Studies of membrane phenomena. Part 4.—Membrane potential and permeability
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Theoretical equations were derived for the membrane potential Δζ which arises between two electrolyte solutions of different concentrations separated by an ionizable membrane and for the permeability Pm of such a membrane to an electrolyte component, using the assumptions of part 3 for the activities and mobilities of small ions in the membrane phase and taking into account the effect of the liquid layer which remains unstirred on the membrane surface. Methods were developed to evaluate all parameters contained in these equations from the measurements of Δζ and Pm at various fixed γ as functions of C1. Here γ=C2/C1, and C1 and C2 are the concentrations of the solutions placed on both sides of the membrane. Such measurements were made with oxidized collodion membranes and four 1 : 1 electrolytes (NaCl, KCl, LiCl and KIO3). The values obtained for the parameters were in good agreement with those derived previously from the measurements of electric resistances of the same membranes in solutions of the same electrolytes. Thus the thermodynamically effective fraction of counterions dissociated from the polyelectrolytes constituting the membrane can permeate through the membrane as if it were not affected by the electrostatic interactions of the polyions. The plots for Pm against C1 calculated using the parameters evaluated by these methods showed a good agreement with the observed data down to a small value of C1, but the corresponding plots for Δζ against C1 agreed with experiment only at relatively high concentrations. The latter fact suggests that some drawback is contained in the assumptions and approximations incorporated in the development of the present theory.