2D modelling of impedance of heterogeneous ion-exchange membranes

Abstract

A two-dimensional mathematical model of the impedance of electromembrane system, composed of an ion-exchange membrane flanked by two diffusion boundary layers, was developed in order to identify differences of the electrochemical behavior of membranes with homogeneous and heterogeneous surface. Due to the absence of direct electric current the chemical reaction on the membrane surface as well as the other coupled effects of concentration polarization were neglected. Heterogeneous surface of the membrane for the sake of simplicity is modeled by a periodic sequence of alternating 1D conducting and insulating segments. For the first time it was shown theoretically that electrical heterogeneity of the membrane surface is a source of deviation of impedance spectra from the linear Warburg-type dependence. This phenomenon occurs on definite time scales corresponding to high-frequency range of finite length Warburg spectrum, depending on the sizes of the conductive and insulating parts of the membrane surface. The proposed model is sensitive to the variation of the control parameter $h$, characterizing the membrane surface conductivity.