Two-dimensional crystals catalyse hydrogen into protons

Domain: physics
Published: 2026-03-28
Editorial outcome: minor_revision

Abstract
Two-dimensional (2D) crystals with atomic-level thickness dramatically shortens the
gas transport pathways, rendering it exceptionally promising for separation membrane
applications. While defect-free 2D crystals such as graphene have long been considered
impermeable to all gases, recent studies show that pristine monolayer graphene permits
room-temperature hydrogen permeation. However, the identity of the permeating species
and its generalizability to other 2D materials remain unclear. Herein, we report hydrogen
permeation behaviour through varying 2D crystals at elevated temperature, and the
hydrogen permeability of graphene can reach up to 1017 s-1m-2 as the form of protons.
This process is evidenced by three critical steps: 2D crystals-assisted catalytic
dissociation of hydrogen into protons, protons permeation through the 2D crystals lattice,
and proton recombination after permeation. Interestingly, the activation energy remains
invariant with the layer number of 2D crystals, but the permeability and activation energy
can be modulated by the type of materials, adsorbed metal nanoparticles, and the
external atmosphere. These findings reveal a catalysis-driven proton permeation
mechanism, and fundamentally deepen the understanding of hydrogen permeation
through 2D crystals.

Introduction
High-performance membranes with exceptional permeability, selectivity and stability are the
cornerstone of membrane separation technology1. Graphene and other two-dimensional (2D)
crystals, featuring atomic-scale thickness, can minimize gas transport pathways and significantly
reduce energy consumption, making them highly promising candidates for next-generation
separation membranes2. Nevertheless, it has been conventionally established that defect-free
graphene exhibits complete impermeability to all gas molecules, attributable to its densely packed
hexagonal lattice and delocalized π-electron cloud3-5. Conventional strategies focus on the
deliberate defect engineering through chemical or structural modifications that disrupt the inherent
atomic arrangement of graphene2,6-12. This leads to uneven pore size while also compromising the
stability and lifespan of graphene1.

Pristine graphene, with its atomically perfect sp2-hybridized hexagonal lattice, uniform pore
distribution, and sub-angstrom structural regularity, represents an ideal framework for molecular
sieving. Emerging experimental studies have begun to explore the separation properties of such
defect-free graphene. Recent work has demonstrated a room temperature (RT) cooperative
catalytic dissociation-permeation process of hydrogen molecules (H ) on defect-free monolayer
2
(1L) graphene13. This finding offers new insights for the development of graphene-based
permeation membranes. A key prerequisite for this process is the catalytic dissociation of H on
2
the surface of graphene, which is traditionally regarded as chemically inert13,14. Building on this
initial report of RT H permeation13, a deeper understanding of the inherent catalytic-permeation
2
properties of defect-free graphene and related 2D crystals is essential. Nevertheless, several critical
issues remain, including: (1) the catalytic-permeation stability of graphene at the elevated
temperatures; (2) the specific species of H dissociation; (3) the influence of material layer number;
2
(4) strategies to regulate the permeation barrier; (5) the universality of 2D crystals. Resolving these
aspects is essential for a deeper mechanistic understanding and for generalizing the observed
behaviour, with potential implications for applications such as high‑temperature
proton‑conducting fuel cells and catalytic membrane reactors in hydrogen‑based processes15-17.
Therefore, it is urgent to systematically investigate the catalytic and permeation properties of
pristine graphene and related 2D crystals.

Results
Realization of H permeating defect-free graphene
2
Figure 1a provides a conceptual overview of this study. Typically, defect-free graphene allows
the permeation of proton (H+), characterized with an energy barrier (E )18-22 (Fig. 1a, Left). In
p
contrast, the permeation of H
2
is expected to follow a catalytic process involving dissociation,
permeation, and subsequent recombination, associated with a distinct energy barrier of E (Fig. 1a,
A
Middle). Moreover, the exact dissociation species during this permeation process remain
unclear13,14. Additionally, while catalytically active metal nanoparticles (NPs) may modulate the
hydrogen catalytic and permeation activity of graphene18, the corresponding energy barrier E
A(NPs)
has yet to be determined (Fig. 1a, Right). Accordingly, we developed an experimental H bubble
2
model to study hydrogen permeation through precisely controlled 2D material membranes, as
shown in Fig. 1b. Based on our previous work, protons from a hydrogen plasma permeate the 2D
crystals lattices at elevated temperature, subsequently recombining into molecular H within the
2
interlayer region, where they gradually accumulate23. A substantial amount of H are confined
2
within the van der Waals interlayers of 2D material to form H bubbles, with a defined layer
2
number of 2D material as the bubble domes, the domes thickness can be confirmed by burst
bubbles23-30. Using graphene as a representative system, these H bubbles demonstrate excellent
2
structural stability at temperatures as high as 400 °C23. By quantitatively monitoring the volumetric
evolution of these bubbles, the catalytic and permeation behaviours of H through defect-free
2
graphene under different conditions can be well investigated. The H bubble regions exhibit clear
2
optical contrast relative to flat zones, as verified by atomic force microscope (AFM), which
provide accurate quantification of volumetric changes (Fig. 1b).

