Re-examination of the potential-step chronoamperometry method through numerical inversion of Laplace transforms. I. General formulation and numerical solution

Re-examination of the potential-step chronoamperometry (PSCA) method through numerical inversion of Laplace transforms is proposed in this work. First, a general expression is derived in the Laplace domain for the current transient following the application of a potential step of arbitrary amplitude. The formulation applies to first-order electrochemical–chemical reactions (E, EC and CE reactions) with one-dimensional mass-transport processes of implicated species in the electrolytic solution or the electrode. Next, numerical inversion of the relevant Laplace transform is performed by the Gaver–Stehfest (GS), Fourier–Euler (FE) and ‘fixed’ Talbot (FT) methods. The so-called GS-, FE- and FT-PSCA algorithms in this work make it possible to investigate a wide range of electrode geometry and chemical, electrochemical and one-dimensional mass-transport processes by the PSCA method. Each algorithm provides a full explicit formulation of Faradaic current with respect to time, applied potential and electrochemical parameters (initial concentrations, geometrical parameter(s), standard potential, electrochemical and chemical rate constants and diffusion coefficients), which greatly simplifies the computation of potentiostatic current transients. Some application examples relative to diffusion equations with spherical electrode geometry will be presented in the second part of this work.