  The penetration of atomic hydrogen through defect-free graphene was generally
predicted to have a barrier of at least several eV, which is much higher than
the 1 eV barrier measured for hydrogen-gas permeation through pristine graphene
membranes. Herein, our density functional theory calculations show that
ripples, which are ubiquitous in atomically thin crystals and mostly overlooked
in the previous simulations, can significantly reduce the barriers for all
steps constituting the mechanism of hydrogen-gas permeation through graphene
membranes, including dissociation of hydrogen molecules, reconstruction of the
dissociated hydrogen atoms and their flipping across graphene. Especially, the
flipping barrier of hydrogen atoms from a cluster configuration is found to
decrease rapidly down to <1 eV with increasing ripples' curvature. The
estimated hydrogen permeation rates by fully considering the distribution of
ripples with all realistic curvatures and the major reaction steps that
occurred on them are quite close to the experimental measurements. Our work
provides insights into the fundamental understanding of hydrogen-gas permeation
through graphene membranes and emphasizes the importance of nanoscale
non-flatness (ripples) in explaining many surface and transport phenomena (for
example, functionalization, corrosion and separation) in graphene and other
two-dimensional materials.
