit cell volume per molecule of T C N Q is 256 A3 in both T C N Q and [ ~ a ' ] [TCNQ-] . For [K'] [TCNQ-] , [ ~ b ' ] [TCNQ] and [Cs+I2[TCNQ-12 [TCNQ], values are 280, 287, and 277 A3 respectively (see Table 5.9 and J. Chem. Soc., Faraday Trans. 92 (1996) 3925). Scanning electyon microscopy and electron probe mic~oanalysis The SEM and electron probe microanalysis (EPM) experiments were undertaken with an in-lens field emission scanning electron microscope (FESEM). To facilitate the transfer of samples from the electrochemical cell to the FESEM chamber, dual-purpose gold substrates were employed that acted both as the electrode and the FESEM sample holder. As with regular electrodes, these substrates were mechanically coated with T C N Q microcrystals before immersion in the electrochemical cell. The T C N Q salts were then generated in situ by electrolysis in 0.1 M Na+, K+, ~ b ' , and Cs+ chloride solutions. After removal from the electrochemical cell, the now T C N Q salt-coated substrates were rinsed with de-ionized water and dried in air at room temperature prior to obtaining FESEM images [37,38]. On a gold An FESEM image of some freshly deposited T C Q microc~stals substrate is shown in Fig. 5.36. The majority of the microcrystals are between 100 and 500 nm in diameter. There are also a few crystals (not shown) of slightly larger dimensions, but as mentioned earlier, these react slowly on the time-scale of voltammetric experiments, and are probably of little statistical significance. Four FESEM images, each recorded after nine and a half continuous voltammetric cycles of the potential in a fferent electrolyte solution9 are shown in Fig. 5.37. The electrolytes are 0.1 N a a 0.1 KC17 0CsC1. It is clear that significan earrangement of solid formation of needle-shaped microcrystals occurs upon cy FESEM micrograph of T C N Q adhered to a gold substrate. The majority of particles are between 100 and 500 nm in diameter. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. Voltar-lznzetry of TCNQ 383 -37 FESEM micrographs of a gold electrode surface containing adhered T C N Q in conith aqueous 0.1 M NaC1, 0.1 M KC1, 0.1 M R b N 0 3 , and 0.1 M CsC1 electrolytes after nine-and-a-half voltammetric cycles of the potential. In all cases needle-shaped highly crystalline phologies have developed from that initially seen in Fig. 5.36. Reproduced by courtesy: Analyst (1998) 1891. Copyright, Royal Society of Chemistry. alyses indicate that the microcrystals contain the corresponding Group from the electrolyte solutions. Anions are absent, demonstrating once ke is negligible. e average lengths, widths, volumes, and aspect ratios of the crystals in the four cases considered in Fig. 5.37. Since the microcrystals are generated by rapid solid-solid phase transe surprising if they were equilibrium morphologies. Most the morphologies are simply those that permit the most reactlon between the oxidized and the reduced forms of the TC needles having average aspect ratios great to-volume ratios higher than the equilibrium ones. en the microcrystals are returned to the electrochemical cell and re- persist even when experiments are repeated many times. It is concluded from these data that after the first few voltammetric cycles, the dominant process is 384 Solid-electvode-solvent intefaces Table 5.8 Average lengths, widths, volumes, and aspect ratios ofneedle-shaped microcrystals of T C N Q salts formed by potential cycling experiments. All the microcrystals are needle-shaped with aspect ratios exceeding 4. See reference 1381 for further details. T C N Q salt Average length (nm) Average width (nm) Average volume (lo6nm3) Average aspect ratio the reversible transformation of the T C N Q microcrystals to the TCNQ-salt rnicrocrystals with minimal change of bulk morpholo&. Even though the majority of the voltammetric response is associated with smaller microcrystals, larger rnicrocrystals (> 1 pm) are not completely inert. particular, outgrowths occur, as shown in Fig. 5.38. Presumably these originate from twin plane defects which commonly arise in high-speed crystal growth. Lacunae can also be observed. These are hollow depressions in the centres of crystal faces caused by the inability of surface diffus;on to transport molecules fist enough from the rapidly growing crystal edges. The fact that many of the outgrowths are hollow is clearly shown in Fig. 5.39. It is evident that electrolyte solution can be trapped inside these structures. The main conclusion from the FESEM studies is that large changes in microcrystal morphology occur during the early stages of voltammetric cycling, leading to the formation of stable, needle-shaped crystals that are retained on the surface of the electrode. Under the same conditions, larger crystals are less morphologically stable, and tend to form hollow outgrowths. X-ray dlffractometry Dual-purpose substrates for electrochemistry and e x situ X-ray diffraction experiments were fabricated from microfoils of 0.05 pm gold on 13 pm mylar. To increase the amount of material available for X-ray analysis, T C N Q was deposited on the gold by evaporation of an ethanolic solution rather than by mechanical attachment. After electrolysis to form the T C N Q salts, each surface was rinsed with de-ionized water and allowed to dry in air. Typically, the diffraction angle was varied from 3" to 32" with a step interval of 0.025". The chemical formulae and crystal structures of the electrogenerated T C N salts were readily established by comparing experimental X-ray diffractograms with a library of diffractograms obtained from the JCPDSACDD Powder Diffraction File [45] or back-computed from published structures [38]. Figure 5.40 is an experimental X-ray diffractogram of T C N Q on a goldmylar substrate prior to electrolysis, and it can be seen that several peaks Voltammetry of TCNQ 385 Fig. 5.38 FESEM images of outgrowths formed during the course of reduction of large T C N Q crystals (> 1 pm) adhered to a gold electrode in contact with (a) 0.1 M NaCl and (b) 0.1 M KC1 aqueous electrolytes. Clearly, the bulk mass of the larger crystals react more slowly than the smaller crystals. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. due to TCNQ are prominent above the background. Indeed, most of the mylar response is concentrated between 22" and 30" and therefore it is easy to exclude this from analysis. Peaks from gold occur above 40" and do not interfere. Figures 5.41(a) and 5.42(a) show the X-ray diffiactograms of TCNQ on gold-mylar substrates before and after electrolysis in solutions of 0.1 M NaCl 386 Solid-electuode-solvent intefaces .39 FESEM images of lacunae formed at the end of needle-shaped outgrowths during the course of reduction of large TCNQ clystals adhered to a gold electrode in contact with 0.1 M NaCI. (b) A close-up image of part of (a) which shows the details of a single lacunae which could trap electrolyte solution. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. and 0.1 M R b N 0 3 , respectively. Equivalent data in 0.1 M KC1 and 0.1 M CsCl have also been obtained and are reported in reference [38].Some peaks due to unreacted T C N Q are evident in all cases, but there are a sufficient number of product peaks to distinguish the freshly formed T C N Q salts from each other and from the inorganic salts in solution. For example, in the case of sodium a e t Before Electrolysis T C N Q from JCPDS 2-0 angle (deg) ig. 5.40 X-ray diffractograms of T C N Q microcrystals on a gold-mylar substrate before electrolysis. Although the mylar contributes a very broad peak between 22" and 30°, the T C N Q peaks are still prominent. Note that the T C N Q peaks are sharp, indicating good internal crystallinity. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. Before Electrolysis After Electrolysis (Na+)(TCNQ-) from JCPDS T C N Q from JCPDS 10 15 2-0 angle (deg) 20 10 15 2-0 angle (deg) 20 Fig. 5.41 X-ray diffractograms observed from T C N Q rnicrocrystals adhered to a gold-mylar substrate in contact with aqueous 0.1 MNaC1 electrolyte before and after reductive electrolysis. (a) Individual intensities. (b) Difference in intensities. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. (Fig. 5.41 (a)),the product peaks match those of [ ~ a +[TCNQ-1. ] This is clearly seen in the difference curves between the diffractograms shown in Fig. 5.41 (b) after background subtraction. A decrease in the amount of T C N Q salts is indicated by the positive peaks. Small discrepancies in the relative peak heights Before Electrolysis After Electrolysis Computed ( ~ b ' )(TCNQ-) T C N Q from JCPDS 10 15 20 2-0 angle (deg) 10 15 20 2-0 angle (deg) Fig. 5.42 X-ray diffractograms observed from TCNQ microcrystals adhered to a gold-mylar substrate in contact with aqueous 0.1 M RbCl electrolyte before and after reductive electrolysis. (a) Individual intensities. (b) Difference in intensities. Reproduced by courtesy: Analyst 123 (1998) 1891. Copyright, Royal Society of Chemistry. between the experimental data and the JCPDS data are not significant and are due to the preferential orientation of crystals. As already shown in the FESEM images, the microcrystals are lying flat on the electrode surface. Consequently, some peaks are stronger while others are weaker than in the case of random orientation. Analogous results are obtained for all the other salts. The most surprising X-ray diffractometryresult is that of rubidium (Fig. 5.42). Of the four known structures for rubidium T C N Q salts, it is the 1 : 1 salt normally found at low temperature (113 K) that forms electrochemically. This result strikingly illustrates the dominance of kinetics over thermodynamics in rapid phase transformation processes. Table 5.9 summarizes the structural parameters of the electrochemically generated T C N Q salts, and Fig. 5.43 show computer-generated perspective views of these structures. Close inspection reveals that three different kinds of lattice rearrangement accompany electrochemical cation ingress: the separation of T C N Q anion stacks (Cs'); the 90" rotation of alternate T C N Q anion stacks accompanied by some lateral compression ( ~ b ' ) , and the 90" rotation of alternative T C N Q anion stacks with some flattening of the layers (Na+ and Kf). Note also that in the cases of ~ a +K+, , and ~ b ' , the reaction stoichiometries are x = 1 and y = 1 (defined in eqn 5.16), whereas in the case of CS+they are x = 3 and y = 2. The reaction for Cs' is therefore + 2~s+(solution)+ 2 e + [Cs+12[TCNQ-12 [TCNQ] (solid) 3TCNQ(solid) (5.29) rather than + TC~Q(so1id) CS+(solution) + e + [cs'] [TCNQ-](solid) (5.30) Voltammetry of TCNQ 389 5.9 Structural parameters derived from X-ray diffraction measurements N Q and its salts of Group I cations, as reported in the literaturea pace group TCNQ monoclinic [~a+] [TCNQ-] triclinic [K+] [R~+I [TCNQ-] [TCNQ-I monoclinic monoclinic [Cs+]2 [TCNQPl2 [TCNQ] monoclinic - a (A) 16.415 b (A) 7.06 c 8.95 a (degree) 90.00 B (degree) 98.65 Y (degree) 90.00 Z 4 Unit cell volume (A3) 1024 Unit cell volume per 256 molecule of TCNQ (A3) Cation radius (A) - (9 'These structures are the ones observed electrochemically at 295 K. Note the complex stoichiometry of the caesiurn salt. The unit cells contain 2, formula units and have dimensions a, b, c with opposite angles of a , p , y , respectively. See reference 1381 for further details. as might have been anticipated. The reason for this is unclear, but is probably related to the fact that CS+has a larger radius than the other cations in Table 5.9, which makes this cation more difficult to accommodate. Structural representations contained in Fig. 5.43 indicate that cation ingress into T C N Q is always accompanied by a significant (though reversible) structural rearrangement of the [TCNQ-] anion stacks. Moreover, there is no evidence of non-integer values of x and y,which would be expected if classical intercalation were occurring. The question therefore arises of whether the electrochemical reaction between Group I cations and T C N Q can be classified as intercalation at all. In the older literature [46], intercalation seems to have meant the reversible insertion of a guest species into a layered host with no orientational rearrangement of the structural features of the host, whereas in the case of T C N Q the reversible insertion of a guest species into a channel host occurs with significant orientational rearrangement of the structural features of the host. This would appear to rule out the use of the word 'intercalation'. However, the definition of intercalation has expanded in the recent literature to include all reversible insertion reactions, even those in which the host and guest experience some degree of perturbation (from subtle to extreme) in their geometric, chemical, electronic, and optical properties [46,47]. If this revised definition is accepted, then eqn. 5.16 would constitute an example of an intercalation reaction that is also a nucleation and growth reaction. Face View Edge View TCNQ Fig. 5.43 Perspective views of the structures of T C N Q and its salts formed electrochemically at 2 2 ° C Atoms not drawn to scale. Reproduced by courtesy: J. Chem. Soc., Faraday Tram. 92 (1996) 3925. Copyright, Royal Society of Chemistry. Voltammetry of TCNQ 39 1 Visualization of the cation channels in [TCNQ-] salts can be achieved by molecular simulation based on the atomic coordinates from X-ray analysis [38]. he results are shown in Fig. 5.44, where it can be seen that even cations hav(see Table 5.9) as large as Cs' (1.67 A) can be accommodated in the -1 channels. It is interesting to note that the cations are unsolvated in the [TCNQ-] channels which implies that they have lost their inner solvation spheres of water molecules at the mouths of the channels. Inside the solid phase, the cations are, of course, stabilized by a 'coordination sphere' of [TCNQ-] anions. Fig. 5.44 Visualization of the cation channels in T C N Q salts made by molecular simulation using atomic coordinates from X-ray analogues. The size of the cations are contained in Table 5.9. Reproduced by courtesy: Analyst 223 (1998) 1891. Copyright, Royal Society of Chemistry. 4.3 Electrochemically driven tran$ormation of microcrystalline TCNQ to tetraalkylamrnonium [TCNQ-] salts13 The metal cations inserted into the [TCNQIOI- system during the course of redox cycling experiments described in Section 5 are relatively small. Questions therefore arise as to whether voltammetry would still be possible when larger ) (Fig. 5.45) have to be transported across tetraalkylammonium ( N R ~ +cations the solid-solution (electrolyte)interface and as to whether systematic thermodynamic and/or kinetic effects attributable to cation size effects can be interrogated by studying the voltammetry of T C N Q adhered to an electrode in contact with aqueous N R 4 + containing electrolytes. 4.3.1 Voltammetry Systematic trends with parameters such as the peak potentials, the peak height, and the gap between reduction and oxidation response are observed in the voltammetry of T C N Q as the chain length of the R group in the NR4+ cation is increased. Voltammograms obtained at a scan rate of 20 mVs-' in the flowing solution configuration with a RAM^^ electrode (Fig. 5.46) clearly confirm that the peak current magnitudes for this electrode-cell configuration are in the order N H ~ ' > NMe4+ > N E ~ ~>+ NPr4+. Indeed, for the NPr4+ case, the current magnitude is very small and more akin in magnitude to that observed with the solid Fig. 5.45 comparison of sizes of some ions that have been used to form T C N Q - salts. Provided by courtesy of P.G. Symons, Monash University, Victoria, Australia. 1 3 ~ .Bond, ~ . S. Fletcher, F. Marken, and P.G. Symons, unpublished studies, 1996-98. Voltammetry of TCNQ 393 NH,+ 5.46 Voltammograms of microcrystals of T C N Q immobilized on a Nafion-coated R A M T M electrode in contact with aqueous 0.1 M NR4C1 electrolyte solutions. Current scales are different for each case. $ed: NH4+, 1.1 PA; NMQ+, 360nA; NEtr+, 210nA; NPr4+, 25nA. (Scan rate 20 mV s-l, third cycle of potential recorded.) Provided by courtesy of P.G. Symons, Monarh University, Victoria, Australia. trarzs-[~r(C0)~ (dpe)$/+ process. For the aqueous 0.1 M NH4Cl electrode voltammograms have similar characteristics to those described case, (Fig. 5.46), reviously in the presence of potassium containing electrolytes (Fig. 5.30). The almost symmetrical reduction and oxidation responses with a large peak-to-peak separation and large peak current values and charges are indicative of extensive solidsolid phase conversion. The data are most simply interpreted in terms of a one-electron reduction accompanied by incorporation of N H ~ +into the solid lattice (eqn 5.31), although XRD data are not available to confirm this stoichiometry. TCNQ(so1id) + e- + N H ~ + ( s o ~ u ~6 ~ o ~ ) [ N H ~ +[TCNQ-] ] (solid) (5.31) or the other electrolytes considered in Fig. 5.46, the extent of electrolysis on the voltammetric time-scale of 20 mV s-' must be far from exhaustive. The critical potentials for the onset of the reduction and re-oxidation response both shift to more positive values upon increasing the size of the electrolyte cation, and the peak separation between the reduction and oxidation components increases slightly with change in cation size. The shifi in ( E F ~ EF)/2 can again be attributed to a change in the formal thermodynamic (reversible) redox potential, for a reaction of the kind given in eqn 5.32. + It therefore may be proposed that a hydrophobic cation, such as NPr4+, will be removed from the aqueous to the solid phase at a more positive potential 394 Solid-electrode-solvent intevfaces than the less hydrophobic NH4+ in accord with data available for the transfer of cations from aqueous into organic phases [19]. Thus, neglecting any solidstate effects, the trend in peak potentials can be explained in terms of increasing to Npr4+ cations. The equivalent effect hydrophobicity in changing from N H ~ + was noted for the t r a n s - [ ~ r ( ~ ~ ) ~ ( d ~process e ) ~ ] ~which '+ involved insertion of anions into the structure. The gap between the reduction and re-oxidation processes, or the so-called 'inert zone', when alkaline metals are the cations, has been attributed to the need to provide a potential to overcome interiacial free energy between differences in the two solid phases by a nucleation-controlled mechanism. Assuming that the formation of solid [NR4+][TCNQ-] requires an increased volume change as the size of the NR4+ cation increases, and therefore a more pronounced lattice mismatch, allows the present results to be explained by a nucleation-growth process. However, details concerning the crystallographic changes accompanying reduction and incorporation of the cation at an electrode surface are series of salts. unknown for the N R ~ + A new feature introduced in the solid-state voltammetry of T C N Q in aqueous 0.1 M N B u ~ +containing electrolyte solution (Fig. 5.47) is the splitting of the reduction response which may be explained in terms of the formation of different phases with distinctly different energies being postulated. The origins of the responses for the first reduction process (IaRdand Ia,,) and the second reduction process (Ibredand Ib,,) (see Fig. 5.47) are summarized in eqns (5.33) and (5.34). A [NBu4+][TCNQ] [ T C N Q ](solid) [NBU~+] [TCNQ] [TCNQ]- (solid) (533) + e + NBu4+(solution) (5.34) - 2[NBu4+][TCNQ-] (solid) A I I I 0.0 0.5 1.O E (V) vs Ag /AgCI (3 M KCI) Fig. 5.47 Cyclic voltammograms obtained at a scan rate of 1 rnV s-' and at 22OC for reduction of T C N Q adhered to a basal-plane pyrolytic graphite electrode placed in contact with aqueous 0.1 M NBu4C1 electrolyte. Provided by courtesy of F. Marken, La Trobe University, Victoria, Australia. Voltawznzetry of TCNQ 4.3.2 395 Scanning electron microscopy canning electron micrographs were obtained after electrochemical reduction of solid T C N Q adhered to a gold electrode in contact with 0.1 M NH4+, ~ e ~ NEt4+, ' , and NBu~' aqueous electrolytes. In the presence of NH4+, ell-defined, elongated, needle-shaped microcrystals of up to 5-pm length were observed after reduction. In NMe4+ containing electrolyte, smaller crystals of approximately 1-pm length, but with a similar shape to the NH4' case were ined. In the presence of N ~ t 4 + even smaller crystals were produced and with 4' the solid formed after reduction retains its non-crystalline appearance. These observations are consistent with a far greater extent of electrolysis in the presence of the smaller N H ~ ' cation and that a rate-determining step is controlled by the cation insertion process in conjunction with crystal growth. .4 Dissolution of solid TCN from electvode sufaces The change from weakly diffracting solid to needle-shaped crystals during the course of potential cycling and/or T C N Q reduction experiments implies that dissolution and probably precipitation reactions are highly significant in early stages of the cyclic voltammetry of microcrystals of T C N Q adhered to electrode surfaces. Indeed, the initial formation of any new solid at an electrode-solidsolution (electrolyte) interface produces very small amounts of material which can be expected to dissolve into the solution phase because the solubility will not be exceeded, unlike the case at later times in the experiment when large amounts of solid are generated. Thus, contribution of dissolution processes need to be considered in any reaction where a solid adhered to an electrode is placed in contact with an electrolyte. Use ofrotating ring-disc electrode and in situ electron spin resonance techniques to detect dissolution processes that accompany the voltammetry ofsolid TCNQ adhered to electrode s ~ f a c e s ' ~ n principle, the use of i n situ rotating ring-disc electrode (RRDE) and 4.4.1 simultaneous electrochemical-electron spin resonance (SEESR) techniques (Section 16.1 in Chapter 2) should enable the detection of solution-soluble products created during electrochemical experiments on T C N Q attached to an electrode surface. Direct detection of products of electrode processes by scan reversal techniques, as used in cyclic voltammetry at a stationary macrodisc electrode, are obviously not available with the rotating disc electrode (RDE), since the product of the electrode reaction is continuously swept away from the surface of the disc (see Section 9.1 in Chapter 2). Thus, at the RDE, reversal of the direction of the potential sweep, under conditions where the scan rate is sufficiently slow 1 4 ~ d a p t e with d permission from J . Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. 396 Solid-electrode-solvent intefaces compared to the rotation rate, will just retrace the curve obtained in the forward scan. Information equivalent to that obtained by cyclic voltammetry at a stationary electrode is obtained in the RDE method by addition of an independent ring electrode surrounding the disc [48-501 to give the so-called RRDE methodMeasurement of the current at the ring electrode with the potential maintained at a given value enables knowledge to be obtained about what is occurring at the disc electrode surface. For example, if the potential of the ring is held at a value at the foot of a reversible reduction wave, any soluble product formed at the disc will be swept over to the ring by the radial flow streams where it will be oxidized back to the starting material or 'collected'. The mass transfer to a ring electrode is larger than that to a disc at a given rotation rate, because flow of fresh solution to it occurs radially from the area adjacent to the ring, as well as normally from the bulk solution. However, the theoretical treatment of ring electrodes is more complicated than that of the RDE, since the radial mass transfer term must be included in the convective-diffusion equation. While the mathematics may be difficult, the results are simple to understand. In the R R D E method, as applied to studies of T C N Q , the solid may be attached to the disc, or so-called generator electrode, and the ring electrode, which is separated from the disc electrode by the solution phase, can then be used as the detector electrode to establish the identity of soluble species that have been transported across the solution phase. In SEESR experiments, compounds to be studied may be attached to working electrode contained in a quartz flat cell which is then used within an electron spin resonance (ESR) cavity [51]. While R R D E experiments allow studies to be undertaken on the voltammetry of components formed either transiently or permanently in solution, ESR measurements should enable a distinction to be made between solution and solid-state surface-confined paramagnetic species. Thus, the combination of these in situ methods enables features of the complex electrode-solid-solvent (electrolyte) interface to be probed. In particular, these techniques may reveal whether extensive or transient dissolution of solids occurs during transformations between oxidized (reduced) and reduced (oxidized) states. RRDE studies on TCNQ Figure 5.48 shows the platinum disc and ring (Pt/Pt) electrode responses (versus disc potential) for reduction of solid microcrystalline T C N Q attached to the disc electrode under conditions of hydrodynamic voltammetry when the electrode is placed in Li+-buffer.15 In this medium, a reduction reaction yielding waterM ~ is) observed soluble [L~+][TCNQ-] (solubility product [52]: 2.2 x with a peak potential Ep = -0.18 V versus Ag/AgCl (Fig. 5.48(a)). The conclusion that dissolved [TCNQ-](solution) is formed is reached on the basis that 1 5 ~ hbuffers e used in the R R D E studies were Britton-Robinson p H 10.0 buffers containing 0.02 M LiOH or K O H which are referred to in the text as ~i+-bufferand K+-buffer, respectively. Voltammetry of TCNQ 397 . 5.48 Pt/Pt R R D E cyclic voltammetry of T C N Q attached to the disk electrode in contact with Li+-buffer using a scan rate of 20 rnV s-I and frequency of rotation of 1000 min-I. (a) Disc current versus disc potential; (b) Ring current versus disc potential, with a ring potential of 0.2 V versus Ag/AgCl; (c) Ring current (five times) versus disc potential, with a ring potential of -0.2 V versus Ag/AgCl. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. no oxidation reaction is detected at the disc electrode during the reverse sweep (Fig. 5.48 (a))and by noting that dissolved solution-soluble [TCNQ-] (solution) is in fact swept past the ring electrode where it is detected via its oxidation response when the ring electrode is held at a potential of f0.2 V versus Ag/AgCl. The observed behaviour at the RRDE is consistent with the reaction sequence + ~i+(solution)+ e- --+ [~i'] [TCNQ-] (solid) [~i'] [TCNQ-] (solid) -+ ~i'(so1urion) + [TCNQ-] (solution) TCNQ(so1id) (5.35) (5.36) No significant response on the ring electrode was detected during a complete cyclic voltammetric sweep when its potential was held at -0.2 V versus Ag/AgCl (Fig. 5.48(c)), where detection of T C N Q could be expected. This is consistent with the absence of transfer of solid T C N Q from the disc to the ring electrode, and that complete dissolution of solid [~i'] [TCNQ-] occurs during one sweep of the potential under conditions of RRDE cyclic voltammetry. Control experiments confirmed that T C N Q remained firmly attached to the disc electrode surface when no reduction potential was applied, even at frequencies of rotation of up to lo4 min-I . Pt/Pt KRDE cyclic voltammetry of T C N Q attached to the disc electrode in contact wit], K+-buffer. Three consecutive scans shown with a scan rate of 20 rnV s-I and frequency of rotation of 1000 min-l. (a) Disc current versus disc ~otential;(b) Ring current ( ~ 2 0versus ) disc potential, with a ring potential of 0.2 V versus Ag/AgC1; (c) Ring current (x20) versus disc potential, with a ring potential of -0.3 V versus Ag/AgC1. