Theoretical investigation of the ionic selectivity of polyelectrolyte multilayer membranes in nanofiltration

Polyelectrolyte multilayer membranes have proven to be promising materials for ion nanofiltration. In this work, we implement a continuum mesoscopic transport model developed in previous works (Szymczyk, A.; Zhu, H.; Balannec, B. Langmuir 2010, 26, 1214; Szymczyk, A.; Zhu, H.; Balannec, B. J. Phys. Chem. B 2010, 114, 10143) to investigate the pressure-driven transport of electrolyte mixtures through this kind of membrane. The model accounts for an inhomogeneous distribution of the fixed charge through an arbitrary number of polyelectrolyte bilayers. We show that accounting for the multiple bipolar charge distribution resulting from the layer-by-layer assembly of polyelectrolytes with opposite charge is responsible for the increase in the Na(+)/Mg(2+) selectivity reported experimentally with respect to conventional nanofiltration membranes. The model also allows the rationalizing of the seemingly contradictory experimental results reported in the literature (i.e., the increase or decrease in the selectivity with the number of bilayers or the existence of an optimum number of bilayers). It is shown, however, that the nonmonotonous variation of the ionic selectivity does not originate from the multibipolar distribution of the fixed charge through polyelectrolyte multilayer membranes but from the existence of an optimum skin layer thickness.