Combining Manning's theory and the ionic conductivity experimental approach to characterize selectivity of cation exchange membranes

The transport selectivity of different cations through cation exchange membranes (CEMs) could be estimated with the partitioning factor (Kji) and mobility ratio in membrane (uim/ujm), which turn can related to corresponding conductivity dimensional swelling data [Journal Membrane Science, 2020, 597, 117645]. This method has been validated two hydrocarbon polymer-based CEMs, obtained K+/Na+ equals one conventional electrodialysis (ED) method. However, perfluorosulfonic acid (PFSA) membranes, bi-/monovalent (Mg2+/Na+) all three types CEMs this ionic experimental approach deviate noticeably from values ED. In work, it is proved that deviation partly due simplification activity coefficients membrane. Here, are calculated according Manning's counter-ion condensation model. model, Manning parameter (?) characterizing dimensionless linear charge density determined by average distance between adjacent fixed sulfonate groups (b) permittivity hydrated (?). assuming homogeneous distribution groups, while PFSA representative structure models employed estimate distance. After accounting for membrane, Mg2+/Na+ gets closer to, but still smaller than ED work shows importance phase interpreting properties, complements proposed characterize ion membranes.