Electrochemical Methods; Fundamentals and Applications (2nd Ed.) - Wiley

851 Pages·2016·22.62 MB·English

by  Bard A.J.

SECOND EDITION
ELECTROCHEMICAL
METHODS
Fundamentals and
Applications
Allen J. Bard
Larry R. Faulkner
Department of Chemistry and Biochemistry
University of Texas at Austin
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Library of Congress Cataloging in Publication Data:
Bard, Allen J.
Electrochemical methods : fundamentals and applications / Allen J. Bard, Larry R.
Faulkner.— 2nd ed.
p. cm.
Includes index.
ISBN 0-471-04372-9 (cloth : alk. paper)
1. Electrochemistry. I. Faulkner, Larry R., 1944- II. Title.
QD553.B37 2000
541.3'7_dc21
00-038210
Printed in the United States of America
10 9 8 7 6 5 4 3 21
PREFACE
In the twenty years since the appearance of our first edition, the fields of electrochemistry
and electroanalytical chemistry have evolved substantially. An improved understanding
of phenomena, the further development of experimental tools already known in 1980, and
the introduction of new methods have all been important to that evolution. In the preface
to the 1980 edition, we indicated that the focus of electrochemical research seemed likely
to shift from the development of methods toward their application in studies of chemical
behavior. By and large, history has justified that view. There have also been important
changes in practice, and our 1980 survey of methodology has become dated. In this new
edition, we have sought to update the book in a way that will extend its value as a general
introduction to electrochemical methods.
We have maintained the philosophy and approach of the original edition, which is to
provide comprehensive coverage of fundamentals for electrochemical methods now in
widespread use. This volume is intended as a textbook and includes numerous problems
and chemical examples. Illustrations have been employed to clarify presentations, and the
style is pedagogical throughout. The book can be used in formal courses at the senior un-
dergraduate and beginning graduate levels, but we have also tried to write in a way that
enables self-study by interested individuals. A knowledge of basic physical chemistry is
assumed, but the discussions generally begin at an elementary level and develop upward.
We have sought to make the volume self-contained by developing almost all ideas of any
importance to our subject from very basic principles of chemistry and physics. Because
we stress foundations and limits of application, the book continues to emphasize the
mathematical theory underlying methodology; however the key ideas are discussed con-
sistently apart from the mathematical basis. Specialized mathematical background is cov-
ered as needed. The problems following each chapter have been devised as teaching tools.
They often extend concepts introduced in the text or show how experimental data are re-
duced to fundamental results. The cited literature is extensive, but mainly includes only
seminal papers and reviews. It is impossible to cover the huge body of primary literature
in this field, so we have made no attempt in that direction.
Our approach is first to give an overview of electrode processes (Chapter 1), show-
ing the way in which the fundamental components of the subject come together in an
electrochemical experiment. Then there are individual discussions of thermodynamics
and potential, electron-transfer kinetics, and mass transfer (Chapters 2-4). Concepts
from these basic areas are integrated together in treatments of the various methods
(Chapters 5-11). The effects of homogeneous kinetics are treated separately in a way
that provides a comparative view of the responses of different methods (Chapter 12).
Next are discussions of interfacial structure, adsorption, and modified electrodes (Chap-
ters 13 and 14); then there is a taste of electrochemical instrumentation (Chapter 15),
which is followed by an extensive introduction to experiments in which electrochemistry
is coupled with other tools (Chapters 16-18). Appendix A teaches the mathematical
background; Appendix В provides an introduction to digital simulation; and Appendix С
contains tables of useful data.
vi • Preface
This structure is generally that of the 1980 edition, but important additions have been
made to cover new topics or subjects that have evolved extensively. Among them are ap-
plications of ultramicroelectrodes, phenomena at well-defined surfaces, modified elec-
trodes, modern electron-transfer theory, scanning probe methods, LCEC, impedance
spectrometry, modern forms of pulse voltammetry, and various aspects of spectroelectro-
chemistry. Chapter 5 in the first edition ("Controlled Potential Microelectrode Tech-
niques—Potential Step Methods") has been divided into the new Chapter 5 ("Basic
Potential Step Methods") and the new Chapter 7 ("Polarography and Pulse Voltamme-
try"). Chapter 12 in the original edition ("Double Layer Structure and Adsorbed Interme-
diates in Electrode Processes") has become two chapters in the new edition: Chapter 12
("Double-Layer Structure and Adsorption") and Chapter 13 ("Electroactive Layers and
Modified Electrodes"). Whereas the original edition covered in a single chapter experi-
ments in which other characterization methods are coupled to electrochemical systems
(Chapter 14, "Spectrometric and Photochemical Experiments"), this edition features a
wholly new chapter on "Scanning Probe Techniques" (Chapter 16), plus separate chapters
on "Spectroelectrochemistry and Other Coupled Characterization Methods" (Chapter 17)
and "Photoelectrochemistry and Electrogenerated Chemiluminescence" (Chapter 18). The
remaining chapters and appendices of the new edition directly correspond with counter-
parts in the old, although in most there are quite significant revisions.
