Understanding Voltammetry: Simulation Of Electrode Processes

Contents
Preface to the Second Edition
Preface to the First Edition
1. Introduction
	1.1. Electrochemical Systems
		1.1.1. Mass transport
		1.1.2. Boundary conditions
		1.1.3. Reaction mechanisms
	1.2. Voltammetric Techniques
	1.3. Finite Difference Methods
	1.4. Voltammetry: A Selected Bibliography
	References
2. Mathematical Model of an Electrochemical System
	2.1. Cyclic Voltammetry
	2.2. Diffusion: Fick’s Second Law
		2.2.1. Equal diffusion coefficients
	2.3. Boundary Conditions
	2.4. Current
	2.5. Dimensionless Parameters
		2.5.1. Electrode surface boundary
		2.5.2. Scan rate
		2.5.3. Current
	2.6. Summary
	References
3. Numerical Solution of the Model System
	3.1. Finite Differences
		3.1.1. Central differencing
		3.1.2. Second derivative
	3.2. Time Evolution: Discretising Fick’s Second Law
		3.2.1. The explicit method
		3.2.2. The implicit method
	3.3. The Thomas Algorithm
	3.4. Simulation Procedure
		3.4.1. Example program
	3.5. Testing Simulations
		3.5.1. General tests
			3.5.1.1. Self-convergence analysis
			3.5.1.2. Unchanging stoichiometry-weighted total number of particles
			3.5.1.3. Unchanging stoichiometry-weighted total concentration
		3.5.2. Specific tests: Analytical solutions and reference values
			3.5.2.1. Any electrode kinetics
			3.5.2.2. Fully reversible electron transfers
		3.5.3. Comprehensive simulation testing
	3.6. Performance and Runtime Analysis
		3.6.1. Memory requirements
	References
4. Diffusion-Only Electrochemical Problems in One-Dimensional Systems
	4.1. Unequally Spaced Grids
		4.1.1. Expanding spatial grid
		4.1.2. Expanding time grid: Chronoamperometry and pulse techniques
		4.1.3. Example program
	4.2. Finite Electrode Kinetics
		4.2.1. The Butler–Volmer model
		4.2.2. Testing Simulations: Specific tests
		4.2.3. The Marcus–Hush model
	4.3. Unequal Diffusion Coefficients
	4.4. Other One-Dimensional Electrode Geometries
		4.4.1. Testing Simulations: Specific tests
			4.4.1.1. Small Tmax limit: Macroelectrodes
			4.4.1.2. Intermediate Tmax regime
			4.4.1.3. Large Tmax limit: Steady state
	References
5. First-Order Chemical Kinetic Mechanisms
	5.1. First-Order ECirre Mechanism: Basic Concepts
		5.1.1. Reaction layer
	5.2. First-Order Catalytic Mechanism: Coupled Equation Systems
	5.3. LU Decomposition and Extended Thomas Algorithm
	5.4. First-Order ECrev Mechanism: Including a Third Species
		5.4.1. Testing Simulations: Specific tests
	5.5. Multiple-Electron Transfer Processes
		5.5.1. Testing Simulations: Specific tests
	5.6. Heterogeneous Chemical Processes
	References
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
	References
7. Electrochemical Simulation in Weakly Supported Media
	7.1. The Nernst–Planck–Poisson Problem
	7.2. Weakly Supported Cyclic Voltammetry and Chronoamperometry
	References
8. Hydrodynamic Voltammetry
	8.1. Rotating Disc Electrodes
		8.1.1. Testing Simulations: Specific tests
	8.2. Channel Electrodes
	References
9. Two-Dimensional Systems: Microdisc Electrodes
	9.1. Microdisc Electrodes: The Model
		9.1.1. Diffusion
		9.1.2. Boundary conditions
		9.1.3. Current
		9.1.4. Normalisation
	9.2. Numerical Solution
		9.2.1. Finite differences in two dimensions
		9.2.2. The ADI method
			9.2.2.1. Z-sweep discretisation
			9.2.2.2. R-sweep discretisation
		9.2.3. Boundary conditions
			9.2.3.1. Implicit terms
			9.2.3.2. Explicit terms
		9.2.4. Flux
	9.3. Implementation
		9.3.1. Multithreading
		9.3.2. Testing Simulations: Specific tests
	9.4. Microband Electrodes
		9.4.1. Numerical solution
		9.4.2. Flux
	References
10. Heterogeneous Surfaces
	10.1. Arrays of Microdisc Electrodes
		10.1.1. Diffusion domain approximation
		10.1.2. Implementation
			10.1.2.1. Simulation procedure
		10.1.3. Diffusional modes
		10.1.4. Random arrays
			10.1.4.1. Partially blocked electrodes
	10.2. Microband Arrays
		10.2.1. Highly ordered pyrolytic graphite
		10.2.2. Interdigitated microbands
	10.3. Porous Electrodes
	10.4. Conclusions
	References
11. Stochastic Electrochemistry
	11.1. Stochastic Electrochemistry and Partial Differential Equations
		11.1.1. Example: Chronoamperometry at Low Concentrations
			11.1.1.1. Implementation in C++
	11.2. Stochastic Electrochemistry and Stochastic Differential Equations
		11.2.1. Theoretical Background
			11.2.1.1. Friction
			11.2.1.2. The Equipartition Theorem
			11.2.1.3. The Langevin Equation
			11.2.1.4. A General Solution to the Diffusion Equation
			11.2.1.5. Einstein-Smoluchowski Relation and Stokes-Einstein Equation
			11.2.1.6. Binomial Distributions and the De Moivre-Laplace Theorem
			11.2.1.7. Construction of the Random Walk
			11.2.1.8. Random Walks in Two and Three Dimensions
		11.2.2. Example: Reversible Voltammetry at a Macroelectrode
			11.2.2.1. Implementation in C++
	References
Appendix A: Review of C++
	A.1. Hello World
	A.2. Variables, Types and Operators
		A.2.1. Arrays, vectors, and strings
	A.3. Logic and Program Control
		A.3.1. The if statement
		A.3.2. The for and while loops
	A.4. Functions
	References
Appendix B: Microdisc Program
	References
Index