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. is significantly different when E voltammetric response of T C , rather than ~ i ' , is present in the electrolyte solution. Figure 5.49 shows disc and ring detector electrod ses during the first three voltammetric sweeps when surlace-attached is reduced when the electrode is in '-buffer. In this c ] salt is sparingly soluble (solueven though the bility product 5 x 1 0 - l ~ ely small level of dissolution of reduced solid occurs. W is present in the electrolyte, the disc electrode response under hydrody nditions (Fig. 5.49(a)) is in fact closely related to that found with static electrodes with a well-defined apparently inert region being detected between the reduction and oxidation peaks, and with a slow decrease in peak height as cycling of the potential occurs. equency of electrode rotation is 3 1000 min-' , a significant amount of ] is detected during the initial stages of the reduction of solid T wever, when repetitive cyclic voltammetric experiments are und (Fig. 5.49(a))only very minor ring electrode responses are prese Apparently, in the initial cycle of the potential, reduction of T -1 which is predominantly 0x1 formation of solid [K+][TC structurally modified or differently adhered form of solid T C N Q , although some dissolution of the adhered salt does occur. In second and subsequent cycles ofthe Voltammetry of TCNQ 399 ptential and after modification of adhered TCNQ, the nucleation and growth reaction interconverting the T C N Q and [K'] [TCNQ-] solids are dominant relative to the dissolution process (eqn 5.37). [K'] [TCNQ-] (solid) + K' (solution) + [TCNQ-] (solution) (5.37) Interestingly, when the ring electrode potential corresponding to the reduction of T C N Q is set at -0.30V versus Ag/AgCl (Fig. 5.49(c)), a small yet significant response indicates that during the first reductive sweep, TCNQ is expelled from the surface of the disc electrode at the same time as reduction of solid T C N Q occurs. T C N Q is also expelled from the sudace during oxidation of solid [K'] [TCNQ-] to TCNQ. Significant expulsion of T C N Q seems to accompany only the initial reductive cycle of the potential (Fig. 5.49(c)). contrast, some T C N Q always appears to be expelled during oxidation of +][TCNQ-] (solid) back to TCNQ(so1id)on the disc electrode during the posive potential oxidative voltammetric scan, (Fig. 5.49(c)). This loss of T C N Q accounts for the decrease in peak height observed in second and subsequent otential cycles of the disc electrode (Fig. 5.49(a)) even though no soluble [TCNQ-] (solution) is detected at the ring electrode (Fig. 5.49(b)). Clearly, the RRDE experiments reveal that significant rearrangement in the nature of adhered T C N Q occurs during potential cycling experiments, as is also demonstrated in the SEM studies described in Section 4 under the headings of scanning electron microscopy and electron probe microanalysis. However, many of the details of the loss of solid accompanying the electrochemistry of T C N Q adhered to electrode surfaces are unknown. SEESR studies on TCNQ The ESR detection of electrochemically generated radical anions (SEESR technique) should be sensitive to the phase of a particular paramagnetic comound. In the case of electrochemically generated [TCNQ-I, a multiple-line SR spectrum would be expected from dissolved [TCNQ-](solution) [54], and a single-line spectrum for a solid phase [TCNQ-] salt [55]. Figure 5.50 shows the solution phase ESR spectrum obtained from chemically synthesized [54] [Li'] [TCNQ-] salt dissolved in Li+-buffer. The simulated ESR spectrum with g = 2.0023, a ( 1 4 ~= ) 0.0985 mT, and a('H) = 0.1435 mT, also included in Fig. 5.50, is fully consistent with published data [54]. The in situ SEESR spectrum shown in Fig. 5.50 was recorded during the course of one-electron controlled-potential electrolysis of surface-attached microcrystalline T C N Q adhered to an electrode in contact with ~i+-buffer.Clearly, the ESR spectra shown in Fig. 5.50(a) and (b) are indistinguishable and there is no ESR evidence to indicate the presence of solid [Li'] [TCNQ-1. Under the thin-layer conditions of the SEESR flat cell used in these experiments, the (solution) and oxidareduction of TCNQ(so1id)to yield dissolved [ ~ i +[TCNQ-] ] tion of dissolved [Li'] [TCNQ-] (solution) back to suriace-attached TCNQ(so1id) is chemically reversible. Figure 5.51 shows a series of ESR spectra recorded Field (mT) Fig. 5.50 Solution-phase ESR spectra of TCNQ-; g = 2.0023, a ( " ~ ) = 0.0985mT, a('~= ) 0.1435 mT. (a) Solid line is the experimental spectrum obtained from 0.1 M [Li+][TCNQ-] in Li+-buffer and the dotted line, which almost completely overlaps experimental spectrum is the simulated spectrum; (b) in situ ESR spectrum recorded during the course of electrochemical reduction of T C N Q adhered to a Pt electrode in contact with Li+-buffer. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. of (a) the initial solution, (b) fully reduced solid T C N Q , (c) fully re-oxidized [TCNQ-](solution), and (d) again fully reduced solid T C N Q in a thin-layer SEESR cell. Optical monitoring of the electrode surface confirms that deposition of a thin yellow layer ofTCNQ(so1id)on the electrode surface occurs upon re-oxidation of the blue solution-soluble [TCNQ-] (solution). When K+-buffer is used as the electrolyte solution, distinctly different SEES behaviour is observed. Figure 5.52 shows the ESR spectra obtained via constant potential electrolysis at four different potential regions. The solution-phase ESR spectrum of [TCNQ-](solution) is observed when the potential is held at the foot of the reduction waves (i.e. prior to the reduction peak potential). The double integral of the spectrum is consistent with the concentration of [TCNQ-](solution) being below that derived from the solubility product of [K'] [TCNQ-] . No clear indication of a solid-state spectrum is evident when Voltammetry of TCNQ 401 Field (mT) Fig. 5.51 In situ generation of solution-phase ESR spectrum of T C N Q - in ~i+-bufferat a Pt electrode. ESR spectrum (a) of initially surface-attached T C N Q ; (b) after complete reduction of TCNQ(so1id) to [TCNQ-](solution); (c) after complete regeneration of TCNQ(so1id); (d) after complete reduction to TCNQ-(solution) after regeneration of T C N Q as in (c). Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. electrolysis is undertaken at this potential, even after leaving the cell switched on for several minutes. However, after applying a potential corresponding to the reduction peak potential (Fig. 5.52(b)),a distortion is observed in the central region of the solution-phase ESR signal. The dominant feature is a single-line ESR spectrum when the potential is adjusted to values more negative than the peak potential (Fig. 5.52(c) and (d)). Furthermore, when the potential was applied at these negative values for increased periods of time, the intensity of the solution-phase ESR spectrum remained constant, whereas the intensity of the solid-state spectrum increased. A comparison with the single-line solidstate ESR spectrum of [K+][TCNQ-] (Fig. 5.53) enables the conclusion to be reached that the in situ ESR spectrum of reduced [TCNQ-] results from the superimposition of solution and solid-state spectra of [ T C N Q - ] ( s o l u t i o n ) and [K'] [TCNQ-] (solid), respectively. In summary, for the [TCNQ]'' system, the combination of R R D E and SEESR experiments shows that microcrystalline T C N Q , when attached to Field (mT) Fig. 5.52 ESR spectra of in situ electrochemically generated TCNQ-(solution) and/or [K+][TCNQ-](solid) from TCNQ(so1id) adhered to a Pt electrode in contact with Kf -buffer. Dependence of ESR response on applied potential is shown (a) prior to peak; (b) at peak; (c) on decreasing part of peak; (d) after peak. The electrolysis potentials were determined from a voltammogram obtained in the SEESR cell at a scan rate of 100mVs-l. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. an electrode surface, is reduced in the solid-state phase. Dissolution may take place up to the point where the solubility product is not exceeded, and when the applied potential is not sufficiently negative to enable nucleation and crystal growth to occur. In the case of ~i+-containingelectrolyte solutions, the solubility product is never exceeded. In contrast, the limited solubility of [K'] [TCNQ-] allows the simultaneous observation of both solid-state reduction and dissolution pathways to be observed. 4.4.2 RRDE and SEESR studies on adhered solid trans- C T ( C O () ~d ~ e ) ~ As shown in Section 3.2.2, although, neither tr~ns-Cr(CO)~(dpe)~ nor the trans-[Cr(CO)2(dpe)2]+ salt show any significant conductivity, the t r a n s - [ ~ r ( ~ ~ ) , ( d ~ eprocess ) ~ ] ~ / in + the surface-attached state is well defined. It is therefore interesting to compare the results from RRDE and SEESR studies with the [TCNQ]O/- process, where semiconducting properties and dissolution processes have been detected, with those for t r a n s - [ ~ r ( ~ 0 ) ~ ( d ~ e ) z 1 0 / + . Figure 5.54 shows GC/GC RRDE voltammograms in 0.1 M aqueous KC1 when microcrystalline tran~-Cr(CO)~(dpe)~ is attached to a GC disc electrode which is rotated at a frequency of 1000 min-'. Clearly, no ring electrode response is detected at a ring potential of either 0.1 or -0.5 V versus Ag/AgC1 Voltammetvy of TCNQ 403 1 gz2.0023 Field (mT) ig. 5.53 Solid-state ESR spectra of [K+][TcNQ-](solid). (a) [K+][TCNQ-] prepared from reaction of KI and T C N Q in acetonitrile; (b) [K' ] [TCNQ-] (solid) prepared by electrochemical reduction of surface-attached T C N Q in contact with K' -buffer. Reproduced by courtesy: J . Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. during the course of either the oxidation or subsequent reduction component of the experiment. This result indicates that neither solid trnn~-Cr(CO)~(dpe)~ nor the trans-[Cr(CO)2(dpe)2]+salt dissolve to any measurable extent so that a dissolution/precipitation mechanism is unlikely to accompany the solid-state voltammetry of the trans-[c~(co), (dpe)2]0"- process. However, the solubility of these chromium carbonyl solids may be enhanced by the addition of organic solvent. Figure 5.55 shows the GC/GC RRDE response for oxiwhen the electrode is placed in a dation of solid trans-Cr(CO)z(dpe)2(~~hd) 1 : 1 aqueous: acetonitrile mixture containing 0.1 M KCI. Upon oxidation of solid tran~-Cr(CO)~](dpe)~ in this mixed solvent medium, quantitative removal of solid t r a n r - [ ~ r ( ~ ~ ) , ( d ~ via e ) ~dissolution ]+ is now observed at a ring electrode potential of -0.5 V versus Ag/AgCl [51]. Partial dissolution of tvan~-[[Cr(CO),(d~e)~]+ can be observed at lower acetonitrile concentrations. At acetonitrile content of up to 50 per cent, no dissolution of neutral t~ans-Cr(CO)~(dpe)~ could be detected on the ring electrode when the ring potential was adjusted to 0.1 V versus Ag/AgCl and the frequency of rotation varied between 100 and 1o4 min-' . Therefore, the electrochemical oxidation of t~ans-Cr(CO)~(dpe)~ in aqueous acetonitrile mixture generates a tvan~-[Cr(CO)~(dpe)~]+ salt which is followed by dissolution of this species. 404 Solid-electuode-solvent intefaces Fig. 5.54 GC/GC R R D E voltammograrns obtained at a scan rate of 2 0 m ~ s - *and frequency of rotation of 1000 min-' for t r ~ n + C r ( C O ) ~ ( d p attached e)~ to the disc electrode in contact with aqueous 0.1 MKCI electrolyte. (a) Disc current versus disc potential; (b) ring current versus disc potential, with a ring potential of 0.1 V versus Ag/AgCl; (c) ring current versus disc potential, with a ring potential of -0.5 V versus Ag/AgCl. Reproduced by courtesy: J. Electrochem. Soc 144 (1997) 1566. Copyright, The Electrochemical Society. Fig. 5.55 GC/GC R R D E voltamn~ogramsobtained at a scan rate of 20 m~ s-* and frequency of rotation of 1000 min-' for tr~ns-Cr(CO)~(dpe)~ attached to the disc electrode in contact with a 1 : 1 mixture ofwater : acetonitrile containing 0.1 M KC1 electrolyte. (a) Disc current versus disc potential; (b) ring current versus disc potential, with a ring potential of 0.1 V versus Ag/AgCl; (c) ring current versus disc potential, with a ring potential of -0.5 V versus Ag/AgCl. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. Voltammetvy of TCNQ 405 Field (mT) Fig. 5.56 In situ electrochemical generation of the solution-phase ESR spectrum of tran~-[Cr(CO)~(dpe)~]' by oxidation of tran~-Cr(CO)~(dpe)~ at a Pt electrode in a 1 : 1 mixture of acetonitrile and aqueous K'-buffer. (a) Surface-attached tran~-Cr(CO)~(dpe)~ prior to oxidation; (b) oxidation of trans-Cr(CO)a (dpe)z to trans-[Cr(CO)z (dpe)2]+; (c) regeneration of solid tran~-Cr(CO)~(dpe)~ by electrochemical reduction of trans-[Cr(C0)2(dpe)2]; (d) re-oxidation of tran~-Cr(CO)~ ( d ~ e to ) ~trans-[Cr(C0)2 (dpe)2If after experiment (c). Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. The solution-phase ESR spectra of trans-[Cr(CO),(dpe)2]+ in acetonitrile is essentially independent of the water content and the origin of the cation (synthesized or generated electrochemically). The g value is 2.012 and the hyperfine splitting parameters a ( 3 1 ~ )= 2.85 mT and a ( 5 3 ~ r )= 0.4 rnT. Under the thin-layer conditions of the SEESR flat cell, the solid-state oxidation of trans-Cr(CO), (dpe), to yield dissolved trans- [Cr (CO), (dpe)2] is chemically reversible in a 1 : 1 mixture of acetonitrile and Kf -buffer. Figure 5.56 shows a series of ESR spectra recorded from (a) the initial solid which prowhen surface attached, (b) fully oxidized tr~ns-Cr(CO)~(dpe)~ duces solution-soluble t r a n s - [ ~ r ( ~ ~ ) ~ d p(c) e ]fully + , reduced solution-soluble t r a n s - [ C r ( ~ O ) ~ ( d ~ ewhich ) ~ ] + produces insoluble trans-Cr(C0)2(d~e)~, and (d) again fully oxidized trans-cr(CO),(d~e)~ produced in (c). As in the case of the [TCNQ]'' process, the dissolved product of the electrochemical reaction in this case, trans-[Cr(CO),(dpe)2]+, can be almost fully restored to insoluble tran~-Cr(CO)~(dpe)~ under thin-layer electrochemical cell conditions to produce a thin orange-red coating of solid on the Pt electrode, resulting in almost complete loss of ESR activity. After oxidation, the full intensity of the ESR spectrum can be recovered. + Solid-electrode-solvent interfaces Field (mT) Fig. 5.57 ESR spectra of t r a n ~ - [ C r ( C O ) ~ ( d ~ e ) ~and/or ]+ trans-[Cr(C0)2(dpe)2][A] (A- = electrolyte anion) generated electrochemically in K+-buffer at a Pt electrode. Dependence of acetonitrile content. (a) 0% acetonitrile, sensitivity x10; (b) 10% acetonitrile x2; (c) 50% acetonitrile, x 1. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. The SEESR behaviour of surface-attached tran~-Cr(CO)~(dpe)~ in different acetonitrile-water mixtures is shown in Fig. 5.57. The potential of the Pt working electrode was held at a value required for the one-electron oxidation of tr~ns-Cr(CO)~(dpe)~. When no acetonitrile is present, the observed broad single-line ESR spectrum (Fig. 5.57(a)) is consistent with an oxidation process proceeding solely in the solid state. No evidence of the characteristic solutionis obvious. However, phase ESR spectrum of tran~-[Cr(CO)~(dpe)~]'(~ol~tion) the situation changes upon increasing the acetonitrile content. At 10 per cent acetonitrile content, a spectrum containing characteristics of both the solid-state and solution-phase ESR spectra is observed (Fig. 5.57 (b)). Upon further increasing the acetonitrile content to 50 per cent, no solid-state ESR signal can be detected (Fig. 5.57(c)) since, as shown above, the oxidized compound dissolves completely. Figure 5.58 shows the single-line solidstate ESR spectra of (a) chemically synthesized trans-Cr(C0)2(dpe)z][I]and (b) trans- [Cr (CO)z( d ~ e )[A] ~ ](A- = electrolyte anion) electrochemically generated by oxidation of solid tr~ns-Cr(CO)~(dpe)~ when attached to a Pt flag electrode in a quartz flat cell. Both ESR spectra are similar, having g values of 2.012. Effects of different molecular packing densities in the differently synthesized solid materials are not as pronounced as in the case of the T C N Q system. Voltammetry of TCNQ I I I I I 330 340 350 360 370 407 Field (mT) ig. 5.58 Solid-state ESR spectra of trans-[Cr(CO)2(dpe)a][A], A- = I- or anion from the electrolyte. (a) Synthesized sample of trans-[Cr(CO)a(dpe)2][I](solid); (b) tran~-[Cr(CO)~ (dpe)2][A](solid) prepared by electrochemical oxidation of surface-attached trans-Cr(CO)2 (dpe)2 at a Pt electrode in contact with K+-buffer, sensitivity x 10. Reproduced by courtesy: J. Electrochem. Soc. 144 (1997) 1566. Copyright, The Electrochemical Society. In summary, the detection of a single-line ESR spectrum observed upon oxidation of surface-attached tr~ns-Cr(CO)~(dpe)~ without any acetonitrile being ~ ] is formed present simply leads to the conclusion that trans-[Cr ( C 0 ) 2( d ~ e )[Cl] as product through a solid-state electrochemical process. In situ R R D E and SEESR measurements demonstrate that microcrystals of organic T C N Q and organometallic tr~ns-Cr(CO)~(dpe)~ mechanically attached to electrodes, in contact with solution (electrolyte) media, follow analogous overall pathways during their solid-state voltammetric reduction and oxidation processes, despite the substantially different physical properties of the solids. Some or all of either compound may be dissolved upon electrochemical reaction, depending on the solubility of the product in the solvent and supporting electrolyte combination. A nucleation/growth-type mechanism may control the electrochemical behaviour of both surface-confined processes, although the rate of electrolysis is probably controlled by the conductivity ofthe solids and the process is probably more confined to the surface in the case of non-conducting crystals. 408 Solid-electrode-solvent intefaces 4.4.3 Use o f i n situ atomic force microscopy (2lFh.I) to detect dissolution and solid-state redistribution veactions that occur during the initial stage of redox cycling experiments at a solid TCNQ-glassy carbon electrode-aqueous (electrolyte) intefafaceJh In order to further characterize the processes that occur during the initial stages of the solid-state T C N Q voltammetry, i n situ rather than e x situ forms of microscopy are needed. The in situ technique of AFM described in Section 19.1 in Chapter 2 is ideally suited to examine the morphological changes that occur on the electrode surface in the initial stage of potential cycling experiments. In the studies described in detail in reference [56], an AFM, operating in the contact mode, was employed to image T C N Q mechanically attached to a 3-mm diameter GC electrode. In all cases, simultaneous recordings of the cyclic voltammograms and conventional AFM topographical images were undertaken using microcrystals of T C N Q attached to a GC electrode. The TCNQ-modified electrode was transferred to the AFM electrochemical cell and the electrochemical reaction was carried out in the presence of aqueous 0.1 M KC1, CsC1, or Et4NC1 electrolyte. During a typical experiment, an electrode area of between 1 x 1pm2 and 50 x 50 pm2 was imaged. Figure 5.59 shows an AFM image (in air) of the particles of T C N Q present after adherence to a GC electrode. The range of sizes of the attached solid 0Pm 5 pm 10 pm Fig. 5.59 AFM image obtained in air of almost amorphous TCNQ particles attached to a GC electrode. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. '%Adapted with permission from J.Solid State Electrochem. 4 ( 1999) 24. Copyright, SpringerVerlag. Voltammetry of TCNQ (d) q 0.1 0 -0.1 -0.2 -0.3 -0.4 -200 0 200 409 400 mv (f) 0.02 0.01 2 -0.01O -0.02 -0.03 . 5.60 Voltammograms obtained at a scan rate of 100 mV s-"after almost amorphous T C N Q adhered to a GC electrode is placed in contact with 0.1 M KC1 (a-c) [(a) first, (b) the third, and (c) the tenth scan respectively] or 0.1 M CsCl aqueous electrolyte (d-!(I [(d) first, (e) the third, and (!(Ithe sixth scan respectively]. The reference electrode was Ag/AgCl. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. particles over the area of electrode imaged is predominantly between 0.1 and 1 pm, but the coverage is lower than used in voltammetric studies described previously (see SEM image shown in Fig. 5.36). Figure 5.60(a)-(c) contains a series of voltammograms obtained in the AFM electrochemical cell for the [ T C N Q ] ~ ' process when the GC electrode is in contact with 0.1 M KC1 as the electrolyte. Clearly, the initial reduction stages with this low coverage produces a complex (and non-reproducible) voltammetric response with current crossover being evident afier reversing the scan direction. However, a stable voltammetric response begins to emerge afier about five cycles. Figure 5.60(d)-(f) show a series of voltammograms obtained during the course of redox cycling experiments with solid T C N Q and with 0.1 M CsCl as the electrolyte. Again the initial voltammograms are very complex, but after six cycles of the potential the voltammetric response expected on the basis Fig. 5.61 Sequences of in situ AFM images obtained when the solid [TCNQ]'' system is attached to a GC electrode in contact with (a-c) 0.1 M CsCl aqueous electrolyte after 0, 2, and 4 potential cycles between 0.4 V and -0.2 V versus Ag/AgCl at a scan rate of 0.1 V s-'. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. of the nucleation-growth mechanism is observed. Additional potential cycling leads to a small decrease in the magnitude of the current, but the principal features of the voltammogram are retained. The AFM images obtained during redox cycling of T C N Q with 0.1 M KC1 as the electrolyte reveal that after two potential cycles between 0.4 and -0.2 V versus A ~ / A & ~ that , the larger sizea particles have either dissolved and/or been transformed to nanometer-sized oarticles. Figure 5.61 shows a seauence of AFM images of T C N Q particles ahhered to ;he electrode surface &ring redox cycling in 0.1 M CsCl. These results show that the three particles in the centre of the figure progressively decrease in size while at the same time, new material becomes evident at the top area of this figure. It is therefore clear that both dissolution and solid-phase redistribution processes, which could involve reprecipitation or surface diffusion are involved at early stages of electrochemical experiments. After 20 cycles of the potential with 0.1 M CsCl as the electrolyte, needle-like crystals similar to those seen previously by the ex situ electron scanning method were evident on the electrode surface as shown in Fig. 5.62(a) and (b). Voltammetry of TCNQ 41 1 . 5.62 (a) Topographic and (b) shaded in situ AFM images of the needle-like crystals formed when the [TCNQ]'/- system is attached to a G C electrode followed by 20 cycles of the potential between 0.4 V and -0.2 V versus Ag/AgCl with aqueous 0.1 M CsCl as the electrolyte. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. (a) $ 0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 (b) 2 (c) 3 0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 ig. 5.63 Voltammograms obtained at a scan rate of 0.1 V s-' after almost amorphous T C N Q is mechanically attached to a GC electrode which is then placed in contact with 0.1 M Et4NC1 aqueous electrolyte (a) first, (b) third, and (c) tenth cycle of the potential respectively). The reference electrode was Ag/AgCl. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. When 0.1 M Et4NCl is the electrolyte, significantly different voltammetric data (Fig. 5.63) were obtained, relative to the case when a metal ion containing electrolyte was used. In this case, the very first scan is exceptionally well defined and only a very small decrease in the peak current was observed on subsequent cycling of the potential. AFM data also revealed that for this system predominantly only the smaller particles were voltammetrically electroactive (Fig. 5.64). The reactivity of the particles is random, but data suggest that the probability of reaction of the smaller sized particles is higher than for the larger sized particles. When the potential was maintained at +0.5 V versus Ag/AgCl, 0 17.12 urn 34.25 Fig. 5.64 Irr situ AFM images ofthe solid [TCNQ]'' system attached to a GC electrode in contact with 0.1 M Et4NC1 aqueous electrolyte after (a) 0, (b) 1, and (c) 2 cycles of the potential at a scan rate of 0.1 V s-* between 0.5 and -0.2 V versus Ag/AgCl. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. very little change occurred in the AFM images over very long time periods (about half an hour). In contrast, when the potential was maintained at -0.2 V versus Ag/AgCl, the larger particles are removed from the surface, but only on the minutes rather than seconds time-scale of voltammetry (Fig. 5.65). The is the C electrolyte ~ different electrochemical behaviour of T C N Q when E ~ ~ N is attributed to very low solubility of the [Et4N+][TCNQ-] salt relative to the metal ion salts. A detailed examination of the electrode surface, with high resolution AF conditions, revealed that in all cases T C N Q particles of submicron size are transformed into a thin layer of material during the initial stages of the redox cycling. The structure of this thin layer of material depends on the electrolyte used. When KC1 is used as an electrolyte, a very regular surface coverage develops over the electrode ('bricks in a wall' model). When CsCl is the electrolyte a very different morphology was observed (dendritic shape). Apparently, during the course of redox cycling experiments on a GC electrode, the initially unstable solid phase of T C N Q is transformed into at least two more energetically stable solid phases of TCNQ; initially a solid thin layer is formed from which the crystalline form with a needle-like shape is evolved. 7 Voltammetry of TCNQ 41 3 ig. 5.65 Sequence of shaded in situ AFM images obtained after (a) 0 s, (b) 162 s, (c) 324 s, and (d) 486 s when initially almost amorphous T C N Q is attached to a GC electrode in contact with 0.1 MEt4NCl is the electrolyte and the potential is stepped from 0.5 to -0.2V versus Ag/AgCl. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. The simultaneous in situ AFM experiments demonstrate that a dissolution reaction makes a significant contribution to the early stage of voltammetric redox cycling experiments involving the chemically reversible conversion of T C N Q to the reduced salt. Thus, features of the voltammetry of T C N Q mechanically attached to an electrode surface may be rationalized as follows: (1) The non-reproducibility found with the first few cycles of the potential is associated with the initial formation and then partial dissolution and reprecipitation of reduced [TCNQ-I . This dissolution-reprecipitation process enables the transformation to occur from a relatively higher energy surface state of immobilized and almost amorphous solid to a lower energy surface state of attached rnicrocrystals. The latter form of attached microcrystals undergo significantly less dissolution during the course of redox cycling at a scan rate of 0.1 V s-' and provide the ideal voltammetric response associated with the nucleation-growth solid-state transformation shown in Fig. 5.26. (2) After conversion to the microcrystalline state, voltammograms are stable in the sense that peak positions and wave shape become almost independent of the number of redox cycles. However, a decrease in the current magnitude of the response may still arise from loss of material to the bulk solution. provides a mechanism for the growth of highly (3) The dissolution crystalline material on an electrode surface. Initially, immobilized material is prepared and attached to an electrode via a non-electrochemical process. The stronger form of adhesion of the electrochemicallyprepared microcrystals minimizes the extent of the dissolution process to a level that at some electrode suriaces it may become lower than that which is voltammetrically detectable. (4) After a significant level of dissolution occurred in the initial stages of redox cycling, diffusion of reduced and dissolved [TCNQ-] (solution) into the bulk solution occurred in a competitive process with precipitation of energetically modified suriace-attached microcrystals. Thus, the relative rates of the physical process of crystallization and diffusion, the strength of adhesion of solid to the electrode surface and the voltammetric scan rate are important factors contributing to the nature of the observed voltammetric response. (5) The presence of an initial dissolution process is consistent with both solution and solid-state phase TCNQ- being detected in the interfacial region during RRDE and in situ electrochemical-ESR spectroelectrochemical experiments. r Diffusion layer Amorphous solid T C N Q Electrochemical dissolution Electrode surface T C N Q + e- TCNQ- Diffusion of TCNQ- Bulk solution Fig. 5.66 Schematic form of representation of the mechanism proposed to account for the electrochemical conversion of almost amorphous particles of solid T C N Q to needle-shaped microcrystals during the initial stages of redox cycling experiments at a GC electrode. Reproduced by courtesy: J. Solid State Electrochem. 4 (1999) 24. Copyright, Springer-Verlag. Voltammetvy of T C N Q 41 5 (6) Figure 5.66 provides a model that can be used to explain the unstable voltammetric responses frequently observed at the early stages of potential cycling experiments. (7) After a period of redox cycling, the response shown in Fig. 5.26 can be achieved. This response can be explained adequately by a simple nucleationgrowth mechanism, where the reduced and oxidized phases can be interconverted without the need to involve the presence of a dissolution process. (8) The time (cycle number) dependence of the voltammetric response on the electrolyte composition is also explained by the presence of an initial dissolution process and the subsequent formation of a stable solid phase on the electrode surface, which is more structurally suited to electrochemical interconversion between the oxidized and reduced forms of the solid. 4.5 Compavison of electvochemical data with micvocvystals and othevforms of suface-conjned T C N Q n addition to studies described above with microcrystals adhered to electrode surfaces, voltammetric studies have been undertaken on single crystals of T C N Q and electrochemically prepared T C N Q 'thin films'. Data obtained with these different forms of adhered solid are presented below and are shown to have a great deal of similarity, implying that a nucleation-growth mechanism is operative in all cases. 4.5.1 Voltammetry ofsingle crystals of T T F . T C N Q One-dimensional organic conductors, such as TTF . T C N Q (where TTF . T C N Q is tetrathiafulvalenium tetracyanoquinodimethanide), can be used as electrode materials [57]. In the study of Bartlett [58] single crystals were grown by interdiffusion of solutions of TTF (tetrathiafulvalene)and T C N Q in acetonitrile and used as electrodes. Figure 5.67 shows a typical cyclic voltammogram in background electrolyte for the single crystal electrode in contact with the aqueous electrolyte. The electrode response is stable when cycled between -200 and +425 mV versus SCE. Potential excursions outside this range lead to oxiand dation (generates T C N Q and TTF~') or reduction (generates T C N Q ~ TTF) of the electrode itself and the deposition of insoluble products ( T C N Q or TTF as appropriate) on the electrode surface. The peaks observed in the cyclic voltammogram shown in Fig. 5.66(b) have been assigned to the oxidation of insoluble T C N Q to insoluble [ ~ a ' ] [TCNQ-] at +267 mV and the reduction of [Na'] [TCNQ-J to T C N Q at -20 mV. Studies revealed that many multilayers of material are involved. Thus, after generation of TCNQ(so1id)by oxidation of the TTF . T C N Q semiconductor electrode, most features observed in the voltammetry correspond to those found in voltammetric studies when microcrystals of T C N Q are directly attached to an electrode as described above. Indeed, cyclic voltammetric and chronoamperometric studies by Scaboo and Chambers [59] on electrodes prepared from needles of T C N Q . TTF single r indicate the presence of nucleation crystals in contact with aqueous 1M 416 Solid-electrode-solvent intefaces Fig. 5.67 Cyclic voltammograms obtained at a scan rate of 20 rnV s-' for a single crystal TTF . T C N Q electrode in a pH 7.2 phosphate buffer containing 0.15 M NaC1. (a) Clean electrode; (b) with insoluble [ ~ a +[TCNQ-]/TCNQ ] present on the surface formed by a potential excursion outside the stable range. Potential axis is V vs Sm.Reproduced by courtesy: J. Electroanal. Chem. 300 (1991) 175. Copyright, Elsevier. and growth mechanisms in the electrochemistry of the [TCNQ]'/- process. In another detailed study with single crystal electrodes, Bartlett and Tong examined the voltammetry in LiCl media and other conditions where dissolution is expected and employed in situ electrochemical STM to explore the details ofthe dissolution processes [60]. In general terms, the voltammograms obtained when TCNQ(so1id)is generated from T C N Q .TTF single crystals have the same characteristics as those obtained when microcrystals of T C N Q are adhered directly to the electrode surface. 