ELECTROCHEMISTRY Principles, Methods, and Applications CHRISTOPHER M. A. BRETT and ANA MARIA OLIVEIRA BRETT Departamento de Quimica, Universidade de Coimbra, Portugal Oxford New York Tokyo OXFORD UNIVERSITY PRESS Oxford University Press, Walton Street, Oxford OX2 6DP Oxford New York Athens Auckland Bangkok Bombay Calcutta Cape Town Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto and associated companies in Berlin Ibadan Oxford is a trade mark of Oxford University Press Published in the United States by Oxford University Press Inc., New York © Christopher M. A. Brett and Ana Maria Oliveira Brett, 1993 First published 1993 Reprinted 1994 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. Within the UK, exceptions are allowed in respect of any fair dealing for the purpose of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms and in other countries should be sent to the Rights Department, Oxford University Press, at the address above. This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Brett, Christopher M. A. Electrochemistry: principles, methods, and applications/ Christopher M. A. Brett and Ana Maria Oliveira Brett. Includes bibliographical references. 1. Electrochemistry. I. Brett, Ana Maria Oliveira. II. Title. QD553.B74 1993 541.3'7-dc20 92-29087 ISBN 0 19 855389 7 (Hbk) ISBN 0 19 855388 9 (Pbk) Printed in Great Britain by Bookcraft (Bath) Ltd., Midsomer Norton, Avon PREFACE Electrochemistry has undergone significant transformations in the last few decades. It is not now the province of academics interested only in measuring thermodynamic properties of solutions or of industrialists using electrolysis or manufacturing batteries, with a huge gulf between them. It has become clear that these two, apparently distinct subjects, and others, have a common ground and they have grown towards each other, particularly as a result of research into the rates of electrochemical processes. Such an evolution is due to a number of factors, but principally the possibility of carrying out reproducible, dynamic experi- ments under an ever-increasing variety of conditions with reliable and sensitive instrumentation. This has enabled many studies of a fundamen- tal and applied nature to be carried out. The reasons for this book are twofold. First to show the all-pervasive and interdisciplinary nature of electrochemistry, and particularly of electrode reactions, through a description of modern electrochemistry. Secondly to show to the student and the non-specialist that this subject is not separated from the rest of chemistry, and how he or she can use it. Unfortunately, these necessities are, in our view, despite efforts over recent years, still very real. The book has been organized into three parts, after Chapter 1 as general introduction. We have begun at a non-specialized, undergraduate level and progressed through to a relatively specialized level in each topic. Our objective is to transmit the essence of electrochemistry and research therein. It is intended that the chapters should be as independ- ent of one another as possible. The sections are: Chapters 2-6 on the thermodynamics and kinetics of electrode reactions, Chapters 7-12 on experimental strategy and methods, and Chapters 13-17 on applications. Also included are several appendices to explain the mathematical basis in more detail. It is no accident that at least 80 per cent of the book deals with current-volt age relations, and not with equilibrium. The essence of any chemical process is change, and reality reflects this. We have not filled the text with lots of details which can be found in the references given, and, where appropriate, we make ample reference to recent research literature. This is designed to kindle the enthusiasm and interest of the reader in recent, often exciting, advances