A Method to Relate Steady-State Ionic Currents, Conductances, and Membrane Potential in Ion Exchange Membranes with Unknown Thermodynamic Properties

A method is presented by which the steady-state properties of an homogeneous, permselective membrane at uniform temperature can be predicted without knowledge of its thermodynamic properties other than assuming that they are functions only of local mole fractions in the membrane. By making this assumption, it is shown how the ionic conductances can be calculated at any point in the membrane from two sets of measurements, (a) Rsymm, the steady-state resistance of the membrane measured between identical solutions and (b) V0, the potential difference between nonidentical solutions for zero current. These two parameters are measured at different external solution compositions (e.g. a varying sodium-potassium ratio ranging from zero to infinity). From these measurements it is shown how the flux equations may be integrated without a knowledge of mobilities, activity coefficients, and other interior membrane parameters. The application of the method to fixed site membranes with variable mobilities is described and the theory for this particular case has also been verified experimentally in glass membranes. A possible application to biological membranes is discussed and a comparison is made between the present treatment and previous treatments used to calculate the steady-state properties of cell membranes, notably the theory of Teorell, Meyer, and Sievers and the constant field theory