A two-dimensional (2D) porous layer can make an ideal membrane for separation of chemical mixtures because its infinitesimal thickness promises ultimate permeation. Graphene--with great mechanical strength, chemical stability, and inherent impermeability--offers a unique 2D system with which to realize this membrane and study the mass transport, if perforated precisely. We report highly efficient mass transfer across physically perforated double-layer graphene, having up to a few million pores with narrowly distributed diameters between less than 10 nanometers and 1 micrometer. The measured transport rates are in agreement with predictions of 2D transport theories. Attributed to its atomic thicknesses, these porous graphene membranes show permeances of gas, liquid, and water vapor far in excess of those shown by finite-thickness membranes, highlighting the ultimate permeation these 2D membranes can provide.

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Driven by the need of maximizing performance, membrane nanofabrication strives for ever thinner materials aiming to increase permeation while evoking inherent challenges stemming from mechanical stability and defects. We investigate this thickness rationale by studying viscous transport mechanisms across nanopores when transitioning the membrane thickness from infinitely thin to finite values. We synthesize double-layer graphene membranes containing pores with diameters from ∼6 to 1000 nm to investigate liquid permeation over a wide range of viscosities and pressures. Nanoporous membranes with thicknesses up to 90 nm realized by atomic layer deposition demonstrate dominance of the entrance resistance for aspect ratios up to one. Liquid permeation across these atomically thin pores is limited by viscous dissipation at the pore entrance. Independent of thickness and universal for porous materials, this entrance resistance sets an upper bound to the viscous transport. Our results imply that membranes with near-ultimate permeation should feature rationally selected thicknesses based on the target solute size for applications ranging from osmosis to microfiltration and introduce a proper perspective to the pursuit of ever thinner membranes.