4.5.2 Voltammetry of TCNQ prepared by oxidation of films of 9-aminoacridine Chambers et al. [611 have also extensively examined the voltammetry of 'films' of solid T C N Q adhered to electrodes in contact with aqueous potassium electrolyte solutions. In these studies, T C N Q was generated by electrochemical oxidation of polycrystalline films of a 9-aminoacridine hydrochloride salt in contact with a carbon electrode substrate. Oxidation of these films at 0.6V versus SCE leads to expulsion of hydrogen ions to form TCNQ(so1id) and to the now familiar voltammograms of the kind shown in Fig. 5.26. The process in the 'thin film7-typeterminology considered in Section 18 in Chapter 2 may be written as TCNQ(surf) + solution) + e ,& [K'] [TCNQ-] (surf) (5.38) Voltammetvy of TCNQ 4 17 This T C N Q form of 'film' electrochemistry has been studied by cyclic voltammetry [61], UV-visible spectroelectrochemisty [62] and Q C microgravimetr[63,64]. At slow scan rates, the charges under the cyclic voltammetric waves correspond to electrolysis of up to 100 monolayers of T C N Q sites, as is the case with studies emanating from adhered microcrystals of T C N Q . Thus, irrespective of whether T C N Q is adhered to an electrode surface as a microcrystal or generated electrochemically from 9-aminoacridine, or from a single crystal of TTF . TCNQ, closely related voltammetry is observed. Chambers et al. [61] have modelled the 'film7 behaviour in several ways. Initially, they considered the possibility that a square scheme is operative. E: (surf) A+e- $ B E; (surf) C-t-e- D EY(~~~Q The assumption of a square scheme [61,62] with < ~ i ( s u r t ) provides , a possible means to rationalize the large peak potential separations, while incorporation of phenomenological 'interaction parameters7into the calculation may be used to account for the narrow peak widths, relative to values expected with conventional thin film theory (Section 18 in Chapter 2). Effectively, this approach extends the treatment of Brown and Anson [65], who considered the extension of a reversible uncomplicated surface-confined redox couple to a square scheme mechanism. The second approach used by Chambers et al. assumed that the wave shapes are a result ofnucleation phenomena and utilized the theory of Camacho and coworkers [66,67] who incorporated nucleation-growth-collision theory into a treatment of surface cyclic voltammetry. Both the square scheme and nucleation approaches predict, under suitable conditions, narrow peak-shaped voltarnmograms that display significant hysteresis between the reduction and oxidation components. Finally, comparison of these interpretations with those emerging from the unusual quasi reversibility (UQR) concept of Feldberg and Rubinstein [68] was considered. Theoretical principles associated with the d f l e m t models considered to explain the voltammetry of T C N Q (thinfilms' The voltammograms modelled via the surface version of the square scheme (eqn 5.39) were calculated using a procedure based on that described in Section 17 in Chapter 2 when the Nernst and kinetic conditions were adjusted to their new values after each measurement of the electrode potential. That is, after each potential step, A E , the surface form of the Nernst condition was satisfied and then the surface concentrations were adjusted for first-order kinetic decay of the intermediate species B and C. The rate constants kl and k2 in eqn (5.39) were chosen to be large enough to produce irreversible voltammograms at the fastest sweep rate employed. In this case, the peak width of a surface-confined voltammetric process is 66/n mV at 25OC. Quasi-reversible voltammograms were calculated in a similar fashion with the assumption of Butler-Volmer kinetics (Section 18 in Chapter 2). In order to match the experimental and calculated voltammograms, it was necessary to assume different values of the ~ double-layer capacity in the oxidized, C:;, and the reduced, C T states. Following Brown and Anson [65], non-ideality effects were Introduced via interaction parameters ei = R T r T r i / F with units of volts in the expression In this equation for the A/B couple, the summation of the surface coverage is taken over all four species, A, B, C, and D in the square scheme. is the total surface coverage, Qi is the fractional coverage for species i, and ri is an adjustable parameter that identifies the magnitude and nature (attractiveor repulsive) of the interaction. A similar expression was used for the C/D couple with a different E'(SUI+) value. The critical condition that leads to narrow voltammetric waves in this model occurs when species in the same oxidation state have greater attractive interactions than species in different oxidation states. This requires that the r values are greater than zero. In the calculations presented by Chambers et al. [61], a single interaction parameter, ci,was used to define the surface voltammograms. As expected, when the interaction parameters are set to zero, the solution to the equations matches the analytical solution of Laviron [69] which was described in Section 17 in Chapter 2. A slightly different treatment of the interaction model has been provided by Chidsey and Murray [70] who employed a statistical mechanics approach to introduce the interaction parameter. In the second model considered by Chambers, the voltammograms were calculated using eqn (5.43) described in reference [GI. 1= *=P RTv exp * [$] In this equation, which is derived [67], assuming a two-dimensional surfacenucleation process, & is the charge required to electrolyse a surface monolayer, b is a kinetic parameter, v is the sweep rate, and X = ( F / R T ) (E - EO (surf)). The kinetic parameter is derived assuming that the surface redox reaction is kinetically controlled by Butler-Volmer kinetics and that the reaction proceeds at the perimeter of expanding nucleation centres. The phases that grow correspond to the two redox states and hence when the growing centres intersect, the current falls back to the baseline. A unity n value is assumed, other terms have their usual significance and the positive sign corresponds to oxidation and the negative sign to reduction. In applying this equation to the T C N Q voltammetry, Qm was set equal to the charge under the peaks in voltammograms. However, it needs to be noted that the two-dimensional nucleation assumption employed in this theory is only approached at very low surface coverages. Voltammetry of TCNQ 419 Theory-experiment comparisons based on voltammetric models igure 5.68 shows an example of a voltammogram calculated via the 'square scheme' model described in eqn (5.39) using positive interaction parameters. The open circles are a 'best fit' calculated voltammogram obtained by trial-and) , (surf), Ci;, c g d ,tox, and tred for a error manipulation of the charge, ~ P ( s ~ r fE: articular set of experimental conditions. Further details of the calculations and L values of the parameters are available in reference [61]. The agreement between the experimental and calculated ('square scheme' model) voltammograms clearly is not completely satisfactory because the theoretically derived voltammograms exhibited greater currents on the rising part of the waves. Thus, to match the peak height and the peak width at half-height, the values of the total charge used in the calculations were arbitrarily adjusted to be significantly larger than the experimental values [61]. Furthermore, the t values, which are due to attractive forces between redox sites of like oxidation state, and which should not be sweep-rate dependent, varied in a systematic fashion with sweep rate. This variation of the calculated E values with sweep rate must be regarded as a failure of the model to account for the voltammetric behaviour. However, it should also be noted that the fit for a classical quasi-reversible 'thin film' voltammogram with n = 1, assuming Butler-Volmer kinetics (Section 18 in Chapter 2) iseven poorer than that se& in Fig. 5.68 [61]. I E (mV versus SCE) Fig. 5.68 Comparison of cyclic voltammograms obtained for the solid [TCNQIOI- process (rT= 7.3 f 0.7 x lops mol ~ m - at~ a) scan rate of 10 mV s-' (filled circles) with a 'film' adhered to a GC electrode of area 0.0707 cm2 in contact with 1.0 M potassium acetate with theory based on the square scheme. Open circles are calculated current values using the 'square' scheme model with p d - 39 mV and &Ox = 36mV. Reproduced by courtesy: J. Electrochem. Soc. 143 (1996) 3039. Copyright, The Electrochemical Society. The second explanation for the narrow peak widths and large peak separations considered by Chambers et al. [61] is the two-dimensional nucleation model. For two-dimensional nucleation, and for overpotentials of less than k 5 0 mV, the theoretically predicted dependence of the peak current, the peak width, and peak separation on the scan rate are u0.67L J O . ~ , and vO.', respectively. Comparison with the experimental data [61] reveals that peak current scan rate dependence (approximately approaches that of theory. However, the peak half-height widths and especially the peak potential separations are significantly less dependent on sweep rate than predicted by this theory [61]. Figure 5.69(a) and (b) shows examples of the reduction and oxidation components of typical voltammograms calculated using two-dimensional nucleation theory. The open circles are best-fit obtained by manipulation of the following parameters: charge, EY(surt), E;(;urt), C:;', C E ~ ,box7 and bred. The agreement between experiment and theory is considerably better than seen for the voltammograms c&ulated assuming the 'square7scheme model. The agreement was especially good for the oxidation process (Figure 5.69(b)),and for both the oxidation and reduction processes the agreement on the rising part of the processes is excellent. Detailed listings of parameters extracted from the experimental voltammograms are available in reference [61] and reveal that the nucleation model does account for the potential dependence of the individual oxidation and reduction process in that the calculated ~ ' ( s u r t ) values are constant. However, unfortunately, the b values are not independent of either the sweep rate or (b) 300 200 n -3 'r 100 I I 300 200 E (mV versus SCE) 100 0 E (mV versus SCE) Fig. 5.69 Comparison of experimental and theoretical (nucleation model) voltammograms obtained for the solid [TCNQ]'/- grocess. (a) Filled circles: reduction component, scan rate = 5 mV s-', r~ = 11.5 f 0.6 x 10- mol crnp2; open circles: calculated using two-dimensional nucleation theory, ele surf) = 55 mV, b = 7.0 x loP5v2sP2. (b) Filled circles: oxidation component, scan rate = 5 mV s-', rT = 11.5 f 0.6 x 1 0 - h o l crnp2; open circles: calculated using two-dimensional nucleation theory, E; (surf) = 210.5 mV, b = 8.5 x 10-6 v2sP2. Reproduced by courtesy: J. Electrochem. Soc. 143 (1996) 3039. Copyright, The Electrochemical Society. - Vo'oltammetvy of TCNQ I 42 1 I 0 1 Fraction oxidized Fig. 5.70 Plot ofpotential versus fraction of [TCNQ-] (solid)oxidized to TCNQ(so1id)via the square scheme with surf surf) = 60 rnV and ~&(surt) = 220 mV. The dotted curves were calculated using these E' (surf) values and two-dimensional nucleation theory with b = v2s - ~ .The curves labelled with N are Nernstian and the dashed curve corresponds to the hypothetical N-shaped free-energy curve of Feldberg and Rubinstein [68]. Reproduced by courtesy: J. Electrochem. Soc. 143 (1996) 3039. Copyright, The Electrochemical Society. the surface coverage, so in this context and others, as noted above, this model does not appear to adequately explain all features of the voltammetry. Feldberg and Rubinstein [68] introduced the idea of U Q R , and this is the third model considered by Chambers et al. [61]. This concept attempts to rationalize cyclic voltammograms with significant hysteresis between coupled oxidation and reduction peaks by invoking an N-shaped free-energy curve. This pathway is depicted in Fig. 5.70 by the dashed line. This figure also shows the Nernstian pathway (labelled N) for a square scheme along with a nucleation pathway calculated using typical b values. Figure 5.70 clearly shows that the nucleation pathway is distinctly different from a hypothetical N-shaped free-energy curve. For a constant value of the kinetic parameter b, the nucleation pathway predicts a v0.4 dependence of the peak potential separation on the scan rate that arises from the assumption of Butler-Volmer kinetics [66]. In contrast, the UQR model predicts that the value of E,O" is independent of scan rate. Inspection of the results [61] shows that' the experimental result is intermediate between these expectations so that again, agreement between theory and experiment with the UQR model is not adequate. ~r~ Compavisons ofpotential step (chronoamperometric) expen'ments and theory based on two- and three-dimensional nucleation models Use of the chronoamperometric current-time response resulting from a potential step avoids the need to consider terms associated with electron-transfer kinetics and this simplification allows different nucleation mechanisms to be more readily distinguished than under voltammetric conditions [711. Figure 5.71 shows a typical current transient experimental response for the reduction of a 'thin' T C N Q film prepared as described above by Chambers et al. [61], after subtraction of the charging current. The signature nucleation response, where the Faradaic current increases from zero at t = 0 to a maximum, then falls back towards the base line, is clearly evident in the 'thin' film case as is the case when microcrystals of T C N Q are adhered to an electrode surface. The experimental current-time transients have been evaluated by Chambers et al. [61] using two- and three-dimensional nucleation models (Fig. 5.71) and it can be noted that a significantly improved fit with the data was obtained using the three-dimensional instantaneous nucleation theory of Isaev and Baraboshkin [72] (Fig. 5.71). Fig. 5.71 Chronoamperometric responses when the potential is stepped from 350 to -90 mV versus SCE for the solid-state [TCNQ]'' reduction process (after subtraction of charging current) when a 'film' of T C N Q is adhered to a GC electrode and which is then placed in contact with 1 M potassium acetate. Filled circles are the experimental data, open circles, which closely match the experimental data, are calculated data using a three-dimensional nucleation model, and the triangles are calculated data using a two-dimensional nucleation model. Reproduced by courtesy: J. Electrochem. Soc. 143 (1996) 3039. Copyright, The Electrochemical Society. Voltammetry of TCNQ 423 Conclusions related to the electrochemistry of TCNQ d to electrode sufaces A]] electrochemical data obtained on the [TCNQ]'/- couple are similar irreve of whether adhered rnicrocrystals, a TTF T C N Q electrode or ochernical oxidation of 9-aminoacridine is used as the source of solid Q . The electrochemical data coupled with spectroelectrochemical and microscopy data all imply that a nucleation-growth process is associated with the rate-determining step, although many complexities are associated with conversion of solid T C N Q to a [TCNQ-] salt and vice versa. In the case of T C N Q voltammetry, it is doubtful that a 'thin film' description of the solid adhered to an electrode surface is adequate and clearly dissolution processes and redistribution reactions occur during the course of potential ling experiments. The modelling of results obtained by cyclic voltammeare therefore exceptionally demanding. Thus, applications of the theory of anchez-Maestre et al. used in Section 4.5 involves assumptions that do not correspond exactly to experiments with TCNQ. Thus, this theory is only valid for relatively low overpotentials of f5OmV and not the large overpotentials encountered experimentally. Furthermore, it is unlikely that the nucleation henomenon that is operative is two-dimensional as assumed in this theory. ather, it is reasonable to assume that the nucleation sites originate at the de-microcrystal interface and grow into the bulk of the solid in a threedimensional manner that allows access for the ion motion which accompanies the electron transfer processes. O n this basis it is expected that incorporation of three-dimensional instantaneous nucleation assumptions into a theory for cyclic voltammetry is required. Even then, it is doubtful that such a model would provide 'perfect' agreement with experiment. Thus, significantly, more development of the theory is required to fully model the plethora of events that occur at the solid-electrode-solvent (electrolyte) interface under conditions of cyclic voltammetry and potential cycling experiments. The discovery of nucleation-growth mechanisms in TCNQ(so1id) electrochemical processes and details of morphology changes illustrate the complexity of the structural factors that may be involved in the electrochemistry of micro or even nanocrystals adhered to a surface. The rich variety of physical phenomena that may be difficult to unravel from sole reliance on solid-state voltammetric experiments is also clearly revealed in the TCNQ(so11d)studies. It is anticipated that in future, the combination of immobilized microcrystal voltammetry, flowcell reaction order measurements, double-potential-step experiments, XRD, and microscopy will be successfully applied to other systems, and thereby uncover the existence of many more nucleative solidsolid phase transformations, as well as shedding further light on the relationship between voltammetric inert zones, specific interfacial free energies, and interfacial structure. For example, nucleation and growth kinetics are probably present in many systems in which they have not been previously suspected. Cases in point include the electrochemical intercalation of metal ions into solid fullerenes [73] where again a large voltammetric inert zone is present and in the oxidation of tetrathiafulvalene [74]. The same class of mechanism would also now appear to be associated with the decamethylferrocene and Cr(C0)2(dpe)2electrochemistries and may also apply to insertion of ~ i that + is important in a range of batteries [75] as well as many other systems where inert zones have been reported. ion transport wit determining where coupled electro microparticle are rate If nucleation growth is not rate determining, then a mechanism that is likely to limit the overall rate of charge transport within a solid is the electron hopping or counterion diffusion/migration processes that must occur to achieve charge neutralization. Studies on adhered solids that probably have layered structures have revealed behaviour converging towards 'thick film' three-dimensional diffusion where coupled electron and ion movement within the solid is rate determining [76,77]. (Fig. 5.72(a)) complex, where In the case of the [O~(bpy)~-4-tet-Cl][ClO~] microparbpy is 2, 2'-bipyridyl and 4-tet is 3,6-bis(4-pyridy1)-1,2,4,5-tetrazine, ticles that have a layered structure have been formed on graphite macrodisc and platinum microdisc electrodes [76]. Images of the solid obtained by SEM reveal that repeated voltammetric cycling of the potential, when the modified electrode is in contact with aqueous sodium perchlorate electrolyte, induces 1 n+ II I N /N 6 Fig. 5.72 Structures of (a) [Os(bpy)a-4-tet-C1](C104) where bpy is 2, 2'-bipyridyl and 4-tet is 3,6-bis(4-pyridy1)-1,2,4,5-tetrazine and (b) [ { ~ - ( b ~ ~ ) ~ } {( p~- '~ () ]bn +~for~ the ) ~ particular } case when M = R u and M' = R u or more generally M or M' = R u or 0 s ; bpy = 2, 2'-bipyridyl; L = 1$-dihydroxy-2,5-bis(pyrazo1-1'-yl)benzene dianion) . Voltammetric studies on systems 425 some crystallization on the electrode surface. However, the voltammetric response does not indicate the presence of a nucleation-crystal growth process when rnicroparticles of solid [Os(bp~)~-4-tet-C1] [C104]( 0 s 2 + ) is oxidized to solid [O~(bpy)~-4-tet-C1] ( ~ 1 0(0s3+). ~ ) ~ In contrast, with perchloric acid as the electrolyte, the rnicroparticles remain apparently 'amorphous' even after several thousand voltammetric cycles of the potential have been undertaken. [C104] The voltammetric responses associated with the [O~(bpy)~-4-tet-C1] complex are close to ideal apparently diffusion-controlled processes when undertaken with the solid adhered to a platinum microdisc electrode. Thus, with a 5-pm radius electrode and at fast scan rates, 'linear diffusion' is dominant, as evidenced by the observation of peak-shaped processes with a square root dependence on scan rate (Fig. 5.73), and the shapes and general characteristics of cvclic voltarnmo~ramsare similar to those observed for com~letelv solution-phase reactions described in Section 8 in Chapter 2 with stationary rnacrodisc electrodes. However, in this case, the current response is controlled by coupled electron transport and diffusion of ClO; within the solid17 rather than diffusion of the anion within the solution phase. As expected with a 2-pm radius electrode and at low scan rates, the current is controlled by a 'radial diffusion' as evidenced by the sigmoidal shape near steady-state respbnse (Fig. 5.74) which is also characteristic of solution-~hasevoltammetrv at microdisc electrodes. The hysteresis in these slow scan rate data shown in Fig. 5.74 may be indicative of small changes in the film structure. Using diffusion-controlled theory, the data obtained from the responses shown in Figs 5.73 and 5.74 (linear and radial diffusion) may be combined to determine the effective concentrations, Ceff, of redox centres within the 'film' (1.8 and 1.6 M for NaC104 and HC104 electrolytes, respectively) and the 'apparent' diffusion coefficients,18 D,,,, for homogeneous charge (coupled electron and ion) transport (2.7 x lo-" and 5.0 x lo-" cm2 s-' for NaC104 and HC104 electrolytes, respectively). This requires adaption of eqns (2.34) (Randle-Sevcik theory) and (2.48) (microelectrode theory) that have previously been presented in Chapter 2 to g v e eqns (5.42) and (5.43) J I U I J I where Dappis the apparent diffusion coefficient and Ceffis the effective concentration of 0 s 2 + centres adhered to the electrode surface, I,, is the steady-state limiting current and all other terms have their usual meaning given in Chapter 2. Thus, in principle, it is possible, when microparticles are adhered to an electrode surface, to have a model of charge transport that resembles behaviour also found 17within the solid structure, electron transport by electron hopping and ion movement must be coupled to achieve charge neutrality. Thus, the apparent diffusion coefficients represent the coupling of the electron and ion charge-transport processes. ''see n. 17. 426 Solid-electrode-solvent (a) intefaces 0.31 Fig. 5.73 Scan rate dependence of the voltammetric response when [O~(bpy)~-4-tet-Cl]ClO~ mechanically attached to a 5-pm radius Pt microdisc electrode is placed in contact with aqueous (a) 1.0M HC104, (b) 1.0 M NaC104 electrolyte. From top to bottom, the scan rates are 1000, 500, 200, and 100 mV s-l. Potential axes are versus SCE. Plots of peak current versus scan rate are linear and pass through the origin as required for a diffusion-controlled process. Reproduced by courtesy: J. Phys. Chem. B 104 (2000) 6389. Copyright, American Chemical Society. in conducting polymers containing redox active centres [78]. Surface coverages studies correspond to several calculated in the [O~(bpy)~-4-tet-Cl]ClO~(solid) hundred monolayer equivalents and almost 100 per cent of the osmium centres are active on the voltammetric time-scale. Raman spectroscopy can be employed to identify the nature of the changes accompanying the surface-confined oxidation process. Figure 5.75(a) and (b) shows the Raman spectra obtained when solid [O~(bpy)~-4-tet-Cl]ClQ~ Voltammetvic studies on systems 427 ig. 5.74 Steady-state voltammograms recorded at a scan rate of 1 rnVsfl when [Os(bpy)z-4-tet-C1]C104 adhered to a 2-pm radius Pt microdisc electrode is placed in contact with 1.0 M HC104 and 1.0 M NaClO4. Potential axis is versus SCE. Reproduced by courtesy: J. Phys. Chem. B 104 (2000) 6389. Copyright, American Chemical Society. Fig. 5.75 Raman spectra obtained when [O~(bpy)~-4-tet-Cl]ClO~ is mechanically attached to a gold disc electrode and the potential is held at (a) -0.2 V in 0.1 M NaC104, (b) 0.4 V in 0.1 M NaC104, (c) -0.2 V in 0.1 M HC104, and (d) 0.4V in 0.1 M HC104. All potentials are versus SCE. The laser excitation wavelength is 632.8 nm. Reproduced by courtesy: J. Phys. Chem. B 104 (2000) 6389. Copyright, American Chemical Society. 428 Solid-electrode-solvent intefaces is immobilized on a gold electrode and the potential is held at -0.2 and 0.4 V versus SCE, respectively while the modified electrode is in contact with aqueous 0.1 M NaC104 electrolyte. The exciting HeNe laser (632.8 nm) used in these Raman experiments is expected to be preresonant with the 0s2+-bpyn* metal to ligand charge transfer (MLCT) transition and this is confirmed with the enhancement of features at 1604, 1550, 1480, 1320, 1268, 1167, and 1015 cm-' , all being associated with the bipyridyl moieties. A weaker feature at 373 cm-' is associated with the 0 s 2 + - N stretch. Two very intense features at 811 and 934 cm-' are attributed to surface-enhanced transitions, possibly due to the tetrazine or its associated free pyridine. These bands are not observed when the bare solid is examined on glass or when the bare electrode is examined, but are observed when the material is adhered to a gold surface and are largely unaffected by switching the oxidation state of the layer. Figure 5.75(c) and (d), illustrates the Raman spectra of the solid material when the electrode potential is held at -0.2 and 0.4 V versus SCE respectively, when aqueous 0.1 A4 HClO, is the electrolyte. In the acid solution, the pyridine group is expected to be fully protonated. The only significant difference between the acidic and neutral medium is the 0s2+-N mode which has shifted to 383 cm-' under acidic conditions. In each case, oxidation of the solid material results in loss of the low-frequency 0s2'-N vibration, consistent with metal oxidation. If oxidation of the metal results in the loss of the MLCT it might be expected that the resonance condition would be lost. However, after oxidation, the laser becomes preresonant with a bpy (n)-0s ligand to metal charge transfer (LMCT) transition and the bpy-based bands continue to be observed even for the oxidized layers, albeit with different relative intensities. While apparently 'diffusion'-controlled processes are observed for the oxidation of the [O~(bpy)~-4-tet-Cl]ClO~ complex, adhered to an electrode, the electrochemistry of a series of 'electrochemically open' [{M(bpy)2){M'(bpy)21 (p-L)](PF,)n complexes (M, M' = R u , 0 s ; bpy = 2, 2'-bipyridyl; L = 1,4-dihydroxy-2,5- bis (pyrazol-1-yl)benzene dianion; n = 2 or 3) at a solid-electrode-aqueous electrolyte interface produces what apparently approaches 'thin film' behaviour [79]. Synthesis of [{M(bpy)2){M'(bpy)z} (p-L)](PF& compounds (structure shown in Fig. 5.72(b)) does not yield well-defined crystalline compounds, and inclusion of solvent and even salts (KN03)has been detected [80]. SEM images (Fig. 5.76) reveal that these solids readily disintegrate into small submicrometre-sized ~articles.to ~ i v ea 'thin film' or laver-like structure. The solid-state voltammetry bf the [ { R ~ ( b p y (p-L)] ) ~ ) ~ (PF6)2 (RuRu), [{os(b~~)2}2(~-L)1(PF6)3 (OSOS), and [{Ru(bpy)2){os(bpy)2)(~-L)](PF6)3 (OsRu) complexes is associated with reversible hydroquinone, semi-quinone, J U Voltammetric studies on adheved micvopavticles 429 . 