Free energies of the ion equilibrium partition of KCl into nanofiltration membranes based on transmembrane electrical potential and rejection

The free energies of ion equilibrium partition between an aqueous KCl solution and nanofiltration (NF) membranes were investigated on the basis of the relationship of the transmembrane electrical potential (TMEP) and rejection. The measurements of TMEP and rejection were performed for Filmtec NF membranes in KCl solutions over a wide range of salt concentrations (1-60 mol·m(-3)) and pH values (3-10) at the feed side, with pressure differences in the range 0.1-0.6 MPa. The reflection coefficient and transport number, which were used to obtain the distribution coefficients on basis of irreversible thermodynamics, were fitted by the two-layer model with consideration of the activity coefficient. Evidence for dielectric exclusion under the experimental conditions was obtained by analyzing the rejection of KCl at the isoelectric point. The free energies were calculated, and the contribution of the electrostatic effect, dielectric exclusion, steric hindrance, and activity coefficient on the ion partitioning is elucidated. It is clearly demonstrated that the dielectric exclusion plays a central role.