Analysis of the salt retention of nanofiltration membranes using the Donnan-steric partitioning pore model

The performance of four commercial nanofiltration membranes was analyzed by the Donnan-steric partitioning pore model (DSPM) that describes solute transport through a membrane using the extended Nernst-Planck equation. Retention measurements were carried out as a function of the permeate flux for uncharged solutes, which allowed characterization of the membranes in terms of an effective membrane pore radius and the ratio of an effective membrane thickness to the porosity. Retention measurements with single salt solutions of NaCl, Na2SO4, MgCl2, and MgSO4 clearly showed the effect of ion concentration and ion valence on the retention. The DSPM model was used to evaluate the effective membrane charge density by analyzing the retention of single salt solutions. The analysis showed that the charge density is not constant but depends very much on the salt and its concentration. This is attributed to ion adsorption on the membrane material. For magnesium salts this could lead to a positive membrane charge. This phenomenon was found for each of the membrane materials.