in the topics described. A major preoccupation was with notation, given the traditionally different type of language that electrochemists have used in relation to viii Preface other branches of chemistry, such as exchange current which measures rate constants, and given differences in usage of symbols between different branches of electrochemistry. Differences in sign conventions are another way of confusing the unwary beginner. We have decided broadly to follow IUPAC recommendations. Finally some words of thanks to those who have helped and influenced us throughout our life as electrochemists. First to Professor W. J. Albery FRS, who introduced us to the wonders of electrochemistry and to each other. Secondly to our many colleagues and students who, over the years, with their comments and questions, have aided us in deepening our understanding of electrochemistry and seeing it with different eyes. Thirdly to anonymous referees, who made useful comments based on a detailed outline for the book. And last, but not least, to Oxford University Press for its interest in our project and enabling us to bring it to fruition. Coimbra C.M.A.B. May 1992 A.M.O.B. ACKNOWLEDGEMENTS Full bibliographical references to all material reproduced are to be found at the ends of the respective chapters. Figure 3.4 is reprinted with permission from D. C. Grahame, Chem. Rev. y 1947, 41, 441. Copyright 1947 American Chemical Society; Fig 7.1 is reprinted with permission from G. M. Jenkins and K. Kawamura, Nature, 1971, 231, 175. Copyright 1971 Macmillan Magazines Ltd; Fig. 8.2c is reprinted by permission of the publisher, The Electrochemical Society Inc., Fig. 9.10a is reprinted with permission from R. S. Nicholson and I. Shain, Anal. Chem., 1964, 36, 706. Copyright 1964 American Chemical Society; Fig. 12.3 is reprinted by permission of John Wiley & Sons Inc. from J. D. E. Macintyre, Advances in electrochemistry and electrochemical engineering, 1973, Vol. 9, ed. R. H. Muller, p. 122. Copyright © 1973 by John Wiley & Sons, Inc.; Fig. 12.15a is reprinted with permission by VCH Publishers © 1991; Fig. 12.15b is reprinted with permission from R. Yang, K. Naoz, D. F. Evans, W. H. Smyrl and W. A. Hendrickson, Langmuir, 1991, 7, 556. Copyright 1991 American Chemical Society; Fig. 15.9 is reproduced from J. P. Hoare and M. L. LaBoda, Comprehensive treatise of electrochemistry, 1981, Vol. 2, ed. J. O'M. Bockris et al., p. 448, by permission of the publisher, Plenum Publishing Corporation; Fig. 16.7 is reproduced by kind permission of the copyright holder, National Association of Corrosion Engineers; Fig. 17.3 is reproduced from S. Ohki, Comprehensive treatise of electrochemistry, 1985, Vol. 10, ed. S. Srinivasan et al, p. 94, by permission of the publisher, Plenum Publishing Corporation; Fig. 17.6 is reproduced from R. Pethig, Modern bioelectrochemistry, ed. F. Gutmann and H. Keyser, 1986, p. 201, by permission of the publisher, Plenum Publishing Corporation; Fig. 17.7 is reprinted with permission from M. J. Eddowes and H. A. O. Hill, /. Am. Chem. Soc, 1979, 101, 4461. Copyright 1979 American Chemical Society; Fig. 17.9 is reproduced from M. Tarasevich, Comprehensive treatise of electrochemistry, 1985, Vol. 10, ed. S. Sriniva- san et al., p. 260, by permission of the publisher, Plenum Publishing Corporation; Fig. 17.11 is reproduced with the kind permission of the Institute of Measurement and Control; Table 2.2 is reproduced by kind permission of Butterworth-Heinemann Ltd; Table 7.1 is reprinted from R. L. McCreery, Electroanalytical chemistry, 1991, Vol. 17, ed. A. J. Bard, p. 243, by courtesy of Marcel Dekker Inc.; Table 7.3 is reprinted by permission of John Wiley & Sons Inc. from D. T. Sawyer and J. L. Roberts, Experimental electrochemistry for chemists, 1974, Copyright © x