  Defect-free graphene is impermeable to all atoms and ions at ambient
conditions. Experiments that can resolve gas flows of a few atoms per hour
through micrometre-sized membranes found that monocrystalline graphene is
completely impermeable to helium, the smallest of atoms. Such membranes were
also shown to be impermeable to all ions, including the smallest one, lithium.
On the other hand, graphene was reported to be highly permeable to protons,
nuclei of hydrogen atoms. There is no consensus, however, either on the
mechanism behind the unexpectedly high proton permeability or even on whether
it requires defects in graphene's crystal lattice. Here using high resolution
scanning electrochemical cell microscopy (SECCM), we show that, although proton
permeation through mechanically-exfoliated monolayers of graphene and hexagonal
boron nitride cannot be attributed to any structural defects, nanoscale
non-flatness of 2D membranes greatly facilitates proton transport. The spatial
distribution of proton currents visualized by SECCM reveals marked
inhomogeneities that are strongly correlated with nanoscale wrinkles and other
features where strain is accumulated. Our results highlight nanoscale
morphology as an important parameter enabling proton transport through 2D
crystals, mostly considered and modelled as flat, and suggest that strain and
curvature can be used as additional degrees of freedom to control the proton
permeability of 2D materials.
