Catalytic ErevCrev′ mechanism at cylindrical wire electrodes: Theory of controlled-potential transients assuming DO = DR, and highly accurate computation of chronoamperograms and cyclic voltammograms

Abstract

There have been surprisingly few theoretical studies devoted to large-signal controlled-potential experiments for the catalytic ErevCrev′ mechanism (containing a reversible charge transfer and a reversible homogeneous reaction) at cylindrical wire electrodes, and their results were partially doubtful. To fill this gap, a general theory is developed, applicable to any such experiments, under the assumption of equal diffusion coefficients of the redox species (DO = DR) and a pseudo-first order homogeneous reaction. Based on the theory, numerical procedures are elaborated and implemented in C++, for computing special functions related to chronoamperometric and cyclic voltammetric currents. The procedures are fairly fast and highly accurate. In the case of chronoamperometry they provide results with moduli of relative errors at the level of 10−18 or smaller. Similar accuracy is achieved for cyclic voltammograms, as long as the current is not too close to zero, or equal zero. In the latter cases the errors may increase considerably, but relative error moduli not bigger than about 10−13 were observed. The procedures can be useful for validating digital simulation methods for electrochemistry, and for the analysis of experimental data. They are freely available.