Automatic solution of integral equations describing electrochemical transients under conditions of internal spherical diffusion

Diffusion of reactants inside spherical spatial domains, in the absence of homogeneous reactions, is characteristic of some electrochemical systems, such as amalgam mercury drop electrodes. Simulation of transient experiments in such systems can be performed by the classical integral equation method [see, for example, R.S. Nicholson, I. Shain, Anal. Chem. 36 (1964) 706]. This requires an accurate computation of a specific integral transformation kernel function and its moment integrals. Based on formerly known series expansions, highly accurate (16 digits) and cost-optimised procedures serving for this purpose have been designed in this work. The procedures have been combined with the adaptive Huber method developed by the present author. The resulting simulation technique has been tested on simple examples of relevant integral equations, including models of potential step chronoamperometry and cyclic voltammetry. The method is shown to provide automatic solutions, with a user-selected target accuracy. Errors corresponding to the range from about 10-2 of the maximum solution value, down to about 10-7 or even smaller, can be easily obtained at a modest computational cost.