  Two-dimensional crystals with angstrom-scale pores are widely considered as
candidates for a next generation of molecular separation technologies aiming to
provide extreme selectivity combined with high flow rates. Here we study gas
transport through individual graphene pores with an effective diameter of about
2 angstroms, or about one missing carbon ring, which are created reproducibly
by a short-time exposure to a low-kV electron beam. Helium and hydrogen
permeate easily through these pores whereas larger molecules such as xenon and
methane are blocked. Permeating gases experience activation barriers that
increase quadratically with the kinetic diameter, and the transport process
crucially involves surface adsorption. Our results reveal underlying mechanisms
for the long sought-after exponential selectivity and suggest the bounds on
possible performance of porous two-dimensional membranes.
