Highly accurate computation of chronopotentiograms for a charge transfer followed by homogeneous dimerization or disproportionation reactions

A theoretical model of constant current chronopotentiometry is considered, for a reversible charge transfer followed by an irreversible homogeneous dimerization or disproportionation reactions at a planar electrode. The model is expressed by a system of two partial differential reaction–diffusion equations, one or both being nonlinear. This system decomposes into two independent initial boundary value problems, which allows one to obtain semi-analytical series solutions of the model. Detailed derivations and analysis of the series are presented. Highly accurate numerical reference solutions are also obtained. Hybrid algorithms are devised for computing electrode potential-time responses. The algorithms combine the series solution for small time, with asymptotic approximants for large time, and fitted polynomials for intermediate time. The algorithms are efficient and highly accurate: the relative error modulus does not exceed ca. $10^{-19}-10^{-18}$$10^{-19}-10^{-18}$, except for the small neighbourhoods of the transition time, and of the time where the potential response passes through zero. A set of C++ routines for these calculations is made available.