A new theory, and automatic computation of reversible cyclic voltammograms at a microband electrode

• New rigorous theory of cyclic voltammetry at microband electrodes
• Applicable to reversible redox couples with equal diffusion coefficients
• Two adaptive calculation routes: by quadratures or by 1D integral equations
• Included a highly accurate procedure for computing integral equation kernel
• Suitable for validation of modelling methods and experimental data analysis

By generalising the recent theory of chronoamperometry [L. K. Bieniasz, Electrochim. Acta 178 (2015) 25], a new, semi-analytical description of reversible cyclic voltammetry at a microband electrode is obtained, assuming equal diffusion coefficients of the species involved in a redox reaction. In contrast to the formerly proposed model [K. Aoki, K. Tokuda, J. Electroanal. Chem. 237 (1987) 163], the new theory does not involve any heuristic approximations. It is based on the formalism of Mathieu equations and functions, and provides rigorous and complete expressions for the voltammetric current, in the form of either a convolution integral or an integral equation. The voltammograms are calculated automatically with a prescribed accuracy, by using either the adaptive integrator dqags from the QUADPACK package, or the adaptive Huber method for integral equations. The two methods are compared, and dqags is found to be more efficient. A highly accurate (relative error about 10− 16) procedure for calculating the kernel function of the integral equation, and its moment integrals, is also described.