Unraveling the ion transport through top and wall coated polyelectrolyte membrane pores

Polyelectrolyte-based nanofiltration membranes are obtained through a layer-by-layer sequential deposition of oppositely charged polyelectrolytes (PEs) onto a porous support structure. The resulting polyelectrolyte membrane offers tailored salt rejections for nanofiltration applications. However, little is known about the exact location of the deposited PEs on top or inside a membrane pore. Also, scarce information is available on the contribution of the different potential PE locations that affect the salt rejection of the overall membrane. Hence, research challenges, such as the influence of (a) an adsorbed PE layer inside the support membrane or (b) the bridging of the original pores and the position of the bridging layer, can only be unraveled through rigorous simulations. We present a significant extension of our previously published model into a two-dimensional modeling framework pE_nPE_nS (pressure p driven transport through n electrolyte layers E_n, n polyelectrolyte layers PE_n, and the support structure S) capable of addressing the selective layer additionally formed on the walls of the support capillary structure. The model solves a set of two-dimensional nonlinear Extended Nernst-Planck-Poisson and Navier-Stokes-Brinkman equations, enabling the prediction of ionic rejections from the top coating, wall coating, and a PE bridging forming inside the capillary. The proposed model framework systematically identifies and quantifies the influence of the capillary coating beneath the top layer on NaCl rejection and addresses the challenge of improving rejection rates. The model reveals that PEs deposited inside the support structure contribute significantly to NaCl rejection. It enables the predictions of differences in the rejection rates depending on the location of the PE coating, the diameter of the support capillary, and the transmembrane pressure. The model gives insight into PE bridging forming inside the support capillary and explains how its position and fixed charge density change ion rejection rates. As such, the model unravels insightful details on the rejection characteristics of coated capillaries, making it a powerful tool for designing polyelectrolyte membranes.