Theoretical modelling in electrochemistry
Keywords: Simulation
Electrochemsitry
Theoretical work
Chronoamperometry
Nanoimpact
Diffusion indicator
Adsorbed enzyme
Cyclic voltammotry

In this thesis, the studies of diffusion and the electrochemical systems based on the modelling and simulation of chronoamperometry and cyclic voltammetry for various novel electrochemical systems are reported and discussed.
In Chapter 1, fundamental and essential concepts and theories in electrochemistry are introduced to provide key background information and to assist the understanding of the later chapters. Similarly, Chapter 2 outlines the introductory aspects for the methodologies of electrochemical modelling and simulation by using the finite difference method to discretise the diffusion equations, together with the methods used for validating and testing the simulations.
Chapter 3 and 4 present the introduction and application of a new physicochemical parameter characterising mass transport, the ”diffusion indicator”, which offers sensitive and comparable information about the changes and trends in chronoamperometric current responses in a simple and straightforward form by distinguishing the relative contributions from linear and convergent diffusion. Based on the analytical and modelling studies of electrochemical systems with four different electrode geometries (spheres, discs, cylinders, and bands), the concept of the diffusion indicator is developed and discussed in Chapter 3. Chapter 4 applies this new parameter to chronoamperometric studies of several cylindrical and ring electrodes, where the comparative studies of the diffusive flux of the analyte toward electrodes with similar but different geometries from different spatial locations are presented.
Chapter 5 discusses the theoretical studies for a particular system regarding the nano-impact method, which involves the electrochemical process of depleting the dopant inside a spherical particle after the particle collides with the electrode and is adsorbed on the electrode surface. Two different theoretical models are adopted and utilised, and a dimensional analysis is presented.
Chapter 6 investigates the cyclic voltammetry of a reversible one-electron-transfer reaction at electrochemical systems with different electrode geometries. A polynomial equation is introduced to describe the forward peak potentials at different scan rates for an ‘infinitely long cylinder’ electrode. Together with literature equations, this introduced equation enables us to produce an evaluation of infinite cylinder approximation for other cylinder-like electrodes of finite length and where the cylinder ends contribute significantly to the net flux.
Chapter 7 applies the diffusion-equation-based simulations to an adsorbed-enzyme-mediated electrochemical system together with the theoretical analysis of cyclic voltammetric current responses on both flat and porous electrodes to understand the role of the Michaelis-Menten kinetics under both diffusional regimes and, in particular, to explore the role of nano-structure in the enzyme-based catalytic reaction. In this study, literature reports of the apparent potential dependent Michaelis constants are explained. Four classes of voltammograms are identified corresponding to qualitatively different current responses. The conditions under which porosity can usefully aid the electro-catalysis are determined providing a basis for scale-up of the enzyme-catalysed redox processes.