Diffusion of Radiotracer Ions in a Cation‐Exchange Membrane

Abstract

The tracer diffusion coefficients of Na + , Cs+ , Sr2 + , and Br− in a homogeneous cation‐exchange membrane have been measured in the homoionic counterion states over the external solution concentration range 0.005–1.0 equiv/liter and in the and heteroionic counterion states over the whole equivalent fraction range at 0.02 and 0.10 equiv/liter total external concentration. Steady‐ and transient‐state permeation and diffusion techniques have been used. The results show that the resin material is essentially uniform apart from a small volume of material of low crosslinking which forms a labyrinthine network interpenetrating the main structure. This labyrinthine network is important mainly in the diffusion of Br− at low external concentrations. In concentrations above about 0.02 equiv/liter the diffusion coefficient DBr of Br− does not vary greatly either with concentration or with counterion type. DBr is greatest in the Cs+ state and least in the Na+ state. These observations and the way in which DBr varies with the equivalent fraction of the counterions in the heteroionic states can be explained by considering the expected frictional interactions between Br− coions and the counterions and by the influence of the local variations in electric potential on the movements of the ions.The diffusion coefficients of all the counterions increase as the external concentration is increased. When these diffusion coefficients are compared with the diffusion coefficients in aqueous solutions Na+ is seen to be the least retarded in the membrane and Sr2+ the most retarded. The observed behavior can be understood qualitatively in terms of the relative roles of “chain” and “volume” diffusion as suggested by Jakubovic et al. (20). A quantitative theory of these mechanisms has not been developed, but the relevance of theoretical treatments of the effects of electric potentials on counterion mobilities in polyelectrolyte and micellar solutions is pointed out. When the membrane is in a heteroionic state the diffusion coefficients of both counterions decrease when the equivalent fraction of Na + , the thermodynamically nonpreferred ion in each mixture, is increased. This behavior is consistent with the mechanism of diffusion discussed above and with the expected distribution of the counterions in a heteroionic state of an exchanger which has the structure deduced from the behavior of the Br− ions.