5.76 SEM images of surface-attached solid [{R~(bpy)~)~(p-L)l(PF~)~ shown in (a) high and (b) lower magnification. Reproduced by courtesy: J. Phys. Chew. B 104 (2000) 1977. Copyright, American Chemical Society. and quinone interconversions of the bridging dioxolene ligand and not a metalbased process as is the case with the [O~(bpy)~-4-tet-Cl]ClO~ compound [77]. Cyclic voltammograms obtained when the complexes are mechanically attached to a basal-plane pyrolytic graphite electrode, which is placed in contact with aqueous 0.1 M KPF6 electrolyte, exhibit two extremely well-defined rocesses which may be modelled by two overlapping Gaussian-shaped or 'thin layer'-type curves (Fig. 5.77). In general, these processes may be written as in eqns (5.44) and (5.45). The individual peak potentials change with scan rate, but as expected, the reversible half-wave potentials, EiI2, measured as the average of the oxidation and reduction peak potentials remain essentially constant [79]. The peak currents increase almost linearly with the scan rate as expected with a 'thin film' and not on the square root of scan rate as in the 'diffusion'controlled [O~(bpy)~-4-tet-C1] [C104] oxidation process. In conjunction with results from Raman spectroscopic [79] analysis of the voltammetric response implies that extensive electrolysis of a thin particulate deposit of compound occurs at the electrode surface on the voltammetric time-scale. Support for this interpretation is also gained by noting that the calculated integrated charge for both R u R u processes (Fig. 5.77) is 0.8 mC (corresponding to 6 pg irrespective of the scan rate over the range of of [{R~(bpy)~}~(p-L)l(PF,), 1mV s-' to 0.1 V s-l. Data obtained with adhered solid and from dimethylformamide [80] solutionphase voltammetric experiments are compared in Table 5.10. Significant differences are detected and the dependence of E;,2 for the solid-state process on the identity and concentration of the electrolyte is characteristic of solid I I I I -0.5 0.0 0.5 1.0 E (V vs SCE) I I I -0.6 -0.4-0.2 I I I I I 0.0 0.2 0.4 0.6 0.8 E (V vs SCE) Fig. 5.77 Cyclic voltammograms (scan rates 100, 50, 20, 10mVs-l) for the oxidation of solid (a) [{Ru(bpy)2)2(p-L)](PF6)2, (b) [{Os(bpy)2){Ru(bpy)2)2(P-L)](PF6)3, and (c) [{0~(bpy)~}~(p-L)](PF~)~ attached to basal-plane pyrolytic graphite electrodes and then placed in contact with aqueous 0.1 M KPF6 electrolyte. Cyclic voltammograms (scan rates 10 mV s-*) with Gaussian curves fitted for the oxidation of solid (d) [{RU(~~~)~}~(~-L)](PF~)~ (e) ] Reproduced by [{Os(bpy)21{Ru(bpy)21(P-L)](PF6)3 and (g [{Os(bpy)212{Ru(bpy)212 ( P - ~ )(PF6)3. courtesy: J. Phys Chem. B 104 (2000) 1977. Copyright, American Chemical Society. state rather than solution-phase [79] processes. Furthermore, considerable differences in the level of stabilization of the semi-quinone intermediate are seen in the solution-phase voltammetry and the solid-state case as evidenced by the significant variation in AEiIz values obtained on comparison of these data in the different phases. (p-L)] (PF,), solids In summary, the conclusion that [{M(bpy)2J{M'(bpy)2) are 'electrochemically open' has been reached on the basis of the high currents observed from essentially bulk conversion of the solid on the voltammetric timescale and the absence of rate-determining nucleation phenomena associated with the formation of new phases. The form of structural features responsible for the fast electron and ion transport and the behaviour approaching that expected for 'thin layer'-type voltammetry appear to be a molecular structure that readily accommodates rapid electron and ion transfer, large molecular ions of low symmetry which aid Coulombic cation-anion-electron interaction and ion exchange across the solid-aqueous solution boundaries, and structural packing which favours salt or solvent inclusion [79]. e 5.10 Reversible potentialsa obtained from cyclic voltammograms of [{M(bpy)2]{M'(bpy)2}(p-L)](PF6), dissolved in dimethylformamide (0.1 M Bu4NBF4)at a platinum disc electrode and as a solid adhered to a basal-plane pyrolytic graphite electrode in contact with aqueous 0.1 M KPF6 electrolyte. Compound Solution phaseb 2 Solid phasec h Ru Ru 0 s Ru 0 s0 s Process I E;/2(V) Process I1 Ei12(V) AEl12 (V) 0.13 0.19 0.23 0.54 0.44 0.42 0.41 0.25 0.19 Process I Process 11 AE1/2 $ AEJJ(V) E;/, (V) w / 2 (V) AEp (V) E;/2 (V) w / 2 (V) (V) 3 2. 0.17 0.13 0.12 0.09 -0.01 -0.01 0.19 0.23 0.15 0.13 0.12 0.13 0.38 0.31 0.12 0.19 0.23 0.15 0.29 0.32 0.13 2 X "Reversible half-wave potentials (Eii2) are V vs Ag/AgCl and calculated as the average of the oxidation and reduction peak potentials, AE1/2 = separation between processes 1 and 2, WIi2 is the half-peak-height width, AEp is the separation of the oxidation and reduction peak potentials. ' ~ a t ataken from reference [79]. Scan rate = 0.1 V s-'. 'Data taken from reference [80]. Scan rate = 0.01 V s-l. 3. n % 2 0 X Q 3 rc % Y 3 F;- 24 2 . n E+ 6.1 Corrzparisorz with the voltammetry ofazurin adhered to an electrode as an ideal thin j l v n Clearly the voltammetry of [{M(bpy)2) {M'(bpy)2) (p-L)](PF6),, while having many of the characteristics of 'thin' film behaviour, is adhered to the electrode in the form of arrays of microparticles (Fig. 5.76) and not as a continuous film. It is therefore interesting to see how the behaviour of this system mimics one that is classically regarded as corresponding to genuinely thin film voltammetry. As noted in Section 18 of Chapter 2, metalloproteins attached to electrode surfaces provide close to ideal 'thin film' voltammetric responses. However, as is the case with voltammetry at microparticle-electrode-electrolyte interfaces, nuances are present in these so-called ideal 'thin film' systems that also have their counterparts in the voltammetry of arrays of [{M(bpy)z}{M'(bpy)2}(p-L)] (PF6), microparticles. T o explore both the excellent conformance to theory, but yet subtle deviation from ideality, similar to that found with the microparticle 'thin film' case, the reduction of azurin, considered in Section 18 in Chapter 2 as a model 'thin film' voltammetric system, is now considered in more detail [81]. A range of methods of forming films of metalloproteins have been described in the literature [81]. Commonly, a few microlitres of dilute protein solution are drawn up into a fine capillary and applied directly onto a freshly polished graphite electrode surface. Scratching the surface with the glass tip induces adsorption, probably by exposing a fresh 'virgin' carbon surface. Co-adsorbates may also be added to both the protein and the buffered electrolyte solution in order to stabilize the adsorbed film, presumably by using positively charged amino groups to form ternary salt bridges between the protein and the negatively charged electrode suriace. For studies on the voltammetry of azurin, polymyxin B sulphate (a complex polypeptide, carrying several amine groups) has been used in some experiments as a co-adsorbate [81]. If polymyxin was not included, the voltammetric peaks are broader, indicating that the co-adsorbate plays a role in directing the formation of a uniform monolayer. An alternative method of preparing a thin film is to simply place the graphite electrode in contact with a dilute solution of azurin and allow spontaneous adsorption to occur. These methods of forming adhered solid are of course significantly different from ~ } (PF6),. mechanical attachment of microparticles of [{M(bpy),}{ M ' ( b ~ y )(p-L)] Figure 5.78 shows cyclic voltammograms obtained as a function of scan rate for azurin surface confined on a graphite electrode in contact with 0.1 M NaCl electrolyte. At slow scan rates of 10 mV s-' , the voltammetric response appears to be close to that predicted for an ideal reversible 'thin film' process, since the reduction and oxidation peak potentials are very similar in value (Section 18.2.1 in Chapter 2). In contrast, at fast scan rates, the shapes and characteristics associated with an irreversible 'thin film' process are evident (Fig. 5.78) and the resemblance to data for the voltammetry of [{M(bpy)2}{M'(bpy),}(p-L)] (PF6), (Fig. 5.77) is obvious. As the scan rate increases, both Butler-Volmer and Marcus theories predict (as described in Section 18.2.3 in Chapter 2) that the reduction and oxidation peaks will separate in potential, and also broaden. Voltammograms in Fig. 5.78 Voltammetricstudies on adhered microparticles 433 Fig. 5.78 Voltammograms obtained at O°C for a thin film of azurin adhered to an edge-plane pyrolytic graphite electrode in contact with 0.1 M NaCl (pH 8.5) at scan rates of 10 mV s-l, 1V s-l, and 100 V s-' (top to bottom). The y axis has the current scale for the background-corrected peaks removed for clarity. The x axis is V versus SHE. Provided by courtesy: F.A. Armstrong and J. Hirst, University of Oxford, England. confirm these predictions as clearly the peaks separate and broaden when the scan analogous rate is increased. In the case of [{M(bpy)2}{M'(bpy)2}(p-L)](PF6), behaviour is observed as the scan rate increases [79]. Figure 5.79 shows the change in the cyclic voltammograms, at a scan rate of 100 V s-' , for reduction of azurin that is surface confined on a graphite electrode and when the electrolyte concentration is changed from 0.1 to 2 M NaCl, while Fig. 5.80 shows the electrolyte concentration dependence for the oxidation of microparticles of [ { R ~ ( b p y )(p-L)] ~ } (PF6)2.In both cases, analogous behaviour is seen to be observed. For azurin, the reversible potential is 40 mV more negative in 0.1 M KC1 than 0.1 M NaC1, and also more negative in 0.1 M NaCIOl than 0.1 M NaCl by 50 mV. A similar variation with electrolyte composition is observed for oxidation of [{Ru(bpy)2}(p-L)] (PF6)2[79]. Apart from the consequences of the Butler-Volmer and Marcus theories and uncompensated resistance, there are at least two other possible reasons why the peaks may display broadening at higher scan rates [81]. The first is thermodynamic dispersion, since different redox centres may have different environments and therefore slightly different free energies and hence different reversible potentials for individual molecules or ions. Analogously, there may be 434 Solid-electvode-solvent intefacer Fig. 5.79 Cyclic voltarnrnograms obtained at O°C for a thin film of azurin adhered to an edge-plane pyrolytic graphite electrode in contact with 0.1 M NaCl and 2 M NaCl (buffered at pH 8.5) at a scan rate of 100 V s-' . The peak separation in 2 M NaCl (34 mV) is less than that in 0.1 M NaCl (86 mV). K is the normalized current relative to that expected for a reversible process (Section 18 in Chapter 2) and the ootential axis is V versus SHE. Provided by courtesy: F.A. Armstrong and J. Hirst, University of 0xfo;d, England. I -0.2 I 0.3 E ( V vs SCE) I 0.8 Fig. 5.80 (a) Cyclic voltammograms (scan rate 1OmVs-l) for the oxidation of solid [ { R ~ ( b p y )(p-L)] ~ } ~ (PF6)z attached to basal-plane pyrolytic graphite electrodes and then placed in contact with aqueous 0.1, 0.02, and 0.005 M KPFh electrolyte. (b) Plot of the peak potentials E r (process 1 (m) and process 2 (A)) and E r d (process 1 (0)and process 2 (A)) versus the logarithm of the concentration of KPF6. The dashed lines show the shift in the reversible half-wave potential (E:~ E,OX)/2. Reproduced by courtesy: J. P h p . Chem. B 104 (2000) 1977. Copyright, American ~ h e m i c Society. d + Voltammetricstudies on adhered microparticles 435 kinetic dispersion in which some individual components can transfer electrons at faster rates than others. Kinetic dispersion cannot be readily distinguished (if at all) from Marcus broadening. For azurin, the peak-to-peak separation at the low scan rate limit is about 10mV rather than OmV and the peak width is 18 mV greater than predicted by the Nernst or equilibrium calculation [81]. Thus, perfect agreement is not achieved with theoretical expectations even for this ostensibly well-behaved 'thin film' voltammetry. In order to model the azurin 'thin film' voltammetry with Butler-Volmer or Marcus models, corrections have been introduced to account for the nonidealities not accommodated by an electron-transfer-only model [81]. After introduction of these corrections, the values of the first-order rate constant for the electron-transfer process (KO) for 'thin film' voltammetry of azurin is approximately 1000 s-' in 0.1 M NaCl and 5000 s-' in 2 M NaCl (Fig. 5.8 1). owever, again after correction for non-ideality, agreement between theory and experiment is still not perfect [81]. Rigorous modelling of the 'thin film' version of voltammetry when microparticles are adhered to an electrode surface, has yet to be undertaken, but probably would produce an analogous set of difficulties if a solely electron-transfer model is used, to those encountered with azurin that have been elegantly addressed by Hirst and Armstrong [811. The suggestion that emerges from the study with [{M(bpy)2}{M'(bpy)2}(p-L)] (PF6)ais that 'thin film' behaviour can be found in cases where arrays of microparticles are present on a surface. The observation of apparently parallel forms of utler -Volmer 0.4 0.6 Potential V Fig. 5.81 Comparison of an experimental voltammogram obtained for azurin which is surface confined on an edge-plane pyrolytic graphite electrode in contact with aqueous 2 M NaCl electrolyte and those predicted using the Butler-Volmer theory (ko = 5000 s-I, a = 0.5) and Marcus theory (A = 0.2 eV and k, = 1.8 x lo5 s-I). The modelled results have been corrected to the same peak height and the same position as the experimental data to allow an exact comparison of wave shape. It is apparent that extra broadening is present in the experimental data and that better agreement is obtained using Marcus theory (with a low reorganization energy or h value). Reproduced by courtesy: Anal. Chem. 70 (1998) 5062. Copyright, American Chemical Society. This reference may be consulted for further details of the significance of the kinetic parameters and for further details of the modelling procedures. - 4 0 1 , -0.6 I -0.4 -0.2 0.0 0.2 Potential (V) 0.4 1 0.6 Fig. 5.82 Calculated reversible (Ej = OV) cyclic voltammograms of differently shaped cuboid particles of constant volume Vnl with height (H) and a square base of length (L) and breadth (B), but of different size. The diffusion coefficients of the electron and cation from the electrolyte used for charge neutralization are both lo-' cm2 s-l, V, = 153.8 cm3 mol-', (a) L = B = 28 prn, H = 10 pm, (b) L = B = H = 20 pm, (c) L = B = 16 pm, H = 31 pm. Reproduced by courtesy: J. Solid State Electrochem. 4 (2000) 314. Copyright, Springer-Verlag. voltammetry, under what appears at first sight to be inherently different forms of surface adherence, raises questions as to whether many so-called thin films, in a microscopic sense, are actually equivalent to arrays of microcrystals, and as to whether examples of genuine thin film formation on electrode surfaces are actually quite rare. Finally, it may be noted that in their description of the voltammetry of a cube-shaped crystal adhered to an electrode surface, Schroder et al. [28] note that the dimensions of the crystal are predicted to be critical in determining the shape of a voltammogram when uptake or expulsion of electrons and electrolyte ions are coupled and their mass transport within the solid is governed by Fick's law of diffusion (see Fig. 5.82). The electrochemical studies described in this chapter that are related to rnicroparticles adhered to electrode surfaces reveal that an order of magnitude of additional complexity is present relative to the case when all species involved in an electrochemical process are solution soluble. Thus, while qualitative understanding of the processes is relatively readily achieved, quantitative comparisons with theory frequently tend to be somewhat disappointing if a wide range of time domains (e.g. scan rates in cyclic voltammetry) are used. The key processes in the dynamic electrochemistry of solid microparticles, adhered to electrode surfaces placed in contact with electrolyte, are the coupling of electron and ion transport required to achieve charge neutralization, the A n overview of techniques 437 movement of ions within and between the solid and solution phases, and any accompanying morphology or other changes in the two solid phases associated with the solid-state redox-based conversion process that takes place. Ratedetermining steps identified in this chapter may involve nucleation-growth processes in the interconversion of oxidized and reduced forms of solids (e.g. the [TCNQ]'' process), and the diffusion of ions, coupled to electron transport (e.g. the 0s2+I3+process). Even 'thin film' behaviour may exist. Numerous possibilities of dissolution, redistribution, and morphological changes were also identified as accompanying or potentially accompanying the solid-solid interconversion of adhered microparticles. The technological importance of studies of adhered microparticles is obvious in electrochromic devices, photovoltaic cells, and other solid-state devices such as batteries and fuel cells (Chapter I), so the rapid increase in studies of solids adhered to surfaces is likely to continue. The voltammetric and related electrochemical techniques employed in studies described in Chapter 5 are generally similar to those used in the solution-phase studies reviewed in Chapters 3 and 4. The techniques and examples of their uses include: (1) transient cyclic voltammetry-useful (2) microelectrode voltammetry-useful for general mechanistic diagnosis; for mechanistic diagnosis, particularly when data are interpreted in conjunction with those obtained from transient techniques at macrodisc electrodes; (3) potential step methods-particularly useful for identifying nucleationgrowth processes; (4) CPE-used to interconvert oxidized and reduced forms of microparticles on long time domains; (5) coulometry-useful for qualifying 'amounts7 of solid being interconverted on an electrode sudace during the course of voltammetric or potential step experiments; (6) RRDE-useful for detection of dissolution processes that may accompany redox-based solid-solid interconversion processes; (7) EQCM-provides useful information on mass changes that accompany surface-based redox processes when ions are involved in the charge neutralization process and when dissolution of solid occurs. Characterization of surface-confined processes by in situ and ex situ techniques used in conjunction with electrochemical methodologies is essentially mandatory if any detailed understanding of inherently complex solid-state processes is to be obtained. 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Fletcher and M.D. Horne, RAM Electrodes-An Introduction, CSIRO Report, Australia, 1994. R.L. Deutscher and S. Fletcher, J. Electroanal. Chem. 239 (1998) 17. S. Fletcher, C.S. Halliday, D. Gates, M. Westcott, T. Lwin, and G. Nelson, J. Electroanal. Chem. 159 (1983) 267. R.A. Swalin, Thermodynamics of solid^, Wiley, New York, 1962, pp. 197-21 3. R.L. Deutscher and S. Fletcher, J. Electroanal. Chem. 277 (1990) 1. C.N.R. Rao and KJ. Rao, Phase Transitions in Solids, ~c~rak- ill, New York, 1978. [45] Joint Committee on Powder Diffraction Standards (JCPDS), International Centre for Diffraction Data (ICDD), Powder Diffraction File 1995, PDF-2, Pennsylvania, USA, 1995, database sets 1-45. [46] M.S. Whittingham, in Intercalation Chemistry, (ed. M.S. Whittingham and A.J. Jacobson), Academic Press, New York, 1982, pp. 1-18. [47] W.R. McKinnon, in Solid State Electrochemistry, (ed. P.G. Bruce), Cambridge University Press, Cambridge, UK, 1995, pp. 163-197. 1481 A.C. Riddiford, Adv. Electrochem. 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Chambers, K. Scaboo, and C.D. Evans, J. Electrochem. Soc. 143 (1996) 3039. [62] R.D. Mounts, K. Widlund, H. Gunadi, J. Perez, B. Pech, and J.Q. Chambers, J . Electroanal. Chem. 340 (1992) 227. [63] C.D. Evans and J.Q. Chambers, Chem. Mat. 6 (1994) 454. Solid-electrode-solvent intefaces C.D. Evans and J.Q. Chambers, J . Amer. Chem. Soc. 116 (1994) 11052. A.S. Brown and F.C. Anson, Anal. Chem. 49 (1977) 1589. M. Sanchez-Maestre, R. Rodriguez-Amaro, E. Munoz, J.J. Ruiz, and L. Camacho, J. Electroanal. Chem. 373 (1994) 31. R . Salas, M. Sanchez-Maestre, R. Rodriguez-Amaro, E. Monoz, J.J. Ruiz, and L. Camacho, Langmuir 11 (1995) 1791. S.W. Feldberg and I. Rubinstein, J. Electroanal. Chem. 240 (1988) 1. E. Laviron, J. Electroanal. Chem. 35 (1972) 333. C.E.O. Chidsy and R.W. Murray, J. Phys. Chem. 90 (1986) 1479. J.A. Harrison and H.R. Thirsk, Elect~oanal.Chem. 5 (1967) 67. V.A. Isaev and A.N. Baraboshkin, J. Electroanal. Chem. 377 (1994) 33. M.F. Suarez, F. Marken, R.G. Compton, A.M. Bond, W. Miao, and C.L. Raston, J. Phys. Chem. B 103 (1999) 5637. S.J. Shaw, F. Marken, and A.M. Bond, Electroanalysis 7 (1996) 1. D.A. Fiedler, J. Solid State Electrochem. 2 (1998) 315. RJ Forster, T.E. Keyes, and A.M. Bond, J . Phys. Chem. B 104 (2000) 6389. T.E. Keyes, R.J.Forster, A.M. Bond, and W. Miao, J . Amer. Chem. Soc. 123 (2001) 2877. M.E.G. Lyons, Electroactive Polymer Electrochemistry, Plenum Press, New York, 1996. A.M. Bond, F. Marken, C.T. Williams, D.A. Beattie, T.E. Keyes, R.J. Forster, and J.G. Vos, J. Phys. Chem. B 104 (2000) 1977. T.E. Keyes, R.J. Forster, P.M. Jayaweerg, C.G. Coates, JJ McGarvey, and J.G. Vos, Inorg. hem. 37 (1998) 5925. J. Hirst and F.A. Armstrong, Anal. Chem. 70 (1998) 5062 (and references cited therein). Introduction As noted in Chapters 3 and 4, voltammetric studies on small redox active inorganic, organometallic, and organic molecules frequently provide an efficient method of obtaining important thermodynamic and kinetic information. Logically, therefore, it would be expected that extensive solution-phase voltammetric studies on important electron-transfer metalloproteins such as the cytochromes, ferredoxins, rubredoxins, plastocyanins, and azurins would have been undertaken almost as soon as these water-soluble biologically important molecules had been isolated and characterized. However, it was in fact only in 1977 that the first reports of well-defined solution-phase voltammograms, which could be used to calculate a reversible potential consistent with that expected on the basis of potentiometric measurements, were published for cytochrome c [I ,2]. Prior to that time, metalloproteins were either reported to be electroinactive under voltammetric conditions or else their voltammetry was described as so complex (highly irreversible, complicated by adsorption) that no useful information could be obtained 13-51. The conundrum of lack of, or ill-defined, solution-phase voltammetry for metalloproteins that are designed for fast and specific electron-transfer reactions in biological systems, was explained initially in terms of protein adsorption or even denaturation at electrode surfaces, very small diffusion coefficients and hence very low currents that are difficult to measure, or an inability of the metal centre to approach close enough to an electrode surface to transfer electrons [3-51. However, after about twenty-five years of intensive research, it has become apparent that voltammetric studies on all electron-transfer metalloproteins, and indeed other highly important redox active metalloproteins such as myoglobin, in both the solution phase or as thin films (Chapters 2 and 5) can in fact produce equally well-defined chemically and electrochemically reversible responses as expected for small organic and inorganic molecules where both halves ofthe redox couple are chemically stable. The 'trick' to obtain well-defined metalloprotein voltammetry is to understand and then model 442 Metalloprotein voltammetry or minimize the influence of undesirable sudace-based processes commonly encountered with these highly surface-active biologically important molecules, as indeed is the case with surface-active ruthenium dyes used in photovoltaic cells (see Section 4 in Chapter 4). In this chapter, some of the key results obtained after twenty-five years of intensive investigation into the electrochemistry of metalloproteins are summarized to highlight both 'heroic failures' and outstanding achievements in this field. Via this approach, the numerous subtleties and nuances of the technique of voltammetry (beneficial and deleterious) not considered in Chapters 1-5 can be introduced. What is noteworthy, is the significant learning that takes place while understanding the progression from initial literature reports of 'bad' or no electrochemistry, to a second batch of publications containing phraseology such as 'transient', 'unstable', 'quasi-reversible', or 'fair' electrochemistry until ultimately, the latest publications are said to contain 'ideal' or almost 'reversible' voltammetric behaviour under carefully specified conditions. The evolutionary pathway towards the attainment of 'ideal' voltammetry is presented in the belief that it provides an ideal teaching tool to elucidate the concept of blocked electrodes, the use of chemically modified electrodes, the importance of functional groups on carbon electrodes and microscopic aspects of voltammetry which always need to be considered when a voltammetric response is found to be unexpectedly complex. Metalloproteins are characterized frequently by high charges (e.g. +7 to +8 for cytochrome c, -8 to -9 for plastocyanin, and -18 to -19 for ferredoxin) with an asymmetric distribution so that they often have large dipole moments [6]. Typically, the metal containing redox active centre is iron or copper which is located within the protein at some distance from the surface. Thus, electron transfer to and from an electrode surface may have to occur over distances of several Angstrom (A). The most widely studied electron-transfer metalloprotein is undoubtedly cytochrome c [7,8]. As noted by Bowden [9], the quintessential cytochrome c protein, whose crystallographic structure was first reported three decades ago [lo], has served as a stalwart model, playground, and testbench for chemists interested in understanding fundamental aspects of biological electron transfer [6-81. Not surprisingly, it has also become a benchmark system in protein electrochemistry [9]. Cytochrome c, an essentially globular protein with a diameter of approximately 30 A. Horse-heart cytochrome c has a molecular weight of 12.4 kDa and contains 104 amino acid residues. It is a very basic protein with an overall charge in the range of +7 to +8 at neutral pH [6]. The protein possesses a Studies on protein-suface attachment 443 heterogeneous surface charge with a predominance of positively charged lysine residues in the vicinity of the partially exposed haem-edge providing 0.6 per cent of the total surface area of the protein. The exposed haem edge is believed to be the site of electron transfer, and electrostatic interactions between the positively charged lysine side chains and, complementary, negatively charged groups on its physiological redox partners (or an electrode surface), induce the electron-transfer process. Some other metalloproteins such as plastocyanins and ferredoxins are highly negatively rather than positively charged in their native forms at neutral pH [6], so that as will be shown later their voltammetry may be different from cytochrome c in situations where the sign of the charges on the protein and on chemically modified electrode surfaces are significant. However, with respect to other structural features, generally analogous characteristics apply to all metalloproteins. Proteins, in general, adsorb strongly to many surfaces, including materials used as electrodes. Solution-phase voltammetric studies on these biologically important molecules are therefore likely to be accompanied by surface interaction of material with the electrode surface. Clearly, the nature and significance of surface interactions will need to be understood in order to elucidate the voltammetry of metalloproteins. In the case of azurin, Hill et al. [ I l l have provided direct evidence of the adsorption of individual molecules of this metalloprotein onto a gold electrode surface by in situ STM (see Section 19.1 in Chapter 2 for details of this scanning probe microscopy (SPM) method). Since gold has been widely used as an electrode material in voltammetric studies of metalloproteins [3,4], significant information relevant to metalloprotein electrochemistry can be expected to emerge in the future from consideration of data obtained from these in situ scanning probe studies. In order to rigidly attach azurin to an atomically flat gold substrate, which constitutes an ideal surface for high resolution SPM, Hill et al. [I 11 replaced the serine in position 118 by cysteine to give the azurin (Pseudomonas aeruginosa) mutant S118C. This modification, which generated a well-defined gold-sulfur interaction on the surface, represents a conservative mutation in that no significant protein structure change is likely to have occurred. Thus, electrochemical activity should be, and indeed is, retained, as will be shown later. The gold [I 111 surface,' onto which azurin S118C could be rigidly attached via anchoring of the thiol group, was prepared by evaporation of gold onto freshly cleaned mica. For STM imaging in air, freshly annealed gold substrate was immersed in a 150 pM azurin solution for 3-12 h, gently rinsed, dried with h he observation [I 11 of atomically flat, hexagonal facets confirmed the presence of a gold [I 111 surface. 