Digital Simulation of Mass Transport to Ultramicroelectrodes

Abstract

The dominant mass transport process at ultramicroelectrodes is diffusion. Different diffusion equations (parabolic differential equations) must be used, depending on the geometry of the electrodes.

As analytical solutions are only available for simple charge-transfer processes, numerical methods - especially finite difference techniques - are favoured for simulating all kinds of electrochemical diffusion problems. Within the different approximations, the Crank- Nicolson (CN) algorithm and the Alternating Direction Implicit (ADD technique are at the moment the methods of choice. For one-dimensional transport phenomena, as is the case with spherical or cylindrical electrodes, the CN algorithm must be applied; for two-dimensional processes, as is the case with band or disc electrodes, the ADI-algorithm is successful. The principles of these difference schemes and their application to all types of electrode reactions, including homogeneous processes, are discussed.