Understanding voltammetry : simulation of electrode processes / by Richard G. Compton (Oxford University, UK, & University of Murcia, Spain), Eduardo Laborda (Oxford University, UK), & Kristopher R. Ward (Oxford University, UK)
1. Introduction. 1.1. Electrochemical systems. 1.2. Voltammetric techniques. 1.3. Finite difference methods. 1.4. Voltammetry: a selected bibliography -- 2. Mathematical model of an electrochemical system. 2.1. Cyclic voltammetry. 2.2. Diffusion: Fick's second law. 2.3. Boundary conditions. 2.4. Current. 2.5. Dimensionless coordinates. 2.6. Summary -- 3. Numerical solution of the model system. 3.1. Finite differences. 3.2. Time evolution: discretising Fick's second law. 3.3. The Thomas algorithm. 3.4. Simulation procedure. 3.5. Checking results. 3.6. Performance and runtime analysis -- 4. Diffusion-only electrochemical problems in one-dimensional systems. 4.1. Unequally spaced grids. 4.2. Finite electrode kinetics. 4.3. Unequal diffusion coefficients. 4.4. Other one-dimensional electrode geometries -- 5. First-order chemical kinetic mechanisms. 5.1. First-order EC[symbol] mechanism: basic concepts. 5.2. First-order catalytic mechanism: coupled equation systems. 5.3. LU decomposition and extended Thomas algorithm. 5.4. First-order EC[symbol] mechanism: including a third species. 5.5. Multiple-electron transfer processes. 5.6. Heterogeneous chemical processes -- 6. Second-order chemical kinetic mechanisms. 6.1. Second-order catalytic mechanism: the Newton-Raphson method. 6.2. Multiple-electron transfers: adaptive spatial grids. 6.3. Adsorption -- 7. Electrochemical simulation in weakly supported media. 7.1. The Nernst-Planck-Poisson problem. 7.2. Weakly supported cyclic voltammetry and chronoamperometry -- 8. Hydrodynamic voltammetry. 8.1. Rotating disc electrode. 8.2. Channel electrode -- 9. Two-dimensional systems: microdisc electrodes. 9.1. Microdisc electrodes: the model. 9.2. Numerical solution. 9.3. Implementation. 9.4. Microband electrodes -- 10. Heterogeneous surfaces. 10.1. Arrays of microdisc electrodes. 10.2. Microband arrays. 10.3. Porous electrodes. 10.4. Conclusion
Summary
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
