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The electrocatalytic activity for oxygen reduction reaction （ORR） at neutral pH of citrate-capped silver nanoparticles （diameter = 18 nm） supported on glassy carbon （GC） is investigated voltammetrically. Novelly, the modification of the substrate by nanoparticles sticking to form a random nanoparticle array and the voltammetric experiments are carried out simultaneously by immersion of the GC electrode in an air-saturated 0.1 M NaC104 solution （pH = 5.8） containing chemically-synthesized nanoparticles. The experimental voltammograms of the resulting nanoparticle array are simulated with homemade programs according to the two-proton, two-electron reduction of oxygen to hydrogen peroxide where the first electron transfer is rate determining. In the case of silver electrodes, the hydrogen peroxide generated is partially further reduced to water via heterogeneous decomposition. Comparison of the results obtained on a silver macroelectrode and silver nanoparticles indicates that, for the silver nanoparticles and particle coverages （0.035%-0.457%） employed in this study, the ORR electrode kinetics is slower and the production of hydrogen peroxide larger on the glassy carbon-supported nanoparticles than on bulk silver.

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).

Numerical simulation is used to characterise double potential step chronoamperometry at a microband electrode for a simple redox process A + e- goes to B, under conditions of full support such that diffusion is the only active form of mass transport. The method is shown to be highly sensitive for the measurement of the diffusion coefficient of both A and B, and is applied to the one electron reduction of decamethylferrocene (DMFc), DMFc - e- goes to DMFc+, in the room temperature ionic liquid 1-propyl-3-methylimidazolium bistrifluoromethylsulfonylimide. Theory and experiment are seen to be in excellent agreement and the following values of the diffusion coefficients were measured at 298 K: D_(DMFc) = 2.50 x 10^(-7) cm^(2) s^(-1) and D_(DMFc+) = 9.50 x 10^(-8) cm^(2) s^(-1).