Numerical simulation of desorption transients at electrodes on the basis of non-linear adsorption isotherms

Abstract

Numerical simulation of desorption transients on the basis of the non-linear Frumkin isotherm is presented. The differential equations which describe the boundary value problem are solved by using the orthogonal collocation technique with expansion of the simulation space with respect to time. The analysis is focused on the desorption process undergone by a modified electrode when it is transferred to a solution containing only electrolyte and a potential step is applied. Three different cases for the kinetics of the desorption/adsorption step are considered: irreversible, quasi-reversible and reversible. In the irreversible case it is shown that the shape of the chronoamperogram is governed by the difference between the interaction parameters involving adsorbate with adsorbate, and activated complex with adsorbate. There is a critical value of this difference above which a maximum in the i–t curve occurs. In the presence of the maximum a transformation of the chronoamperograms is proposed which allows one to define a unique curve regardless of the value of the kinetic and interaction parameters. In the quasi-reversible case, for certain values of the rate constants, an initial decay of the current before the appearance of the maximum is predicted. Under certain conditions for high coverage (θ≈ 1) two maxima are observed. The effect of the potential on the logarithm of the maximum current and the time at which the maximum occurs is considered. At a more negative potential a limiting linear relationship between both quantities and electrode potential is predicted.