Measuring the characteristics of electroosmotic flow in a polyelectrolyte grafted nanopore by molecular theory approach

Abstract: In this paper, we present a molecular theory analysis of ions and potential distribution, degree of ionization of polyelectrolyte (PE) brushes, velocity profile, volumetric flow rate, ionic selectivity, ionic conduction and advection by electroosmotic flow in poly-acid (PA)/poly-base (PB) grafted nanopores. The generated conformations by the Rotational Isomeric State model are used in performing the minimization of the free energy functional of the system including the effects of the Born energy arising from the variation of permittivity, pH of the electrolyte, grafting density of weak PE brushes, ion partitioning and ionic size. Then, the velocity field is obtained in the process of solving the Navier-Stokes-Brinkman equation by considering the interfacial fluid/wall slippage. Also, the accuracy of the numerical solutions is examined by comparing the present results of ionic conductivity with the existing experimental data for a nanopore grafted with 4PVP brushes used as a synthetic proton-gated ion channel. The application of the present methodology enables us to describe the electrohydrodynamic characteristics of electroosmotic flow in PE grafted nanopores in terms of different factors including the pH of the electrolyte, bulk salt concentration and the grafting density of PE brushes. We show that the dependency of the quantities of interest are essentially rely on the type of the polymer chains. For instance, increasing the pH of the electrolyte results in an increase/decrease of the degree of charged sites in the PA/PB brushes, and there exists a minimum/maximum point in the variation of magnitude of the ion selectivity of PA/PB grafted nanopore with the pH of the electrolyte. However, for both types of PA and PB grafted nanopores, ionic conduction and advection are approximately the ascending function of the bulk salt concentration and low range grafting density of the PE layer.