On the diffusion coefficients of cations in sulfonic cation exchangers

Abstract

The article provides the first theoretical interpretation of the results of the widely known experimental work by B. Soldano, which has not yet been explained and described theoretically. This result was obtained using a model of diffusion of ions with different charges inside polymer ion exchangers, developed on the basis of a new theory of ion exchange, developed by the authors in a number of works published in recent years. The theory describes the equilibrium and kinetics of ion exchange depending on the nature and concentration of the functional groups of the ion exchanger, the swelling capacity of its polymer matrix and the parameters of ions, such as charge, ionic radius and hydrophilicity. Important elements of the theory are the dependences of the local permittivity of the liquid dielectric, the model of ion hydration and the relationship between the swelling capacity of the hydrophilic polymer and the degree of its crosslinking. The developed theory allows one to derive an expression for the ion exchange constant, the formula for the distribution coefficients of ions between the phases inside the ion exchanger following from it. In addition, the model presented in this paper contains a formula previously proposed by one of the authors of the article for the relationship between the diffusion coefficients in ion exchangers and the tabular values ​​of the self-diffusion coefficients of ions in water. As a result, the model allows one to explain the relationships between the particle diffusion coefficients and the characteristics of ions, temperature, and the degree of cross-linking of the polymer base of the ion exchanger. It is shown that the dependence of the internal diffusion coefficients of ions on the cross-linking of a strongly acidic ion exchanger is determined mainly by the effects of ion hydration inside the polymer matrix, which, in turn, are associated with the sizes of non-hydrated ions and their charges.