Development of a Randles-Ševčík-like equation to predict the peak current of cyclic voltammetry for solid metal hexacyanoferrates

A mathematical model, derived from Fick’s second law for planar and spherical coordinates, is presented and solved to obtain novel equations that satisfactorily predict the charge transfer and peak current observed in cyclic voltammetry of solid hexacyanoferrates. For a planar geometry, two cases are considered. The first one takes into account the effect of the evolution of the activities of the oxidized and reduced phases of the hexacyanoferrates on the peak currents, while in the second one, the activities of both phases were considered as a constant. In the first case, an analysis of charges involved in the reaction is required to obtain the molar fractions of the oxidized and reduced forms of the hexacyanoferrates. In this case, the solution of the model is obtained numerically using the lines method. In the second case, the model is analytically solved obtaining a Randles-Sevcik-like equation. When spherical coordinates are considered, the activities of the solid phase are assumed to be constant and the model is analytically solved. In this way, other novel equations allowing the calculus of the electroactive electrode area and the diffusion coefficient of the alkali ions are presented. The advantages of an analytical expression for the peak current as a function of the square root of the potential scan rate, instead of a numerical solution, are analyzed. The validity of each model is proven by its comparison with experimental measurements for peak currents in a carbon paste electrode containing nickel hexacyanoferrate immersed in a 0.5M KNO3 solution.