Perfect proton selectivity in ion transport through two-dimensional crystals

Defect-free monolayers of graphene and hexagonal boron nitride are surprisingly permeable to thermal protons, despite being completely impenetrable to all gases. It remains untested whether small ions can permeate through the two-dimensional crystals. Here we show that mechanically exfoliated graphene and hexagonal boron nitride exhibit perfect Nernst selectivity such that only protons can permeate through, with no detectable flow of counterions. In the experiments, we use suspended monolayers that have few, if any, atomic-scale defects, as shown by gas permeation tests, and place them to separate reservoirs filled with hydrochloric acid solutions. Protons account for all the electrical current and chloride ions are blocked. This result corroborates the previous conclusion that thermal protons can pierce defect-free two-dimensional crystals. Besides the importance for theoretical developments, our results are also of interest for research on various separation technologies based on two-dimensional materials. Introduction Proton transport through two-dimensional (2D) crystals has recently been studied, both experimentally and theoretically1,2,3,4,5,6,7,8,9. As for the experiment, it was found that proton permeation through mechanically exfoliated crystals is thermally activated with energy barriers of ?0.8?eV for graphene and ?0.3?eV for monolayer hexagonal boron nitride (hBN)1. Further measurements using deuterons, nuclei of the hydrogen isotope deuterium, show that quantum oscillations raise the energy of incoming protons by 0.2?eV2. This correction yielded the total barriers of ?0.5?eV for monolayer hBN and ?1?eV for graphene. From a theoretical perspective, the latter value is notably lower (by at least 30% but typically a factor of 2) than that found in density-functional calculations for graphene3,4,5,6,7. To account for the difference, a recent theory suggests that graphene can be partially hydrogenated during the measurements, which makes its lattice slightly sparser; thus, making it more permeable to protons8,9. An alternative explanation put forward attributes the observed proton currents to atomic-scale lattice defects, including vacancies10,11. This was argued on the basis of ion-selectivity measurements using chemical-vapor-deposited (CVD) graphene11. Indeed, CVD graphene is known to possess a large density of atomic-scale defects that appear during growth12,13,14. Such defects are generally absent in mechanically exfoliated 2D crystals, which was proven conclusively in gas-leak experiments using the so-called nanoballoons15,16,17. Even a single angstrom-sized vacancy per micrometer-size area could be detected in those experiments16,17. Whereas it is plausible that vacancies and similar defects played a dominant role in experiments using CVD graphene10,11, extrapolation of those results to mechanically exfoliated 2D crystals is unjustifiable. To resolve the controversy, it is crucial to carry out similar ion-selectivity studies using mechanically exfoliated crystals with little or no defects1,2,15. Here we report ion-selectivity measurements using mechanically exfoliated graphene and hBN monolayers. The crystals are found to be perfectly selective with respect to protons. The latter can permeate through the 2D membranes, whereas even such small ions as chlorine are blocked. The results support the previous conclusion1 that transport of thermal protons through high-quality graphene and hBN occurs through their bulk and does not involve vacancies and other atomic-scale defects.by K. Gopinadhan et al