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UNDERSTANDING VOLTAMMETRY

by Richard G Compton (University of Oxford, UK) & Craig E Banks (University of Oxford, UK)

Table of Contents (64k)
Preface (31k)
Chapter 1: Equilibrium Electrochemistry and the Nernst Equation (1,095k)

The power of electrochemical measurements in respect of thermodynamics, kinetics and analysis is widely recognized but the subject can be unpredictable to the novice even if they have a strong physical and chemical background, especially if they wish to pursue quantitative measurements. Accordingly, some significant experiments are perhaps wisely never attempted while the literature is sadly replete with flawed attempts at rigorous voltammetry.

This textbook considers how to go about designing, explaining and interpreting experiments centered around various forms of voltammetry (cyclic, microelectrode, hydrodynamic, and so on). The reader is assumed to have a knowledge to Masters level of physical chemistry but no exposure to electrochemistry in general, or voltammetry in particular. While the book is designed to 'stand alone', references to important research papers are given to provide an entry into the literature.

The book gives clear introductions to the theories of electron transfer and of diffusion in its early chapters. These are developed to interpret voltammetric experiments at macro-electrodes before considering microelectrode behavior. A subsequent chapter introduces convection and describes hydrodynamic electrodes. Later chapters describe the voltammetric measurement of homogeneous kinetics, the study of adsorption on electrodes and the use of voltammetry for electroanalysis.
Contents
Preface                v
1        Equilibrium Electrochemistry and the Nernst Equation        1
        1.1        Chemical Equilibrium                 1
        1.2        Electrochemical Equilibrium: Introduction                 5
        1.3        Electrochemical Equilibrium: Electron Transfer       
                at the Solution¨CElectrode Interface                 9
        1.4        Electrochemical Equilibrium: The Nernst Equation                 11
        1.5        Walther Hermann Nernst                 17
        1.6        Reference Electrodes and the Measurement of Electrode Potentials        19
        1.7        The Hydrogen Electrode as a Reference Electrode                 26
        1.8        Standard Electrode Potentials and Formal Potentials                 27
        1.9        Formal Potentials and Experimental Voltammetry                 30
        1.10        Electrode Processes: Kinetics vs. Thermodynamics                 32
2        Electrode Kinetics        35
        2.1        Currents and Reaction Fluxes                 35
        2.2        Studying Electrode Kinetics Requires Three Electrodes                 37
        2.3        Butler¨CVolmer Kinetics                 40
        2.4        Standard Electrochemical Rate Constants and Formal Potentials        43
        2.5        The Need for Supporting Electrolyte                 45
        2.6        The Tafel Law                 46
        2.7        Julius Tafel                 47
        2.8        Multistep Electron Transfer Processes                 49
        2.9        Tafel Analysis and the Hydrogen Evolution Reaction                 52
        2.10        B. Stanley Pons                 57
        2.11        Cold Fusion¨CThe Musical!                58

x Understanding Voltammetry
        2.12 Why are Some Standard Electrochemical Rate Constants Large but Others Slow? The Marcus Theory of Electron Transfer: An       
        Introduction                 60
        2.13        Marcus Theory: Taking it Further. Inner and Outer Sphere       
                Electron Transfer                 66
        2.14        Marcus Theory: Taking it Further. Adiabatic and Non-Adiabatic       
                Reactions                 67
        2.15        Marcus Theory: Taking it Further. Calculating the Gibbs Energy       
                of Activation                 70
        2.16        Relationship between Marcus Theory and Butler¨CVolmer Kinetics        73
        2.17 Marcus Theory and Experiment. Success!                74
3        Diffusion        77
        3.1        Fick¡¯s 1st Law of Diffusion                 77
        3.2        Fick¡¯s 2nd Law of Diffusion                 79
        3.3        The Molecular Basis of Fick¡¯s Laws                 81
        3.4        How Did Fick Discover His Laws?        83
        3.5        The Cottrell Equation: Solving Fick¡¯s 2nd Law                 88
        3.6        The Cottrell Problem: The Case of Unequal Diffusion Coefficients        92
        3.7        The Nernst Diffusion Layer                 94
        3.8        Mass Transfer vs. Electrode Kinetics: Steady-State       
                Current-Voltage Waveshapes                 97
        3.9        Mass Transport Corrected Tafel Relationships                 100
4        Cyclic Voltammetry at Macroelectrodes        107
        4.1        Cyclic Voltammetry: The Experiment                 107
        4.2        Cyclic Voltammetry: Solving the Transport Equations                 109
        4.3        Cyclic Voltammetry: Reversible and Irreversible Kinetics                 111
        4.4        What Dictates ¡®Reversible¡¯ and ¡®Irreversible¡¯ Behaviour?                 119
        4.5        Reversible and Irreversible Behaviour: The Effect of Voltage       
                Scan Rate                 120
        4.6        Reversible versus Irreversible Voltammetry: A Summary                 126
        4.7        The Measurement of Cyclic Voltammograms: Three Practical       
                Considerations                 127
        4.8        The Effect of Unequal Diffusion Coefficients, DA =~ DB                 129
        4.9        Multiple Electron Transfer: Reversible Electrode Kinetics        . . . .        133
        4.10        Multiple Electron Transfer: Irreversible       
                Electrode Kinetics                 142
        4.11        The Influence of pH on Cyclic Voltammetry                 147

