Counterion Transference Numbers in the Cell Model of a Charged Membrane

Abstract

The paper suggests exact formulae for calculating the electromigration, diffusion and convective numbers of counterion transport in the cell model of a charged membrane depending on the physicochemical parameters and the equilibrium concentration of the electrolyte. The cell model was previously developed to calculate all the kinetic coefficients of the Onsager matrix and the asymmetry of the cross coefficients was established. The limiting case of an ideally selective membrane is studied in detail, for which approximate formulae for transference numbers are obtained. The obtained dependences are illustrated by graphs using the example of the MK-40 cation-exchange membrane after conditioning at room temperature. The proposed method for calculating the transference numbers is applicable to any single-layer membranes in binary electrolyte solutions.