LSV modelling of electrochemical systems through numerical inversion of Laplace transforms. I - The GS-LSV algorithm

Semi-analytical modelling of electrochemical reactions in the time domain generally requires prior knowledge of the inverse Laplace transform of the so-called mass-transfer function, M-X(s) (with s being the variable of Laplace transform), which depends on the electrode geometry, the mass-transport process, the boundary conditions and the possible presence of coupled (homogeneous) chemical reactions. Oldham and co-workers have developed efficient convolution algorithms. Unfortunately, the semi-analytical approach becomes ineffective when the inverse transform of M-X(s) cannot be derived analytically. Hence, a new approach of the dynamics of electrochemical systems is proposed in this work. The method is based on numerical inversion of Laplace transforms, and, more especially, on the Gaver-Stehfest inversion formula. The simple algorithm, proposed in this work, makes it possible to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by potential-controlled techniques, and more especially linear scan and cyclic voltammetry (LSV and CV). (c) 2007 Elsevier B.V. All rights reserved.