Acknowledgements 191A by John Wiley & Sons, Inc.; Tables 9.1 and 9.2 are reprinted with permission from R. S. Nicholson and I. Shain, Anal. Chem., 1964, 36, 706. Copyright 1964 American Chemical Society; Table 9.3 is reprinted with permission from R. S. Nicholson, Anal. Chem. y 1965, 37, 1351, copyright 1965 American Chemical Society, and from S. P. Perone, Anal. Chem.y 1966, 38, 1158, copyright 1966 American Chemical Society; Table 15.2 is reprinted by permission of the publisher, The Electrochem- ical Society Inc.; Table 17.1 is reproduced from H. Berg, Comprehensive treatise of electrochemistry, 1985, Vol. 10, ed. S. Srinivasan et al., p. 192, by permission of the publisher, Plenum Publishing Corporation; Table 17.2 is reproduced from S. Srinivasan, Comprehensive treatise of electrochemistry, 1985, Vol. 10, ed. S. Srinivasan et al. y p. 476, by permission of the publisher, Plenum Publishing Corporation. The following are also thanked for permission to reproduce or reprint copyright material: Bioanalytical Systems Inc. for Fig. 14.8; Elsevier Science Publishers BV for Figs 8.3, 8.4, 8.6, 8.7, 11.7, Tables 8.1 and 8.2; Elsevier Sequoia SA for Figs 9.11, 9.12, 9.15, 12.4, 12.8, 12.20, and 14.3; Journal of Chemical Education for Fig. 9.13a; Kluwer Academic Publ- ishers for Fig. 3.10; R. Kotz for Fig. 12.1; Oxford University Press for Figs 2.11, 2.12, and 17.10; Royal Society of Chemistry for Table 14.2. Although every effort has been made to trace and contact copyright holders, in a few instances this has not been possible. If notified the publishers will be pleased to rectify any omission in future editions. CONTENTS Notation and Units xxi Main Symbols xxii Subscripts xxvi Abbreviations xxvii Fundamental physical constants xxix Mathematical constants xxix Useful relations at 25°C (298.15 K) involving fundamental constants xxix 1 INTRODUCTION 1 1.1 The scope of electrochemistry 1 1.2 The nature of electrode reactions 1 1.3 Thermodynamics and kinetics 2 1.4 Methods for studying electrode reactions 5 1.5 Applications of electrochemistry 5 1.6 Structure of the book 6 1.7 Electrochemical literature 7 PART I Principles 2 ELECTROCHEMICAL CELLS: THERMODYNAMIC PROPERTIES AND ELECTRODE POTENTIALS 13 2.1 Introduction 13 2.2 The cell potential of an electrochemical cell 14 2.3 Calculation of cell potential: activities or concentrations? 16 2.4 Calculation of cell potential: electrochemical potential . 18 2.5 Galvanic and electrolytic cells 20 2.6 Electrode classification 21 2.7 Reference electrodes 22 2.8 Movement of ions in solution: diffusion and migration . 25 2.9 Conductivity and mobility 26 2.10 Liquid junction potentials 32 2.11 Liquid junction potentials, ion-selective electrodes, and biomembranes 33 2.12 Electrode potentials and oxidation state diagrams 34 References 38 xii Contents 3 THE INTERFACIAL REGION 39 3.1 Introduction 39 3.2 The electrolyte double layer: surface tension, charge density, and capacity 39 3.3 Double layer models 44 the first models: Helmholtz, Gouy-Chapman, Stern, and Grahame 45 Bockris, Devanathan, and Muller model 51 'chemical' models 52 3.4 Specific adsorption 54 3.5 The solid metallic electrode: some remarks 56 3.6 The semiconductor electrode: the space-charge region . 58 3.7 Electrokinetic phenomena and colloids: the zeta potential 64 electrophoresis 66 sedimentation potential 67 electroosmosis 67 streaming potential 68 limitations in the calculation of the zeta potential . . 68 References 68 4 FUNDAMENTALS OF KINETICS AND MECHANISM OF ELECTRODE REACTIONS 70 4.1 Introduction 70 4.2 The mechanism of electron transfer at an electrode . . 