A new theory and automatic computation of reversible cyclic voltammograms at an inlaid disk electrode

Abstract

By generalising the recent theory of chronoamperometry [L. K. Bieniasz, Electrochim. Acta 199 (2016) 1], a new, semi-analytical description of reversible cyclic voltammetry at an inlaid disk electrode is obtained, assuming equal diffusion coefficients of the electroactive species. In contrast to some former modelling studies, the new theory does not involve simplified or low-accurate approximations to the chronoamperometric current or integral transformation kernel, but it is mathematically rigorous. An explicit expression for the voltammetric current function is derived, in the form of an inverse Laplace transform of an infinite series involving spheroidal wave functions. An equivalent formula involving convolution integrals, more suitable for calculations, is also obtained, as well as an integral equation for the current function. The voltammograms are calculated automatically with a prescribed accuracy, by using either the adaptive integrator INTDE based on double exponential formulas, or the adaptive Huber method for integral equations. INTDE is more efficient, allowing one to compute a current function value with a relative error as close to ±10−16 as is possible, in a computing time of ca. 1 ms on a contemporary laptop computer.