ELECTROCHEMICAL METHODS Fundamentals and Applications - Allen.J.Bard

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MAJOR SYMBOLS Listed below are symbols used in several chapters or in large portions of a chapter. Symbols 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. Parsons et al., Pure Appl. Chem., 37, 503 (1974).]; however there are exceptions. A bar over a concentration or a current [ej*., C o (x, s)] indicates the Laplace transform of the variable. The exception is when / indicates an average current in polarography. STANDARD SUBSCRIPTS a с D d anodic (a) cathodic (b) charging disk diffusion dl eq f / double layer equilibrium (a) forward (b) faradaic limiting 0 P R r pertaining to species 0 in О + ne ±± R peak (a) pertaining to species R in О + ne ^ R (b) ring reverse ROMAN SYMBOLS Symbol Meaning Usual Units Section References С C B c d c't (a) area (b) cross-sectional area of a porous electrode (c) frequency factor in a rate expression (d) open-loop gain of an amplifier absorbance (a) internal area of a porous electrode (b) tip radius in SECM activity of substance j in a phase a aFv/RT capacitance series equivalent capacitance of a cell differential capacitance of the double layer integral capacitance of the double layer concentration of species; bulk concentration of species; concentration of species; at distance x cm 1.3.2 cm 2 11.6.2 depends on order 3.1.2 none 15.1.1 none 17.1.1 cm 2 11.6.2 16.4.1 none 2.1.5 s" 1 6.3.1 mol/cm 2 13.5.3 F 1.2.2, 10.1.2 F 10.4 F, F/cm 2 1.2.2, 13.2.2 F, F/cm 2 13.2.2 M, mol/cm 3 M, mol/cm 3 1.4.2, 4.4.3 M, mol/cm 3 1.4
Major Symbols Symbol Meaning Usual Units Section References CjCx = 0) Cj(x, t) Cj(O, f) Cj(y = 0) Csc С Dj(A, E) D M £s d *\ E AE E % % E £° AE° E° E 0 ' E A E ac E b Edc concentration of species j at the electrode surface concentration of species у at distance x at time t concentration of species у at the electrode surface at time t concentration of species у at distance у away from rotating electrode surface concentration of species у at a rotating electrode space charge capacitance pseudocapacity speed of light in vacuo diffusion coefficient for electrons within the film at a modified electrode diffusion coefficient of species у concentration density of states for species у model diffusion coefficient in simulation diffusion coefficient for the primary reactant within the film at a modified electrode distance of the tip from the substrate in SECM density of phase у (a) potential of an electrode versus a reference (b) emf of a reaction (c) amplitude of an ac voltage (a) pulse height in DPV (b) step height in tast or staircase voltammetry (c) amplitude (1/2 p-p) of ac excitation in ac voltammetry electron energy electric field strength vector electric field strength voltage or potential phasor (a) standard potential of an electrode or a couple (b) standard emf of a half-reaction difference in standard potentials for two couples electron energy corresponding to the standard potential of a couple formal potential of an electrode activation energy of a reaction ac component of potential base potential in NPV and RPV dc component of potential M, mol/cm 3 M, mol/cm 3 M, mol/cm 3 M, mol/cm 3 M, mol/cm 3 F/cm F cm/s cm /s cm 2 /s cm 3 eV~ ! none cm 2 /s /xm, nm g/cm 3 V V V mV mV mV eV V/cm V/cm V V V V eV V kJ/mol mV V V 1.4.2 4.4 4.4.3 9.3.3 9.3.4 18.2.2 10.1.3 17.1.2 14.4.2 1.4.1,4.4 3.6.3 B.1.3.B.1.8 14.4.2 16.4.1 1.1,2.1 2.1 10.1.2 7.3.4 7.3.1 10.5.1 2.2.5, 3.6.3 2.2.1 2.2.1 10.1.2 2.1.4 2.1.4 6.6 3.6.3 2.1.6 3.1.2 10.1.1 7.3.2, 7.3.3 10.1.1
Page 1 and 2: SECOND EDITION ELECTROCHEMICAL METH
Page 3 and 4: PREFACE In the twenty years since t
Page 5: CONTENTS MAJOR SYMBOLS ix STANDARD
Page 9 and 10: xii Major Symbols Symbol Meaning Us
Page 11 and 12: xiv Major Symbols Symbol Meaning Us
Page 13 and 14: xvi Major Symbols Symbol Meaning Us
Page 15 and 16: xviii Major Symbols Symbol Meaning
Page 17 and 18: xx Major Symbols Abbreviation Meani
Page 19 and 20: CHAPTER 1 INTRODUCTION AND OVERVIEW
Page 21 and 22: Pt H 2 1.1 Introduction 3 Zn Ag С
Page 23 and 24: 1.1 Introduction 5 Power supply -Ag
Page 25 and 26: 1.1 Introduction 7 idation of Br~ t
Page 27 and 28: 1.1 Introduction Hg/I-Г, ВГ(1 М
Page 29 and 30: 1.2 Nonfaradaic Processes and the N
Page 37 and 38: 1.3 Faradaic Processes and Factors
Page 47 and 48: 1.4 Introduction to Mass-Transfer-C
Page 55 and 56: 1.5 Semiempirical Treatment of Nems
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1.6 The Literature of Electrochemis
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1.6 The Literature of Electrochemis
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1.8 Problems 43 1.6 For the electro
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Thus the net cell reaction is 1 Zn
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2.1 Basic Electrochemical Thermodyn
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2.2 A More Detailed View of Interfa
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(a) Properties of the Electrochemic
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2.3 Liquid Junction Potentials л :
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2.3 Liquid Junction Potentials < 65
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2.3 Liquid Junction Potentials 67 T
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2.3 Liquid Junction Potentials 69 W
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2.3 Liquid Junction Potentials «I
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2.3 Liquid Junction Potentials : 73
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2.4 Selective Electrodes \ 75 Ag wi
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2.4 Selective Electrodes 77 The fir
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Other Ion-Selective Electrodes 2.4
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2.4 Selective Electrodes •« 81 (
