Electric circuits modelling the low-frequency impedance of ideal ion-exchange membrane systems

A network model to represent the low-frequency electrochemical impedance of a diffusion boundary layer (DBL) in an ideal ion-exchange membrane system with simultaneous direct electric current has been proposed. This network model with elements distributed in space is obtained using the principles of the network simulation method in a system constituted by a cation-exchange membrane and two boundary layers adjacent to the membrane, from the Nernst–Planck flux equations, the electrical neutrality condition in the DBL and the Donnan equilibrium relations at the membrane|solution interface. The proposed network model is simulated by using the PSpice electrical network simulation program, not only in systems with symmetric 1:1 electrolytes but also in those with asymmetric 2:1 electrolytes. The results of the simulation for the electrochemical impedance are compared with those obtained from a simplified equivalent electric circuit with lumped parameters constituted by the series association of the ohmic resistance of the system and the well-known Warburg-type impedance. It has been found that for the highest values of the direct current, the low-frequency impedance is constituted by a straight line at relatively high frequencies and a semicircle at vanishing frequencies. The slope of the straight line is higher than 45°, the radius of the semicircle is higher than that of the Warburg impedance at low frequencies, but the characteristic frequency of this arc is not a function of the direct current.