                Contents        xi
5        Voltammetry at Microelectrodes        153
        5.1        The Cottrell Equation for a Spherical or Hemispherical Electrode        153
        5.2        Potential Step Transients at Microdisc Electrodes                 158
        5.3        Microelectrodes have Large Current Densities and       
                Fast Response Times                 159
        5.4        Applications of Potential Step Chronoamperometry Using       
                Microdisc Electrodes                 161
        5.5        Double Potential Step Microdisc Chronoamperometry Exploring       
                the Diffusion Coefficient of Electrogenerated Species                 164
        5.6        Cyclic and Linear Sweep Voltammetry Using Microdisk Electrodes        172
        5.7        Steady-State Voltammetry at the Microdisc Electrode                 182
        5.8        Microelectrodes versus Macroelectrodes                 183
        5.9        Ultrafast Cyclic Voltammetry: Megavolts per Second Scan Rates .        187
        5.10        Ultrasmall Electrodes: Working at the Nanoscale                 188
6        Voltammetry at Heterogeneous Surfaces        193
        6.1        Partially Blocked Electrodes                 193
        6.2        Microelectrode Arrays                 209
        6.3        Voltammetry at Highly Ordered Pyrolytic Graphite Electrodes. .        215
        6.4        Electrochemically Heterogeneous Electrodes                 219
        6.5        Electrodes Covered with Porous Films                 222
        6.6        Voltammetric Particle Sizing                 224
        6.7        Scanning Electrochemical Microscopy (SECM)                 228
7        Cyclic Voltammetry: Coupled Homogeneous Kinetics and Adsorption        233
        7.1        Homogeneous Coupled Reactions: Notation and Examples        . . .        233
        7.2        Modifying Fick¡¯s Second Law to Allow for Chemical Reaction . .        235
        7.3        Cyclic Voltammetry and the EC Reaction                 236
        7.4        How Do The Parameters K1 and A Emerge?                 240
        7.5        Cyclic Voltammetry and the EC2 Reaction                 243
        7.6        Examples of EC and EC2 Processes                 246
        7.7        ECE Processes                 254
        7.8        ECE vs DISP                 262
        7.9        The CE Mechanism                 264
        7.10        The EC¡¯ (Catalytic) Mechanism                 266
        7.11        Adsorption                 268
        7.12 Voltammetric Studies of Droplets and Solid Particles                 277

xii Understanding Voltammetry
8 Hydrodynamic Electrodes        285
8.1 Convection          285
8.2 Modifying Fick¡¯s Law to Allow for Convection          287
8.3 The Rotating Disc Electrode: An Introduction          288
8.4 The Rotating Disc Electrode ¡ª Theory          289
8.5 Osborne Reynolds (1842¨C1912)          293
8.6 The Rotating Disc Electrode ¡ª Further Theory          293
8.7 Chronoamperometry at the Rotating Disc Electrode: An
Illustration of the Value of Simulation          300
8.8 The Rotating Disc and Coupled Homogeneous Kinetics          303
8.9 The Channel Electrode: An Introduction          306
8.10 The Channel Electrode: The Levich Equation Derived          309
8.11 Channel Flow Cells and Coupled Homogeneous Kinetics . . .          310
8.12 Chronoamperometry at the Channel Electrode          316
8.13 The Channel Electrode is not ¡°Uniformly Accessible¡±          318
8.14 Channel Microelectrodes          319
8.15 Channel Microband Electrode Arrays for Mechanistic
Electrochemistry          321
8.16 The High Speed Channel Electrode          325
8.17 Hydrodynamic Electrodes Based on Impinging jets          327
8.18 Sonovoltammetry          329
9 Voltammetry for Electroanalysis        341
9.1 Potential Step Voltammetric Techniques          341
9.2 Differential Pulse Voltammetry          342
9.3 Square Wave Voltammetry         344
9.4 Stripping Voltammetry          345
9.5 Sono-electroanalysis          352
Appendix Simulation of Electrode Processes        361
A.1 Fick¡¯s First and Second Laws          361
A.2 Boundary Conditions          362
A.3 Finite Difference Equations          362
A.4 Backward Implicit Method          363
A.5 Conclusion          365

[ Last edited by yjfeng2000 on 2010-4-3 at 19:05 ]
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