Pressure-driven ion separation through a pH-regulated cylindrical nanopore

Abstract

The ion rejection performance of a pH-regulated cylindrical nanopore is studied comprehensively. We show that this performance can be assessed by the ion selectivity of the nanopore. A larger ion selectivity yields a greater electric potential difference across the nanopore to balance ion transport, thereby lowering the rate of salt transport. Although the electrostatic interaction between mobile ions and the nanopore surface leads to salt rejection, increasing the surface charge density and/or the nanopore length raises the rejection only up to a certain extent. Due to the decrease in the ion selectivity and the increase in the strength of the induced electric field having a direction opposite to that of the liquid flow, the shorter the nanopore the smaller the rejection. In this case, the volumetric flow rate deviates more significantly from Hagen-Poiseuille equation than pores with length ranging from 100 nm to few micrometers. The radius of a nanopore is more significant than its length in influencing the rejection. Depending upon the value of nanopore radius, the rejection shows either an asymptotic value or a local maximum as the applied transmembrane pressure increases. The rejection can be improved remarkably by lowering the nanopore radius because the electrostatic interaction between mobile ions and the nanopore surface increases significantly. Nonintuitively, larger pores show better rejection performance in low-pressure filtration than smaller pores. The asymmetric fixed charge distribution on the nanopore surface arising from its pH-regulated nature is capable of tuning the net ion concentration gradient inside it.