Microdisc Electrodes The Model

A microdisc electrode is a micron-scale flat conducting disc of radius r. that is embedded in an insulating surface, with the disc surface flush with that of the insulator. It is assumed that electron transfer takes place only on the surface of the disc and that the supporting smlace is completely electroinactive under the conditions of the experiment. These electrodes are widely employed in electrochemical measurements since they offer the advantages of microelectrodes (reduced ohmic drop and capacitive effects, miniaturisation of electrochemical devices) and are easy to fabricate and clean for surface regeneration. In Chapter 2, we considered a disc-shaped electrode of size on the order of 1 mm. In that case we could approximate the system as one-dimensional because the electrode was large in comparison to the thickness of the diffusion layer, such that the current was essentially uniform across the entire electrode surface. Due to the small size of the microdisc, this approximation is no longer valid so we must work in terms of a three-dimensional coordinate system. While the microdisc can 

In this system, an axis passes through the centre of the disc perpendicular to the plane of its surface, r is the radial distance from the axis, z is the perpendicular distance from the surface and j is the angle around the axis. The origin is at the centre of the disc. 

While it is true that the current at the electrode surface will vary with radial coordinate, r, it can be seen that there will be no variation with angle cf), 

Fick s second law predicts how diffusion causes the concentration to change with time. In general, this may be stated as 

Transforming this equation into cylindrical polar (r, z, 4 ) coordinates gives 

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