AN INTEGRAL-EQUATION METHOD FOR COMPUTING THE TRANSIENT CURRENT AT MICROELECTRODES

The integral equation method (IEM) is an efficient method for computin g the transient current at microelectrodes under conditions of converg ent diffusion. The IEM is a hybrid analytical-numerical method consist ing of three parts: (1) Laplace transforming the diffusion equation an d reducing it to an integral equation, the kernel of which is characte rized by the cell geometry and is independent of the electrode geometr y; (2) numerical solution of the integral equation for the (Laplace tr ansformed) current <(i)over cap(s)>; (3) numerical inversion of <(i)ov er cap(s)> for the current i(t). The method is applicable to a wide ra nge of electrode-cell geometries and electrode reactions. Furthermore, calculations are reduced from the cell interior to the electrode surf ace, and various steps in the calculation can be reduced to a concise explicit form (e.g. kernel calculations). These computational steps ha ve a similar form across all problems which allows the repeated use of the same algorithms. For these reasons, the method shows promise of e xceptionally high efficiency. In this paper, we present an overview of the IEM: a theoretical formulation in physical and dimensionless vari ables for electrode-cell geometries in general; introduction of Neuman n kernels and reduction to an integral equation; explicit Neumann kern els for a range of electrode-cell geometries; and some remarks on nume rical methods for solution of the integral equation and for Laplace in version of the transformed current.