Complex Conductivity in Saturated Porous Media: Role of Membrane Polarization

We quantitatively explain the origin of complex conductivity of a porous medium made of non-conductive grains, saturated with a binary electrolyte. The medium is assumed to possess a heterogeneous immobile charge density, and to interact with ions in the electrolyte only through electrostatic interactions. We establish a theoretical framework relating spectral complex conductivity in these systems to the geometry and intrinsic properties of the materials, and validate the results with experiments on model systems. We conclude that complex conductivity arises due to concentration (membrane) polarization, which is driven by spatial inhomogeneity in the ionic transferences, i. e., the proportion of current carried by the cation vs. the anion. We obtain quantitative agreement between experiment and theory, not just for characteristic frequencies and amplitudes, but for the entire spectral shape of the phase angle between electric field and current density. The amplitude, scaling of the characteristic frequency with feature size, and the spectral shape of the phase angle differ markedly from complex conductivity associated with dispersed electronic conductors.