Linear and non-linear analysis using the Oldham–Zoski steady-state equation for determining heterogeneous electrode kinetics at microdisk electrodes and digital simulation of the microdisk geometry with the fast quasi-explicit finite difference method

Abstract

Abstract A procedure which utilizes a linearized version of the Oldham–Zoski current-potential equation has been developed for the evaluation of electrode kinetic parameters from near-steady state voltammograms obtained at microdisk electrodes. The inherent advantage of the method is its mathematical simplicity relative to the other procedures already available in the literature. The procedure is applied to synthetic data obtained under near-steady state conditions from the fast quasi-explicit finite difference simulation of quasi-reversible electron transfer at a microdisk electrode. A procedure using non-linear optimization based on the Marquardt algorithm is also applied to the simulated data. Near-steady state voltammograms showing the effect of a potential dependent charge transfer coefficient are presented and analyzed. The robustness of the analysis is tested with voltammograms containing a random noise component and the near-steady state terms inherently present in experimental data. Application of the Oldham–Zoski equation to the simulated voltammograms enables the fidelity of both methods to be established over a wide range of heterogeneous kinetic conditions.