Despite being only one-atom thick, defect-free graphene is considered to be completely impermeable to all gases and liquids1,2,3,4,5,6,7,8,9,10. This conclusion is based on theory3,4,5,6,7,8 and supported by experiments1,9,10 that could not detect gas permeation through micrometre-size membranes within a detection limit of 105 to 106 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 are capable of discerning (but did not observe) permeation of just a few helium atoms per hour, and this detection limit is also valid for all other gases tested (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. This 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 transport11,12. 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.
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All the mentioned data to support this study and its conclusions are available upon request from P.Z.S. (email@example.com).
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This work was supported by the Lloyd’s Register Foundation, the European Research Council (grants ARTIMATTER and VANDER), Graphene Flagship and the Royal Society. S.J.Y. acknowledges support from the National Key R&D Program of China (grant 2018YFA0305800) and Supercomputing Center of Wuhan University.
The authors declare no competing interests.
Peer review information Nature thanks Rohit Karnik, Valentina Tozzini and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
a, Graphite or hBN monocrystals are obtained by mechanical exfoliation. Micrometre-size wells are then made by e-beam lithography and ion etching. Monolayer graphene is transferred on top to seal the wells. b, Optical micrograph of a set of hBN microcontainers. The dashed curve indicates the position of monolayer graphene.
a, A microcontainer with d = 0.5 μm. Such images were taken only after finishing measurements to avoid electron-beam damage. b, Example of a broken graphene seal: the membrane was damaged after a thermal cycle to 80 °C.
a, Changes in δ(0) measured for two containers with d = 1 μm; AFM scans were taken every hour. b, Representative profiles δ(x) for a. c, Long-term variations in δ for 12 different containers kept in air. d, Permeation rates evaluated from the evolution of Δδ with time in c. e, Δδ for 16 different devices placed in helium at 3 bar. f, Permeation rates for the data in e. In c, e, different symbols denote different microcontainers made from graphite (empty symbols) and hBN (solid). The dashed lines in c, e indicate maximum changes detected for representative devices (colour coded). In d, f, the colour represents the same-colour device as in c, e, respectively. Error bars are standard deviation for fitting δ with a linear time dependence. Grey areas are the overall statistical accuracy obtained using all our devices measured in air and helium at 3 bar.
a, AFM micrographs of the same container sealed with bilayer graphene before (left) and after (right) its exposure to molecular hydrogen at 1 bar at 50 °C for 3 d. White curves show the profiles along the membrane’s diameter. No changes in membrane positions could be detected within our experimental accuracy. b, Same experiment for monolayer MoS2. No changes could be noticed either. c, For comparison, we show the simultaneous experiment for a microcontainer covered with monolayer graphene. The membrane clearly bulged out after the exposure, similar to the case of Fig. 2a. All scale bars, 1 μm. After the experiment, the bulging membrane in c was kept under ambient conditions and found to slowly deflate over months, in agreement with the room-temperature permeation rates reported in the main text.
Symbols are measurements at room temperature. Error bars are standard deviation using a minimum of ten devices in each case. Solid curve is the best fit to the square-root dependence.
a, b, Reaction of molecular hydrogen with graphene for t/D = 7.5% if adatoms are adsorbed in the central (a) and bridge (b) positions. Insets: atomic configurations of the initial, maximum-energy and final states (marked by the orange dots). The simulated size D is 2–3 nm. c, The dissociation barrier as a function of ripples’ curvature. Insets show top view of the bridge and central positions for hydrogen adatoms. d, The dissociation energy barrier as a function of biaxial strain. The inset shows schematic showing the direction of applied strain in our simulations.
a, Typical snapshot of graphene membrane at 300 K using molecular dynamics simulations. b, Density of ripples with t/D ≥ 7% (most chemically active). Symbols are the calculations for different T. Solid curve is a guide to the eye. c, Statistical distribution of intrinsic ripples with different t/D.
Time evolution of Δδ for ten different devices (different colours) exposed to deuterium at 1 bar at room temperature (295 ± 2 K). All the devices are hBN containers sealed with monolayer graphene. The dashed lines indicate maximum changes detected for the device coded with the same colour. The random fluctuations are close in amplitude to those shown in Fig. 1e for helium.
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Sun, P.Z., Yang, Q., Kuang, W.J. et al. Limits on gas impermeability of graphene. Nature 579, 229–232 (2020). https://doi.org/10.1038/s41586-020-2070-x