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2.5 References 83 8. M. W. Chase, J
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2.3 Devise a cell in which the foll
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3 KINETICS OF ELECTRODE REACTIONS I
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3.1 Review of Homogeneous Kinetics
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3.2 Essentials of Electrode Reactio
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3.3 Butler-Volmer Model of Electrod
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3.4 Implications of the Butler-Volm
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Г " т - ') = e f(E-E«) ( 3 A 2 7
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3.5 Multistep Mechanisms 107 -200 -
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3.5 Multistep Mechanisms 109 one-st
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3.5 Multistep Mechanisms 111 which
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3.5 Multistep Mechanisms 113 dent o
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3.6 Microscopic Theories of Charge
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3.7 References 133 17. J. A. V. But
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3.8 Problems 135 Use a spreadsheet
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CHAPTER 4 MASS TRANSFER BY MIGRATIO
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4.2 Migration 139 component at any
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4.3 Mixed Migration and Diffusion N
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4.4 Diffusion i 147 -5/ -41 -31 -21
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4.4 Diffusion 149 net mass-transfer
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4.4 Diffusion 151 X IТ i i i \ \\
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4.5 References i 153 4.4.4 Solution
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4.6 Problems 155 4.4 The mobility,
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5.1 Overview of Step Experiments 15
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5.1 Overview of Step Experiments 15
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5.2 Potential Step Under Diffusion
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and inversion produces the current-
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5.3 Diffusion-Controlled Currents a
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Responses to a Large-Amplitude Pote
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5.4 Sampled-Current Voltammetry for
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5.6 Multicomponent Systems and Mult
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5.7 Chronoamperometric Reversal Tec
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5.7 Chronoamperometric Reversal Tec
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5.8 Chronocoulometry 211 nal-to-noi
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5.8 Chronocoulometry 213 100 200 30
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5.8 Chronocoulometry «i 215 The ap
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5.9 Special Applications of Ultrami
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5.9 Special Applications of Ultrami
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5.10 References « 221 would diffus
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5.11 Problems 223 0.2, 0.5, 1, 2, 3
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5.11 Problems < 225 5.19 G. Denault
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6.1 Introduction -I 227 0 t E t E°
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6.2 Nemstian (Reversible) Systems 2
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6.2 Nemstian (Reversible) Systems <
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6.2 Nernstian (Reversible) Systems
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where Introducing E(t) from (6.2.1)
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6.4 Quasireversible Systems *4 237
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6.5 Cyclic Voltammetry 239 Figure 6
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6.5 Cyclic Voltammetry 241 0.5 -0.3
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6.7 Convolutive or Semi-Integral Te
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6.8 Cyclic Voltammetry of the Liqui
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6.9 References 255 100 I -100 I I I
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6.10 Problems 257 20 r- 15 /, цА
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6.10 Problems *« 259 -0.8 -1.0 -1.
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CHAPTER 7 POLAROGRAPHY AND PULSE VO
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7.1 Behavior at Polarographic Elect
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7.2 Polarographic Waves 273 Kouteck
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7.3 PULSE VOLTAMMETRY 7.3 Pulse Vol
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7.3 Pulse Voltammetry 277 -0.4 -0.6
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7.3 Pulse Voltammetry < 279 • Dro
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7.3 Pulse Voltammetry 281 Potential
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7.3 Pulse Voltammetry 283 duration
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7.3 Pulse Voltammetry \. 285 cant c
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7.3 Pulse Voltammetry < 287 Second
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7.3 Pulse Voltammetry 289 The shape
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7.3 Pulse Voltammetry I 291 one ref
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7.3 Pulse Voltammetry 293 effects o
