Effects of unstirred layers or transport number discontinuities on the transient and steady-state current-voltage relationships of membranes.

The effects of current-induced electrolyte accumulation and depletion on the electrical properties of a two-layered membrane system have been examined. The membrane consisted of a charged, ion permselective layer and an uncharged, non-selective layer. The model was designed to reveal the properties of membranes possessing long pores with ionic charges at one end or of ion-selective membranes bounded by highly unstirred aqueous layers. Electrolyte concentration profiles in the inert layer and their time-dependent changes were obtained from solutions of the diffusion equation under the condition of constant current. The profiles were then used to calculate the voltage developed across the membrane at various times after the current is switched on. The theoretical results are presented in the form of i-V curves with reduced coordinates that can be used to obtain time-current-voltage relationships for membranes of the type considered having any thickness of the non-selective layer and bathed in any concentration of any 1:1 electrolyte. Experimental results on a model composite membrane were in good agreement with calculations that assume that ion transport occurs only under the influence of electrical potential and concentration gradients, suggesting that in such systems, the combined effects of convection, osmosis, electro-osmosis, and concentration-dependence of diffusion coefficients, activity coefficients, and transference numbers are small. Voltage fluctuations in the form of periodic spikes were observed experimentally at the limiting current density (the current density at which the electrolyte concentration at one surface of the selective layer goes to 0). These phenomena were not seen when the current was in the direction leading to accumulation of electrolyte in the non-selective (unstirred) layer. Such composite membranes can exhibit S-shaped and N-shaped i-V curves under ramp-voltage and ramp-current clamps, respectively.