Saltwater transport through pristine and positively charged graphene membranes

Transport of saltwater through pristine and positively charged single-layer graphene nanoporous membranes is investigated using molecular dynamics simulations. Pressure-driven flows are induced by motion of specular reflecting boundaries at feed and permeate sides with constant speed. Unlike previous studies in the literature, this method induces a desired flow rate and calculates the resulting pressure difference in the reservoirs. Due to the hexagonal structure of graphene, the hydraulic diameters of nano-pores are used to correlate flow rate and pressure drop data. Simulations are performed for three different pore sizes and flow rates for the pristine and charged membrane cases. In order to create better statistical averages for salt rejection rates, ten different initial conditions of Na⁺ and Cl^- distribution in the feed side are used for each simulation case. Using data from 180 distinct simulation cases and utilizing the Buckingham Pi theorem, we develop a functional relationship between the volumetric flow rate, pressure drop, pore diameter, and the dynamic viscosity of saltwater. A linear relationship between the volumetric flow rate and pressure drop is observed. For the same flow rate and pore size, charged membranes exhibit larger pressure drops. Graphene membranes with 9.90 Å pore diameter results in 100% salt rejection with 163.2 l/h cm² water flux, requiring a pressure drop of 35.02 MPa.