70 4.3 The mechanism of electron transfer in homogeneous solution 71 4.4 An expression for the rate of electrode reactions 72 4.5 The relation between current and reaction rate: the exchange current 76 4.6 Microscopic interpretation of electron transfer 77 References 81 5 MASS TRANSPORT 82 5.1 Introduction 82 5.2 Diffusion control 83 5.3 Diffusion-limited current: planar and spherical electrodes 85 5.4 Constant current: planar electrodes 90 5.5 Microelectrodes 92 5.6 Diffusion layer 94 Contents xiii 5.7 Convection and diffusion: hydrodynamic systems 95 5.8 Hydrodynamic systems: some useful parameters 97 5.9 An example of a convective-diffusion system: the rotating disc electrode 98 References 102 KINETICS AND TRANSPORT IN ELECTRODE REACTIONS 103 6.1 Introduction 103 6.2 The global electrode process: kinetics and transport . . 103 6.3 Reversible reactions 106 6.4 Irreversible reactions 109 6.5 The general case Ill 6.6 TheTafellaw 113 6.7 The Tafel law corrected for transport 115 6.8 Kinetic treatment based on exchange current 115 6.9 The effect of the electrolyte double layer on electrode kinetics 116 6.10 Electrode processes involving multiple electron transfer 119 6.11 Electrode processes involving coupled homogeneous reactions 122 References 126 PART II Methods ELECTROCHEMICAL EXPERIMENTS 129 7.1 Introduction 129 7.2 Electrode materials for voltammetry 129 metals 130 carbon 130 other solid materials 133 mercury 133 7.3 The working electrode: preparation and cleaning . . . 134 7.4 The cell: measurements at equilibrium 136 7.5 The cell: measurements away from equilibrium 137 electrodes 137 supporting electrolyte 138 removal of oxygen 140 7.6 Calibration of electrodes and cells 142 7.7 Instrumentation: general 142 xiv Contents 7.8 Analogue instrumentation 143 potentiostat 146 galvanostat 147 compensation of cell solution resistance 148 7.9 Digital instrumentation 148 References 149 8 HYDRODYNAMIC ELECTRODES 151 8.1 Introduction 151 8.2 Limiting currents at hydrodynamic electrodes 155 8.3 A special electrode: the dropping mercury electrode . . 157 8.4 Hydrodynamic electrodes in the study of electrode processes 163 reversible reaction 163 the general case 164 8.5 Double hydrodynamic electrodes 165 8.6 Multiple electron transfer: the use of the RRDE 167 consecutive reactions 168 parallel reactions 168 consecutive and parallel reactions 169 8.7 Hydrodynamic electrodes in the investigation of coupled homogeneous reactions 169 8.8 Hydrodynamic electrodes and non-stationary techniques 171 References 172 9 CYCLIC VOLTAMMETRY AND LINEAR SWEEP TECHNIQUES 174 9.1 Introduction 174 9.2 Experimental basis 175 9.3 Cyclic voltammetry at planar electrodes 176 reversible system 177 irreversible system 181 quasi-reversible system 183 adsorbed species 185 9.4 Spherical electrodes 187 9.5 Microelectrodes 188 9.6 Systems containing more than one component 188 9.7 Systems involving coupled homogeneous reactions . . . 189 9.8 Convolution linear sweep voltammetry 191 9.9 Linear potential sweep with hydrodynamic electrodes . 193 9.10 Linear potential sweep in thin-layer cells 194 References 197 [...]... Gileadi, E Kirowna-Eisner, and J Penciner, Interfacial electrochemistry An experimental approach, Addison-Wesley, Reading, MA, 1975 W J Albery, Electrode kinetics, Clarendon Press, Oxford, 1975 A J Bard and L R Faulkner, Electrochemical methods, fundamentals and applications, Wiley, New York, 1980 A M Bond, Modern polarographic methods in analytical chemistry, Dekker, New York, 1980 Southampton Electrochemistry. .. instrumental methods in electrochemistry, Ellis Horwood, Chichester, 1985 J Goodisman, Electrochemistry: theoretical foundations, WileyInterscience, New York, 1987 8 Introduction J Koryta, Principles of electrochemistry, Wiley, Chichester, 1987 P H Rieger, Electrochemistry, Prentice-Hall International, Englewood Cliffs, NJ, 1987 D R Crow, Principles and applications of electrochemistry, 3rd edn, Chapman and. .. Admittance and its use 236 11.8 A.c voltammetry 238 11.9 