Low-frequency impedance of ion-exchange membrane with electrically heterogeneous surface

Abstract

Understanding of the effect of membrane/electrode surface heterogeneity on the electrochemical behavior of membrane/electrode systems in conditions of current-induced concentration polarization is an important issue. In this paper, low-frequency electrochemical impedance spectra (EIS) of electrically heterogeneous ion-exchange membranes (IEMs) are studied experimentally and theoretically. A 2D model for calculating these spectra is proposed. Non-stationary ion transport through a heterogeneous membrane and two adjacent diffusion layers is studied. The corresponding mathematical problem is solved numerically and analytically under conditions of zero DC bias of the applied AC signal. It is shown that at sufficiently low frequencies, the impedance spectrum of a heterogeneous IEM is described by the finite-length-Warburg-type impedance. However, in the range of relatively high frequencies, a nose-shaped element appears on the complex plane plot. This element reflects an increase in the system resistance due to a higher concentration polarization of the boundary solution caused by nonconductive surface areas. An exact analytical solution describing the impedance is found in the case where the diffusivities of anion and cation are the same. The form of this solution is convenient for the experimental data analysis. A good quantitative agreement between the calculated and experimental impedance spectra for several commercial and specially prepared heterogeneous membranes is established.