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7.3 Pulse Voltammetry 295 In genera
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7.3 Pulse Voltammetry < 297 1.0 i
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7.3 Pulse Voltammetry 299 (d) Appli
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7.4 References 301 Therefore, the b
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7.5 Problems < 303 49. L. Ramaley a
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8 CONTROLLED-CURRENT TECHNIQUES 8.1
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8.2 General Theory of Controlled-Cu
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8.2 General Theory of Controlled-Cu
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8.2.3 Programmed Current Chronopote
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8.3 Potential-Time Curves in Consta
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8.3 Potential-Time Curves in Consta
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8.4 Reversal Techniques 317 connect
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8.6 The Galvanostatic Double Pulse
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8.7 Charge Step (Coulostatic) Metho
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8.9 Problems 329 electrolysis time
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CHAPTER 9 METHODS INVOLVING FORCED
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9.2 Theoretical Treatment of Convec
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9.3 Rotating Disk Electrode 335 9.3
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9.3 Rotating Disk Electrode 337 Fig
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9.3 Rotating Disk Electrode i 339 T
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9.3 Rotating Disk Electrode 341 For
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9.3 Rotating Disk Electrode 343 1 0
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9.3 Rotating Disk Electrode 345 to
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7iim» o f j lim =l№l(i u /A)s l/
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9.4 Rotating Ring and Ring-Disk Ele
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9.4 Rotating Ring and Ring-Disk Ele
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9.5 Transients at the RDE and RRDE
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9.5.2 Transients at the RRDE 9.5 Tr
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9.6 Modulated RDE «1 357 600 400 -
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9.6 Modulated RDE < 359 Full-wave r
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9.7 Convection at Ultramicroelectro
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9.8 Electrohydrodynamics and Relate
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9.10 Problems 365 40. D. A. Saville
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9.10 Problems 367 +1.0 -0.2 Figure
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ЮЛ Introduction 369 Potentiometer
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10.1 Introduction 371 Figure 10.1.3
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10.1 Introduction 373 In this way w
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10.1 Introduction 375 *I_L -3 -2 -1
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10.2 Interpretation of the Faradaic
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10.2 Interpretation of the Faradaic
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10.3 Kinetic Parameters from Impeda
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10.4 Electrochemical Impedance Spec
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10.5 ас Voltammetry < 389 voltamm
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10.5 ас Voltammetry «I 391 exper
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10.5 ас Voltammetry 393 heterogen
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10.5 ас Voltammetry 395 This maxi
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10.5 ас Voltammetry < 397 The str
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10.5 ас Voltammetry -Щ 399 peak
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10.6 Higher Harmonics -m 401 f В R
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10.6 Higher Harmonics 403 Output H
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10.7 Chemical Analysis by ac Voltam
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10.8 Instrumentation for Electroche
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10.8 Instrumentation for Electroche
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10.9 Analysis of Data in the Laplac
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10.9 Analysis of Data in the Laplac
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10.11 Problems « 415 22. J. Vareec
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CHAPTER 11 BULK ELECTROLYSIS METHOD
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General Considerations in Bulk Elec
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General Considerations in Bulk Elec
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Controlled-Potential Methods < 423
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Controlled-Potential Methods 425 lo
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11.3.3 Electroseparations Controlle
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Controlled-Potential Methods 429 ur
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Controlled-Current Methods ^ 431 Ba
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Controlled-Current Methods i 433 Th
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Electrometric End-Point Detection 4
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Electrometric End-Point Detection i
