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In this thesis, mathematical modelling is used to theoretically investigate the electrochemical behaviour of surfaces which can be broadly classified as being ‘electrochemically heterogeneous’. Simulated voltammetry is used in the exploration of a number of specific systems as listed below. The cyclic voltammetry of electrodes composed of two different electroactive materials that differ in terms of their electrochemical rate constants towards any given redox couple. The effect of the distribution of the two materials was investigated and the occurrence of split peak cyclic voltammetry where two peaks are observed in the forward sweep, was studied. The technique was specifically applied to the modelling of highly-ordered pyrolytic graphite (HOPG). The steady-state voltammetry of a conducting spherical particle resting on an insulating supporting surface. An algebraic expression that completely describes the voltammetric waveform in the limit of irreversible kinetics was developed. The cyclic voltammetry of the EC′ (catalytic) mechanism at a regularly distributed array of hemispherical particles on an insulating supporting surface. Particular attention was paid to the ‘split-wave’ phenomenon, where two peaks are observed in the forward scan of a cyclic voltammogram and the conditions under which these peaks are resolvable were elucidated. The linear sweep voltammetry of micro- and nano-particle modified electrodes and other electrodes of partially covered and non-planar geometry. It was demonstrated that the apparent electrochemical rate constant of the reaction and thus the peak position of the voltammetry is dependent only on the relative electroactive surface area of the particles on the surface and not upon their shape or distribution. This has wide reaching implications as it can be used to explain some instances of a purported nano-catalytic effect without appeal to altered properties at the nanoscale. The linear sweep voltammetry of the interior of a partially electroactive cylindrical pore. Four limiting cases were observed and fully characterised. The linear sweep voltammetry of porous surfaces. It was established that if the pores are less than a certain threshold depth, then a porous surface will also display an apparent catalytic effect that is dependent on the relative electroactive surface area (including the area in the interior of the pores).