SPC/E model 42 was used for water molecules. Carbon atoms of PG membranes and of pistons were modeled as uncharged Lennard-Jones (LJ) interaction sites with the parameters listed in Table 1. Na+ and Cl¬ ? ions were also described by charged LJ particles (Table 1). The cutoff distance for LJ potential was set to 10 Å. The Lorentz-Berthelot mixing rule 43 was employed for the LJ interactions between different sites. The columbic interactions were taken into account using Coulomb law with the cuto? radius of 15 Å. The long range columbic interactions beyond the Coulomb cuto? distance were also calculated using the particle-particle particle-mesh (PPPM) method 44. The validity of the potential model and the parameters used in the present study were presented in the supporting information (SI).
In order to get a deep knowledge on the desalination mechanism, we have analyzed the passageways of water molecules through the membrane channels based on the density distribution profile (DDP). Furthermore, we have computed the potentials of mean forces (PMFs) for water and ions across the PG membranes to evaluate the corresponding passing free energy barriers (PFEBs). The PMFs were calculated by means of steered molecular dynamics (SMD) 46. For this goal, a virtual spring with harmonic potential of U = 1/2K(r – r0)2 was used with K equal to 1.0 eV Å-2. The end of the spring was considered to move with fixed velocity of 0.01 Å ps-1 which is slow enough for reversible pulling. Also, 10 independent simulations runs were performed to generate a reliable PMF profile.