Theory of chronoamperometry for the catalytic EC′ mechanism at a band electrode: Highly accurate and efficient computation of the Faradaic currents

Abstract

Rigorous theoretical expressions are derived, for chronoamperometric limiting currents in the case of the catalytic EC′ mechanism at an infinite inlaid band electrode. Transient and steady state currents (per unit length of the electrode) are considered. Identical diffusion coefficients of the members of the redox pair are assumed. By extending the former theory for uncomplicated charge transfers [L. K. Bieniasz, Electrochim. Acta 178 (2015) 25, J. Electroanal. Chem. 760 (2016) 71], the currents are expressed in terms of series expansions involving Mathieu functions. With the help of the formalism obtained, reference current values having at least 20 accurate significant digits are computed. The reference values are further used to develop numerical procedures (written in C++) for calculating the currents efficiently (a single value requiring about 1–103 microseconds on a modern laptop) and with a high accuracy (relative error moduli not exceeding about 10−15). Apart from their utility for the analysis of experimental data, the procedures should be particularly suitable for validating algorithms and software for electroanalytical simulations and modelling.