An examination of the finite difference numerical approach to the solution of electrochemically-induced diffusive transport at stationary solid cylinder electrodes: Single sweep voltammetry of reversible systems

Abstract

Extensive computational testing of a finite-element Galerkin/B-spline (GBS) numerical model of electrochemical transport recently developed in this laboratory yielded results which agreed with predictions for planar and spherical hydrodynamics but were in disagreement with M.M. Nicholson's explicit finite difference (CEFD) model for the important case of nernstian boundary conditions at stationary solid cylinder electrodes. This disparity prompted a detailed re-examination of both models. We shown in this note that the CEFD approach was imprecise in its formulation of the first-order space derivative and was incorrect in applying established criteria for computational stability. Our re-examination of the same problem using implicit (IFD) and modified explicit finite difference (EFD) methods gave stable solutions which agreed fairly closely with each other; the GBS model agreed with the IFD solution to within ±0.3%. We are thus obliged to conclude that attempts to use the original non-dimensionalized cylindrical CEFD model to calculate concentration profiles, surface fluxes, and current-voltage curves are destined to yield incorrect results except for large radii, fast potential scan rates, or both, in which cases transport occurs essentially by planar diffusion which this model adequately describes.