Efficient and highly accurate calculation of chronoamperometric currents for the CrevErev and ErevCrev reaction mechanisms at planar, spherical, and cylindrical electrodes

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. 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 gamma. 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(-1)5 in absolute value, for function arguments from almost the entire range [10(-4932), 10(4932)] 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.

Automated summary

This paper investigates the single potential step chronoamperometry for the CrevErev and ErevCrev reaction mechanisms at planar, spherical, and cylindrical electrodes involving reversible electrochemical and reversible homogeneous chemical reactions. The study finds that for a given electrode type, the currents for both reaction mechanisms can be described by the same mathematical function dependent on a mechanism-specific parameter gamma. Formulas for Laplace transforms of these functions are determined for the three electrode types studied. Numerical algorithms are described to calculate these functions reliably, efficiently, and accurately. The algorithms provide a maximum relative error of about 10(-15) and take computational time ranging from 10(-6) s to 10(-2) s per single function value. A C++ code implementing these algorithms is provided.