On the equivalence between specific adsorption and kinetic equation descriptions of the admittance response in electrolytic cells

Abstract

The response of an electrolytic cell, in the shape of a slab, is analyzed in the framework of the Poisson-Nernst-Planck model in the limit of full dissociation. Two different types of boundary conditions on the electrodes are compared. One type describes the exchange of charges between the volume and the external circuit, in the form originally proposed by Chang and Jaffé and later extended to include specific adsorption, where the surface current density is proportional to the variation of the surface bulk density of ions with respect to the value of equilibrium. The other one describes the surface adsorption, in the limit of Langmuir. We show that in the simple case where the ions dissolved in the insulating liquid are identical in all the aspects, except for the sign of the charge, the two models are equivalent only if the phenomenological parameter entering the boundary condition of the Chang-Jaffé model, κ, is frequency dependent, and related to the adsorption coefficient, k(a), in the form κ = iωτ/(1 + iωτ)k(a), where τ is the desorption time and ω the circular frequency of the applied voltage, as proposed long ago by Macdonald.