Graphene is impermeable to all gases and liquids 1-3 , and even such a small atom as hydrogen is not expected to penetrate through graphene's dense electronic cloud within billions of years 3-6 . Here we show that monolayers of graphene and hexagonal boron nitride (hBN) are unexpectedly permeable to thermal protons, hydrogen ions under ambient conditions. As a reference, no proton transport could be detected for a monolayer of molybdenum disulfide, bilayer graphene or multilayer hBN. At room temperature, monolayer hBN exhibits the highest proton conductivity with a low activation energy of 0.3 eV but graphene becomes a better conductor at elevated temperatures such that its resistivity to proton flow is estimated to fall below 10 -3 Ohm per cm 2 above 250°C. The proton barriers can be further reduced by decorating monolayers with catalytic nanoparticles. These atomically thin proton conductors could be of interest for many hydrogen-based technologies.Graphene has recently attracted renewed attention as an ultimately thin membrane that can be used for development of novel separation technologies (for review, see refs. 7,8). If perforated with atomic or nanometer accuracy, graphene may provide ultrafast and highly selective sieving of gases, liquids, ions, etc. 2,9-19 However, in its pristine state, graphene is absolutely impermeable for all atoms and molecules moving at thermal energies [1][2][3][4][5][6][7] . Theoretical estimates for the kinetic energy E required for an atom to penetrate through monolayer graphene vary significantly, depending on the employed model, but even the smallest literature value of 2.4 eV for atomic hydrogen 3-6 is 100 times larger than typical k B T which ensures essentially an impenetrable barrier (k B is the Boltzmann constant and T the temperature). Therefore, only accelerated atoms are capable of penetrating through the one atom thick crystal 20,21 . The same is likely to be valid for other two dimensional (2D) crystals 22,23 , although only graphene has so far been considered in this context. Protons can be considered as an intermediate case between electrons that tunnel relatively easily through atomically thin barriers 24 and small atoms. It has been calculated that E decreases by a factor of up to 2 if hydrogen is stripped of its electron 4,5 . Unfortunately,

Nanometre-scale pores and capillaries have long been studied because of their importance in many natural phenomena and their use in numerous applications. A more recent development is the ability to fabricate artificial capillaries with nanometre dimensions, which has enabled new research on molecular transport and led to the emergence of nanofluidics. But surface roughness in particular makes it challenging to produce capillaries with precisely controlled dimensions at this spatial scale. Here we report the fabrication of narrow and smooth capillaries through van der Waals assembly, with atomically flat sheets at the top and bottom separated by spacers made of two-dimensional crystals with a precisely controlled number of layers. We use graphene and its multilayers as archetypal two-dimensional materials to demonstrate this technology, which produces structures that can be viewed as if individual atomic planes had been removed from a bulk crystal to leave behind flat voids of a height chosen with atomic-scale precision. Water transport through the channels, ranging in height from one to several dozen atomic planes, is characterized by unexpectedly fast flow (up to 1 metre per second) that we attribute to high capillary pressures (about 1,000 bar) and large slip lengths. For channels that accommodate only a few layers of water, the flow exhibits a marked enhancement that we associate with an increased structural order in nanoconfined water. Our work opens up an avenue to making capillaries and cavities with sizes tunable to ångström precision, and with permeation properties further controlled through a wide choice of atomically flat materials available for channel walls.

One-atom-thick crystals are impermeable to atoms and molecules, but hydrogen ions (thermal protons) penetrate through them. We show that monolayers of graphene and boron nitride can be used to separate hydrogen ion isotopes. Using electrical measurements and mass spectrometry, we found that deuterons permeate through these crystals much slower than protons, resulting in a separation factor of ≈10 at room temperature. The isotope effect is attributed to a difference of ≈60 milli-electron volts between zero-point energies of incident protons and deuterons, which translates into the equivalent difference in the activation barriers posed by two-dimensional crystals. In addition to providing insight into the proton transport mechanism, the demonstrated approach offers a competitive and scalable way for hydrogen isotope enrichment.

