Beyond the Laviron Method: A New Mathematical Treatment for Analyzing the Faradaic Current in Reversible, Quasi-Reversible, and Irreversible Cyclic Voltammetry of Adsorbed Redox Species

A new algorithm that describes the faradaic current for elementary redox reactions in the cyclic voltammetric responses of persistently adsorbed species on metal electrodes at any scan rate is presented. This work does not assume electrochemical reversibility and instead demonstrates a set of equations that encapsulate how the forward and back charge-transfer rate constants influence the data as a function of the experimental time scale. The method presented here is compared against other approaches that rely on either finite-difference calculations or that require numerical approximation of improper integrals (i.e., +/- infinity as a bound). The method here demonstrates that the current-potential data can be described by incomplete gamma functions, whose two arguments capture the relevant kinetic variables. Following the notation for the Butler-Volmer model of charge transfer, exact solutions are presented for the cases of the charge-transfer coefficient, alpha, equal to 1 or 0. A related algorithm based on these results affords calculation of current-potential data for 0 < alpha < 1, allowing comprehensive analysis (i.e., point by point) of voltammetric data throughout the reversible, quasi-reversible, and irreversible regimes. Accordingly, this work represents an alternative to the method of Laviron, i.e., analyzing just the peak splitting values, for experimentalists to understand and interpret their voltammetric data in totality.