Low-frequency impedance of an ion-exchange membrane system

A 1D mathematical description of low-frequency impedance is presented for a system including an ion-exchange membrane, two adjacent diffusion boundary layers (DBLs) and two layers of bulk solution. Electrolyte concentration may vary within the DBLs under the action of a direct current (DC) and a small sinusoidal current perturbation imposed on the DC. The description is based on the Nernst–Planck equations and the local electroneutrality assumption, which are believed correct at current densities lower than the limiting one. The results of calculations are compared with experimental data obtained for an AMX anion-exchange membrane installed in a cell with a well specified forced laminar flow of a 0.02 M NaCl solution. For each applied DC density, two fitting parameters, the DBL thickness and the ohmic resistance of the membrane and two bulk solution layers are found. It is shown that the experimental spectra are well described by the model. The hyperbolic tangent element, tanh α/α, acts an important role in the impedance behavior of membrane system, similar as in electrode systems with an open diffusion layer of a finite thickness, or O element, which provides a “finite thickness porous Warburg” impedance. The relevant parameter found by fitting the experimental data is the thickness of depleted DBL, which increases slightly with increasing DC density, but remains close to Nernst's DBL thickness calculated by using the 2D convective-diffusion model. It is found that the main contributions to the impedance are the Donnan contribution, which is due to the variation of interfacial potential drops caused by boundary concentration variations, and the “conductivity” contribution becoming important at high currents. The last contribution, first considered in this paper, is due to the variation of the solution conductivity resulting from the concentration variation caused by an increment of alternative current (AC).