444 Metallopvotein voltammetry argon, and immediately imaged. Solution studies were carried out in the same way, with the exception that the gold substrate was removed from the protein solution, gently rinsed, then immediately immersed under pure water or buffer, and then imaged [I 11. Imaging in air of gold substrate that had been placed in contact with azurin S118C demonstrated that the surface was covered with a significant amount of material. At high magnification, some of this material could be resolved into regularly sized, quasi-spherical molecules [I 11. Since such features were not observed if the substrate was immersed in protein-free deionized water and imaged under the same conditions, these are in all probability, azurin molecules. This conclusion is further supported by the fact that the smallest, clearly resolved features were approximately 4 nm in diameter (the long axis of the azurin molecule is about 4 nm in length). Images of similarly treated substrate taken under solution were even sharper than those obtained in air and under these conditions individual molecules, and/or small aggregates could be resolved [ l I]. The detection of aggregates is, of course, noteworthy as it raises the question as to whether these could give rise to different voltammetry relative to that observed with individual protein molecules, as assumed to be present in 'thin film7studies on adsorbed azurin (Section 18 in Chapter 2 and Section 4.8.1 in Chapter 5). Figure 6.l(a-g) shows images taken under solution at specified times after the gold substrate was in contact with a solution containing approximately 70 yM protein. The sequence of images shows a clear evolution over time, with the amount of adsorbed azurin steadily increasing. Images of individual isolated molecules are presented in Fig. 6.2.2 A comparison with a space-filling computer graphical model of a single molecule is presented in Fig. 6.2(c). If the models are orientated so as to direct the exposed surface cysteine residue towards an underlying substrate, the correlation, in terms ofboth size and shape, with the STM images is excellent. The STM results on azurin demonstrate that the S118C mutant has a high affinity for a gold electrode surface. Friis et al. [12] have published a combined AFM/STM (Section 19.1 in Chapter 2) study of wild type or native azurin on a gold surface and concluded that the protein chemisorbs on the substrate surface via its disulfide group (Cys3-Cys26). However, since this interpretation may not represent the complete story [Ill, the full relevance of these open-circuit potential ex situ images to voltammetric data has yet to emerge. The difficulty in assigning the full details of the form of surface attachment is that the adsorption and immobilization of protein at a solid/liquid interface remains a poorly understood process [13,14] in which van der Waals, electrostatic and hydrophobic forces, amongst others, play a role [15-171. At the present time, few analytical methods exist that enable adsorption process to be studied at a molecular level [18]. However, SPM now offers the ability to carry out such studies in an in situ mode and at a truly molecular level, so that in future, the molecular level details required to fully understand what 'see http://www.rsc.org/suppdata/njc/l998/ 1119 for full colour venions of Fig. 6.2(a-c). Fig. 6.1 Constant-current STM images of the in situ adsorption of azurin S118C on an Au[l 111 surface under pH 7 phosphate buffer. (a) The annealed gold substrate surface prior to the introduction of protein, x-scale 0-2.5 nm; (b) 3 min after the injection of 100 p1 of 100 pM S118C solution; (c) 5 min after protein injection; (d) 10 min after protein injection; (e) 15 min after protein injection; (018 min after protein injection; (g) 32 min after protein injection. Reproduced by courtesy: New J. Chem. (1998) 1119. Copyright, Royal Society of Chemistry. 446 Metalloprotein voltammetry Fig. 6.2 STM images of immobilized azurin S118C on an A u [ l l l ] surface. (a) In situ constant current image; (b) a three-dimensional, constant-current image; (c) a comparison of constant height images of two azurin Sl l 8 C molecules and orientated space-filling models of the protein. Reproduced by courtesy: New J. Chem. (1998) 1119. Copyright, Royal Society of Chemistry. occurs at gold and other electrode surfaces as a function of potential should be revealed. While the above report focuses on adsorption of azurin on gold, molecular details on azurin, plastocyanin, ferredoxin, cytochrome c, and other metalloproteins attached to gold and other surfaces such as carbon ultimately should become available by scanning probe techniques. At present, all that can be noted from observations made with other proteins, such as cytochrome c [I2,191 is that the affinity for a gold substrate varies significantly with the nature of the metalloprotein. Nevertheless, a fact to emerge from all the studies is that metalloproteins in contact with a gold or other surface will almost invariably become attached as both single molecules and as aggregates and that surface interactions related to these observations almost certainly will influence the voltammetry. Influence ofru$ace attachment 447 f a metalloprotein in solution is strongly adsorbed or chemically attached Q electrode surfaces, as frequently appears to be the case, then clearly the voltammetric response should be modified from that expected for a purely iffusion-controlled solution-phase response. Three likely scenarios arising under these circumstances are: If essentially all of the metalloprotein becomes surface attached and retains the structure of the native form, then ideal 'thin film' voltammetry of the kind exhibited by azurin at carbon electrodes (Section 18 in Chapter 2 and Section 4.8.1 in Chapter 5) may be anticipated. If the surface-attached metalloprotein exhibits a modified structure3 from that of the native form present in the solution phase and if the modified form (e.g. an aggregate) is electroinactive in the reversible potential region of the native form, then electrode blockage could occur, so that no voltammetry is observed. However, in this case, it is also possible that the voltammetric response for the modified surface-attached metalloprotein may be detected at a different potential to that of the native form of the metalloprotein. If both solution phase and surface-confined metalloprotein are present in their native form, then mixtures of thin film and diffusion-controlled voltammetry could be expected, with the relative contributions being a complex function of voltammetric technique (time domain) and protein concentration (Section 18.4 in Chapter 2). General features of voltammetry of metalloproteins at bare (unmodijied) gold electrodes At an edge-plane graphite electrode, the voltammetry ofboth native and S118C forms of azurin exhibit essentially classical diffusion-controlled solution-phase responses (Fig. 6.3(a) and (b)). That is, the peak height is proportional to the square root of scan rate (Fig. 6.3(c)) and the reversible potential is about 90 mV versus SCE. Equation 6.1 describes the azurin voltammetry at graphite electrodes. Az [Cu (11)](solution) + e- + Az [Cu(I)](solution) (6.1) In contrast, at bare gold electrodes (Fig. 6.4(a) and (b)),but not at a modified gold electrode (Fig.6.4(c))the processes are significantly more complex than implied by eqn (6.1). This raises the question of why the use of carbon or chemically modified gold surfaces simplify the voltammetry relative to that observed at a 'bare' gold metal electrode. 3~nteraction with the electrode surface may, for example, lead to unfolding of the structure and subsequently to denaturation of the rnetalloprotein. 448 Metallopotein voltammetvy -200 0 200 mV vs SCE 0 0.05 0.1 0.15 0.2 0.25 Scan ratex (V/s)% mV vs SCE Fig. 6.3 Close to ideal reversible voltammetry obtained for azurin at a polished edge-plane graphite electrode (a) cyclic voltammogram of 100pM wild-type azurin (pH 8, 0.1 M KC1, scan rate 10 mV s-l); (b) cyclic voltammetry of 60 yM S118C azurin (pH 7, 0.1 M KC1, scan rate 20 mV s-l); (c) plot of peak height versus square root of scan rate for 76 yM wild-type azurin (pH 7, 0.1 M KCl). Adapted from: Coord. Chem. Rev.200-202 (2000) 41 1. Copyright, Elsevier. The SPM clearly reveals that azurin and the S118C mutant become attached to a gold substrate and presumably this factor is related to the observation of their complex voltammetry at gold electrodes. The voltammetry of native or wildtype azurin at a 'bare' gold electrode, as shown in Fig. 6.4(a), is very transitory in nature and also occurs at more positive potentials than the reversible process detected at other surfaces (Figs 6.3(a) and 6.4(c)). In the case of the S1l 8 C mutant, a stable, but not diffusion-controlled (shape and scan rate dependence consistent with surface confinement) cyclic voltammetric response shown in Fig. 6.4(b) is observed at a potential that is again significantly more positive than expected for a reversible diffusion-controlled process (compare Figs 6.3(b) with 6.4(b)).The role of the surface cysteine present in the azurin S118C in this behaviour may be demonstrated through the addition of B-alenoyl maleimide to the cell. Removal of the free surface thiol, through its reaction with the maleimide results in a dramatic change in electrochemical response to give a cyclic voltammogram that resembles the transient behaviour observed with the wild-type protein [I I]. Since the voltammetric response of the mutant protein is stable to continual scanning of the potential, the surface attachment occurs with retention of electrochemical activity. In contrast, wild-type azurin, which presumably is attached to the gold surface in a different manner, becomes electroinactive in the Faradaic sense on cycling of the potential. However, note in Fig. 6.4(c), 449 Influence ofsuface attachment (b) I I 0 I I I 400 -100 I 200 (mV) vs SCE I -100 I I 0 100 (mV) vs SCE I I 100 300 (mV) vs SCE I 500 I 200 Fig. 6.4 Voltammograms of azurin at a gold electrode (a) 76 pM wild-type azurin (pH 7, 0.1 M KCl, scan rate 20 mV s-') showing the first (I), second (2), and fifth (5) cycles ofpotential; (b) 60 pM S118C azurin (pH 7, 0.1 M KC1, scan rate 20 mV s-l) showing the initial 20 cycles of potential; (c)wild-type azurin at an SS-bpy-modified gold electrode (pH 6, 50 mM phosphate buffer, scan rate 20 mV s-I). Adapted from: Coord. Chem. Rev. 200-202 (2000) 41 1. Copyright, Elsevier. that at a SS-bpy (4,4'-bipyridyl disulfide or bis(Cpyridy1 disulfide) modified gold electrode, a diffusion-controlled ideal process is observed as is the case at an edge-plane graphite electrode (Fig. 6.3(a)). The voltammetry of ferredoxins, rubredoxins, plastocyanins, and myoglobins on 'bare' gold electrodes is essentially the same as that for wild-type azurin in the sense that no stable welldefined solution-phase diffusion-controlled processes have been reported unless chemically modified gold or other electrode surfaces are used. The electrode dependence clearly needs to be explained. While images of azurin on gold surfaces are impressive, inadequate data are available to elucidate all the nuances of azurin voltammetry. In contrast, imaging data on cytochrome c is not yet of the same quality as for azurin but a great deal more is known about the voltammetry of cytochrome c. Importantly, many features analogous to those described above for azurin, are associated with the cytochrome c process given in eqn (6.2) cyt c[Fe(III)](solution) + e + cyt c[Fe(II)](solution) (6.2) 450 Metalloprotein voltammetry Consequently, a detailed overview of the voltammetry of this metalloprotein is presented, with the presumption being that analogous considerations apply to the surface interactions and voltarnrnetry of azurin. 4.2 The transient nature of the voltammetry ofcytochrome c at 'bare' gold electrodes: an explanation based on a se& blocking mechanism4 Recently, Hill et al. [20] have introduced the concept of a self-blocking mechanism to explain the difficulty associated with obtaining well-defined and stable electrochemical responses for cytochrome c at bare gold electrodes. 4.2.1 Important experimental details In order to obtain the results reported below, extensive cytochrome c purification, specific gold electrode treatment, and specific cytochrome c transferral procedures to the electrochemical cell were used. Brief details of these procedures relevant to the voltammetry described at bare gold electrodes are as follows: (1) Tuna-heart cytochrome c and horse-heart cytochrome c, unless otherwise specified, were purified by fast protein liquid chromatography. (2) Before each set of experiments, the 4-mm diameter gold disc electrode was electrochemically cleaned by cycling the potential between -0.45 and +1.45 V versus SCE in 1 M sulfuric acid solution for 10 min at a scan rate of 0.1 v s - l . (3) Before polishing, the electrode was initially dipped into concentrated nitric acid for 30 s and then in ethanol for 3 min. (4) A mirror-like surface was obtained by polishing on a Buehler ~ i c r o c l o t h ~ ~ with a water-alumina (0.03pm) slurry, followed by 3 min of sonication. (5) A drop of water was left on the surface of an inverted electrode during transfer but was shaken off before the electrode was placed in the cell. (6) Experiments were undertaken at 21°C. 4.2.2 Studies with potassium chloride and sodiumjuoride electrolytes When voltammetric experiments are undertaken using conventional conditions (gold electrode placed in solution and experiments are commenced after the electrode has been in contact with the solution for a period in excess of a minute), no significant Faradaic current is observed at the reversible potential of about OV versus SCE for the process given in eqn (6.2) when potassium chloride is the electrolyte [20]. That is, the response is essentially indistinguishable from that obtained with the electrolyte alone (compare Fig. 6.5(a) and (b)), except for a slight suppression of the background current which may be attributed to adsorption of native cytochrome c or other material. This is, 4 ~ d a p t e with d permission from J. Electroanal. Chem. 436 (1997) 17. Copyright, Elsevier. InJuence ofsurface attachment I -60 I I I I I I I 0 60 mV vs SCE I I 1 120 -60 I 1 1 1 0 1 1 1 1 60 mV vs SCE 1 1 1 120 I -60 I I I I I I I 0 60 mV vs SCE 45 1 I I I 120 Fig. 6.5 Cyclic voltammograms obtained at a scan rate of 20 mV s-I in 0.08 M potassium chloride solution (a) electrolyte alone, (b)-(h) electrolyte containing 110 pM horse-heart cytochrome c and a time delay after the gold electrode came into contact with the solution before scanning commenced of (b) 120 s, (c) 2 s, (d) 10 s, (e) 20 s, (f) 30 s, (g) 40 s, (h) 60 s. The numerals 1, 2, 3, etc. indicate the number of cycles. Reproduced by courtesy: J. Elect~oanal.Chem. 436 (1997) 17. Copyright, Elsevier. data are obtained which are equivalent to the (lack of) voltammetric responses reported in studies prior to 1977. However, if the same 'bare' gold electrode is treated and repolished according to the procedure described above and the potential scan is commenced within 2 s of the electrode coming into contact with the cytochrome c solution, then the voltammogram seen in Fig. 6.5(c) is obtained. Despite the fact that the response is sigmoidal rather than the predicted peak shape, and is only observed for about 3 cycles of the potential, the halfwave potential does occur at potentials that are close to the thermodynamically expected reversible value of about 0 V versus SCE. Clearly, the almost sigmoidal shape of the voltammetric response differs considerably from the peak-shaped response predicted for a diffusion-controlled process at a fully electroactive 4-mm diameter gold macrodisc electrode. Electrode blockage is implicated. Figure 6.6 shows how radial diffusion and hence a sigmoidal-shaped voltammogram may occur with high blockages when each bare electrode site remaining is small and no overlap of diffusion layers occurs. However, if only a small extent of blockage occurs or long time domain experiments are undertaken, then overlap of diffusion layers may occur to give a peak-shaped curve associated with linear diffusion. The maximum current observed for the transient response is actually only about 35 per cent of the value calculated on the basis of the reported diffusion I Electrode Redox active site Redox inactive part of electrode Fig. 6.6 Illustrations of the overlap of diffusion layers which takes place (a) as time increases or (b) the spacing between electroactive sites decreases in a situation where electrode blockage leads to formation of an array of electroactive microelectrodes. 6 is the diffusion-layer thickness. coefficients for cytochrome c and assuming that the entire geometric area is electroactive and that linear diffusion is the dominant mode of mass transport (Table 6.1). Thus, substantial electrode blockage appears to have occurred. A time dependence study (Fig. 6.5(d-h)) reveals no detectable response if the gold electrode is left in contact with the solution for about 30 s prior to commencing the scan. Results obtained with horse-heart and tuna-heart cytochrome c, used as supplied by the manufacturer, differ to those obtained for purified samples, in that the duration for which the transient response is observed is longer in the latter case [20]. Additionally, if the extensive cleaning, maintenance, and electrode transferral procedures detailed in Section 4.2.1 are not used, then the duration of the measurable response also decreases. Adsorption of solution contaminants could represent one form of electrode blockage [21]. Deaminated and oligomeric forms of cytochrome c adsorbed on the electrode surface also may lead to electrode blockage [22] as has been elegantly demonstrated in voltarnmetric studies on cytochrome c at indium oxide electrodes. However, it may be noted that at least one adsorbed form of cytochrome c, which will have a different structural form to the soluble native protein [23-261, and which may be related to the reduced high p H form [27], can undergo irreversible electron transfer at gold electrodes at a potential of about -400mV versus SCE which is quite negative with respect to Influence ofsuface attachment Table 6.1 Half-wave potentials, peak-to-peak separations, and current ratios obtained from voltammetric experiments on a gold electrode using a scan rate of 20 mV s-' in different electrolytes containing 0.1 mM cytochrome ca Electrolyte 0.08 M KC1 (SS-bpy-modified electrode) 0.08 M K2HP04-KH2P04' 0.10 M tris-cacodylatee 0.08 M KCle 0.10 M NaFe 30 35 35 40 35 60 65 70 70 75 1.OO 0.83 0.64 0.34 0.24 'Data taken from reference [20]. b ~ l (+5 p mV) calculated from the average of the oxidation and reduction peak potentials when peak-shaped curves are observed, or from the potential at half the limiting current value when sigmoidal-shaped curves are observed. 'versus SCE. d ~ u r r e nobserved t relative to that expected for an entirely electroactive electrode surface area and linear diffusion. eFirst full cycle. the reversible potential of the native protein [27,28]. Figure 6.7 reveals that if the potential is scanned to this negative potential region so that reduction of adsorbed, presumably non-native form of cytochrome c occurs, then apparently some displacement of material is achieved thereby partially restoring the voltammetry of native cytochrome c at about 0 V versus SCE. A large positive charge (about +8 for the native horse-heart ferricytochrome c) would be expected for both native and adsorbed forms of cytochrome c, although the distribution of charge may differ. Blocking of the electrode surface may occur in a more uniform manner with highly charged species than with non-charged species [29], since coulombic forces will influence the orientation and spacing. These electrostatic constraints between adsorbed and native forms may also limit the number of surface-active sites, which can become occupied by cytochrome molecules, and determine their spacing, although eventually sufficient blocking may be achieved so that current flow at the formal potential of cytochrome c, cannot be detected. The lowering of the background current on the gold electrode in the presence of cytochrome c (Fig. 6.5(a) and (b)) shows that the capacitance and the surface area is reduced [30-321 probably due to adsorption of material on the electrode surface. A self-blocking model, also explains how the sigmoidal-shaped response associated with a partially blocked electrode, may be transformed to an ideal linear diffusion model peak-shaped response (Fig. 6.4(c)) by addition of surface-active SS-bpy. SS-bpy which was used to minimize surface interactions of ruthenium photovoltaic dye-sensitizers in Section 2.5 in Chapter 4 is covalently bound to gold surfaces but, in contrast to adsorbed cytochrome c material, does not block electron transfer [32]. 454 Metallopvotein voltammetvy I I I I I I I -400 -300 -200 -100 0 100 200 mV vs SCE Fig. 6.7 Cyclic voltammograms recorded at a gold electrode using a scan rate of 20 mV s-' in (a) 0.08 M potassium phosphate buffer solution, (b) with 120 pM horse-heart cytochrome c added and cycling over the potential range of -100-220 mV versus SCE, with scanning of the potential commencing immediately after the electrode comes into contact with the solution, (c) as for (b), but potential range extended to encompass the range -500 to 250mV versus SCE, (d) response obtained over the extended potential range after five cycles. Reproduced by courtesy: J. Electroanal. Chem. 436 ( 1997) 17. Copyright, Elsevier. Figure 6.8 shows the shape-time dependence of the voltammetry on addition of SS-bpy to a blocked gold electrode, which initially exhibits no detectable Faradaic response. O n addition of SS-bpy, a sigmoidal response becomes apparent after a few minutes and, in time, this becomes peak-shaped in character. O n repolishing the electrode, an even more pronounced peak-shaped response is observed immediately (Fig. 6.8). Apparently, polishing instantaneously removes the strongly adsorbed molecules and provides electroactive sites to which the SS-bpy may bind and hence protect the gold surface from further adsorption of cytochrome c. If electrolyte anion adsorption is an important parameter in the observed voltammetric response, then replacing the chloride containing electrolyte with Influence of sugace attachment -100 -50 0 50 100 455 150 mV vs SCE ig. 6.8 Cyclic voltammograms for 110 pM horse-heart cytochrome c at a gold electrode obtained in 0.08 M potassium chloride electrolyte at a scan rate of 20 mV s-' after addition of SS-bpy. The transient response obtained without SS-bpy was first allowed to decay (not shown), then 20 cycles (solid line) of the potential were recorded after addition of 10 mM SS-bpy. Finally, the electrode was repolished to give the response shown with the dashed line. Reproduced by courtesy: J. Electroanal. Chem. 436 (1997) 17. Copyright, Elsevier. one containing fluoride would be expected to lead to a decrease in the stability of the transient cytochrome c electrochemical response since the fluoride ion is known to be even more weakly adsorbed than chloride at a gold surface [33]. The cyclic voltammetry of cytochrome c in a sodium fluoride electrolyte is shown in Fig. 6.9. The response is indeed more transient than when chloride electrolyte is employed and, at a scan rate of 20 mV s-' , not identifiable within two cycles. The peak current obtained from the first scan in the fluoride electrolyte is only about a quarter that expected if the electrode were fully electroactive and mass transport were to occur solely by linear diffusion (see Table 6.1). 4.2.3 Studies with phosphate and tris-cacodylate buffered electrolytes The self-blocking array-type model suggests that a more stable response would be achieved by addition of an electrolyte containing a highly charged anion which may be adsorbed onto the electrode or present in the double-layer region of the electrode-solution interface. The voltammetry of cytochrome c when 456 Metallopvotein voltammetry I I -50 0 I I 50 100 mV vs SCE Fig. 6.9 Cyclic voltammograms (first 5 cycles) of 95 pM horse-heart cytochrome c in 0.1 M sodium fluoride, recorded with a scan rate of 20 mV s-I at a gold electrode. Scanning commenced immediately after the electrode came into contact with the solution. Reproduced by courtesy: J. Electroanal. Chem. 436 (1997) 17. Copyright, Elsevier. the potassium chloride electrolyte is replaced with a phosphate buffer5 is shown in Fig. 6.10. Instead of the first scan being small and sigmoidal shaped, it now possesses a peak current about 80 per cent that expected for a fully electroactive electrode under reversible conditions with linear diffusion (Table 6.1). While subsequent scans still eventually become sigmoidal shaped, the response for an approximately 100 pM cytochrome c solution is now identifiable above the background for many cycles (also see references [33-361). Employing a triscacodylate electrolyte (the anion present in solution being [Me2As02]-), as in the work of Bowden et al. [24], produces (Fig. 6.1 1) a similar kind of response for cytochrome c as with the use of a phosphate buffer. The cacodylate anion would be expected to show enhanced adsorption properties relative to phosphate at a gold surface, but is only singly charged. Clearly the nature of the electrolyte is significant in voltammetric studies of cytochrome c as is adsorption and the presence of electrode modifiers such as SS-bpy. 4.2.4 Conclusions devivedfrom voltammetn'c studies at 'bare' gold electrodes The transient nature of the diffusion-controlled component of the electrochemistry of cytochrome c observed at a 'bare' macrodisc gold electrode may be explained in terms of a microscopic model of electron transfer occurring at sites remaining unblocked by time-dependent adsorption of positively-charged non-native forms of cytochrome molecules. he phosphate ion is present as a mixture of [ H P O ~ ] ~and - [H2P04]- at pH 7 and therefore possesses a slightly greater charge per unit concentration than the chloride or fluoride ions. Influence of suIface attachment 457 inset I I I -150 -100 50 0 I I I 50 100 150 mV vs SCE ig. 6.10 Cyclic voltammograms (first 20 cycles) of 100pM horse-heart cytochrome c solution recorded with a scan rate of 20 mV s-I at a gold electrode in a 0.08 M potassiunl phosphate buffer. Scanning commenced immediately after the electrode came into contact with the solution. Inset: first 4 scans over a limited potential range detailing the peak-to-sigmoidal shape progression of the response and concomitant shift in the peak potential. Reproduced by courtesy: J. Electroanal. C h e m . 436 ( 1997) 17. Copyright, Elsevier. The proposed self-blocking model also explains why not even a transient response due to cytochrome c could be detected at the reversible potential at a gold disc microelectrode (5 pm radius) [37] since almost complete blocking of the small electrode surface by adsorbed protein molecules would be very rapidly achieved and the current at the residual part of the bare gold surface of the microelectrode would be too small to measure. The work of Shibata et al. [38] reports the enhancement of the electrochemical response of cytochrome c at a gold electrode by the addition of ad-atoms to the electrode surface which suppress the gold-protein interactions and simultaneously decrease the electrostatic repulsion between native protein in solution and a partially covered electrode surface. This current enhancement is accompanied by a change from sigmoidal to peak-shaped curves. The concept of ad-atoms constituting unblocked or arrays of electroactive sites is consistent with the blocked electrode model. Similarly, the microscopic model may also be applied to explain the observation of transient electrochemical responses reported with cytochrome c at other unmodified metal [21,24,39] and some metal oxide [40] electrodes. Effectively it has been proposed [20] that fast electron transfer takes place at suitable sites and no electron transfer at blocked sites. 458 Metalloprotein voltammetry I I I I I -50 0 50 100 150 mV vs SCE Fig. 6.11 Cyclic voltammograms (first 5 cycles) of a 107 pM horse-heart cytochrome c solution, recorded with a scan rate of 20 mV s-' at a gold electrode in a 0.1 M tris-cacodylate buffer. Scanning commenced immediately after the electrode came into contact with the solution. Reproduced by courtesy: J. Electroanal. Chem. 436 (1997) 17. Copyright, Elsevier. Of course, localized variation in electron-transfer kinetics has of course been considered in other systems where it has been pointed out that measurement of total current only provides an average picture of the surface heterogeneity [41]. Finally, it may be noted that voltammetric responses at variable phosphate buffer concentrations [35,36] also reveal the importance of electrolyte concentration and oligomers, with again the shape of many of the curves being explicable in terms of a partially blocked electrode surface. In the future, it is probable that these surface-based reactions will be directly observable using SPM, so that more detailed explanations of the surface-based processes will become available. 4.2.5 Electrode blockage at indium oxide electrodes Taniguchi [42] has recently stressed the role of the electrode and protein interactions that may give rise to a partially blocked electrode. In the case of cytochrome c, indium oxide is another electrode surface at which ideal essentially diffusion-controlled voltammetric responses can be observed provided purified samples are used [22]. In contrast, on In203, as with a bare gold electrode, commercially available samples of cytochrome c only yield unstable, ill-defined voltammograms [22]. Voltammograms obtained with commercially available and purified samples are shown in Fig. 6.12. Deliberate addition of deamidated and oligomeric components, which are contained in commercially available samples in small amounts, leads to a change in wave shape (Fig. 6.13), and ultimately, if sufficient of these compounds are added, the voltammetric electrode is eliminated [22]. In contrast, at an SS-bpy response on an h203 modified electrode, no change in the voltammetry occurs on addition of these structurally different forms of cytochrome c [22]. These non-native components adsorb so strongly onto the electrode surface that the electrode reaction of native cytochrome c is blocked. In contrast, at the chemically modified Metalloproteins at gold electrodes 459 (4 0.2 yA E (V) vs Fig. 6.12 Cyclic voltammograms (-) obtained at a scan rate of 20 mV s-' of (a) commercially available cytochrome c, (b) approximately 0.1 rnM purified cytochrome c, in a pH 7 phosphate buffer solution containing 0.1 M NaCl at 25°C. (- - - - -) represents the background response. Adapted from: Denki Kagaku 60 (1992) 1043. Fig. 6.13 Changes in shape of the cyclic voltammograms obtained at a scan rate of 20 mV s-' for (-) approximately 0.1 mM purified cytochrome c after adding (- - - - -) (a) approximately 20 pM deamidated and (b) approximately 10 pM oligomeric cytochrome c in a phosphate buffer solution containing 0.1 M NaCl (pH 7) at 25OC. Adapted from: Denki Kagaku 60 (1992) 1043. electrode, SS-bpy molecules adsorb more strongly onto the gold electrode surface than any component of cytochrome c and, thus, no strong adsorption of deamidated and oligomeric cytochrome c occurs. This observation further supports the concept that exclusion of strong adsorption of non-native forms of cytochrome c onto the electrode is one of the important requirements to obtain a completely electroactive surface. Similar behaviour indicating the importance of purification of sample was also observed for myoglobin electrochemistry at electrode [42]. an h203 As noted above, the difficulty in undertaking voltammetric studies of metalloproteins on a 'bare' gold electrode has been attributed to adsorption of the protein itselc a denatured form of the protein or impurity present in the electrolyte solution or in the protein, which produces either a completely blocked and electroinactive gold electrode surface, or a partially blocked electrode with 6~ections5 and 6 have been adapted with permission from Anal. Proc. 29 (1992) 132, 30 (1993) 218 and Coord. Chem. Rev. 200-202 (2000) 411. Copyright, Royal Society of Chemistry and Elsevier. 