Numerical simulation of microelectrodes

Abstract

This thesis considers the numerical simulation of chronoamperometric measurements at disc shaped microelectrodes (microdiscs). Due to the inherent symmetry of microdiscs, a two-dimensional simulation can be used to predict their Faradaic response. Various two-dimensional simulation techniques are reviewed and the final choice of the Alternating Direction Implicit (ADI) method is discussed.

The ADI simulation is adapted to be better able to simulate long times by the use of expanding finite difference grids in space and time. The simulation domain is extended to cover concentrations round the edge of the insulating sheath allowing the effect of sheath thickness to be modelled. The high stability and accuracy of the new method is demonstrated.

The simulation is modified to model Scanning Electrochemical Microscopy (SECM) experiments by considering the proximity of various types of substrate. It is found that the spatial and topographical sensitivity of the SECM not only depends upon tip - substrate distance but also on the tip geometry.

The algorithm is used to model cyclic voltammetry. One and two-dimensional simulations are developed and the results are analysed successfully using diagnostic tests. The two-dimensional simulation is then adapted to model a combined SECM/EQCM (Electrochemical Quartz Crystal Microbalance) instrument. A novel mathematical treatment, called 'Double Implicit ADI' , is developed to predict both current and mass measurements from the instrument. The simulation correctly predicts the shape and magnitude of the experimental cyclic voltammograms. Mass measurement predictions are within an order of magnitude to those obtained experimentally.

Finally, coupled homogeneous kinetics are added to the simulation. Two-dimensional simulations for E_rC_i and E_rC_i' reactions are developed and the results are discussed with reference to those found in the literature. This algorithm is then adapted to simulate approach curves to immobilised enzymes exhibiting Michaelis Menten kinetics. The Double Implicit ADI method is used again to demonstrate that many of the features and trends of experimental approach curves can be predicted using the simulation.

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