Proton transport through nanoscale corrugations in two-dimensional crystals

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.