The mathematical notation is uniform throughout the book and there is minimal du-
plication of symbols. The List of Major Symbols and the List of Abbreviations offer defi-
nitions, units, and section references. Usually we have adhered to the recommendations of
the IUPAC Commission on Electrochemistry [R. Parsons et al., Pure Appl. С hem., 37,
503 (1974)]. Exceptions have been made where customary usage or clarity of notation
seemed compelling.
Of necessity, compromises have been made between depth, breadth of coverage, and
reasonable size. "Classical" topics in electrochemistry, including many aspects of thermo-
dynamics of cells, conductance, and potentiometry are not covered here. Similarly, we
have not been able to accommodate discussions of many techniques that are useful but not
widely practiced. The details of laboratory procedures, such as the design of cells, the
construction of electrodes, and the purification of materials, are beyond our scope. In this
edition, we have deleted some topics and have shortened the treatment of others. Often,
we have achieved these changes by making reference to the corresponding passages in the
first edition, so that interested readers can still gain access to a deleted or attenuated topic.
As with the first edition, we owe thanks to many others who have helped with this
project. We are especially grateful to Rose McCord and Susan Faulkner for their consci-
entious assistance with myriad details of preparation and production. Valuable comments
have been provided by S. Amemiya, F. C. Anson, D. A. Buttry, R. M. Crooks, P. He,
W. R. Heineman, R. A. Marcus, A. C. Michael, R. W. Murray, A. J. Nozik, R. A. Oster-
young, J.-M. Saveant, W. Schmickler, M. P. Soriaga, M. J. Weaver, H. S. White, R. M.
Wightman, and C. G. Zoski. We thank them and our many other colleagues throughout
the electrochemical community, who have taught us patiently over the years. Yet again,
we also thank our families for affording us the time and freedom required to undertake
such a large project.
Allen /. Bard
Larry R. Faulkner
CONTENTS
MAJOR SYMBOLS ix
STANDARD ABBREVIATIONS xix
1 INTRODUCTION AND OVERVIEW OF ELECTRODE PROCESSES 1
2 POTENTIALS AND THERMODYNAMICS OF CELLS 44
3 KINETICS OF ELECTRODE REACTIONS 87
4 MASS TRANSFER BY MIGRATION AND DIFFUSION 137
5 BASIC POTENTIAL STEP METHODS 156
6 POTENTIAL SWEEP METHODS 226
7 POLAROGRAPHY AND PULSE VOLTAMMETRY 261
8 CONTROLLED-CURRENT TECHNIQUES 305
9 METHODS INVOLVING FORCED CONVECTION—HYDRODYNAMIC
METHODS 331
10 TECHNIQUES BASED ON CONCEPTS OF IMPEDANCE 368
11 BULK ELECTROLYSIS METHODS 417
12 ELECTRODE REACTIONS WITH COUPLED HOMOGENEOUS CHEMICAL
REACTIONS 471
13 DOUBLE-LAYER STRUCTURE AND ADSORPTION 534
14 ELECTROACTIVE LAYERS AND MODIFIED ELECTRODES 580
15 ELECTROCHEMICAL INSTRUMENTATION 632
16 SCANNING PROBE TECHNIQUES 659
17 SPECTROELECTROCHEMISTRY AND OTHER COUPLED CHARACTERIZATION
METHODS 680
18 PHOTOELECTROCHEMISTRY AND ELECTROGENERATED
CHEMILUMINESCENCE 736
APPENDICES
A MATHEMATICAL METHODS 769
В DIGITAL SIMULATIONS OF ELECTROCHEMICAL PROBLEMS 785
С REFERENCE TABLES 808
INDEX 814
MAJOR SYMBOLS
Listed below are symbols used in several chapters or in large portions of a chapter. Sym-
bols similar to some of these may have different local meanings. In most cases, the usage
follows the recommendations of the IUPAC Commission on Electrochemistry [R. Par-
sons et al., Pure Appl. Chem., 37, 503 (1974).]; however there are exceptions.
