An integral equation approach to the study of the steady state current at surface microelectrodes

Abstract

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 arbitrarily shaped planar electrode, including both surface and bulk reactions. In this work, results for the electrode current are presented for typical values of the dimensionless surface and bulk reaction constants for (1) the common case of an isolated disc-shaped microelectrode imbedded in an insulating plane substrate and (2) two identical disc-shaped microelectrodes at arbitrary separations in an insulating plane. The numerical results for the isolated disc problem are in excellent agreement with both the recent asymptotic approximations of Phillips and a new four-term expansion derived herein for conditions which are surface-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 rings or arrays of circular microelectrodes, for which characterization of the mass transport process for the two-disc configuration is a first step.