Biological membranes allow permeation of water molecules but can reject even smallest ions. Behind these exquisite separation properties are protein channels with angstrom-scale constrictions (e.g., aquaporins). Despite recent progress in creating nanoscale pores and capillaries, they still remain distinctly larger than protein channels. We report capillaries made by effectively extracting one atomic plane from bulk crystals, which leaves a two-dimensional slit of a few Å in height. Water moves through these capillaries with little resistance whereas no permeation could be detected even for such small ions as Na + and Cl -. Only protons can diffuse through monolayer water inside the capillaries. The observations improve our understanding of molecular transport at the atomic scale and suggest further ways to replicate the impressive machinery of living cells.It has long been an aspirational goal to create artificial structures and devices with separation properties similar to those of biological membranes 1-5 . The latter utilize a number of separation mechanisms but it is believed that angstrom-scale constrictions within protein channels 6,7 play a key role in steric (size) exclusion of ions with the smallest hydration diameters D H  7 Å, typically present in biofluids and seawater 8,9 . Such constrictions are particularly difficult to replicate artificially because of the lack of fabrication tools capable to operate with such precision and, also, because the surface roughness of materials is typically much larger than the required angstrom scale 1 . Nonetheless, several artificial systems with nanometer and sub-nanometer dimensions were recently demonstrated, including narrow carbon and boron-nitride nanotubes 5,10,11 , graphene oxide laminates 12,13 and atomic-scale pores in graphene and MoS 2 monolayers 3,4,14 . The resulting devices exhibited high selectivity with respect to certain groups of ions (for example, they blocked large ions but allowed small ones 12,13 or rejected anions but allowed cations and vice versa 2,3,5 ). Most recently, van der Waals assembly of two-dimensional (2D) crystals 15 was used to make slit-like channels of several Å in height 16,17 . They were atomically smooth and chemically inert and exhibited little ( 10 -4 C cm -2 ) surface charge 17 . The channels allowed fast water permeation 16 and blocked large ions with a complete cutoff for diameters larger than 10 Å (ref. 17 ). Small ions (for example, those in seawater with D H of 7 Å) still permeated through those channels with little hindrance, showing that an angstrom-scale confinement comparable to that in aquaporins 6,7 is essential for steric exclusion of small-diameter ions. In this report, we describe 2D channels with the height h of about 3.4 Å (ref. 18), which are twice smaller than any hydrated ion (smallest ions are K + and Clwith D H  6.6 Å) 8,19 but sufficiently large to allow water inside (effective size of water molecules is 2.8 Å). The achieved confinement matches the size of protein constrictions in biological ...

Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids [1][2][3][4][5][6][7][8][9][10] . This conclusion is based on theory 3-8 and supported by experiments 1,9,10 that could not detect gas permeation through micrometre-size membranes within a detection limit of 10 5 to 10 6 atoms per second. Here, using small monocrystalline containers tightly sealed with graphene, we show that defect-free graphene is impermeable with an accuracy of eight to nine orders of magnitude higher than in the previous experiments. We could discern permeation of just a few helium atoms per hour, and this detection limit is also valid for all other tested gases (neon, nitrogen, oxygen, argon, krypton and xenon), except for hydrogen. Hydrogen shows noticeable permeation, even though its molecule is larger than helium and should experience a higher energy barrier. The puzzling observation is attributed to a two-stage process that involves dissociation of molecular hydrogen at catalytically active graphene ripples, followed by adsorbed atoms flipping to the other side of the graphene sheet with a relatively low activation energy of about 1.0 electronvolt, a value close to that previously reported for proton transport 11,12 . Our work provides a key reference for the impermeability of two-dimensional materials and is important from a fundamental perspective and for their potential applications.From a theory standpoint, monolayer graphene imposes a very high energy barrier for penetration of atoms and molecules. Density-functional-theory calculations predict that the barrier E is at least several eV 2-6 , which should prohibit any gas permeation under ambient conditions. Indeed, one can estimate that at room temperature T it would take longer than the lifetime of the universe to find an atom energetic enough to pierce a defect-free membrane of any realistic size. These expectations agree with experiments that reported no detectable gas permeation through mechanically-exfoliated graphene. The highest sensitivity was achieved using micrometersize wells etched in oxidized silicon wafers, which were sealed with graphene 1,9,10 . In those measurements, a pressurized gas (e.g., helium) could permeate along the SiO 2 layer and gradually fill the microcontainers making so-called 'nanoballoons'. Their consecutive deflation in air could be monitored using atomic force microscopy (AFM), and it was shown that the leakage occurred only along the SiO 2 surface, within several minutes but independently of the number of graphene layers used for the sealing 1 . These studies allowed a conclusion that graphene membranes were impermeable to all gases, at least with the achieved accuracy of 10 5 -10 6 atoms s -1 . This was further corroborated by creating individual atomic-scale defects in graphene nanoballoons, which resulted in their relatively fast deflation/inflation and confirmed the high sensitivity of the method 9,10 .