An Attempt to Formulate a Quantitative Theory of Membrane Permeability

The fundamental theories of electrolyte diffusion (Nernst, 1 Planck 2 ) take into account the electrostatic forces that coöperate with the “osmotic” forces to cause the migration of ions. In these theories, however, no assumption has to be made as to the origin of the charge on the particles in the solution. Accordingly, we may expect that their predictions regarding ionic diffusion may be extended to include other cases of diffusion, where other charged elements are present, regardless of the constitution, shape, etc., of these elements.

Diffusion of an electrolyte through a membrane may be such a case. The membrane may be regarded as having a charge due either to “adsorption,” “dissociation,” or “polar character,” etc., but it is not necessary to make any further assumptions as to its nature. The effect of the membrane is regarded as that of an “added ion.”

In order to demonstrate the usefulness of treating permeability problems as cases of simple diffusion we shall—for the sake of clarity, in a highly simplified way—try to show that the so-called “concentration effect” when NaCl diffuses across a “negative” membrane is theoretically predictable:

From one side of the membrane, NaCl, having the activity a ₁, diffuses to the other side where the activity is a ₂. The membrane may be represented as consisting of negative, immobile ions of the activity X, which is assumed to be constant throughout the membrane. In the steady state the ionic activities in the membrane surface layers may be Na₁, Cl₁ and Na₂, Cl₂. For electroneutrality it may be assumed that Na₁ = (Cl₁ + X) and Na₂ = (Cl₂ + X). Although the concentration of Na in the membrane differs from that of Cl the flux will be equal because the forces (“osmotic” plus electrical) operating on them are not equal.