According to the Teorell Meyer Sievers (TMS) model and the nonlinear least squares procedure, volumetric charge densities of five commercial nanofiltration membranes (NTR 7450, ESNA 1, ESNA 1-LF, LES 90 and UTC 60) can be obtained by measuring the membrane potentials (MP) of NaCl and KCl solutions across these membranes. The simulation was calculated under two kinds of initial conditions: a uniform and an exponential variation of volumetric charge density with the bulk electrolyte concentration. The results suggested that the exponential variation of volumetric charge density with the bulk electrolyte concentration is more favorable to describe the membrane potential and to evaluate the induced fixed charge density. MP was dependent on the concentration ratio of electrolyte solutions of each side. In the high concentration region, MP also relied on ionic diffusion coefficient, and its value would be reversed if the diffusion coefficient ratio of co-ion to counter-ion was larger than 1.0. While in the intermediate concentration region, MP as a function of electrolyte concentration was almost linear.

Key words: Teorell Meyer Sievers model, nonlinear least squares procedure, charged membrane, membrane potential, volumetric charge density