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Electrometric End-Point Detection <
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Flow Electrolysis 441 11.6 FLOW ELE
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Flow Electrolysis ) = nFv dC o (x)
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Flow Electrolysis 445 This allows t
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Flow Electrolysis ^ 447 I Solution
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Flow Electrolysis 449 Spacer Auxili
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Flow Electrolysis 451 are much high
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Thin-Layer Electrochemistry 453 Mic
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Thin-Layer Electrochemistry 455 thr
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Thin-Layer Electrochemistry 457 -0.
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Stripping Analysis 459 Deposition (
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Stripping Analysis 461 -0.6 Figure
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Stripping Analysis 463 0 -0.2 1 1 1
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References 465 7. N. Tanaka, op. ci
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Problems 467 1.0 +0.8 +0.6 +0.4 +0.
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Problems 469 are equal and (b) thos
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CHAPTER 12 ELECTRODE REACTIONS WITH
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12.1 Classification of Reactions i
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12.1 Classification of Reactions 47
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12.2 Fundamentals of Theory for Vol
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(as above) дС т д2 С т С О2
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12.2 Fundamentals of Theory for Vol
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12.3 Theory for Transient Voltammet
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Catalytic Reaction—E r Cj 12.3 Th
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Icurr< 12.3 Theory for Transient Vo
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12.4 Rotating Disk and Ring-Disk Me
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12.7 Controlled-Potential Coulometr
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12.8 References « 529 12.8 REFEREN
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12.9 Problems =4 531 92. G. Denuaul
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12.9 Problems 533 12.11 Consider cu
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13.1 Thermodynamics of the Double L
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13.1 Thermodynamics of the Double L
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13.2 Experimental Evaluation of Sur
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13.2 Experimental Evaluation of Sur
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13.2.3 Relative Surface Excesses 13
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13.3 Models for Double-Layer Struct
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The total charge per unit volume in
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13.4 Studies at Solid Electrodes 55
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13.5 Extent and Rate of Specific Ad
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13.6 Effect of Adsorption of Electr
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13.7 Double-Layer Effects on Electr
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13.7.2 Double-Layer Effects in the
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13.8 Referencess 575 / / / 4 —% -
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13.9 Problems 577 64. D. M. Mohilne
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13.9 Problems 579 13.13 Aramata and
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14.2 Types, Preparation, and Proper
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14.3 Electrochemical Responses of A
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14.4 Overview of Processes at Modif
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where the permeation current, ip, i
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14.5 Blocking Layers 619 One can al
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14.5 Blocking Layers 621 current at
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14.5 Blocking Layers 623 The parame
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14.5 Blocking Layers 625 at the ele
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14.6 Other Methods of Characterizat
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14.7 References . 629 (b) H. S. Whi
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14.8 Problems 631 15 20 25 [ВГ],
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15.1 Operational Amplifiers 633 +15
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15.2 Current Feedback 635 (f) Other
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15.2 Current Feedback < 637 i Figur
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15.3 Voltage Feedback * 639 This ki
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15.4 Potentiostats 641 Counter Work
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15.4 Potentiostats -4 643 I Potenti
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15.6 Difficulties with Potential Co
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15.7 Measurement of Low Currents
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15.8 Computer-Controlled Instrument
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15.9 Troubleshooting Electrochemica
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15.11 Problems 657 25. P. He, J. P.
