STUDIES OF MEMBRANE PHENOMENA .7. EFFECTIVE CHARGE DENSITIES OF MEMBRANE

Measurements were made of the emf which arose between aqueous solutions of KCl of different concentrations (C1 and C2) separated by a layer of aqueous solution of potassium polystyrenesulfonate (KPSS) as a function of C1 at various equivalent concentrations, X, of KPSS, keeping the ratio of C2 to C1 at several given values. The data obtained were analyzed in terms of the theory developed in part IV of this series after it had been modified to suit the present experimental condition that the stagnant layers of liquid outside the polyelectrolyte region were fairly thick, and a value of about 0.4 was obtained for the parameter φ′. Here φ′ characterizes the hydrodynamically effective charge density of KPSS in aqueous KCl. A simple equation was derived for use in the determination of φ from the measurement of the Donnan equilibrium potential, where φ is the parameter which characterizes the thermodynamieally effective charge density of a polyion in salt solution. Necessary data for the Donnan potential were obtained over a wide range of C and for several values of X, where C is the concentration of KCl in the phase containing no KPSS. It was found that the resulting values of φ varied with log (C/X) following a sigmoid-shaped curve, approaching about 0.4 and 0.2, respectively, in the upper and lower limits of C/X. Thus the ratio of φ to φ′ tends to approach unity at high concentrations of KCl. Finally, an approximate method was proposed for the calculation of membrane potentials under conditions where φ depends on electrolyte concentration, and it was demonstrated that a better fit to observed data is obtained by this method than by our previous treatment which did not take the concentration dependence of φ into account.