460 Metallopvotein voltammetry an array of electroactive sites. Commonly, in order to overcome problems with electrode blockage, a chemically modified electrode surface is used to achieve stable well-defined voltammetry at or near to the reversible potential. SS-bpy has already been shown above to enable well-defined voltammetry to be observed, even when voltammetric studies are undertaken on unpurified cytochrome c solutions. Central to the action of these surface-modifying molecules appears to be the ability to prevent direct adsorption of the metalloprotein on to the bare electrode suriace 1431 as well as the maintenance of the protein structure in a configuration which allows rapid electron transfer between the chemically modified surface and the protein redox site. In achieving these two functions, the chemically modified surface appears to 'promote' or facilitate the observation of the direct electrochemistry of metalloproteins. A basic mechanism for the interaction between the 'promoter' (facilitator) and cytochrome c [44-471 is schematically reproduced in Fig. 6.14.~It encompasses diffusion of metalloprotein to the surface, adsorption to the facilitating adlayer in a favourable orientation, electron transfer, desorption, and then diffusion of the protein away from the electrode surface. Figure 6.15 shows STM images of a single-crystal gold SS-bpy modified electrode surfaces which clearly change on addition of cytochrome. O n some occasions in these experiments, which are described in more detail in reference [47], it was possible to resolve small structures, which could be assigned to individual cytochrome molecules. Though these observations are consistent with the electrode-facilitator-protein model shown in Fig. 6.14, it is not clear whether the adsorbed metalloprotein sits on top of or slowly displaces the facilitating adlayer of SS-bpy. As anticipated, polycrystalline gold electrodes, after polishing with an alumina slurry (as typically used in electrochemical studies), are seen to be far from flat on a micrometre scale. In addition to the presence of 'rounded hill' surface features, 100-200 nm in diameter (r.m.s. roughness 15-30 nm), defects and polishing scratches are also evident (Fig. 6.16). In view of the relative complexity and roughness of these surfaces, the adsorption of protein at polycrystalline gold electrodes cannot be studied directly. However, one would expect [47] that protein adsorption/aggregation on these rough surfaces would be even greater than that observed on atomically flat single crystalline electrodes of the same nominal geometric area. Figure 6.17 illustrates the cyclic voltammogram obtained at a gold electrode in the presence of the modifier 4,4'-bip~ridine.This form of surface modification was used in one of the first publications where well-defined voltammetry was reported [2] for cytochrome c. The contrast with voltammetric data contained at ' ~ tshould be noted that figures used to depict these adlayer-protein interactions are obviously idealized models. The electrode surface, in reality, is a complex mixture of topographies. Protein-surface interactions will similarly be highly variant. The experimentally determined electrode potentials and heterogeneous electron-transfer rate constants will therefore reflect a distribution of all those Val& actually present [47]. Metallopvoteins at gold electrodes 461 0 Horse-heart cytochrome c Adsorption _______) Electron transfer 'QL cytochrome c Fig. 6.14 (a) Schematic representations of the interaction between a 4-pyridyl thiolate modified gold electrode surface and a cytochrome c nlolecule. Shown on the right (b) is an STM image of a facilitating 2-mercaptopyrimidine adlayer on gold (with the protein structure superimposed). (c) A schematic depiction of the processes associated with redox protein electron transfer at an electrode/electrolyte interface. Reproduced by courtesy: Coord. Chem. Rev. 200-202 (2000) 41 1. Copyright, Elsevier. 'bare' gold electrodes in Section 4 is most pronounced. Subsequently, numerous organic compounds have been examined [48] specifically in terms of their ability to achieve ideal electrochemistry of horse-heart cytochrome c at a modified gold electrode. Consequently, the structural requirements for successful promotion of the voltammetric response are now well known [49]. Figure 6.18 provides a schematic illustration of the nature of the modified electrode surface as deduced from the various studies [49]. Effectively, an array of adsorbed molecules at the electrode interface provides the electroactive sites rather than the bare gold electrode. The electrochemical implication of this arrangement is illustrated in Fig. 6.19. Thus, linear diffusion of cytochrome c to and from what is effectively a fully electroactive macrodisc electrode may only occur if a monolayer of greater coverage of surface modifier is present or if the sizes of the newly created electroactive sites are large so that the spacing between electroactive sites is small. It therefore follows that the model of electron transfer of proteins at chemically modified gold electrodes may be based on radial diffusion to microscopic active 462 Metalloprotein voltammetry rnV vs SCE Fig. 6. I§ (a) STM image of an SS-bpy adlayer on Au[l 11] in 0.05 M HC1O4 solution. (b) Constant current electrochemical STM image of a SS-bpy modified Au[l11] electrode about 3 min after the addition of approximately 100p1 of 2OOpM cytochrome c solution to the STM cell. Scale bar 4 nm. (c) The simultaneously recorded voltammetric response obtained at a scan rate of 21 mV s-l. Reproduced by courtesy: Coord. Chern. Rev. 200-202 (2000) 41 1. Copyright, Elsevier. sites in instances where surface coverage by the modifier is incomplete, and that electron transfer does not occur to any significant extent at the unmodified part of the gold electrode, which is presumably blocked by adsorbed protein material. Figure 6.20 contains examples of the time dependence of the voltammetry of cytochrome c after a gold electrode modified ex situ with SS-bpy (an excellent promoter of cytochrome c voltammetry) is placed in a solution of another modifier (relatively poor promoter). The transition from a peak to sigmoidalshaped voltammogram followed by a decrease in the limiting current is readily understood in terms of gradual displacement of adsorbed SS-bpy from the electrode surface coupled with the implications that are inherent in the microscopic model. An analogous time dependence is observed when an ex situ modified Metallopvoteins at gold electvodes 463 Fig. 6.16 Ambient contact AFM image of a polished polycrystalline gold electrode surface. x-range 0-400 nm, scan size 3.6 x 3.6 p.m. Reproduced by courtesy: Coord. Chem. Rev.200-202 (2000) 41 1. Copyright, Elsevier. gold electrode is placed in solution and a change in wave shape and decrease in peak height occur as the modifier dissolves from the sudace of the electrode. In the case of azurin, chemical modification of a gold electrode with SS-bpy also produces a stable almost ideal chemically and electrochemically reversible voltammetric process (Fig. 6.4(c)).The reduction of spinach plastocyanin at gold electrodes modified with 2-mercaptoethylamine, 2,2'-dithiobis(ethy1amine) and other compounds has been described in considerable detail [50,51]. Application of the linear diffusion model, which is valid at high coverage (see above), leads to the conclusion that fast electron transfer is associated with the voltammetry of plastocyanin at a suitably modified electrode. However, under some conditions, reduction of plastocyanin exhibits characteristics of a contribution from radial diffusion, as shown by a full analysis of the wave shape and scan-rate dependence. For example, time-dependent [50] studies of plastocyanin voltammograms at a PATS-2-modified electrode (PATS-2 being 2-pyridylaldehyde thiosemicarbazone), prepared in the ex situ mode, reveals a change from a peak-shaped to a sigmoidal-shaped curve (Fig. 6.21(a)), which is attributable to gradual loss of the modifier. In contrast, if PATS-2 is present in the bulk solution, a persistent response is observed (Fig. 6.21 (b)), corresponding closely to the linear diffusion mass-transport model at a highly covered surface [50]. Finally, it may be noted that the electrochemistry of the very negatively (- 19) charged ferredoxin at PATS-modified gold electrodes has also been interpreted as poor [50], since the Faradaic response is hardly, if at all, detectable above 464 Metallovrotein voltammetry Fig. 6.17 Cyclic voltammograms obtained at a gold electrode for horse-heart cytochrome c (5 r n g m ~ ~ in ' ) 0.1 M NaC104-0.02M phosphate buffer at pH 7.0, in the presence of 10 rnM 4,4'-bipyridyl over the potential range from +0.20 to -0.20 V versus SCE, at scan rates of (1) 20, (2) 50, and (3) 100 mV s-' . Provided by courtesty: H.A.O. Hill, University of Oxford, England. the background current (Fig. 6.22). However, after correcting for the background current, the response again can be regarded as reversible according to a model in which electron transfer only occurs at microscopically-sized chemically modified electroactive sites. 6 Voltammetry o f erately functionalize s at naturally an on electrodes In Section 5, well-defined electrochemistry at gold macrodisc electrodes has been shown to be routinely achieved, provided, modified surfaces are prepared with suitable materials. At carbon electrodes, metalloprotein voltammetry without deliberate addition of modifier is often possible, but a wide range of shapes and scan-rate dependence are observed depending on the exact nature of the electrode and its treatment, and the metalloprotein. Figure 6.23 shows, for example that the details of the voltammetric shape depends on the identity of the protein, whether edge or basal-plane pyrolytic graphite is used, the pH and the nature of the modification. Under some conditions, gven in detail in the captions to Figs 6.23 and 6.24 it can be seen that sigmoidal rather than peak-shaped voltammograms are observed and that the dependence ofthe peak current is not always a function of the square root of scan rate, as required by the macroscopic model where mass transport is assumed to occur by linear diffusion and the entire electrode surface is assumed to be electroactive. Thus, a close relationship is noted with voltammetry at modified gold electrodes. Metalloproteins at carbon electvodes 465 Fig. 6.18 Schematic illustration of an array of adsorbed molecules on a chemically modified gold electrode surfice. The proven or anticipated mode of adsorption is given for each of the surface modifiers: (a) 1,2-bis(4-pyridy1)ethylene; (b) SS-bpy (4,4-bipyridyl disulfide); (c) PATS-4 (4-pyridylaldehydethiosemicarbazone); (d) CATS-4 (thiodemicarbazone; 4-carboxybenzaldehyde); (e) thiophenol; (0 2-mercaptoethylamine. Reproduced by courtesy: J. Electroanal. Chem. 217 (1987) 141. Copyright, Elsevier. The need to again introduce the concept of a microscopic electrode array model can be appreciated readily by noting the remarkably close relationship of metalloprotein electrochemistry at carbon as well as gold electrode surfaces with voltammograms obtained for the oxidation of ferrocene at arrays of platinum microelectrodes having both spacing between electrodes and sizes of the electrodes themselves in the micrometre size range (Fig. 6.25). It may be deduced from this comparison, that if protein electrochemistry occurs only at electroactive sites of micrometre size with non-electroactive sites constituting the remainder of the surface, then a better theoretical description of the observed voltammetry will be obtained than is the case when the entire electrode surface is assumed to be electroactive. The use of an electrode microarray-type model of course poses the question of why only parts of the electrode surface are electroactive and other parts are 466 Metallopvotein voltammetry Electrode sudace Surface potential \ E734 \ otential drop across the adlayer rotein molecule Facilitating fun'ctionalized adlayer (b) Electrode surface \ Partial coverage of facilitating adlayer Fig. 6.19 Metalloprotein electron transfer processor at a chemically modified electrode. Model (a) illustrates the situation where the electrode surface area is both flat and uniformly electroactive over its entirety. In the case if the surface is modified with a monolayer coverage of facilitating adlayer, the drop in potential across this must be taken into account when interpreting subsequently obtained protein voltammetry. Model (b) illustrates the situation where the electrode surface is functionalized, but not uniformly. Electron transfer accordingly takes place preferentially at localized sites on the surface. A schematic illustration of an array of adsorbed facilitating molecules on a gold electrode surface for each of the surface modifiers shown in Fig. 6.18: clockwise from top centre SS-bpy, PATS-4, CATS-4, 2-mercaptopyrimidine, 2-mercaptoethylamine, 1,2-bis(4-pyridy1)ethylene.Reproduced by courtesy: Coord. Chem. Rev.200-202 (2000) 41 1. Copyright, Elsevier. blocked at a carbon electrode. In Section 4.1 when describing the voltammetry of metalloproteins at bare gold electrodes it was implied that the electrode was being blocked by adsorbed or denatured proteins or impurities. However, details of the nature of the postulated microscopically small active sites that represent Metalloproteins at carbon electrodes 467 0.0 rnV vs SCE Thiophenol v 2-mercaptoethylarnine Fig. 6.20 Cyclic voltammetry with a scan rate of 20 mV sf1 for 0.4 mM cytochrome c in a pH 7, 20 mM phosphate buffer containing 100 mM NaC104, using a gold electrode modified ex situ with SS-bpy (a) and the effect of increasing exposure time to thiophenol (b,c) and 2-mercaptoethylamine (d,e). Reproduced by courtesy: Eur. J. Biochem. 191 (1990) 737. Copyright, Blackwell Science. the unblocked part of a carbon electrode surface now need to be considered. Because of its highly ordered structure, pyrolytic graphite is anisotropic and has two distinctive types of surfaces, depending on the plane along which it is cleaved [52]. The basal plane formed by cutting along the aromatic ring is relatively inert. In contrast, cutting the graphite across the aromatic rings results in an edge face that is relatively reactive. In the presence of oxygen, this leads to the formation of surface sites associated with various carbon-oxygen (C-0) functional groups. The surface-oxidized functional groups, which are ideally localized at the edge plane, impart considerable hydrophilicity and ionic character to the surface and may form the sites where protein electrochemistry takes place, either because protein adsorption is minimal at such sites or because specific interactions occur at these sites which enable electron transfer to take place. From the point of view of the microscopic theory of electron transfer, the new feature being introduced is the assumption that electron transfer occurs only at the functionalized (unblocked) sites and that these sites are microscopically 468 Metalloprotein voltammetry I I -100 rnV +300 mV E (vs SCE) Fig. 6.21 Voltammetry at a scan rate of 20 mV S-I for 0.25 mM spinach plastocyanin in a pH 8.0 buffer. (a) Gold electrode modified ex situ with PATS-2; (b) as for (a) but in presence of 0.1 mM PATS-2 in the bulk solution. Reproduced by courtesy: Eur. J. Biochern. 191 (1990) 737. Copyright, Blackwell Science. small. The functionality may be naturally imparted by spontaneous formation of functional groups on carbon or by deliberate modification of gold surfaces. It may be argued that with the localized active site model, reduction of a protein such as cytochrome c should not occur at the basal-plane electrode because there should be (ideally) no electroactive sites at which the electron transfer can take place. That is, because this electrode should be purely carbon in nature, adsorption of protein should occur on all points on this interface, and no reduction of native protein should take place at this fully blocked surface. In contrast, the observed electrochemistry at the edge plane would depend on the number of redox active sites per unit area that were not blocked. In reality, a basal-plane graphite electrode will have a more dilute number of active sites than the edgeplane electrode because of non-idealities introduced either in its manufacture or during the cleavage process. Thus, the inherent difference between a basal plane and an edge-plane electrode in a real experimental situation should be the surface density of electroactive sites. Data obtained from X-ray photoelectron spectroscopy and other studies have established the presence of C - 0 functional groups on the graphite Metalloproteins at carbon electrodes Bare Au 0.4 469 p~l -350 mV vs SCE Fig. 6.22 The voltammetry of Clostridiumpasteurianum ferredoxin at (a) a bare gold electrode and (b,c,d) the same electrode modified ex situ with different isomers of PATS. Reproduced by courtesy: Eur. J. Biochem. 191 (1990) 737. Copyright, Blackwell Science. surface: carbonyl, phenolic, carboxylic, and ether-like groups are all thought to be present. At the basal-plane electrode, the oxygen-to-carbon ratio at the surface is very low (O/C = 0.02) [53]. O n polishing, this increases to 0.1 1 [53] and, with an edge plane, the ratio may be as high as 0.33 [53]. The surface density of active sites and the shape of the cyclic voltammograms is therefore predicted to be a function of the method of fabrication and history of the electrode according to the microscopic model. Highly oriented pyrolytic graphite (HOPG) is a substrate commonly used in SPM because it is easily cleavable to produce a surface which is atomically flat 470 Metalloprotein voltammetry PGE, pH 5.0 PGE + PGE PGE PGE, pH 4.0 10.25 1 1 ~ Fig. 6.23 Modifications of the edge-plane pyrolytic graphite electrode (PGE)-solution interface and their effect on the voltammetry oE (a) 150 pM cytochrome c in 5 mM Tricine-100 mM NaCl buffer (pH 8.0) at Ph3Si-modified PGE electrode; scan rate 20 mV s-'; temperature 20°C; (b) as in (a) at bare PGE electrode; (c) 50 pM cytochrome c in 5 mM Tricine-100 mM NaCl buffer (pH 8.0) at a [ ~ r ( N ~ ~ ) ~ ] ~ + - r n o PGE d i f i eelectrode; d scan rate 20 mV s-'; temperature 25°C); (d) as in (c) at bare PGE electrode; (e) 25 pM plastocyanin in 5 rnM acetate-1 mM KC1 buffer (pH 5.0) at bare PGE electrode; scan rate 20 mV s-I; temperature 3°C); (0as in (e) at pH 4.0; (g) 30 yM plastocyanin in 5 mM HEPES-100 mM KC1 buffer (pH 7.0) at bare PGE electrode; scan rate 20 mV s-' ; temperature 20°C; (h) as in (g) at [ ~ r ( N ~ ~ ) ~ ] ~ + - r n o PGE d i f i eelectrode. d The marked region (f) corresponds to a potential of 0 V versus SCE and zero current. Reproduced by courtesy: J.Am. Chem. Soc. 111 (1989) 9185. Copyright, American Chemical Society. over several square micrometres (Fig. 6.26(a)). HOPG has been used successfully in the AFM/STM imaging of proteins and enzymes and is equivalent to the basal-plane graphite surfaces commonly used in electrochemical investigations [3,4]. High-resolution STM images of horse-heart cytochrome c, deposited on a HOPG surface, are presented in Fig. 6.27. Individual molecules (with dimensions very close to those determined by X-ray diffraction) of the cytochrome are clearly evident. Interestingly, and of likely electrochemical significance, the protein molecules preferentially aggregate at defect sites and step edges in the surface (Fig. 6.27(a)) which are likely to possess hydrophilic, 'anchoring' oxygen-based functionalities. An equivalent situation is thereby observed, on at least part of the electrode surface, to that at a deliberately modified gold electrode surface. Metallovvoteins at carbon electvodes d I 0 471 0.2 0.4 Scan rate 'V (V s-')' The radial limit I Fig. 6.24 Cyclic voltammograms (scan rate = 20 mV s-I) for reduction of 150 pM cytochrome c (pH = 8.0) at (a) a polished edge-plane pyrolytic graphite electrode, and (b) a freshly cleaved basal-plane pyrolytic graphite electrode; scan rate 20 mV s-I; temperature 2 0 ° C Also shown are a plot of peak current for the reduction process at the edge-plane electrode versus the square root of the scan rate, d l 2 , verieing the predominance oflinear diffusion for (a) and a plot of log[(^,,, - I)/I] versus the potential, E, at the basal-plane electrode, verieing the predominance of radial diffusion for (b). Reproduced by courtesy: J. Am. Chem. Soc. 111 (1989) 9185. Copyright, American Chemical Society. Edge-plane graphite electrodes used in voltammetric studies are, in stark contrast to HOPG, very rough (Fig. 6.26(b)).The act of polishing adds further to this in the creation of surface scratches of variable diameter and depth. Further to this, edge-plane graphite surfaces, polished in air, possess a high density of various carbon oxide functionalities and approach the situation depicted in Fig. 6.14 at a modified gold electrode. 6.1 Cytochrorne c The observation of an almost sigmoidal-shaped curve for reduction of cytochrome c at a basal-plane electrode (Fig. 6.24(b)) with an ElI2 value equal to the standard redox potential E ~ O , and a linear plot of E versus - I)/I] (E denotes potential, I, the current, and him, the limiting current) with a slope 0.002 V) over the temperature range 15--25"C, is consistent of 2.303 R T I F (f with a reversible process at an array of microscopically small and well-spaced 472 Metalloprotein voltammetry Macroelectrode r=0.5 ~ ~ 0 . 1 pm UMA pm UMA Macroelectrode rz0.5 r=O.l pm U M A pm UMA l Potential (V) vs SCE I Potential (V) vs SCE Potential (V) vs SCE log (v)/log(mV s-I) Fig. 6.25 Cyclic voltammograms for oxidation of low3M ferrocene at arrays of Pt microelectrodes and a conventionally sized Pt disc electrode of the same geometric area in acetonitrile (0.1 M Bu4NC104).(a) Scan rate 5 mV s-' for typical array elements of radius 0.1 (right) and 0.5 pm (centre) with a total area of 0.5 cm2 and for a macro-sized Pt electrode (left) of area 0.5 cm2. (b) Influence of scan rate at the 0.5 pm array electrode. (c) as for (a) but with a scan rate, V,of 20 V s-I where Ip is the peak oxidation current. (d) Plot of log Ip versus log v for data obtained in parts (a), (b), and (c). Macroelectrode; A radius of array element = 0.1 pm; 0radius of array element = 0.5 pm. UMA represents ultramicroelectrode array. Reproduced by courtesy: Anal. Chem. 59 (1987) 2625. Copyright, American Chemical Society. electroactive sites. In contrast, the peak-shaped response at the edge-plane electrode (Fig. 6.24(a)), with an average of the reduction and oxidation peak potentials giving an E ~ O value equal to the value obtained for Eli2 at a basalplane electrode (within the experimental error of A5 mV) also is consistent with a reversible process, but under conditions where diffusion layers overlap to give the equivalent of linear diffusion. The polished basal-plane electrode represents an intermediate case of behaviour, but the electron-transfer process always appears to be reversible on the time-scale of the voltammetric experiments. T o support the applicability of the microscopic model at carbon electrodes, the obvious experiments to consider are those which deliberately alter the surface density of electroactive sites at the edge-plane electrode. For cytochrome c, it has been proposed that positively charged groups around the active haem edge site interact with deprotonated C - 0 functional groups at the electrode surface [53]. If this idea is correct, then blocking agents which can bind preferentially to the oxygen groups on the surface decrease the surface density of suitable sites at which electron transfer to the protein can take place. Comparison of Fig. 6.23(a) and (b) shows the influence on the electrochemistry of cytochrome c when trimethylsilane or triphenylsilane blocking groups are attached [54]to a Metalloproteins at carbon electrodes 473 Fig. 6.26 (a) A constant-current STM image of the single crystal HOPG electrode surface. x-range 0-4 nm, scan size 2 x 2 pm. (b) Low-resolution contact AFM image of a polished edge-plane graphite electrode surface. x-range 0-250 nm, scan size 6 x 6 pm. Reproduced by courtesy: Coord. Chern. Rev.200-202 (2000) 41 1. Copyright, Elsevier. carbon electrode. According to the microscopic model, the almost sigmoidal, rather than peak-shaped, curves that are observed in the presence of silane blocking groups are not the result of slow electron transfer as previously proposed [54]. Rather, a decrease in the number of active sites leads to a predominance of radial diffusion over linear diffusion but the rate of electron transfer remains extremely fast. Thus, a plot of E versus log[&, - I)/I] is linear, with a slope of 2.303 RT/F 0.002V) at 20" C, and Ellz = E ~ O with an experiment error of f5 mV at the silane-derivatized electrodes. This latter result is closely related to the reduction of cytochrome c at a basal-plane electrode, where the surface density of active sites, present as electrode imperfections, is also postulated to be low. + 0 10.0 20.0 nM Scale bar 3.5 nm Fig. 6.27 Constant-current ambient STM images of molecules of horse-heart cytochrome c deposited from aqueous solution onto a freshly cleaved highly ordered pyrolytic graphite electrode surface. (a) Illustrates the obvious preferential accumulation of the protein at step edges on the, otherwise pristine, surface. x-range 0-5 nm, scan size 80 x 80 nm. (b) Shows three individual cytochrome molecules. x-range 0-5 nm, scan size 25 x 25 nm. Scale bar 3.5 nm. Reproduced by courtesy: Coord. Chem. Rev. 200-202 (2000) 41 1. Copyright, Elsevier. Armstrong et al. also showed [55] that it is possible to attach positively charged chromium(1II) complexes to the C - 0 functional groups at an edgeplane graphite electrode. Figure 6.23(c) and (d) shows the cyclic voltammograms for reduction of cytochrome c in the presence and absence of a positively charged [ c ~ ( N H ~ ) ~modified ] ~ + surface. As was the case after the introduction of a silane blocking agent, the peak-shaped voltammogram observed in the absence of modification is transformed into a fully reversible steady-state sigmoidal-shaped response corresponding to reversible charge transfer at a low density of electroactive sites of microscopic dimension. Cytochrome c is a positively charged protein and addition of groups of the same charge to the electrode surface has the effect of decreasing the surface density of electroactive sites. The addition or P~(NH~):+ also causes a change in shape from the reversible linear of &lg2+ diffusion model to the reversible radial diffusion model. Metalloproteins at carbon electrodes 475 6.2 Plastocyanin The copper protein plastocyanin (PC),which like azurin exhibits a CU"-CU' redox process, has an overall highly negative charge of about -9 at pH 7 in contrast with cytochrome c, which has a very positive charge of approximately +8 at the same pH value. Effects related to charge therefore should occur in an opposite sense if the microscopic model is valid. The functional groups, where it is possible that the electron transfer takes place at the pyrolytic graphite electrode, are pH dependent. At pH values less than about 5, it has been suggested that considerable protonation of electrode surface functional groups takes place [53]. Thus, if electrostatic terms are important in the negatively charged plastocyanin, the electrochemistry should appear to be pH dependent. Figure 6.23(e) and (f) shows the cyclic voltammetric response for reduction ofplastocyanin as the pH is varied. The sigmoidal shape of the response at pH 5 (Fig. 6.23(e)) can be attributed to a low concentration ofwell-separated suitable sites for electron transfer which are of microscopic dimension in size, whereas the peak shape at pH 4 (Fig. 6.23(f)) may be associated with an increase in the density of suitable surface-active sites, giving rise to a predominance of linear diffusion rather than radial diffusion. Figure 6.23(g) shows the response of the negatively charged plastocyanin in the presence of positively charged chromium ammine complexes. The situation is now reversed from that observed for positively charged cytochrome c (Fig. 6.23(c) and (d)), where the addition of [ c ~ ( N H ~ ) ~leads ] ~ + to the change from a peak to a sigmoidal-shaped curve. The positively charged domains formed from [ c ~ ( N H ~ ) ~treatment ]~' of the electrode surface promote reversible binding with negatively charged plastocyanin, so that a high density of active sites is achieved and a peak-shaped curve is found instead of the sigmoidal response shape for plastocyanin at an unmodified electrode (Fig. 6.23(g)). The iron-containing ferredoxing proteins are extremely negatively charged and the shapes of cyclic voltammograms can also be extensively modified by addition of positively charged species such as [ c ~ ( N H ~ ) ~to ] ~the + surface (Fig. 6.28), in an analogous way to that previously described for negatively charged plastocyanin. The electrochemistry of ferredoxin at a freshly cleaved basal-plane graphite electrode in the presence of [ c ~ ( N H ~ ) ~ions ] ~ is + reversible, as is shown by the R T I n F slope of the plot oflog[(Ili, -I)/I] versus the potential, E , (Fig. 6.29(a)), although the dependence of the current on scan rate, v , is clearly sensitive to the density of surface-active sites (compare Fig. 6.29(a) and (b) at polished edge and basal-plane electrodes). 