VOLTAMMETRIC MODELING VIA EXTENDED SEMIINTEGRALS

The modelling of many voltammetric experiments can be carried out expe ditiously by making use of semiintegration or its converse, simediffer entiation. The virtue of this approach is that the modelling, be it al gebraic, simulative or numerical, takes place in one dimension only--t hat of time--rather than in the dual dimensions of space and time. How ever, the applicability of pure semiintegration is limited to experime nts in which transport is by planar semiinfinite diffusion, preceded b y a state in which no current flows, and without concurrent homogeneou s reactions. In this article it is demonstrated that all these limitat ions may be overcome by broadening the concept of semiintegration to i nclude other convolutions that reduce to semiintegration in the short- time limit. Appropriate convolutions are derived for spherical and cyl indrical geometries, for thin-layer and Nernst-layer electrodes, for f aradaic processes complicated by homogeneous reactions of the EC, CE a nd ECE varieties, and for voltammetry preceded by a steady state, but this list does not exhaust the possibilities. Although controlled-curr ent experiments are most readily modelled by the extended semiintegral approach, a powerful procedure is described by which numerical one-di mensional modelling is applicable to controlled-potential voltammetry. Three worked examples are presented in detail: constant-current chron opotentiometry at a wire electrode; a Nernst diffusion layer problem i n which the current is shared by a faradaic path and by double-layer c harging; and cyclic voltammetry complicated by a following chemical re action. (C) 1998 Elsevier Science S.A. All rights reserved.