Diffusion to electrodes
Keywords: Stochastic arrivals
Numerical simulations
Diffusion of particles
Electrodes

This thesis develops diffusion models for modern electrochemical experiments involving the transport of particles to electrodes and adsorbing surfaces. In particular, the models are related to the 'impact' method where particles stochastically arrive at an electrode and detected electrochemically. The studies are carried out using numerical simulations and also analytical methods.
Chapter 1 is introductory and outlines some fundamental concepts in mass transport and kinetics, and their relation to electrochemical measurements which are of importance for the reader. Chapter 2 describes the numerical methods which are used for electrochemical simulations. Chapter 3 focuses on a specific two dimensional simulation system and the development of a high performance voltammetry simulation.
Chapters 4 and 5 study the stochastic impacts of particles at an electrode surface. In Chapter 4, a 'diffusion only' model is developed using a probabilistic study and random walk simulations in order to provide expressions that can be used in so-called `impact' experiments. In Chapter 5, the practical cases of microdisc and microwire electrodes are investigated. Expressions for the number of impacts are developed and the concept of the lower limit of detection in ultra-dilute solutions is introduced. Then, a comparison study between the microwire electrode and the microdisc electrode explores a geometrical effect and its implications for experimental setups.
In Chapter 6, a numerical and analytical study is developed to examine the effect of hindered diffusion as a particle moves close to an adsorbing surface. The study identifies the conditions under which this hindered diffusion is signiffcant even in a non-confined space. The study shows that the domination of hindered diffusion is strongly dependant on the sizes of both the particle and the target. The study focuses on a variety of target shapes and allows the number of hits/impacts to be estimated in practical 'impact' experiments. Moreover, a drastic effect on the calculation of the mean first passage time is observed for a sub-micron sized target, showing the importance of this effect not only for electrochemistry but also in biological systems.
Chapters 7 and 8 investigate the properties of an adsorbing insulating surface adjacent to an electrode. In Chapter 7, a numerical study of the effect of 'shielding' by the insulating sheath is carried out. The study examines the in uence of this effect on the magnitude of the current in chronoamperometry experiments. Chapter 8 explores the case of reversible adsorption on the insulating surface for voltammetric enhancement by pre-concentration on the sheath surface. The results identify the conditions under which enhancement of the voltammetric signal can be observed.
Finally, Chapter 9 looks at geometrical effects on the current response of insulating particles modified with an electroactive surface layer. Numerical models are developed to model the diffusion of charge transfer between electro-active sites on a modified surface of insulating particles. The current-time responses are simulated for particles with the shape of a sphere, a cube/cuboid, and a cylinder on an electrode. The characteristic currenttime responses are calculated for the various shapes. The observations show that the model can be utilised in experiments to determine the coverage or the diffusion coeficient of charge dissipation on modified insulating particles and, in some situations to identify the particle shape.