We report selective ionic transport through controlled, high-density, subnanometer diameter pores in macroscopic single-layer graphene membranes. Isolated, reactive defects were first introduced into the graphene lattice through ion bombardment and subsequently enlarged by oxidative etching into permeable pores with diameters of 0.40 ± 0.24 nm and densities exceeding 1012 cm–2, while retaining structural integrity of the graphene. Transport measurements across ion-irradiated graphene membranes subjected to in situ etching revealed that the created pores were cation-selective at short oxidation times, consistent with electrostatic repulsion from negatively charged functional groups terminating the pore edges. At longer oxidation times, the pores allowed transport of salt but prevented the transport of a larger organic molecule, indicative of steric size exclusion. The ability to tune the selectivity of graphene through controlled generation of subnanometer pores addresses a significant challenge in the development of advanced nanoporous graphene membranes for nanofiltration, desalination, gas separation, and other applications.

Graphene and other two-dimensional materials offer a new approach to controlling mass transport at the nanoscale. These materials can sustain nanoscale pores in their rigid lattices and due to their minimum possible material thickness, high mechanical strength and chemical robustness, they could be used to address persistent challenges in membrane separations. Here we discuss theoretical and experimental developments in the emerging field of nanoporous atomically thin membranes, focusing on the fundamental mechanisms of gas- and liquid-phase transport, membrane fabrication techniques and advances towards practical application. We highlight potential functional characteristics of the membranes and discuss applications where they are expected to offer advantages. Finally, we outline the major scientific questions and technological challenges that need to be addressed to bridge the gap from theoretical simulations and proof-of-concept experiments to real-world applications.

We report graphene composite membranes with nominal areas more than 25 mm(2) fabricated by transfer of a single layer of CVD graphene onto a porous polycarbonate substrate. A combination of pressure-driven and diffusive transport measurements provides evidence of size-selective transport of molecules through the membrane, which is attributed to the low-frequency occurrence of intrinsic 1-15 nm diameter pores in the CVD graphene. Our results present the first step toward the realization of practical membranes that use graphene as the selective material.

We present an investigation of molecular permeation of gases through nanoporous graphene membranes via molecular dynamics simulations; four different gases are investigated, namely helium, hydrogen, nitrogen, and methane. We show that in addition to the direct (gas-kinetic) flux of molecules crossing from the bulk phase on one side of the graphene to the bulk phase on the other side, for gases that adsorb onto the graphene, significant contribution to the flux across the membrane comes from a surface mechanism by which molecules cross after being adsorbed onto the graphene surface. Our results quantify the relative contribution of the bulk and surface mechanisms and show that the direct flux can be described reasonably accurately using kinetic theory, provided the latter is appropriately modified assuming steric molecule-pore interactions, with gas molecules behaving as hard spheres of known kinetic diameters. The surface flux is negligible for gases that do not adsorb onto graphene (e.g., He and H2), while for gases that adsorb (e.g., CH4 and N2) it can be on the order of the direct flux or larger. Our results identify a nanopore geometry that is permeable to hydrogen and helium, is significantly less permeable to nitrogen, and is essentially impermeable to methane, thus validating previous suggestions that nanoporous graphene membranes can be used for gas separation. We also show that molecular permeation is strongly affected by pore functionalization; this observation may be sufficient to explain the large discrepancy between simulated and experimentally measured transport rates through nanoporous graphene membranes.

Graphene and other two-dimensional materials offer a new class of ultrathin membranes that can have atomically defined nanopores with diameters approaching those of hydrated ions. These nanopores have the smallest possible pore volumes of any ion channel, which, due to ionic dehydration and electrokinetic effects, places them in a novel transport regime and allows membranes to be created that combine selective ionic transport with ultimate permeance and could lead to separations and sensing applications. However, experimental characterization and understanding of sub-continuum ionic transport in nanopores below 2 nm is limited. Here we show that isolated sub-2 nm pores in graphene exhibit, in contrast to larger pores, diverse transport behaviours consistent with ion transport over a free-energy barrier arising from ion dehydration and electrostatic interactions. Current-voltage measurements reveal that the conductance of graphene nanopores spans three orders of magnitude and that they display distinct linear, voltage-activated or rectified current-voltage characteristics and different cation-selectivity profiles. In rare cases, rapid, voltage-dependent stochastic switching is observed, consistent with the presence of a dissociable group in the pore vicinity. A modified Nernst-Planck model incorporating ion hydration and electrostatic effects quantitatively matches the observed behaviours.