Studies of membrane phenomena. Part 3.—Electric resistance of membranes

Abstract

A theory was developed for the electric resistance r of a charged membrane immersed in aqueous solutions of a uni-uni-valent electrolyte, on the basis of appropriate assumptions for the activities and mobilities of small ions in the membrane. Thus the “additivity” rule, known for dilute polyelectrolyte solutions containing an added electrolyte, was assumed for the single-ion activities. Adequate linear plots were derived by which to evaluate three basic parameters contained in the theory from experimental data for r and the equivalent conductivity of the external solution. Such data were obtained with oxidized collodion membranes of different charge densities in solutions of KCl, LiCl and KIO₃ at 30°C, and the values of the three parameters for each pair of membrane and electrolyte were determined. From these results it was found that the thermodynamically “effective” concentration and the hydrodynamically “effective” one of the counterions dissociated from the polyelectrolyte constituting the membrane were nearly independent of electrolyte species for a fixed membrane and, moreover, their ratio was almost equal to unity for membranes of different charge densities. Comparison of the calculated and observed values of r showed that the present theory applies except at very low concentrations of the external electrolyte solution.