Three infinite series and integral formulations for the voltammetric responses of reversible electrochemical reactions at a rotating disk electrode. Discrimination using the method of lines, and generalization to the integral equation method with finite kinetics, Ohmic potential drop and (pseudo-) capacitive interfacial behaviour

Abstract

Given the closed-form expression of the mass transfer function pertaining to one-dimensional mass transport conditions in the electrolyte, the voltammetric response of one-step reversible electrochemical (E r ) reactions to a linear potential ramp can be derived first as an infinite series well suited to formal analysis, and then as an integral formulation well suited to numerical calculation. This approach applies in this article to the E r reaction studied on a uniformly accessible Rotating Disk Electrode (RDE). Using three closed-form approximations of the mass transfer function, three infinite series and three integral formulations can be derived for the Faradaic current response versus the electrode potential. Discrimination of the approximating formulations of the voltammetric response can be performed by comparison to benchmark voltammetric data obtained using the numerical method of lines to solve the relevant partial differential equation for diffusion-convection at RDE. Once the best approximating model is selected, based on its voltammetric features, the appropriate mass transfer function can be used together with the inverse Laplace transformation to derive the kernel function involved in the Integral Equation method. Application to the E reaction investigated by cyclic voltammetry on RDE is an illustration example in this article, first disregarding and then taking into account Ohmic drop and double-layer charging effects with capacitive or pseudo-capacitive (constant phase element) interfacial behaviour. • Infinite series formulations of the voltammetric response for the E r reaction on RDE . • Integral formulations of the voltammetric response for the E r reaction on RDE . • Derivation of a new kernel function for the dissolved species reacting on RDE. • Application to the Integral Equation method for cyclic voltammetry on RDE. • Voltammetric modelling of Ohmic drop and double-layer (capacitance/CPE) effects.