476 Metallopvotein voltammetry 1rnM -350 mV vs NHE I NaCl 100 mV n Fig. 6.28 Cyclic voltammograms for reduction of 67 pM Clostridium yasteurianum ferredoxin in a pH 6.0 buffer containing 1 rnM NaCl at an edge-plane pyrolytic graphite electrode in the presence of increasing concentrations of [ c ~ ( N H ~ ) ~ ] Scan ~ ' . rate 20 rnV s-' ; temperature 25°C. Reproduced by courtesy: J. Electroanal. Chem. 217 (1987) 331. Copyright, Elsevier. 6.4 General conclusions concerning the voltammetry of metalloproteins at carbon electrodes Numerous studies are available that describe the influence of added charged species on the voltammetry of redox proteins at graphite and other forms of carbon electrode. The general observation can be made, using the microscopic model, that the observed response lies within the limit expected for 100 per cent radial (microscopicmodel) or 100 per cent linear (macroscopicmodel) diffusion with reversible electron transfer [56,57]. uantitative use of a microscopic model to in the unusual features of metalloprotein voltammetry at car An array of microelectrodes represents a demanding electrode configuration to model, but significant advances in the area have been made which enable many aspects of metalloprotein solution-phase voltammetry to be quantified [58,59]. ' ~ d a ~ t ewith d permision from J. Electroanal. Chem. 314 (1991) 191. Copyright, Elsevier. Also see Inorg. Chem. 31 (1992) 5007. Quantitative use of micvoscopic model 477 Scan rate v112/(vs-')ll2 I -400 mV vs SCE 2 0.6 \ ? ' j 0.5 4w 5 0.4 lz 0.3 d .2 0.2 1 a 2 0.1 I 0.0 0.1 0.2 0.3 0.4 Scan rate v112/(vs-')lI2 Fig. 6.29 Cyclic voltammograms for 50 pM Clostridiurn pasteurianurn ferredoxin in a pH 6.4 20 mM HEPES/100 rnM NaCl buffer (6 mM [ c ~ ( N H ~ ) ~ ]scan ~ + rate ; 20 mV s-l; temperature 20°C) at (a) freshly cleaved and (b) polished basal-plane graphite electrodes. Plots of reduction current, Ired, versus square root of scan rate, v1I2, (shown as e) and, in the case of (a), a plot of log[(hi, - I)/I] versus the potential E (shown as o) is also included. Reproduced by courtesy: J. Am. Chern. Soc. 111 (1989) 9185. Copyright, American Chemical Society. 7.1 Cytochrome c voltammetry at carbon macrodisc electrodes In cyclic voltammetry, and if the process were in fact quasi-reversible, as has been assumed in most reports on the voltammetry of cytochrome c [3,4], the separation of the reduction and oxidation peak potentials A Ep and the wave shape at suitably modified macrodisc electrodes would be expected to be independent of the solution concentration of the electroactive species (Section 8 in Chapter 2). However, for cytochrome c, a significant concentration dependence is observed at graphite macrodisc electrodes which is not explained by the macroscopic linear diffusion model. The peak separation value, AEp = (E;~ - EpO"),which has commonly been used to determine the standard heterogeneous charge-transfer rate constant, ko, at E: when mass transport occurs solely by linear diffusion (Section 8 in Chapter 2), actually increases as the bulk cytochrome c concentration increases. For example, with a 2.4-mm radius basal-plane graphite disc electrode a low concentration of cytochrome c (cc,,,) ( t 2 0 pM), the peak separation (AE,) = 58 f 2 mV (see Figs 6.30 and 6.31), which is, in fact, the value expected for a reversible electron transfer when mass transport occurs 478 Metallopvo tein voltammetvy I -0.3 0.0 I I 0.3 -0.3 I I I 0.0 I I I 0.3 Potential (V) (vs Ag/AgCl) Fig. 6.30 Cyclic voltammograms of cytochrome c at a polished basal-plane pyrolytic graphite electrode in a 100 mM NaC104 5 mM phosphate buffer (pH 7) as a function of scan rate. (a) c,,,., 860 pM; (b) c,,,,, 21 pM. Reproduced by courtesy: J. Electroanal. Chem. 314 (1991) 191. Copyright, Elsevier. log v (mV s-I) Fig. 6.31 Reduction and oxidation peak separations (AEp values) obtained from cyclic voltammograms of cytochrome c at a polished basal-plane pyrolytic graphite electrode in a 100 mM NaC104 5 rnM phosphate buffer (pH 7), as a function of scan rate. Symbols (experimental data): A, c,,,,, 860 pM; B, c,,,.,, 380 pm; C, icy,,,, 122 pm; D, cCYt., 41 pm; E, cCyt,,, 17 pm. Solid lines (simulated data): A, Q = 0.992; B, 6' = 0.975; C, Q = 0.85; D, 6' = 0.35; E, Q = 0.2. Other simulation parameters are in Table 6.2. Reproduced by courtesy: J. Electroanal. Chem. 314 (1991) 191. Copyright, Elsevier. by linear diffusion (Section 8 in Chapter 2). With increasing concentrations (20 pM < cCytc < 900 pM), enhancement of the peak separation for a given scan rate is observed and AE, values of up to 200 mV (see Fig. 6.31) can be obtained under some conditions. Typically, a change from peak to sigmoidal-shaped voltammograms is observed with scan rates v 3 0.5 V s-' and for concentrations of cCy,., > 500 pM. The concentration dependence of AE, and voltammetric shape cannot be explained with a conventional model for a charge-transfer-controlled process where mass transport to the electrode surface occurs via linear diffusion. Such an interpretation would imply different charge-transfer rates (ko values, see Section 7.2 in Chapter 2) for different concentrations (slower rates for Quantitative use of micvoscopic model 479 higher concentrations), a proposal which is inconsistent with a first-order heterogeneous charge-transfer process.9 An alternative interpretation of the experimental data, which does not require the value of ko to be a function of concentration, can be obtained if the surface of the graphite electrode is assumed to have the property ofheterogeneous electroactivity, which is a function of the bulk cytochrome c concentration. That is, if only part of the surface is electroactive, non-linear mass-transport patterns (e.g. microscopic radial diffusion) may be induced. Neglect of these non-linear diffusion terms can strongly influence the apparent kinetics of the electrode interface if the purely linear diffusion model is applied erroneously. In summary, if a model is developed in which the cytochrome c bulk concentration is linked to the fraction of blocked electrode surface, with the higher concentration leading to a higher fraction of surface being blocked, then it follows that the larger peak separation values at higher concentration can be attributed to a higher fraction of blocked electrode sudace rather than to a change in the heterogeneous rate of electron transfer (ko value). The model for partially blocked electrodes, proposed by Matsuda et al. [60,61] can be adapted relatively easily to quantify the relation between surface coverage and cytochrome c concentration. This model is based on a regular hexagonal blocking pattern with circular active sites,'' and the geometry of the pattern is defined by the radius of the active site r;, and the half-distance between active sites ro (see Fig. 6.32). The fractional coverage 8 is given by the expression - <)/$. ASshown in reference [60], a set of values for the parameters, Ti, Q, and 8 , can be found which give excellent agreement1' between theory and experiment (Fig. 6.33 and Table 6.2). The results in Table 6.2 are consistent with the active sites having average sizes in the micrometre and sub-micrometre range. It must be emphasized that these calculated sizes are actually average values, for the time-scale of slow scan rate cyclic voltammetric experiments, and are expected to be dependent on the nature of the model. Realistically, random sizes, forms, and spacing rather than a uniform surface are present. The fractional coverage, 8 , exhibits values close to 1 for concentrations of c,,,., > 300 pM. This situation corresponds to an almost completely blocked electrode surface. With very dilute solutions of cytochrome c, 8 has a value close to zero, which corresponds to a situation where most of the surface is electroactive. Simulated cyclic voltammograms for a fractional coverage of 8 = 0.922 and a rate constant ko = 1.0 cm s-' are shown in Fig. 6.33 as a function of a scan (vi 9k0has the units of cm s-' (Section 7.2 in Chapter 2) and is therefore a first-order process. 'ONthough the regularity of the blocking pattern of this model may be a simplification of the randomly blocked surface situation applying to cytochrome c, differences in the (microscopic) non-linear diffusion patterns between model and real surfaces have only a minor influence on calculated parameters [58,62]. he diffusion coefficient used in these calculations was D = 8 x low7cm2 s-' because this value provided excellent agreement between thory and experiment. See reference [63] for a discussion of the values reported in the literature. 480 Metallopvotein voltammetvy (4 Fig. 6.32 Modelling of partially blocked electrode surfaces: (a) infinitely extending pattern of electroactive disc sites with radius ri and half average distance ro, as used in the model proposed by Matsuda et al. (see text for details) for conventionally sized electrodes; (b) a finite number of non-interacting electroactive microdisc sites of radius rSwithin a microdisc electrode of r a d m r: shaded part of the microelectrode is electroinactive. Reproduced by courtesy: J. Electroanal. Chem. 3 14 (1991) 191. Copyright, Elsevier. rate.12 The change in shape from peaked to sigmoidal form with increasing scan rate closely matches the experimental data for a cytochrome c concentration of 860 pM (Fig. 6.30(b)). Simulated and experimental voltammograms obtained at other concentrations are also in excellent agreement over the scan rate range of 10-1000 mV sP1. The rate of electron transfer used in these calculations essentially corresponds to a reversible process, implying that the rate of electron transfer is very fast at electroactive sites and zero at blocked sites which are electrochemically insulating. 7.2 Cytochrome c voltammetry at carbon microdisc electrodes The electrochemical properties of cytochrome c also have been investigated at carbon disc microelectrodes which had an electrochemically calibrated radius of 6.3 pm. In cyclic voltammetric experiments at these rnicroelectrodes, no Faradaic response was detected when solutions were prepared directly from commercially supplied sample [58]. Due to its much smaller surface area, a microelectrode is expected to be far more sensitive to the presence of surfaceaffecting impurities present in the bulk solution than are normal-sized electrodes. Therefore, the cytochrome c solutions were purified by charcoal filtration to remove surface-active trace impurities estimated to be present in all lyophilized samples [21,39,40]. At the microdisc electrode, under conditions of cyclic voltammetry with purified samples, bulk cytochrome c concentration-dependent voltammetric behaviour was observed, as was the case for normal-sized electrodes. For con< 250 pM and with scan rates 0.05 ( v 5 1.O V s-', the centrations of c,,, system showed the peak-shaped curves (see Fig. 6.34(a)) theoretically expected for the given disc size and diffusion coefficient where all the electrode is 1 2 ~ h double e layer capacitance of 8 pF ~ m added - ~ to the simulated data was estimated from experimental curves. Quantitative use of microscopic model 48 1 Fig. 6.33 Simulations of cyclic voltammograms at a partially covered electrode as a function of scan rate, using the model of Matsuda et al. (see text for details). Parameters used in calculations: 19,0.992; Q, 4.0~"; D, 8.0 x lov7 cm2 spl; kO, 1.0cms-l, a , 0.5; electrode area, 1.0crn2; concentration of redox active species, 1.0 rnM; double-layer capacity, 8 pF cmP2. Reproduced by courtesy: J. Electroanal. Chem. 314 (1991) 191. Copyright, Elsevier. Table 6.2 Calculated geometric parameters 8 , ro, and ri for a partially blocked graphite electrode surfacea obtained as a function of cytochrome c concentration. Values of parameters used in the calculation are D = 8.0 x loy7cm2s-'; k0 = 1.0 cm s-'; a = 0.5 - aData obtained from reference [58]. Symbols are defined in the text; a is the charge-transfer coefficient. b ~ deviation o from an ideal reversible system (linear diffusion) within experimental error. 482 Metalloprotein voltammetry Potential (V vs Ag/AgCl) Fig. 6.34 Cyclic voltammograms for reduction of cytochrome c at a carbon microdisc electrode with r = 6.3 pm in a 100 mM NaC104 5 pm phosphate buffer (pH 7), as a function of scan rate. For clarity only the (reduction) negative scan direction is shown, (a) cCyt.,, 150 yM; (b) cCy,.,,660 pM. Scan rates: (al)v = 50mVs-l; (a2,bl)v = 1 0 0 m V ~ - ~(as, ; ba)v = 500rnVs-I. Reproduced by courtesy: J. Electroanal. Chem. 3 14 (199 1) 191. Copyright, Elsevier. surface active. However, for concentrations ccyt., > 500 pM, and for the same scan rates, steady-state behaviour (sigmoidal-shaped curves) was observed (Fig. 6.34(b)).Analysis of these steady-state curves (ccyt., = 660 pM) gave values for the shift ofthe half-wave potential, E l p , from the reversible value (E: -E1p) of (5 & 4) mV and for the Tomes potential criteria (EIl4- E3/4) of (63 & 4) mV. As with the conventionally sized graphite disc electrode, this concentrationdependent voltarnmetric behaviour can be explained by partial self-blocking of the electrode surface. Because there is no rigorous theoretical treatment available to describe the diffusion properties of partially blocked microelectrodes, a simple approximation may be made to describe the observed response. It can be assumed that by blocking parts of the microelectrode surface an array of noninteracting smaller electroactive sites of circular shape remains (Fig. 6.32 (b)) with the mass transport to each site being by radial diffusion. With this model, the number and size of these microactive sites, and therefore the limiting current, depends on the cytochrome c bulk concentration because the blocked fraction of the surface is a function of this concentration. Theoretical calculations using the above approximate model were made by digital simulation [58] (also see Section 12.2 in Chapter 2). Simulated curves for different k0 values and electroactive sizes are shown in Fig. 6.35. For a microelectrode of given radius, the number of active sites within the partially covered rnicrodisc can be determined from the limiting current and must be equal, according to the proposed model, to the sum of the calculated limiting currents ofthe individual active sites. The limiting current to a single disc-shaped Quantitative use of microscopic model 483 Fig. 6.35 Simulations of cyclic voltammograms at microdisc electrodes with radii (a) r, = 0.1 pm, (b) r, = 5 pm, as a function of rate constant. For clarity, on1 the (reduction) negative potential scan direction is shown: rate constants (al,bl) kO = oo; (aa,b2) k = 1.0 cm s-l; (as,bS) ko = 0.1 cm s-l; cm2 s-l ; a , 0.5; scan rate, (a4,b4) kO = 0.01 cm s-l . Other simulation parameters: D, 8.0 x 0.5 v s-' . Reproduced by courtesy: J. Electroanal. Chern. 314 (1991) 191. Copyright, Elsevier. 7i active site is of course independent ofthe electrode kinetics and can be calculated according to the equation (Section 10 in Chapter 2) where I& is the limiting current, n the number of electrons (1for cytochrome c), D the diffusion coefficient, F the Faraday constant and rs is the radius of the electroactive site. The number of active sites j, is therefore given by where I;: is the experimentally determined limited current. All other symbols have their normal meaning. The fractional coverage, 6 , of the microdisc electrode can be obtained from where r is the radius of the microdisc. The fractional coverage of the normal-sized graphite electrodes has been determined as a function of the cytochrome c bulk concentration (see Table 6.2). If similar fractional coverages are also assumed to apply for the partially blocked microdisc electrode, then by use of eqns (6.3) and (6.4), the size of the active sites in the microdisc can be calculated for experimentally determined values 484 Metallopvotein voltammetvy 1 t -0.3 t 0 Potential (V vs Ag/AgCI) I 0.3 Fig. 6.36 Cyclic voltammograms at microdisc electrodes; experimental (+) and simulated (-) data. For clarity only the (reduction) negative scan direction is shown. Experimental conditions: 660 pm cytochrome c in 100 rnM NaC104, 5 rnM phosphate buffer (pH 7) at a carbon microdisc electrode with r , 6.3 pm; scan rate v , 0.5 V s-l. Simulation parameters: 5, 0.14 pm; js, 25; D, 8.0 x cm2s-'; a , 0.5; v , 0 . 5 ~ s - l ;rate constants A, kO = m; B , k0 = l.0cms-l; C, kO = 0.1 cms-I; D, kO = 0.01 cm s-l. Reproduced by courtesy: J. Electroanal. Chem. 314 (1991) 191. Copyright, Elsevier. 4:;. of Values lie within the range calculated at the large electrodes. The size of the active sites is important because the kinetic sensitivity of the electrode to the rate of electron transfer is directly related to it. The smaller the active sites, the higher the kinetic sensitivity of the electrode (Section 14 in Chapter 2). This fact is illustrated in Fig. 6.36, where it is shown that for a site size v, = 5 pm, the voltammetric curves are indistinguishable for rate constants oo 2 ko 2 0.1 cm s-' , whereas when r, = 0.1 prn, even the curve for 1.0 cm s-' is well resolved from the reversible case. The value of ko as a function of vs [64] is calculated by where K O is a dimensionless parameter and has been defined [64] as a function of the half-wave potential (E: - Ell2)and the Tomes potential criterion E3/4). For the experimental values cyt.c = 660 pM, (E: = (5 f.4) mV and (E1/4-E3/4) = (63k4) mV, the parameter K O is given by log K O = 0.9A10.3. The resulting calculated heterogeneous charge-transfer rate constants, ko, for a range of fractional coverages similar to those obtained at the conventionally sized graphite electrodes are presented in Table 6.3. Figure 6.36 shows that an excellent fit of the proposed model with experimental data is obtained for a very fast rate of electron transfer in the sense Quantitative use of micvoscopic model 48 5 Table 6.3 Heterogeneous charge-transfer rate constants calculated for horse-heart cytochrome c for a range of surface parameters of a partially blocked carbon disc microelectrode" "Data obtained from reference [58]. b ~ a d i uof s the active site. "umber of active sites calculated by use of eqn (6.4) and an experimentafly determined limiting current of 72pA (660pM cytochrome c in 0.1 M NaC104, 5 mM phosphate buffer, p H 7). d~alculated by use of eqn (6.5). eCalculated by use of equation (6.6) for D = 8.0 x lop7 cm2 s-' and l o g ~ O= 0.9. f 19value obtained by interpolating values in Table 6.2 for cCY,,, = 660 pM. that the experimental curve lies very close to the simulated curves for ko = oo (fully reversible) and ko = 1.0 cm s-', but is considerably removed for the cases ko = 0.1 and ko = 0.01 cm s-l. The conclusion is therefore reached that the process is close to reversible and certainly much faster than 0.1 cm s-l. The value for ko calculated assuming a similar coverage as at a large graphite electrode is >0.4 cms-', which, as shown from data contained in Table 6.3 is about two orders of magnitude higher than the values previously calculated by using models in which ideal linear mass transport to a fully active electrode surface is assumed [58]. Further support for the presence of partially blocked microelectrodes also comes from data provided by Hill et al. [65] who studied the voltammetry of cytochrome at a very large assembly of more than 8000 carbon-fibre microdisc electrodes. At this very large array of microdisc electrodes, high quality near steady-state voltammograms were observed (Fig. 6.37) down to cytochrome c concentrations of 1 pM. However, the response deteriorated as cycling of the potential progressed as expected when time-dependent adsorption of denatured or other forms of cytochrome c occurs. Furthermore, curvature is evident in the limiting current versus concentration plot (Fig. 6.37) again as expected when cytochrome c concentration-dependent electrode blockage occurs. 7.3 Conclusions derived fvom modelling the voltammetry of cytochrome c at carbon electrodes The electrochemistry of cytochrome c at carbon electrodes can be explained in terms of a model where the electrode surface is partially blocked, presumably Metalloprotein voltanzmetry -150 0 -300-200-100 0 100 200 300 400 Potential (mV) 60 Concentration (pM) Fig. 6.37 The non-linear diffusion-limited current versus concentration plot obtained from voltammograms of horse-heart cytochrome c (5 mM sodium phosphate buffer (pH 7.0)/100 mM NaC1) using a large assembly of carbon-fibre microdisc electrodes (scan rate 20 mV s-l). Inset: A cyclic voltammogram obtained at the same electrode assembly with a scan rate of 10 mV s-' for the reduction of 49.6 yM horse-heart cytochrome c and a cyclic voltammogram of the buffer solution alone. Adapted from: Lab on a Chip. 1 (2001) 127. by the presence of some form of adsorbed protein. Under conditions where electrode blockage is substantial, this self-inhibition process may dominate the voltammetric behaviour of the interiace because the Faradaic process can take place only at the few remaining active sites of the electrode surface. The nonlinear mass transport to these extremely small active sites then contributes significantly to the voltammetry observed for cytochrome c. An equivalent model to that used to explain cytochrome c voltammetry also has been successfully applied to the voltammetry of plastocyanin at carbon electrodes [59]. ence that chernica e surface can a ification of the In the preceding part of this chapter, the voltammetric response of metalloproteins has been described at chemically modified or functionalized electrode surfaces. Until now, the question as to whether the compounds used to modify the electrode surface are innocent in the thermodynamic sense has not been raised. However, it will now be demonstrated that positively charged 13~dapted from Electrochem. Commun. 1 (1999) 309 Chemical modification of electrode su$ace 487 compounds used to modify graphite electrode surfaces, may alter the measured redox potential of both negatively changed recombinant and mutant forms of rubredoxin and ferredoxin from Clostridium pasteurianum (Cp). This view contrasts to the frequently held assumption that modifiers are thermodynamically innocent. 8.1 The thermodynamic effects of chemical modijcation of graphite electrodes on rubredoxin electrochemistry No Faradaic voltammetric response is observed when a freshly polished pyrolytic graphite electrode is placed in contact with a recombinant rubredoxin (Rd) solution. However, after the electrode is modified ex situ by dipping into a 10 rnM solution of highly charged cationic poly(L-lysine) (degree ofpolymerization, 20) for 2min, followed by rinsing carefully with distilled water, a very welldefined voltammogram is observed in the reversible potential region. When the electrode is modified ex situ with 160 mM tris(l,2-diaminoethane)chromium chloride, [Cr (en)3]C13l 4 solution, again a well-defined voltammogram is observed. In contrast, after using ex situ modifications with very high concentrations of Mg2+, only a very weak response is observed. Figure 6.38 contains a comparison of square-wave voltammograms15obtained when poly(L-lysine), [ ~ r ( e n ) ~ ]and ~ +Mg2+ , ex situ modified graphite electrodes are placed in contact with a rubredoxin solution. The fact that these charged electrode surface modifiers are not thermodynamically innocent is revealed by noting that the reversible potentials obtained by square-wave voltammetry using in situ modified electrodes depend on the molar ratio of cationic modifier to rubredoxin. A positive potential shift is always observed with increasing concentrations of modifier but the magnitude of the shifts varies with the identity of the cation. The shifts in reversible potential are significant at low poly(L-lysine) to rubredoxin ratios, but approach a limiting value as the ratio is increased (Fig. 6.39(a)). The peak potentials are also positively shifted as the concentration of [Cr(en)3I3+ is increased. However, the magnitude of the shifts are much smaller than when poly(L-lysine) is used under the same conditions (Fig. 6.39(b)). The measured peak potentials for [modifier]/ [Rd] extrapolated to zero modifier concentration are essentially identical for both poly(L-lysine) and [cr(en)313+ (Fig. 6.39(b)). The extrapolated value is believed to represent the 'correct' E,O value of the rubredoxin redox process. 14[cr(en)313+in water undergoes hydrolysis to form an equilibrium containing mononuclear and binuclear ions [66]. However, for conciseness, this form of electrode modification will be referred to as [cr(en)313+. 1 5 ~ hsquare-wave e technique is described in Section 4.1 in Chapter 2 and for a reversible process the peak position is located at E ~ O [67]. Furthermore, the same shape applies irrespective of whether a macroscopic or microscopic electrode model applies, provided the process is reversible as appears to be the case with square-wave voltammograms for both rubredoxin and ferredoxin [68]. 488 Metallopvotein voltammetvy -500 -480 -360 -240 -120 0 Potential (mV) vs Ag/AgCl Fig. 6.38 Square-wave voltammograms of 80 pM recombinant Clostridium Pasteurianum rubredoxin in a 30 mM tris-HC1/0.1 M NaCl (pH 7.4) buffer at an edge-plane pyrolytic graphite electrode modified by dipping into a solution of (a) 2mM poly(L-lysine); (b) 0.16M [Cr(en)3]C13; and (c) 0.20 M MgC12. Square-wave amplitude 50 mV, frequency 43 Hz. Provided by courtesy: Z. Xiao and A.G. Wedd, University of Melbourne, Australia. 8.2 Thevmodynamic effects of chemical mod$cation of graphite electrodes onfervedoxin electvochemistry Observations on the electrochemistry of recombinant ferredoxin Fd at an in situ modified pyrolytic graphite electrode in the presence of modifiers are similar to the rubredoxin case (compare Figs 6.39(a) and 6.40). The shift in reversible potential of recombinant ferredoxin with increased modifiers concentration was found to be greater in magnitude with poly(L-lysine) as the modifiers than with [cr(en)3I3+.Total shifts were found to be f 3 0 and +15 mV respectively for [promoter]/[Fd] = 12.0 (Fig. 6.41). Reversible electrochemistry can also be obtained by ex situ modification of the electrode by dipping into a concentrated solution of 160 mM [cr(en)313' or 10 mM poly(L-lysine). Under these conditions, the peak current is constant for up to 20 scans when poly(L-lysine) is used but decreases rapidly with repeat scans in the case of [ ~ r ( e n ) ~ ]That ~ + .is, [cr(en)313+incorporated onto/into the graphite electrode slowly dissolves from the surface into the interfacial region and the bulk solution and it is the surface-confined state of the complex that leads to the promotion of the voltammetry of ferredoxin. Chemical modification of electrode Potential (mV) vs SHE (b) -80 1 I I I 0 5 10 15 Ipromoter]:[r-Rd] Fig. 6.39 Dependence of the reversible square-wave peak potentials (Epvalue) of 80 pM recombinant rubredoxin (r-Rd) obtained at an in situ poly(L-1ysine)-modified pyrolytic graphite electrode on the solution-phase concentrations of modifier and protein: (a) square-wave voltammograms at different solution-phase poly(L-lysine) concentrations; (b) plots of Ep versus [modifier]/[protein] concentration ratio. Voltammetric conditions are as in Fig. 6.38. Reproduced by courtesy: Electrochem. Comm. 1 (1999) 309. Copyright, Elsevier. The electrochemistry of mutant D33,35,39N ferredoxin (charge -8 relative to -11 on the recombinant form) was also measured [68] to determine whether a change in total protein charge would influence the efficiency of promotion or the magnitude of potential shifts. [cr(en)313+was added in the same [protein]/[modifier] ratios as for the native protein (Fig. 6-41(c)). The Metallopvotein voltammetvy Potential (mV) vs Ag/AgCl Fig. 6.40 Square-wave voltammograms of 80 yM recombinant Clostridiumpasteurianurn ferredoxin in a 30 rnM tris HCV0.1 M NaC1, (pH 7.4) buffer at a pyrolytic graphite electrode, showing the dependence of the reversible peak potentials (EP)on poly(L-lysine): R d molar ratios; where [poly(L-lysine)]/[Rd] = 0.25; 0.50; 1.O; 2.0; 4.0; 8.0; 12. Other voltammetric conditions are as in Fig. 6.38. Provided by courtesy: Z. Xiao and A.G. Wedd, University of Melbourne, Australia. maximum change in measured potential was approximately +6 mV in this case which is significantly smaller than obtained with recombinant rubredoxin. Also, in contrast to the work on the rubredoxin protein, the measured potential was 4.0 d ]and above. constant for [ ~ r ( e n ) ~ ] ~ + /=[ ~ 8.3 Conclusions concerning the dependence of the reversible potential on the presence of a su?face modijier The surface of a freshly polished pyrolytic graphite electrode contains negative patches due to the formation of carboxylate functionalities on the surface that result from oxidation of carbon in the presence of air. Consequently, the electrode can be modified by the incorporation of cationic species such as [cr(en)3I3+and poly(L-lysine) onto the surface to give favourable electroactive sites that do not readily become blocked by adsorption of protein. Modification of the electrode can be achieved by dipping it into a concentrated solution of cations. This contact with positive-charged species apparently results in association of the cation onto the electrode surface causing the electrode surface Chemical mod$cation of electrode surface 49 1 10 [Modifier]/ [Fd] Fig. 6.41 Dependence of reversible square-wave voltammetric peak potentials (Ep)on modifier: ferredoxin molar concentration ratios for (a) 80 pM recombinant ferredoxin in the presence of poly(L-lysine), (b) 80 pM recombinant ferredoxin in the presence of [ ~ r ( e n ) ~ and ] ~ +(c) 80 pM D33/35/39N ferredoxin in the presence of [cr(en)313+.Voltammetric conditions as in Fig. 6.38. Provided by courtesy: Z. Xiao and A.G. Wedd, University of Melbourne, Australia. to have favourable electroactive sites with which the negatively charged proteins can interact, without encountering electrostatic repulsion or electrode blockage. Reversible electrochemistry results at these favourable sites. However, it is important to note that the use of these modifiers may cause shifts in the measured redox potentials of proteins, with the magnitude of the shifts being dependent on the molar ratio of modifier to protein when an in situ form of electrode modification is used. It is possible that these shifts in potential are due to ion-pair formation between the protein and modifier molecules such that the reduced form of the protein is stabilized (causingthe protein to be more difficult to oxidize and thus making the reversible potential more positive). As may be expected ifbinding is electrostatic in origin, the strength of binding of modifier to protein and hence the shift in potential as a function of modifier concentration seems to depend on the protein charge. This is shown by comparison of data obtained in the [ ~ r ( e n ) ~titration ]~+ experiments with the D33/35/39N Fd mutant and recombinant ferredoxin [68]. The mutant has a total charge of -8 at pH 7.5 as compared to the charge on the native protein of - 11. The addition of [cr(en)3I3+caused a smaller shift and ] ratios. The approaches a limiting value at lower [ ~(en):' r ] / [ ~ dconcentration dependence of modifiers on the reversible potential of other metalloproteins also 492 Metalloprotein voltammetry has been noted [69-721 and it always must be remembered that modification of the electrode surface cannot be assumed to be an innocent activity in the thermodynamic sense. 