New approach of electrochemical systems dynamics in the time-domain under small-signal conditions. I. A family of algorithms based on numerical inversion of Laplace transforms

Dynamic modelling of electrochemical systems in the time-domain generally requires the inversion of Laplace transforms. Unfortunately, many practical systems exist for which the inverse transforms cannot be derived analytically. A new approach of the dynamics of electrochemical systems, investigated under small-signal conditions, is proposed in this work. The method is based on numerical inversion of Laplace transforms and, more especially, on the Gaver-Stehfest (GS) inversion formula. General and explicit formulations of the time-domain responses of stable systems to a small potential step/ramp and to a small current step/pulse are derived in part I of this work from linear combinations of values of the system immittance that is the admittance for potential-controlled techniques and the impedance for current-controlled techniques. The GS approach of system dynamics is illustrated by taking the example of finite-space diffusion of electroactive species. Application to corrosion systems, polymer exchange membrane fuel cells and thin-film ion-insertion electrodes will be presented in the next parts of this work. (C) 2008 Elsevier B.V. All rights reserved.