Ultrafast ion sieving in two dimensional graphene oxide membranes

Ultrahigh water permeance, together with a high rejection rate through nanofiltration and separation membranes1,2, is crucial but still challenging for multivalent ion sieving in water treatment processes of desalination, separation, and purification3,4. To date, no theory or equation has ever been quantitatively clarified the mechanism of water permeance in two-dimensional (2D) membranes, despite intensive and prolonged searches. Here, we established a new general equation of permeation through 2D membranes, and experimentally achieved unprecedented advances in water permeance one to two orders of magnitude higher than state-of-the-art membranes while simultaneously maintaining high ion rejection rates for multivalent metal ions, by staking nano-sized reduced graphene oxide (nano-rGO) flakes into nanofiltration membranes. The equation is simply based on a fundamental steady-state flow assumption and provides an essential description of water permeance through 2D membranes, demonstrating that the ultrahigh water permeance is attributed to the high effective channel area and shortened channel length elicited from the nano-sized-flake stacking effects in nano-rGO membranes, consistent with our theoretical simulations and previous experiments. These results pave the way for fabrication of advanced 2D nanofiltration membranes to realize a breakthrough in water permeance with exceptional ion sieving performance.