The steady-state current for a ring-like microelectrode under non-diffusion-controlled conditions

The steady-state current for a 'ring-like' microelectrode is considered, when the electrode reaction rate is not sufficiently large that the diffusion of the electroactive species is the rate-limiting transport process. This régime is particularly relevant for micro-ring electrodes (which the present formulation includes), because the criterion for diffusion-limited transport is much more stringent for a thin micro-ring electrode than for a micro-disc of comparable size. First an approximate solution is presented for the steady-state current for a ring-like microelectrode, valid for any value of the electrode reaction rate provided the ring is thin. For the special case of a thin, plane-mounted micro-ring electrode, numerical results are given and the surface current density distribution is shown. In this case the total current is found to be in close agreement with a semi-empirical approximation due to A. Szabo (J. Phys. Chem., 91 (1987) 3108). A micro-ring electrode with an arbitrary ratio of inner to outer radius is then considered, and the steady-state current is calculated numerically as a function of the electrode reaction rate for a range of geometries, extending from a complete disc to a thin ring.