AN INTEGRAL-EQUATION APPROACH TO THE STUDY OF THE STEADY-STATE CURRENT AT SURFACE MICROELECTRODES

An efficient and accurate numerical procedure using integral equation methods is described for solving steady state microelectrode transport problems. The approach is applicable to the general case of an arbitr arily shaped planar electrode, including both surface and bulk reactio ns. In this work, results for the electrode current are presented for typical values of the dimensionless surface and bulk reaction constant s for (1) the common case of an isolated disc-shaped microelectrode im bedded in an insulating plane substrate and (2) two identical disc-sha ped microelectrodes at arbitrary separations in an insulating plane. T he numerical results for the isolated disc problem are in excellent ag reement with both the recent asymptotic approximations of Phillips and a new four-term expansion derived herein for conditions which are sur face-reaction limited. For the more typical diffusion-limited reaction conditions studied by Phillips, a numerically based correction to the asymptotic series is proposed, thereby extending the range of utility of the analytical approximation. Overall, the numerical method allows straightforward investigation of mixed boundary value problems and is applicable to other surface transport problems, e.g. microelectrode r ings or arrays of circular microelectrodes, for which characterization of the mass transport process for the two-disc configuration is a fir st step.