Ion mobility and partition determine the counter-ion selectivity of ion exchange membranes

Ion (perm)selectivity and conductivity are the two most essential properties of an ion exchange membrane, yet no quantitative relation between them has been suggested. In this work, the selectivity between two different counter-ions is correlated to the membrane conductivity. We show that the counter-ion selectivity measured by conventional electrodialysis (ED) can be expressed by the product of two parameters: (a) the mobility ratio between these two different counter-ions in the membrane and (b) their partition coefficient between the solution and the membrane. This is reminiscent of the classical solution-diffusion model. Via the counter-ion mobility in the membrane, the selectivity could be simply expressed with the membrane conductivity and dimensional swelling degree at pure counter-ion forms and at mixed counter-ion form when the membrane has been equilibrated with 1:1 equivalence ratio of the two counter-ions in the solution. This correlation is validated experimentally for the ion selectivity of K+/Na+ in two commercial hydrocarbon-based cation exchange membranes (CEMs). For K+/Na+ in a commercial perfluorosulfonic CEM, and for Mg2+/Na+ in all the three types of CEMs, the correlation could predict the counter-ion partition very well; but there is an underestimation of the K+/Na+ and Mg2+/Na+ mobility ratios afforded by this correlation, which might be due to simplification of the cation activity coefficients in CEMs. This work offers a convenient method to decouple experimentally the effect of partition and mobility in controlling the membrane selectivity, and also proposes a new perspective to study the selectivity as well as conductivity of ion exchange membranes.