The electrostatic and steric-hindrance model for the transport of charged solutes through nanofiltration membranes

Nanofiltration (NF) membranes possess the intermediate molecular weight cut-off between reverse osmosis membranes and ultrafiltration membranes, and also have rejection to inorganic salts. So one can assume that NF membranes have charged pore structure. We have developed the electrostatic and steric-hindrance (ES) model from the steric-hindrance pore (SHP) model and the Teorell-Meyer-Sievers (TMS) model (Wang et al., J. Chem. Eng. Japan, 28 (1995) 372) to predict the transport performance of charged solutes through NF membranes based on their charged pore structure. In this article, by doing the permeation experiments of aqueous solutions of neutral solutes and sodium chloride, the structural parameters (the pore radius and the ratio of membrane porosity to membrane thickness) and the charge density of NF membranes (Desal-S, NF-40, NTR7450 and G-20) were estimated on the basis of SHP model and the TMS model, respectively. Then, we selected an solution of different tracer charged solutes (sodium benzenesulfonate, sodium naphthalenesulfonate and sodium tetraphenyl-borate) and a supporting salt (sodium chloride) to verify the ES model. The prediction based on the ES model was in good agreement with the experimental results.