A bar over a concentration or a current [ej*., C(x, s)] indicates the Laplace trans-
o
form of the variable. The exception is when / indicates an average current in polaro-
graphy.
STANDARD SUBSCRIPTS
a anodic dl double layer 0 pertaining to species 0 in О + ne ±± R
с (a) cathodic eq equilibrium P peak
(b) charging f (a) forward R (a) pertaining to species R in О + ne ^ R
D disk (b) faradaic (b) ring
d diffusion / limiting r reverse
ROMAN SYMBOLS
Section
Symbol Meaning Usual Units References
(a) area cm 1.3.2
(b) cross-sectional area of a porous cm2 11.6.2
electrode
(c) frequency factor in a rate expression depends on order 3.1.2
(d) open-loop gain of an amplifier none 15.1.1
absorbance none 17.1.1
(a) internal area of a porous electrode cm2 11.6.2
(b) tip radius in SECM 16.4.1
activity of substance j in a phase a none 2.1.5
aFv/RT s"1 6.3.1
mol/cm2 13.5.3
С capacitance F 1.2.2, 10.1.2
C series equivalent capacitance of a cell F 10.4
B
differential capacitance of the double F, F/cm2 1.2.2, 13.2.2
layer
integral capacitance of the double layer F, F/cm2 13.2.2
c
d concentration of species; M, mol/cm3
bulk concentration of species; M, mol/cm3 1.4.2, 4.4.3
concentration of species; at distance x M, mol/cm3 1.4
c't
Major Symbols
Section
Symbol Meaning Usual Units References
CjCx = 0) concentration of species j at the M, mol/cm3 1.4.2
electrode surface
Cj(x, t) concentration of species у at distance x M, mol/cm3 4.4
at time t
Cj(O, f) concentration of species у at the M, mol/cm3 4.4.3
electrode surface at time t
concentration of species у at distance у M, mol/cm3 9.3.3
away from rotating electrode
Cj(y = 0) surface concentration of species у at a M, mol/cm3 9.3.4
rotating electrode
Csc space charge capacitance F/cm 18.2.2
pseudocapacity F 10.1.3
С speed of light in vacuo cm/s 17.1.2
diffusion coefficient for electrons within cm /s 14.4.2
the film at a modified electrode
diffusion coefficient of species у cm2/s 1.4.1,4.4
Dj(A, E) concentration density of states for species у cm3eV~! 3.6.3
D model diffusion coefficient in simulation none B.1.3.B.1.8
M
£s diffusion coefficient for the primary cm2/s 14.4.2
reactant within the film at a modified
electrode
d distance of the tip from the substrate in /xm, nm 16.4.1
SECM
density of phase у g/cm3
*\
E (a) potential of an electrode versus a V 1.1,2.1
reference
(b) emf of a reaction V 2.1
(c) amplitude of an ac voltage V 10.1.2
AE (a) pulse height in DPV mV 7.3.4
(b) step height in tast or staircase mV 7.3.1
voltammetry
(c) amplitude (1/2 p-p) of ac excitation mV 10.5.1
in ac voltammetry
E electron energy eV 2.2.5, 3.6.3
% electric field strength vector V/cm 2.2.1
% electric field strength V/cm 2.2.1
E voltage or potential phasor V 10.1.2
£° (a) standard potential of an electrode or V 2.1.4
a couple
(b) standard emf of a half-reaction V 2.1.4
AE° difference in standard potentials for V 6.6
two couples
E° electron energy corresponding to the eV 3.6.3
standard potential of a couple
E0' formal potential of an electrode V 2.1.6
E activation energy of a reaction kJ/mol 3.1.2
A
E ac component of potential mV 10.1.1
ac
E base potential in NPV and RPV V 7.3.2, 7.3.3
b
Edc dc component of potential V 10.1.1
Major Symbols xi
Section
Symbol Meaning Usual Units References
Е equilibrium potential of an electrode V 1.3.2,3.4.1
щ
E Fermi level eV 2.2.5, 3.6.3
F
Em flat-band potential V 18.2.2
bandgap of a semiconductor eV 18.2.2
Eg
E; initial potential V 6.2.1
