Unraveling the impact of ion adsorption and dielectric exclusion on nanofiltration through pH-regulated cylindrical nanopores

We theoretically investigate the effects of ion adsorption on nanofiltration by simultaneously solving the modified Navier-Stokes, Poisson, and Nernst-Planck equations. Considering the confined space in the nanopore and the layered structure of water near the nanopore surface, hindered transport and anisotropic dielectric exclusion are separately incorporated to demonstrate the corresponding influences on salt rejection. For symmetric electrolytes, ion adsorption decreases the rejection of NaCl slightly but alters the rejection performance of CaSO₄ significantly. In particular, ion adsorption improves the rejection of asymmetric electrolytes due to the charge polarity reversal. With ion adsorption, the susceptibility of rejection to pH changes diminishes, and the dependence of rejection on feed concentration decreases. Owing to the counteracting effects of increased surface charge density and more pronounced ion screening as feed concentration rises, the rejection of CaCl₂ and Na₂SO₄ exhibits a maximum under specific pH ranges. 2D surface plots illustrate the dependence of rejection on concentration and pH. In addition, the effect of hindered transport is beneficial to rejection. As the diffusivities of ionic species drop or the diffusivity ratio of co-ions (relative to the surface charge polarity) to counterions decreases, the rejection increases pronouncedly. Lastly, dielectric exclusion in the nanopore results in a more negative surface charge density due to the repulsion of protons from the surface, thereby causing a shift of the isoelectric point towards lower pH values. The effect of the reduction in the perpendicular dielectric permittivity may be enhanced or offset partially by that of the increase in the parallel dielectric permittivity.