Analysis of transmembrane electrical potential across nanofiltration membranes based on electrostatic and steric-hindrance model

Abstract

Transmembrane electrical potential (TMEP) across nanofiltration (NF) membranes was calculated analytically in single electrolyte solution -– NF membranes systems with electrostatic steric-hindrance (ES) model in this study. Moreover, a simplified expression with average membrane parameters was obtained to give explicit explanations by combining ES model and irreversible thermodynamics. The effects of electrolyte species with common co-ion Cl^_ (KCl and MgCl₂), electrolytes concentration c, diffusion coefficient ratio of co-ion over counterion D₂/D₁ , pore radius r_p , ratio of membrane thickness over porosity ?x/A_k , effective volume charge density X_w on TMEP were investigated. The results showed that with the existence of membrane potential, dependencies of TMEP on solution flux were nonlinear. When ξ_f ^-1 (z₁v₁c_f/X_w ) was larger than 50 for 1-1 electrolytes and 100 for 2-1 electrolytes, TMEP tended to be constant and three potentials (TMEP, membrane potential and convection potential) crossed at D₂/D₁D_i = 1.0, which implied that the electrostatic effect could be neglected. When the isoelectric point of membranes is judged in different pH based on the zero point of TMEP, solutes with D₂/D₁ = 1.0 is recommendatory. Because when D₂/D₁ > 1.0, the zero point will locate on where X_w is negative, and when D₂/D₁ < 1.0, zero points will appear when X_w is positive, and only when D₂/D₁ = 1.0, the zero point of TMEP appears when membrane is neutral (X_w is zero). Moreover, a sufficient condition t_1m/z₁+t_2m/ z₂ = 0 was proposed to explain the coincidence of zero point of membrane potential and minimum of reflection coefficient.

Keywords:

• Transmembrane electrical potential
• Nanofiltration membranes
• The electrostatic and steric-hindrance model
• Irreversible thermodynamics