Analytical modelling of membrane polarization with explicit parametrization of pore radii and the electrical double layer

Processes related to the membrane-like behaviour of pore throats are generally considered relevant for the induced polarization of granular media. A model to describe the impedance of membrane polarization analytically was suggested previously for a 1-D system, consisting of a sequence of narrow and wide pores of different lengths. In that model, the membrane effect is caused by different mobilities of the ion species, resulting in different ion transference numbers in the two pore types. We extend the model by explicitly including the properties of the electrical double layer and the pore radii into the impedance calculation. Our basic assumption is that in a cylindrical pore system, the ion concentrations in the direction perpendicular and parallel to the pore are independent of each other. We then obtain concentrations averaged over the pore section from known theories of the charge distribution in a cylindrical pore. We also include the effect of the Stern layer in form of a partition coefficient. Our extension enables us to use the analytical expression of the impedance, but with an extended parametrization of the transference numbers. We demonstrate the validity of our approach by comparing the results of our calculations with previously published numerical simulations for a particular model. The usefulness of our method is illustrated with parameter studies that illustrate the possible dependence of relaxation times on pore radii.