Osmotic Properties of Polyelectrolyte Membranes: Positive and Negative Osmosis

Abstract

A method is proposed and tested experimentally to predict the concentration dependence of the osmotic properties of a given cation exchange membrane with an inhomogeneous structure which separates two aqueous solutions of a single electrolyte. These properties are characterized by the reflection coefficient σ s. The prediction of the concentration dependence of σ s is based on a modified version of the "model of the membrane with narrow pores." In its original form this model assumes a homogeneous structure of the membrane matrix. The influence of structural inhomogeneities is taken into account by using an effective fixed ion concentration X eff instead of the analytically determined fixed ion concentration X a ( X eff < X a ) in the calculation of σ s. The value of X eff is obtained from independent experiments. From measurements of tracer flow across the membranes used in this study it is known that the value of the ratio of the effective diffusion coefficients (Ď -/Ď +) in the membrane phase has approximately the same value as the ratio of the diffusion coefficients ( D -/ D +)∞ in free solution at infinite dilution. Using values of X eff and ( D -/ D +)∞, the theoretically predicted concentration dependence of σ s for aqueous solutions of three 2, -1 valent electrolytes is in satisfactory agreement with the experimentally determined concentration dependence. Positive and negative osmosis is predicted and found experimentally.