Second-order effects 240 higher harmonics 240 other second-order methods 241 faradaic rectification 242 demodulation 242 xvi Contents 11.10 More complex systems, porous electrodes, and fractals 244 11.11 Нуdrodynamic electrodes and impedance 248 11.12 Transforms and impedance 249 References 251 12 NON-ELECTROCHEMICAL PROBES OF ELECTRODES AND ELECTRODE... potential and of the electrode material at or outside equilibrium (as in potentiometric, amperometric, voltammetric, and enzyme sensors) Thus the range of applications is vast Electroanalysis, potentiometric and voltammetric; industrial electrolysis, electroplating, batteries, fuel cells, electrochemical machining, and many other related applications, including minimization of corrosion; biosensors and bioelectrochemistry... reversible and irreversible reactions, the overpotential having a relatively small value, so that with this extra potential reactions can be reversed The potential-dependent expression for the rate constant of an electrode reaction is, for a reduction, kc = k0 exp [-acnF(E - E^')/RT] (1.4) and for an oxidation k.A = k0 exp [aanF(E - E^')/RT] (1.5) In these equations occ and ara are the cathodic and anodic... amplitude and/ or frequency • impedance methods: increasing perturbation frequency, registering higher harmonics, etc The type of technique chosen will depend very much on the timescale of the electrode reaction Non-electrochemical methods can and should be used for studying electrode surfaces and the interfacial region structure, particularly in situ in real time where this is possible 1.5 Applications of electrochemistry. .. New York Volumes 1-9 , ed P Delahay and C W Tobias; Volumes 1 0-1 3, ed H Gerischer and C W Tobias Advances in electrochemical science and engineering, ed H Gerischer and С W Tobias, VCH, Weinheim (continuation of Adv Electrochem Electrochem Eng.\ 1 volume until end 1991) Comprehensive treatise of electrochemistry, ed J O'M Bockris, В Е Conway, E Yeager et al., Plenum, New York, Volumes 1-1 0 Comprehensive... photochemical effects on electrode reactions— photoelectrochemistry In the third part of the book areas in which there are important applications of electrochemistry are described Chapters 13 and 14 look at potentiometric and amperometric/voltammetric sensors respectively, focusing particularly on recent developments such as new electrode materials and miniaturization Electrochemistry in industry, which produces... instrumental methods in electrochemistry, Interscience, New York, 1954 K J Vetter, Electrochemical kinetics Academic Press, New York, 1967 R N Adams, Electrochemistry at solid electrodes, Dekker, New York, 1969 J O'M Bockris and A N Reddy, Modern electrochemistry, Plenum, New York, 1970 J Newman, Electrochemical systems, Prentice Hall, Englewood Cliffs, NJ, 1973 D T Sawyer and J L Roberts, Experimental electrochemistry. .. 221 applications of pulse techniques 222 References 222 11 IMPEDANCE METHODS 224 11.1 Introduction 224 11.2 Detection and measurement of impedance 225 a.c bridges 225 phase-sensitive detectors and transfer function analysers 227 direct methods 228 11.3 Equivalent circuit of an electrochemical cell 229 11.4 The faradaic impedance for a simple electrode process 230 11.5 The faradaic impedance, Z f , and . frequency — Nm" 1 — mol m~ 2 m m n^mol" 1 Fin" 1 Fm" 1 — — V — V Pas — — Sm" 1 s S m 2 mol Jmol" 1 Jmol" 1 s" 1 — m 2 s" x Qm kgm" 3 Cm" 2 s" 1 s V V V V rads" 1 rads" 1 . Publication Data Brett, Christopher M. A. Electrochemistry: principles, methods, and applications/ Christopher M. A. Brett and Ana Maria Oliveira Brett. Includes bibliographical references. 1. Electrochemistry. . ELECTROCHEMISTRY Principles, Methods, and Applications CHRISTOPHER M. A. BRETT and ANA MARIA OLIVEIRA BRETT Departamento de Quimica, Universidade