Щ junction potential mV 2.3.4
E membrane potential mV 2.4
m
E peak potential V 6.2.2
P
A£P (a)|£pa-£pc|inCV V 6.5
(b) pulse height in SWV mV 7.3.5
Ep/2 potential where / = /p/2 in LSV V 6.2.2
£pa anodic peak potential V 6.5
£pc cathodic peak potential V 6.5
staircase step height in SWV mV 7.3.5
£ potential of zero charge V 13.2.2
Z
*л switching potential for cyclic voltammetry V 6.5
Еф quarter-wave potential in V 8.3.1
chronopotentiometry
E\I2 (a) measured or expected half-wave V 1.4.2,5.4,5.5
potential in voltammetry
(b) in derivations, the "reversible" V 5.4
half-wave potential,
Eo> + (RT/nF)\n(D /D)l/2
R 0
Ещ potential where i/i^ =1/4 V 5.4.1
ЕЪ1А potential where ///d = 3/4 V 5.4.1
e (a) electronic charge с
(b) voltage in an electric circuit V 10.1.1,15.1
e\ input voltage V 15.2
e output voltage V 15.1.1
0
voltage across the input terminals of an /xV 15.1.1
amplifier
ег%) error function of x none A.3
erfc(x) error function complement of x none A.3
F the Faraday constant; charge on one С
mole of electrons
f (a) F/RT V"1
(b) frequency of rotation r/s 9.3
(c) frequency of a sinusoidal oscillation s-1 10.1.2
(d) SWV frequency s-1 7.3.5
(e) fraction titrated none 11.5.2
/(E) Fermi function none 3.6.3
fUk) fractional concentration of species / in none B.1.3
boxy after iteration к in a simulation
G Gibbs free energy kJ, kJ/mol 2.2.4
AG Gibbs free energy change in a chemical kJ, kJ/mol 2.1.2,2.1.3
process
G electrochemical free energy kJ, kJ/mol 2.2.4
G° standard Gibbs free energy kJ, kJ/mol 3.1.2
xii Major Symbols
Section
Symbol Meaning Usual Units References
AG° standard Gibbs free energy change in a kJ, kJ/mol 2.1.2,2.1.3
chemical process
standard Gibbs free energy of activation kJ/mol 3.1.2
дс! j standard free energy of transfer for kJ/mol 2.3.6
transfer, j
species j from phase a into phase /3
(a) gravitational acceleration cm/s2
(b) interaction parameter in adsorption J-cm2/mol2 13.5.2
isotherms
H (a) enthalpy kJ, kJ/mol 2.1.2
s-l/2 5.5.1
Mi enthalpy change in a chemical process kJ, kJ/mol 2.1.2
A#° standard enthalpy change in a chemical kJ, kJ/mol 2.1.2
process
standard enthalpy of activation kJ/mol 3.1.2
Planck constant J-s
corrected mercury column height at a DME cm 7.1.4
/ amplitude of an ac current A 10.1.2
/(0 convolutive transform of current; C/s1/2 6.7.1
semi-integral of current
/ current phasor A 10.1.2
7 diffusion current constant for average ^A-s1/2/(mg2/3-mM) 7.1.3
current
diffusion current constant for maximum M-s1/2/(mg2/3-mM) 7.1.3
current
peak value of ac current amplitude A 10.5.1
current A 1.3.2
А/ difference current in SWV = if — i A 7.3.5
r
8i difference current in DPV = /(r) - Z(r') A 7.3.4
/(0) initial current in bulk electrolysis A 11.3.1
characteristic current describing flux of the A 14.4.2
*А
primary reactant to a modified RDE
anodic component current A 3.2
(a) charging current A 6.2.4
(b) cathodic component current A 3.2
(a) current due to diffusive flux A 4.1
(b) diffusion-limited current A 5.2.1
average diffusion-limited current flow A
7.1.2
over a drop lifetime at a DME
Od)max diffusion-limited current at t . at a A
m dX 7.1.2
DME (maximum current)
characteristic current describing diffusion A
14.4.2
of electrons within the film at a
modified electrode
(a) faradaic current A
(b) forward current A 5.7
kinetically limited current A 9.3.4
characteristic current describing A 14.4.2
cross-reaction within the film at a
modified electrode