Understanding Voltammetry: Simulation Of Electrode Processes

by Richard Guy Compton, Eduardo Laborda, Kristopher R Ward

Overview

This is the first textbook in the field of electrochemistry that will teach experimental electrochemists how to carry out simulation of electrode processes. Processes at both macro- and micro-electrodes are examined and the simulation of both diffusion-only and diffusion-convection processes are addressed. The simulation of processes with coupled homogeneous kinetics and at microelectrode arrays are further discussed. Over the course of the book the reader's understanding is developed to the point where they will be able to undertake and solve research-level problems. The book leads the reader through from a basic understanding of the principles underlying electrochemical simulation to the development of computer programs which describe the complex processes found in voltammetry.This is the third book in the “Understanding Voltammetry” series, published with Imperial College Press and written by the Compton group. Other books in the series include “Understanding Voltammetry”, written by Richard G Compton with Craig Banks and also “Understanding Voltammetry: Problems and Solutions” (2012) written by Richard G Compton with Christopher Batchelor-McAuley and Edmund Dickinson. These are and continue to be successful textbooks for graduates in electrochemistry and electroanalytical studies.

Product Details

ISBN-13:	9781783263233
Publisher:	Imperial College Press
Publication date:	01/23/2014
Pages:	260
Product dimensions:	6.20(w) x 9.10(h) x 0.80(d)

Table of Contents

Preface v

1 Introduction 1

1.1 Electrochemical Systems 2

1.2 Voltammetric Techniques 19

1.3 Finite Difference Methods 20

1.4 Voltammetry: A Selected Bibliography 22

References 23

2 Mathematical Model of an Electrochemical System 25

2.1 Cyclic Voltammetry 25

2.2 Diffusion: Fick's Second Law 28

2.3 Boundary Conditions 32

2.4 Current 34

2.5 Dimensionless Coordinates 35

2.6 Summary 42

References 43

3 Numerical Solution of the Model System 45

3.1 Finite Differences 45

3.2 Time Evolution: Discretising Fick's Second Law 50

3.3 The Thomas Algorithm 54

3.4 Simulation Procedure 57

3.5 Checking Results 61

3.6 Performance and Runtime Analysis 66

References 69

4 Diffusion-Only Electrochemical Problems in One-Dimensional Systems 71

4.1 Unequally Spaced Grids 71

4.2 Finite Electrode Kinetics 81

4.3 Unequal Diffusion Coefficients 87

4.4 Other One-Dimensional Electrode Geometries 90

References 96

5 First-Order Chemical Kinetic Mechanisms 99

5.1 First-Order EC_ire Mechanism: Basic Concepts 99

5.2 First-Order Catalytic Mechanism: Coupled Equation Systems 107

5.3 LU Decomposition and Extended Thomas Algorithm 112

5.4 First-Order EC_rev Mechanism: Including a Third Species 114

5.5 Multiple-Electron Transfer Processes 116

5.6 Heterogeneous Chemical Processes 119

References 121

6 Second-Order Chemical Kinetic Mechanisms 123

6.1 Second-Order Catalytic Mechanism: The Newton-Raphson Method 123

6.2 Multiple-Electron Transfers: Adaptive Spatial Grids 131

6.3 Adsorption 136

References 143

7 Electrochemical Simulation in Weakly Supported Media 145

7.1 The Nernst-Planck-Poisson Problem 146

7.2 Weakly Supported Cyclic Voltammetry and Chronoamperometry 153

References 158

8 Hydrodynamic Voltammetry 161

8.1 Rotating Disc Electrode 163

8.2 Channel Electrode 169

References 174

9 Two-Dimensional Systems: Microdisc Electrodes 175

9.1 Microdisc Electrodes: The Model 175

9.2 Numerical Solution 181

9.3 Implementation 191

9.4 Microband Electrodes 194

References 198

10 Heterogeneous Surfaces 201

10.1 Arrays of Microdisc Electrodes 202

10.2 Microband Arrays 216

10.3 Porous Electrodes 222

10.4 Conclusion 225

References 225

Appendix A Review of C++ 229

A.1 Hello World 229

A.2 Variables, Types and Operators 231

A.3 Logic and Program Control 234

A.4 Functions 236

References 238

Appendix B Microdisc Program 239

References 246

Index 247