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Proton transport through one-atom-thick crystals


Graphene is increasingly explored as a possible platform for developing novel separation technologies1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19. This interest has arisen because it is a maximally thin membrane that, once perforated with atomic accuracy, may allow ultrafast and highly selective sieving of gases, liquids, dissolved ions and other species of interest2,9,10,11,12,13,14,15,16,17,18,19. However, a perfect graphene monolayer is impermeable to all atoms and molecules under ambient conditions1,2,3,4,5,6,7: even hydrogen, the smallest of atoms, is expected to take billions of years to penetrate graphene’s dense electronic cloud3,4,5,6. Only accelerated atoms possess the kinetic energy required to do this20,21. The same behaviour might reasonably be expected in the case of other atomically thin crystals22,23. Here we report transport and mass spectroscopy measurements which establish that monolayers of graphene and hexagonal boron nitride (hBN) are highly permeable to thermal protons under ambient conditions, whereas no proton transport is detected for thicker crystals such as monolayer molybdenum disulphide, bilayer graphene or multilayer hBN. Protons present an intermediate case between electrons (which can tunnel easily through atomically thin barriers24) and atoms, yet our measured transport rates are unexpectedly high4,5 and raise fundamental questions about the details of the transport process. We see the highest room-temperature proton conductivity with monolayer hBN, for which we measure a resistivity to proton flow of about 10 Ω cm2 and a low activation energy of about 0.3 electronvolts. At higher temperatures, hBN is outperformed by graphene, the resistivity of which is estimated to fall below 10−3 Ω cm2 above 250 degrees Celsius. Proton transport can be further enhanced by decorating the graphene and hBN membranes with catalytic metal nanoparticles. The high, selective proton conductivity and stability make one-atom-thick crystals promising candidates for use in many hydrogen-based technologies.

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Figure 1: Proton transport through 2D crystals.
Figure 2: Proton barrier heights and their catalytic suppression.
Figure 3: Current-controlled hydrogen flux.


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This work was supported by the European Research Council, the Royal Society, the Office of Naval Research, the Air Force Office of Scientific Research and the National Science Foundation of China. M.L.-H. acknowledges a PhD studentship provided by the Consejo Nacional de Ciencia y Tecnología (Mexico).

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Authors and Affiliations



A.K.G. designed the project and directed it with help from S.H. and M.L.-H., who fabricated devices, performed measurements and carried out data analyses. H.A.W. and F.C.W. provided theoretical support. M.L.-H., H.A.W., I.V.G. and A.K.G. wrote the manuscript. All authors contributed to discussions.

Corresponding authors

Correspondence to M. Lozada-Hidalgo or H. A. Wu.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Microfabrication process flow.

(1) An etch mask is made by photolithography. (2) RIE is used to remove the exposed SiNx layer. (3) Si underneath is etched away by wet chemistry. (4) By repeating steps 1 and 2, a hole is drilled through the membrane. (5) The 2D crystal is transferred to cover the etched hole. (6) Nafion is deposited on both sides of the wafer. (7) PdHx electrodes are attached. Bottom right, optical photo of the final device. Scale bar, 1 cm.

Extended Data Figure 2 SEM images of suspended 2D crystals.

a, Monolayer graphene with some accidental contamination. One of the particles away from the edge is marked with a white circle. b, Suspended graphene with pillars of hydrocarbon contamination intentionally induced by a focused electron beam. The inset shows a crack in the membrane; scale bar, 100 nm.

Extended Data Figure 3 Dependence of proton conductance on aperture size.

a, A bare-hole device exhibits a linear dependence of σ on the aperture diameter, as expected for this geometry35. The inset is a sketch of such a device. b, Proton conductance through monolayer hBN scales quadratically with membrane diameter, that is, linearly with membrane area. The inset shows examples of IV characteristics for four hBN monolayer devices with different D values, from 1 to 4 µm.

Extended Data Figure 4 Reproducibility of proton barrier heights for different devices.

Activation temperature dependences for three bilayer hBN devices (symbols are the experimental data; lines are the best fits). Inset: equivalent data for four monolayer graphene devices, three of which could be measured only within limited T intervals before they failed. The blue line is the best fit to the Arrhenius-type dependence; the other lines are guides to the eye indicating that all the devices exhibit practically the same E.

Extended Data Figure 5 Proton transport through 2D crystals in electrolytes.

a, Examples of IV characteristics for mono-, bi- and trilayer hBN membranes covering an aperture 2 µm in diameter. The inset shows a sketch of the liquid-cell set-up. To match the proton concentration in our Nafion experiments, we used a 0.1 M HCl solution in both containers. An additional polymer seal (yellow) is used to avoid leakage along the 2D crystal/substrate interface11. Ag/AgCl electrodes are placed inside each reservoir to measure ionic currents. In the case of trilayer hBN, the measured current falls within the range given by leakage currents. b, Histograms for the 2D crystals that exhibited unambiguous proton conductivity in the liquid-cell set-up. Each bar represents a different 2 μm membrane. The shaded area shows our detection limit.

Extended Data Figure 6 Electron clouds of 2D crystals.

Integrated charge densities for graphene, monolayer hBN (nitrogen is indicated by blue balls; boron in pink) and monolayer MoS2 (S is in yellow; Mo in brown).

Extended Data Figure 7 Slow deflation of micro-balloons rules out atomic-scale pinholes.

a, Height profiles for a typical graphene membrane over 24 h of observation. b, Maximum height as a function of time. The inset shows a typical AFM image of a pressurized graphene microcavity (colour scale, 0–130 nm). We measured six graphene membranes and all of them showed the same deflation rates, independently of whether or not Pt was deposited on top. Similar behaviour was observed for hBN monolayers.

Extended Data Figure 8 Nafion-limited conductivity for Pt-activated hBN.

Temperature dependences for a bare-hole device (constriction with Nafion only), a Nafion/Pt/Nafion device (no 2D membrane present) and a membrane device with catalytically activated monolayer hBN. The nominal conductivity is calculated as the measured conductance S divided by the aperture area A.

Extended Data Figure 9 Simulations of proton transport through 2D crystals.

a, b, Profiles of energy as a function of the distance of the proton to the centre of the hexagonal ring in graphene (a) and hBN (b), calculated using the CI-NEB method. Carbon atoms are shown in cyan, nitrogen in blue, boron in pink and protons in white. c, The influence of catalytic nanoparticles used in the experiment is mimicked by placing four Pt atoms at a distance of 4 Å from the graphene sheet. d, Trajectory of protons with an initial kinetic energy of 0.7 eV (the other two Pt atoms cannot be seen because of the perspective). The bent trajectory indicates that the decrease in barrier height is due to interaction of protons with Pt. Carbon atoms are shown in cyan, Pt in ochre and protons in white.

Extended Data Figure 10 Hydrogen flow detection.

a, Schematics of our devices for mass spectroscopy measurements. b, Example of the observed hydrogen flow rates as a functions of time for different negative biases on the graphene membrane. The voltage was applied in steps and resulted in the current values indicated next to the steps.

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Hu, S., Lozada-Hidalgo, M., Wang, F. et al. Proton transport through one-atom-thick crystals. Nature 516, 227–230 (2014).

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