Isotope effect
The proposed mechanism of hydrogen permeation involves several
steps: dissociation of molecular hydrogen on graphene ripples lead-
ing to a finite coverage of the surface with hydrogen atoms; flipping
of the atoms across the membrane in a proton-like transfer pro-
cess; and their recombination and desorption as molecular hydro-
gen. Only the chemisorption and flipping are expected to involve
sufficiently high energy barriers as discussed in the main text. To
determine which of these two key barriers limits the observed
permeation, we performed experiments using deuterium. To this
end, ten microcontainers were sealed with monolayer graphene
and exposed to deuterium at 1 bar at room temperature. Δδ was
monitored as a function of time. In stark contrast to our molecular
hydrogen experiments, the devices did not show any discernible
changes in Δδ (Extended Data Fig. 8). The absence of deuterium
permeation was further verified in elevated-T tests such as those
in Fig. 2a. Several devices were exposed to deuterium at 50 °C for
3 d, but none exhibited any bulging, in contrast to the molecular
hydrogen experiments of Fig. 2a.
To understand the isotope effect, we carried out DFT calculations for
chemisorption of deuterium on rippled graphene. After including cor-
rections due to zero-point oscillations, we found little difference in the
dissociation energies with respect to molecular hydrogen (Extended
Data Fig. 6). However, desorption of deuterium from the graphene
surface should be slower because of the same quantum corrections.
Hence, surface coverage for deuterium atoms should be higher than
that for hydrogen. The latter isotope effect is well known for both gra-
phene and graphite^47 ,^48 and implies that, if chemisorption were the rate-
limiting process, higher permeation rates would have been expected for
deuterium rather than molecular hydrogen, contrary to our observa-
tions. The latter conclusion indicates again that the limiting process is
the proton flipping. Indeed, in this case, one expects another isotope
effect analogous to that observed in the transport experiments of refs.
12 , (^49) where deuterons exhibited ten times lower conductivity through
graphene than protons. The reduction factor R has been attributed to
the fact that deuterons have a lower energy in their initial bound state
in Nafion^12 ,^49 , which results in an effectively higher barrier for flipping
(by ΔE ≈ 60 meV). This energy shift leads to the ratio between hydrogen
and deuterium permeation, which is given by R = exp(ΔE/kBT) ≈ 10 (ref.
(^12) ). For the case of atomic hydrogen/deuterium adsorbed on graphite,
ΔE was found^48 to be around 90 meV. Assuming the same value for
graphene, this shift should result in about 35 times slower permeation
of deuterons with respect to protons. Because of the detection limit
of about 10^9 s−1 m−2, we can only conclude from our experiments that
R ≥ 20, in good agreement with the above expectations. This supports
the proposed scenario in which the flipping step limits hydrogen per-
meation through monolayer graphene.
Data availability
All the mentioned data to support this study and its conclusions are
available upon request from P.Z.S. ([email protected]).
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Acknowledgements 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.
Author contributions A.K.G. suggested and directed the project with help from P.Z.S., Q.Y. and
F.C.W. P.Z.S., Q.Y., W.J.K. and Y.V.S. fabricated the devices, performed measurements and
analysed the data. W.Q.X., J.Y., M.I.K., S.J.Y. and F.C.W. provided theoretical support. I.V.G., R.R.N,
F.C.W. and M.L.-H. contributed to interpretation of the experimental results. A.K.G., P.Z.S., I.V.G.
and M.L.-H. wrote the manuscript. All authors contributed to discussions.
Competing interests The authors declare no competing interests.Additional information
Correspondence and requests for materials should be addressed to S.J.Y. or A.K.G.
Peer review information Nature thanks Rohit Karnik, Valentina Tozzini and the other,
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