Water transport and desalination through double-layer graphyne membranes.

Non-equilibrium molecular dynamics simulations of water-salt solutions driven through single and double-layer graphyne membranes by a pressure difference created by rigid pistons are carried out to determine the relative performance of the membranes as filters in a reverse osmosis desalination process. It is found that the flow rate of water through a graphyne-4 membrane is twice that of a graphyne-3 membrane for both single and double-layer membranes. Although the addition of a second layer to a single-layer membrane reduces the membrane permeability, the double-layer graphyne membranes are still two or three orders of magnitude more permeable than commercial reverse osmosis membranes. The minimum reduction in flow rate for double-layer membranes occurs at a layer spacing of 0.35 nm with an AA stacking configuration, while at a spacing of 0.6 nm the flow rate is close to zero due to a high free energy barrier for permeation. This is caused by the difference in the environments on either side of the membrane sheets and the formation of a compact two-dimensional layer of water molecules in the interlayer space which slows down water permeation. The distribution of residence times of water molecules in the interlayer region suggests that at the critical layer spacing of 0.6 nm, a cross-over occurs in the mechanism of water flow from the collective movement of hydrogen-bonded water sheets to the permeation of individual water molecules. All membranes are demonstrated to have a high salt rejection fraction and the double-layered graphyne-4 membranes can further increase the salt rejection by trapping ions that have passed through the first membrane from the feed solution in the interlayer space.