9 Long-range electron-transfer effects encountered in cytochrome c voltammetry at long-chain alka modified electrodes In Section 18.2.3 in Chapter 2 it was noted that electron-transfer reactions that occur over long distances lead to slow rates of electron transfer that may be analysed in terms ofMarcus theory. In principle, voltammetry of metalloproteins at suitable chemically modified electrode surfaces could lead to this situation being achieved. For example, the schematic diagrams used in Figs 6.14 and 6.19 to explain the voltammetry of cytochrome c at partially blocked electrodes could lead to electron transfer over long distances if the electrode modifier had had significantly larger dimensions than SS-bpy and other electrode modifiers considered so far. In Section 18 in Chapter 2, the voltammetry of cytochrome c at SAMs was considered when long-chain alkane thiolates were attached to gold electrodes. It can now be noted that use of these SAMs, discussed in Chapter 2, in the case of metalloprotein electrochemistry, represents in reality a special case of chemically modified electrodes that both inhibits problems with electrode blockage, and which concomitantly leads to electron transfer over long distances. This aspect of cytochrome c electrochemistry considered in Chapter 2, can now be revisited to further illustrate that metalloprotein voltammetry, after allowing for the nuances, is in fact not significantly different from that obtained with smaller molecules. In particular, additional discussion of Figs 2.92-2.95 of Chapter 2 will be considered in this context. If cytochrome c becomes attached to the SAM, as in the studies of Bowden et al. [9], cytochrome c electrochemistry, instead of being undertaken in diffusional mode as described above and with all the electrode-blockage problems, can be performed in a diffusionless mode, in which a monolayer or submonolayer of the protein is immobilized on top of the alkane thiolate modified electrode surface (Fig. 2.93). As discussed in Chapter 2 and elsewhere [73], reaction schemes become considerably simplified upon exclusion of rate limitations arising from mass transfer and adsorption/desorption processes, leaving a particularly simple overall reaction to characterize in which the measured rate constants (ko), with units of s-l, is that of the fundamental electron-transfer step itself (assuming that conformational changes or other complications are not a factor), and surf denotes a surface-confined species. Alternatively, of course, if cytochrome c is not immobilized onto the modified surface, then diffusion-controlled theory can apply, but the heterogeneous electron-transfer rate will again be slow with ko values having the units of Long-range electron-transfer effects 493 centimetre per second being measurable. In both the diffusional and diffusional modes of metalloprotein voltammetry at these chemically modified electrodes, Marcus theory can now be expected to be used when highly irreversible voltammograms are observed as a result of very slow electron transfer being introduced by the long distance required for electron transfer. Figure 2.94 shows some typical cyclic voltammograms (CV) obtained from diffusionless cytochrome c voltammetry experiments using SAMs of two different thicknesses constructed using COOH-terminated alkanethiols. As noted in Chapter 2, the area under the voltammetric peaks provides a direct measure of the number of electroactive cytochrome molecules on the surface r(mol/cm2); the sudace formal potential ([Efo](suq)can be obtained from reversible or nearreversible cyclic voltammograms as the midpoint between the peak potentials; the peak separation can be used to determine the standard electron-transfer rate constant (ko) for reaction (6.7). As noted in Chapter 2, there are always complications associated with these analyses, since the redox proteins are confined to heterogeneous solid surfaces, thus giving rise to thermodynamic and kinetic dispersions and other phenomena [74,75]. Nevertheless, for voltammograms of the quality shown in Fig. 2.94, the complications are not overly serious, and f , ko can readily be obtained using the fairly accurate values for I?, [ ~ f o ] ~and simple physical models presented in Chapter 2. The two cyclic voltammograms shown in Fig. 2.94 show that as the alkyl chain of the thiolate molecule is lengthened, the peak separation increases due to a decrease in electron-transfer rate. The distance dependence of the electrontransfer rate for the cytochrome c modified gold electrode system has been studied [76-781 by systematically varying the number of methylenes (n) in the COOH-terminated alkanethiol spacer molecule. For n > 8, the exponential decay of electron-transfer rate with distance shown in Fig. 2.95, which signifies a non-adiabatic electron-transfer process involving long range electron transfer. The tunnelling decay parameter obtained from these experiments [9] are consistent with through-bond tunnelling of electrons along the alkane chains forming the modified gold electrode and are consistent with comparable studies of small molecule electroactive SAM [79]. However, for cytochrome c, adsorbed on thinner alkane thiolates (n 5 8), there is disagreement at present as to whether the electron-transfer rate continues to decay exponentially or levels off as the distance continues to decrease [9]. As noted in Chapter 2, peak separations for cyclic voltammograms such as shown in Fig. 2.94 can be used with the simple Butler-Volmer model, described in the seminal work by Laviron [go], to readily give ko values used to construct Fig. 2.98. These values of ko (s-l) are uniquely those for zero overpotential, [Efolsurf, where the rate is controlled by the intrinsic free-energy barrier [81]. Also as noted in Chapter 2, the other activation issue to consider is the driving force or potential dependence of the rate of electron transfer. In order to extract the reorganization energy (A)and the intrinsic activation barrier for the redox protein, theoretical linear sweep voltammetric treatments of the kind described in Chapter 2 and references [82,83] have been applied to cytochrome c adsorbed 494 Metallopvotein voltammetvy on self-assembled alkane thiolate monolayers [84]. A value for h of 0.3 eV was determined based on fitting the theoretical analytical expression to the voltammetric data, but the presence of non-ideal peak broadening dictates that this value be considered as a lower limit to the true h [9]. A second approach to achieve long-distance electron transfer, developed by Miller's group [85,86], does not rely on cytochrome c immobilization to circumvent the mass-transfer problem, but using the hydroxy-terminated long-chain alkane thiol surface modification to slow the normally rapid heterogeneous electron-transfer kinetics (rate constants having cm s-' units) to sufficiently low values. This strategy has the effect of shifting the voltammetry wave to irreversible potentials (Fig. 2.92), well into the Marcus inverted region, whereupon current-voltage data can be acquired at the foot of the voltammetric wave, where mass-transport limitations are minimal (see Fig. 2.92). This approach has been used to measure the reorganization energy for several species of cytochromes and values of around 0.6 eV have been found [86]. Determination of reorganization energies for redox proteins has been a challenge for decades, as evidenced by a lack of consensus regarding such a fundamental kinetic parameter as the reorganization energy for cytochrome c [9]. With these electrochemical approaches using chemically modified electrodes, the prospects for this important measurement becoming routine have brightened considerably [9]. 10 Voltammetry of metalloprotei surfactant environments In the preceding part of this chapter, almost ideal voltammograms of metalloproteins have been obtained using highly purified protein solutions or chemically modified or functionalized electrode surfaces. An alternative method of achieving well-defined voltammetry for metalloproteins is to undertake studies with material trapped in surfactants that are cast as thin films on electrode surfaces [87]. Again, as with the case of a chemically modified electrode, in this environment, no direct interaction of a metalloprotein with an electrode surface occurs to block electron transfer and reversible well-defined electrode processes are observed. This surfactant actually provides a medium akin to the lipid bilayer biomembrane-like environment [87] in which many metalloproteins exist in nature [88]. In living organisms, biomembranes are about half-phospholipids and halfprotein and generally exist in a partly fluid, semi-permeable state [87-891. In the early 1980s, Kunitake and co-workers showed that ordered films of waterinsoluble surfactants can be cast onto solid surfaces from organic solvents or aqueous vesicle dispersions [87,90]. Evaporation of solvent leaves thin, selfassembled multi-bilayer films, similar to stacks of biomembranes. Similar films can be made with surfactants and polymers [91-931. Several research groups have described the reversible electrochemistry of small molecules in the liquid crystal Metallopvoteins in sufactant envi~onments 495 state present in these cast multi-Maya surfactantfilms [%-I021 and this concept has been extended to achieve well-defined metalloprotein voltammetry. Waterinsoluble surfactants are used in these studies, usually with two alkyl chains, with an example being the surfactant DDAB (Fig. 6.42). The work of Hawkridge and co-workers [87] shows that myoglobin (Mb) in solution-phase voltammetry, like cytochrome c and other metalloproteins, gives ill-defined voltammetry on bare metal electrodes, although it is detected with reasonable definition on indium tin oxide electrodes [103-1051. In contrast, direct reversible electron transfer between pyrolytic graphite, Au, or Pt electrodes and myoglobin is readily obtained in water-insoluble films of DDAB (Fig. 6.43) [I O4,106,lO7] immobilized onto the electrode surface, which is in turn in contrast with an aqueous electrolyte media. In order to achieve charge balance the electrode reaction requires a proton from the solution phase, and the process can be represented as [Fe(II)](surfactant) (6.8) didodecyldimethylammonium bromide (DDAB) Fig. 6.42 Structure of the surfactant didodecyldimethylammonium bromide (DDAB). I I I I I -0.40 -0.20 0.00 E (V) vs SCE 0.20 0.40 Fig. 6.43 Cyclic voltammograms at 100rnVs-l in pH 5.5 buffer: (a) pH 5.5 buffer on a bare pyrolytic graphite electrode; (b) 0.5 mM m~oglobinin buffer on bare pyrolytic graphite; (c) myoglobin-DDAB film on pyrolytic graphite in buffer, no myoglobin in solution. Adapted from: Anal. Chem. 67 (1995) 2386; Electrochem. Inteface 6(4) (1997) 26. 496 Metallopvotein voltammetry In a qpical experiment [87] a solution of DDAB in chloroform is spread on an electrode surface and the solvent is allowed to evaporate. The surfactantcoated electrode is then placed in an electrochemical cell containing a solution of myoglobin, and the protein is taken up rapidly into the film. Diffusion of myoglobin within the film accounts for the fast uptake. Diffusion of protons also accounts for proton charge transport during cyclic voltammetry [I061 so that a diffusion-controlled form of voltammetry is observed as also can occur with microcrystals adhered to electrode surfaces and in contact with aqueous electrolyte (Chapter 5). A wide range of other water-insoluble surfactants can be used to make liquid crystal Glms in which myoglobin gives reversible electron transfer [87,106-112]. Use of insoluble surfactant films appears to be a relatively general way of obtaining well-defined voltammetry for metalloproteins as evidenced by the measurement of reversible processes for cytochrome P450,,, (Fig. 6.44), haemoglobin, cytochrome c, and Chlorella ferredoxin in films of various surfactants [112-1161 or composites of DDAB and Nafion [117]. Bianco et al. reported reversible electrochemistry for cytochrome c, cytochrome c3, and cytochrome ~ 5 5 3in lipid films doped with lauric acid [I 18-1 201, and for spinach ferredoxin in phosphatidylcholine-cholesterol films doped with dodecylamine or didodecyldimethylammonium bromide [I 2 11. A question that arises is: why is voltammetry so well defined and reversible when proteins are in surfactant films compared to proteins in solution with a bare electrode? Again to answer probably is associated with avoidance of electrode blockage. Reversible electron transfer is found on bare electrodes only when -10 1 I -0.80 I I I I -0.60 -0.40 -0.20 0.00 E (V) vs SCE Fig. 6.44 Cyclic voltammograms on basal-plane pyrolytic graphite electrodes obtained at a scan rate of 100 mV s-' in pH 7 buffer containing 0.1 M KC1: (a) substrate-free cyt P450Cam-DMPC film in oxygen-free buffer containing no enzyme; (b) bare electrode in oxygen-free buf-fer containing 40 pM cyt P450Cam; and (c) DMPC film in oxygen-free buffer containing no enzyme. Adapted from: J. Chem. Soc., Faraday Trans. 93 (1997) 1769; Electrochem. Inteface 6(4) (1997) 26. References 497 myoglobin is purified by chromatography immediately before the experiment, and only on hydrophilic tin-doped indium oxide [l 03,1041 or pyrolytic graphite electrodes [122]. As is the case with cytochrome c (Section 4.2.5) exposure of these electrodes to constituents present in partly purified protein solutions blocks electron transfer to myoglobin (Fig. 6.43(b)) [l 221. Reflectance-absorbance FTIR and X-ray photoelectron spectroscopy reveals the presence of protein containing adsorbed material on pyrolytic graphite and Pt electrodes exposed to these partly purified solutions of myoglobin [122]. Adsorption of this material blocks electron transfer to myoglobin and even ferricyanide [122]. Exposure of the same electrodes with solutions of cationic surfactants removes the macromolecular adsorbates, allowing well-defined voltammetric peaks for Mb to be observed. Thus, electron transfer in myoglobin containing surfactant films is facilitated partly by strong adsorption of surfactants at the electrodefilm interface, which in turn inhibits adsorption of protein macromolecules from myoglobin solutions, thereby preventing the blockage of electron transfer between the metalloprotein and the electrode [l 031. 11 Conclusions related to t etalloproteins The major factor that inhibits electron transfer between electrodes and metalloproteins is adsorption onto electrodes of macromolecular impurities or denatured or non-native forms of the metalloprotein itself. This adsorption can create a passive layer that blocks electron transfer. Clearly, the most straightforward way to overcome this problem, at least in principle, is to use highly purified protein solutions and well-cleaned electrodes. Alternatively, the electrode can be coated with a suitable monolayer of a redox-inactive surface modifier, or naturally functionalized electrodes containing suitable non-blocked electrontransfer sites can be employed. A novel extension of the surface modification method employs long-chain alkylthiol monolayers on gold electrodes with end functional groups that may even be capable of binding proteins with strong electrostatic interactions or even covalent bonds. Finally, use of surfactants may also lead to prevention of electrode blockage and well-defined voltammetry. In summary, after accounting for all the nuances, the voltammetry of metalloproteins can be conducted under conditions that are characterized by well-defined current-voltage curves that are characterized by rapid electrontransfer reactions, as would be expected from electron transfer and structurally related metalloproteins. [I] P. Yeh and T. Kuwana, Chem. Lett. (1977) 1145. [2] MJ. Eddowes and H.A.O. Hill, J . Chem. 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Chem. 67 (1995) 2386. ndex AC, see alternating current voltammetry accumulation potential 282, 307, 312 activation parameters 124 active sites 483 activity 11, 14, 17, 336, 347 activity coeffkient 14, 15 ad-atoms 457 adhered solid 334, 339, 369 adlayers 460, 461, 462 adsorption 130, 149, 151, 168, 249, 265, 277, 312, 314, 432, 450 array of molecules 461, 465 azurin 444 cytochrome c 153, 454 facilitating molecules 466 influence on voltammetry 150 isotherm 149 metal complexes 283, 312 prevention 460 protein 441, 486 solution contaminants 452 adsorptive stripping chronopotentiometry 310 adsorptive stripping voltammetry 283, 301, 307, 310, 319 AFM polished edge-plane graphite electrode image 473 polished polycrystalline gold electrode image 463 topographical images of T C N Q 408, 410, 41 1, 412,413 see also atomic force microscopy A ~ / A ~reference + electrode 39 Ag/AgCl reference electrode 38 alkane thiols 139, 140, 150, 494 alternating current voltammetry 33, 35, 41 amalgams 282, 284, 286, 290, 295, 297, 298 analysis of whole blood 328, 329 angular velocity 68, 71 anode 6,24, 26,27 anodic stripping voltammetry 282-301 Anson plot 266 apparatus considerations 101 array of adsorbed molecules 461, 465 array of electrodes carbon 286, 287, 293, 294 disc 24, 284, 288 platinum 465, 472 see also microarray electrodes array of microcrystals or microparticles 267, 336, 338, 369 Arrhenius equation 136 aspect ratios of crystals 383, 384 Atkins, P.W. 3, 4 atomic force microscopy 156, 159, 160, 408, 438 see also AFM atomically flat gold 443 attachment of solids to electrodes 334 auxiliary electrodes, see counter electrodes Azurin 131, 146, 443-450, 463 background current 35, 36, 46, 48, 103, 286, 450,463 see also non-Faradaic current background subtraction 281, 286 band electrodes 79 Barker, G.C. 2 basal plane graphite electrodes 338, 369, 464, 468, 471, 473, 477 batteries 1, 5, 9, 10, 23, 25, 26, 437 Becquerel, E. 2, 28 Berzelius, J.J. 2, 11, 13, 14 biologically important processes or molecules 131, 441, 442,443 biosensors 249, 319, 321, 322 see also glucose biosensor 4,4'-bipyridyl disulfide, see SS-bpy blocking of electrodes 442, 453, 479, 482, 485, 497 see also self-blocking processes Boltzmann constant 141 boundary conditions 60, 62, 90 bulk electrolysis 41, 100, 102-107, 115, 212, 253, 256,257,308-310 at dropping mercury electrodes 308 at gauze or mesh electrodes 107 at mercury pool electrodes 308 cells 104-106, 208, 212 see also exhaustive electrolysis n B ~ 3 P234,241-243 Butler-Volmer theory 54, 63, 64, 88, 136, 138, 140, 141, 142, 143, 144, 146, 418, 419,432,433 cadmium amalgam 299 cadmium ion reduction 305 calibration curves in analysis 285 Index calomel reference electrode 38, 39 capacitance 4, 5, 6, 38, 82, 192, 220, 338, 453 see also double layer capacitance current 47, 48, 58, 65, 68, 77, 101, 152 carbon electrodes 4, 33, 36 fibre 24, 25 microdisc 24 see also basal plane, diamond, edge plane, glassy carbon, graphite, HOPG and pyrolytic electrodes carboxylate functionalities on electrode surfaces 490 Carlisle, A. 2, 27 catalytic processes 26, 130, 146, 148, 149, 178, 255, 256,303, 324, 326,327 catalytic electrodes 26 cathode 6, 23, 24, 26, 27 cell time constant 82 cells, see electrochemical cells centre line velocity parameter 72 channel electrodes 52, 71-75, 90, 94, 98, 108, 109, 110, 112, 113, 117,230-235, 240, 244 channel flow-spectroelectrochemical cells 108 charge 84, 102, 164, 336, 352 see also coulometry charge density 194, 372 charge neutralization process 129, 336, 436 charge on the electron 141 charge-transfer process 11, 14, 83, 478 charge-transfer coefficient 54, 141, 182 charging current 47, 78, 80 see also background current and double layer current chemical current 312 chemical energy 26 chemical potential 21 chemical reactions coupled to electron-transfer processes 65, 146 chemical reversibility 55, 57, 83 chemical synthesis based on knowledge of electrochemical data 213 chemically irreversible processes 57, chemically modified electrodes 33, 130, 442, 443, 460,465,486, 487,492,494 see also functionalised electrodes and modified electrodes chronoamperometry 376 see also double-potential step experiments chronocoulometry 266, 267 chronopotentiometry 310 chronopotentiometric adsorptive stripping analysis 310 Clark oxygen electrode, see oxygen electrodes closed system 21 cobalt dimethylglyoxime 301-319 cobalt ion reduction 306 collection of products at ring electrodes 396 combinations of techniques used to elucidate mechanisms 243-245 comparison of experimental and theoretical voltammograms 181, 186, 187, 189, 191, 222,261, 293,299 comparison of voltammetric techniques 95-100 composite electrodes 4, 336 concentration distributions 88, 90, 194 concentration gradients 52 conditional potential 15 see also formal potential conducting polymers 130, 168, 336, 425 constant current electrolysis 103, 310, 312, 314 constant potential electrolysis, see controlled potential electrolysis controlled potential electrolysis 102, 103, 208, 227, 309,310, 400, 437 convection 10, 49, 51, 52, 68, 69, 75, 77, 89, 93, 109,284,396 see also natural convection convergent diffusion 79 see also radial diffusion convolution voltammetry 83, 88 see also Semi-integration copper deposition 23-25, 92, 93 copper nail experiment 7, 19 Cottrell equation 95 Cottrell, F.G. 2 coulometric stripping chronopotentiometry 310-314 coulometric titration 210, 21 1 coulometry 102, 104, 116,227,308-313,437 microcoulometry 308, 309 counter electrodes 7, 34, 35, 106, 407 counterion diffusion/migration 424 coupled electron and ion transport 362, 365, 367, 424, 425,436 coupled electron and proton-transfer 179, 195 CPE, see controlled potential electrolysis Cr(C0)3(C6Me6) 114, 115 cis and trans-Cr(C0)2 (Ph2PCH2CH2PPh2)2 345-365,402-407 [cr(en)313+-modified electrode 488-491 [ ~ r ( ~ H ~ ) ~ ] ~ + - m o electrode d i f i e d 470 critical potentials 372, 373, 374, 375, 379, 380 critical radius 379 cross redox reactions 188, 224, 250 Cruikshanks, W. 2 crystals and their role in electrochemistry 361, 382-395,408-416, 437,438 crystal sensitivity factor 166 Index current density 79, 80, 287 current-time relationships 103, 104, 422 cyclic voltammetry 41, 43, 45, 46, 47, 56, 57-68, 98, 101, 197-203, 244 chemical reactions coupled to electron transfer 65-68 depletion 75 derivative 88, 89 fast scan rate 80, 82, 83, 113, 280, 281 irreversible processes 62-64 quasi-reversible processes 64, 65, 85 reversible processes 60-62, 84, 85, 86 theory 59-68, 128-152 1,2-cyclooctanedione dioxime 3 16-3 18 cylindrical electrodes 78 cytochrome c 150, 152, 153, 154, 442, 449, 450-459,460,461, 464, 467,468, 470, 471, 474,477-486, 492-494,496 cytochrome c3 496 cytochrome P450 496 Dalton 14 data analysis service 91 Davy, H. 2, 11, 13, 14 decameth~lferrocene213-21 5, 337-345, 361 decay constant 143 defect sites 460, 470 density of electronic states 143 depletion 75, 288 deposition step 282 derivative cyclic voltammetry, see cyclic voltammetry 2,3-diaminobutane 303, 315 diamond electrodes 4 didodecyldimethylammonium bromide 495, 496 differential pulse voltammetry 41, 42 diffusion 10, 49, 50, 52, 62, 68, 75, 79, 89, 90, 93, 161 coefficients 49, 184, 193, 205, 270, 276, 284, 425 coupled with electron transport 425 layer 81, 161, 452 of ions within a solid 364, 425 semi-infinite 50, 52, 84 surface 367 three-dimensional 52, 424 two-dimensional 52, 101 diffusionless voltammetry 129, 133, 144, 154, 493 digital simulations, see simulations 2,3-di(hydroxy1amino)butane 303, 306, 315, 319 dimensionless variables 96, 98, 130, 290 dimethylglyoxime 30 1-306 disc electrodes 37 505 see also microdisc, rotated disc and inlaid disc electrodes disproportionation 18, 19, 111, 188, 192, 207, 238,243,250, 264 dissolution 168, 336, 343, 367, 395, 396, 397, 398, 413, 414, 423, 437, 438 and precipitation processes 403, 405, 413 and redistribution reactions 408, 410 distance dependence of the rate of electron transfer 140, 154 see also Marcus theory distance scale 286, 287 DME, see dropping mercury electrodes double layer 35, 82, 152 capacitance 46, 65, 182, 260 current 46, 312 see also charging current effects 204 double-potential step experiments 266, 352, 353, 354, 357, 358, 376,378 drop time of mercury electrode 305, 308, 318 dropping mercury electrodes 293, 308 dye sensitized cells 28, 29 E~O,see formal potential EiI2, see reversible half-wave potential Ell2 87, 91, 96, 102, 202, 218, 274 see also half-wave potential E1/4 76, 87 E3/4 76, 87 E3/4-E1/4 or E1/4-E3/4 76, 204, 218, 271, 276, 482, 484 edge-plane graphite electrode 433, 448, 464, 468, 470, 471 electrochemical cells 7, 9, 11, 16, 21, 22, 23, 26 high pressure 129 voltammetric 34-36 see also bulk electrolysis and non-isothermal electrochemical cleaning 450 electrochemical-ESR experiments 108-1 13, 317 see also ESR, EPR and SEESR electrochemical quartz crystal microbalance 155, 162, 164-171, 264-266, 269, 276-278, 335, 349-358, 437 electrochemical rate constants dependence on potential, see Butler-Volmer theory and Marcus theory electrochemical reversibility 55, 56 electrochemical series 11, 12, 13, 14 electrochemical stripping techniques 283 see also stripping voltammetry electrochemical synthesis 6, 100, 104, 196, 21 1, 212,226-230 see also bulk electrolysis Index electrochemical technology 29 electrochromic devices 437 electrocrystallization 152 electrodes 4, 6 see also band, bulk electrolysis, carbon, channel, composite, diamond, dropping mercury, gauze, glassy carbon, gold, graphite, hanging mercury drop, hemi-cylinder, hemispherical, hydrodynamic, indium oxide, ion-selective, lead, macrodisc, mercury, mercury pool, mercury thin-film, mesh, metal, micro jet, microarray, microband, microdisc, microhemispherical, microring, modified, optically transparent, oxygen, planar, platinum, polycrystalline gold, polymer modified, pyrolytic graphite, quasi-reference, RAM, reference, ring, rotating disc, rotating ring-disc, sacrificial, semiconducting, silver, smart, spherical, titanium, wall-jet working electrode area 47, 54, 76, 80, 95, 103, 182, 189, 220,286,288 see also many equations that contain this term electrode blockage 204, 447, 451, 452, 458, 460, 486 electrode edge effects 287 electrode fouling 4, 6, 203, 204 see also blocking electrode functionality 442 electrode kinetic effect 204 electrode mechanisms 43, 68 CE 73 CECE 234, 235 CECEC 233 C2E 240 EC 55, 57, 66, 82, 96, 111, 126, 130, 146, 217, 259 EC2 83 EC2E 96, 97, 100 ECE 55, 56, 66, 67, 68, 69, 78, 80, 81, 82, 96, 99, 102, 104, 111, 149,217 Eccatalpic 130 EE 130,217 ErevCirrevErev 55 see also square reaction schemes electrode passivation 232, 234 see also blocking of electrode electrode potentials 3, 19 see also standard potentials electrode radius 79, 287 electrode rotation 69-71 electrode size 3, 4, 80 electrode surface loadings 313 see also surface coverage electrodes, practical considerations 101 electrodeposition 23, 24, 25, 287 electrode-solution interface 91, 92 electrolysis 3, 11, 14,24,33,79, 104, 113, 115, 116, 122, 313 see also bulk electrolysis electrolyte 27, 28, 113, 205, 342-345, 347-349 electrolytic cell 7, 10, 31 electron hopping 365, 424 electron microprobe X-ray analysis, see electron probe analysis electron paramagnetic resonance 108-1 13, 207, 208, 210, 211, 395, 396, 399-403, 405-407, 438 electron probe analysis 341, 342, 352, 356, 382 electron scanning microscopy 145, 367, 382-386 see also scanning electron microscopy electron spin resonance, see electron paramagnetic resonance electron transfer 52-54 long-range 492-494 electronic conductor 92 electronic coupling 143 electronic spectra 226 see also UV-visible spectroelectrochemistry electronic states 144 electron-transfer processes 14, 23, 48, 62, 90, 131, 140,436 electrorefining 1, 23 electrospray mass spectrometry 119, 122, 123, 258 electrostatic force microscope 156 electrosynthesis, see el