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CHAPTER 16 SCANNING PROBE TECHNIQUE
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16.2 Scanning Tunneling Microscopy
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16.3 Atomic Force Microscopy 667 no
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16.4 Scanning Electrochemical Micro
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16.6 Problems 679 tip and the subst
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17.1 Ultraviolet and Visible Spectr
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17.2 Vibrational Spectroscopy 701 R
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17.2 Vibrational Spectroscopy ; 703
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17.2 Vibrational Spectroscopy 705 h
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17.2 Vibrational Spectroscopy 707 0
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17.3 Electron and Ion Spectrometry
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17.4 Magnetic Resonance Methods 723
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17.5 Quartz Crystal Microbalance 72
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17.5 Quartz Crystal Microbalance ;
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17.6 X-Ray Methods 729 few millimet
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17.7 References 731 17.7 REFERENCES
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17.7 References =- 733 87. D. M. Ko
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17.8 Problems 735 17.2 Given D = 6.
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18.1 ElectrogeneratedChemiluminesce
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18.2 Photoelectrochemistry at Semic
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18.3 Electrochemical Detection of P
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18.3 Electrochemical Detection of P
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18.4 References ! 765 41. L. L. Shu
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18.5 Problems 767 18.4 The transien
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А Р Р #Й D IX А MATHEMATICAL M
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АЛ Solving Differential Equations
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А. 1 Solving Differential Equation
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А. 1 Solving Differential Equation
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А.2 Taylor Expansions 777 10 Figur
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А.З The Error Function and the Ga
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А.5 Complex Notation «i 781 A val
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А.8 Problems 783 In most applicati
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APPENDIX В DIGITAL SIMULATIONS OF
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ut the definition of a derivative a
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B.I Setting Up the Model 789 1. C*
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B.I Setting Up the Model 791 could
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В.2 An Example < 793 and imax « 6
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В.2 An Example « 795 mensionless
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В.З Incorporating Homogeneous Kin
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В.4 Boundary Conditions for Variou
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В.4 Boundary Conditions for Variou
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В.6 Miscellaneous Digital Simulati
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В.6 Miscellaneous Digital Simulati
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В.8 Problems 807 / B vs. x f° r t
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TABLE C.I (continued) Reaction 2H +
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Reference Tables 811 TABLE C.3 Esti
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Referem TABLE C.4 Selected Diffusio
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816 • Index Blocking polymers, 58
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818 Index Convective-diffusion equa
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820 Index Dropping mercury electrod
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822 ; Index Ellipsometry, described
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824 Index Instrumentation (continue
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826 Index Multicomponent systems: m
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828 Index Potential step methods (c
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830 • Index Sampled-current volta
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832 Index Thin-layer electrochemist
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ELECTROCHEMICAL METHODS Fundamentals and Applications - Allen.J.Bard

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