Efficient and highly accurate calculation of chronoamperometric currents for the [formula omitted] and [formula omitted] reaction mechanisms at planar, spherical, and cylindrical electrodes

Abstract

The theory is considered, of single potential step chronoamperometry for the CrevErev and ErevCrev reaction mechanisms (involving reversible electrochemical and reversible homogeneous chemical reactions) at planar, spherical, and cylindrical electrodes. Diffusional transport with identical diffusion coefficients is assumed. It is found that for a given electrode type the currents for both reaction mechanisms are described by the same mathematical function, dependent on a mechanism-specific parameter γ. Formulae for Laplace transforms of such functions are determined for the three electrode types studied. Numerical algorithms are described, enabling a reliable, efficient, and highly accurate calculation of these functions. The algorithm for the spherical electrode case makes use of a novel rigorous integral formula. The algorithm for the cylindrical electrode case is a generalization and improvement of the algorithm for the ErevCirr mechanism, formerly published by the author and co-workers. Relative errors of the computed functions do not exceed about 10−15 in absolute value, for function arguments from almost the entire range 10−4932,104932 of extended precision variables available in contemporary computers. Computational time (per single function value) varies between 10−6 s and 10−2 s. A C++ code implementing the algorithms is provided.