Figure 1c and Supplementary Fig. 1a, b plots the volumetric changes of H bubbles after
2
annealing at different temperature, and their volumes progressively decreases once the temperature
exceeds a threshold value, until the bubbles disappear entirely. Throughout these processes, the
high-to-radius ratios of the bubbles remain constant (h/R ~ 0.125). Figure 1d summaries the
volumetric changes of a certain H bubbles after annealing at different temperature, and the bubble
2
volume diminution starts above the critical temperature of 700 °C. Raman spectroscopy confirms
that throughout this volume evolution, the graphene bubble dome shows no signs of hydrogenation
or structural damage, as indicated by its characteristic peaks (Supplementary Fig. 1c)31. High-
resolution AFM imaging of regions where H bubbles disappeared reveals no detectable damage
2
or wrinkles, confirming the structural integrity of the graphene membrane after H permeation
2
(Supplementary Fig. 2). Similar changes could be observed in trilayer (3L) graphene, hBN, MoS
2
and MoSe
2
, accompanied by different critical temperatures (Supplementary Fig. 3–6), indicating
the universality of H permeation behaviour across 2D crystals.
2
To directly confirm the catalytic dissociation of H on 2D crystal surfaces, we used H bubbles
2 2
on hBN as a model system. Their Raman spectra are free from interference by H
2
and HD
vibrational modes and remain stable under intense laser irradiation. We introduced deuterium ions
(D⁺) into pre-existing H bubbles at elevated temperature. Subsequent Raman spectroscopy
2
revealed two distinct vibrational peaks: a newly emerged HD peak at ~3632 cm-1 coexisting with
the original H
2
peak at ~4153 cm-1 (Fig. 1f)32. The HD signal originates from recombination
between injected D+ and hydrogen species produced through catalytic dissociation of pre-existing
H
2
. This phenomenon provides direct evidence that 2D crystals can catalytically dissociate
hydrogen molecules. Nevertheless, the hydrogen permeation pathway and the specific dissociation
species involved await further clarification.

Identification of permeating hydrogen species
Furthermore, the areal density evolutions of H bubbles are monitored, indicating no observable
2
evidence of proton transporting through the vdW interlayers (Supplementary Fig. 7). Then, we
further apply the electric field with different direction to regulate the proton permeation, and find
the parallel electric field have no effect on the H permeation (Supplementary Fig. 8a–e). However,
2
the perpendicular electric field can markedly reduce the H permeation temperature and enhance
2
the permeation rate (Supplementary Fig. 8f–j). All these experimental results together confirm that
the permeating species are charged and migrates through the 2D materials lattice rather than along
the vdW interlayer space.

We continue to utilize the focused lasers to heat the 2D crystals (Supplementary Fig. 9) with
sub-micron regions to investigate the local permeation behaviour, as illustrated in Fig. 2a. The
height evolution of the H bubble in 1L MoS under different laser irradiation duration is plotted
2 2
in Fig. 2b. It is worth noting that the laser power is moderate and does not damage the MoS lattices,
2
and this power is insufficient to induce hydrogen permeation of bubbles in graphene or hBN
(Supplementary Fig. 10). The disappearance of a given H
2
bubble had no effect on adjacent bubbles
(Supplementary Fig. 11 and 12). Considering that if molecular H inside the bubble undergo the
2
leakage behaviour through interlayer, it will significantly affect the size of adjacent bubbles33.
Therefore, this phenomenon also confirms that H permeation occurs across the lattice of 2D
2
crystals rather than transport through the vdW interlayer gaps.

We also use the polymethyl methacrylate (PMMA) and Nafion proton exchange membrane
(PEM) films to distinguish the permeating hydrogen species, where protons can permeate PEM
but PMMA cannot (Supplementary Fig. 13)18,34. Both films, ~340 nm-thick PMMA and ~320 nm-
thick Nafion are separately coated on the H
2
bubbles in MoS
2
, followed by identical local laser
heating. Figure 2c plots the height evolution of shrinking H bubbles covered by PEM, which
2
maintains their morphological integrity. In contrast, PMMA exhibits local rupture at the irradiation
region as the underlying bubble diminished (Fig. 2d), and this phenomenon persisted across
varying PMMA thicknesses (Supplementary Fig. 14). After removing the PMMA, the originally
illuminated bubbles are found to completely disappear (Supplementary Fig. 15). Given that the
comparable Young’s moduli of PMMA and PEM, their different structural responses can be
attributed to the interaction with catalytically dissociated hydrogen species. Protons cannot
permeate PMMA and thus accumulate at the interface between MoS and PMMA, where they
2
recombine into molecular H . Once the pressure of recombined H is high enough, the rupture of
2 2
PMMA happens. In contrast, protons can readily permeate PEM, allowing the hydrogen species to
pass through without inducing rupture. This comparison clearly reveals that the catalytically
dissociated species of H on the surface of 2D crystals should be protons.
2
Brief summary, we can conclude two critical findings: (1) H permeation occurs across the
2
crystalline 2D lattices rather than interlayer pathways; (2) the complete permeation of H involves
2
catalytically dissociation into protons, subsequent lattice permeation, and eventual recombination.

Quantification of H permeation
2
We quantify the H permeation rate (Г ) by tracing the volumetric changes of dozens of H
2 P 2
bubbles after thermal annealing for a specific duration (details refers to Methods). Figure 3a
summarizes the measured Г
P
values for bilayer (2L) graphene at different temperatures. The
temperature-dependent Г follows the Arrhenius law,
P
Г = A  e x p ( − E / k T ) (1)
P A B
where k is the Boltzmann constant, A is pre-exponential factor, T is the permeation temperature
B
and E is the activation energy. Numerical fitting yields an E of 1.7 ± 0.1 eV for H permeation
A A 2
2L graphene. In contrast, the E for D permeating 2L graphene is fitted to be 2.1 ± 0.2 eV
A 2
(Supplementary Fig. 16), which is a little higher than that for H . This isotopic trend aligns with
2
prior observations for H+ and D+ permeation through 1L graphene13,19.

Using the consistent statistical methodology, the temperature-dependent Г for 3L graphene and
P
1–3L MoS are summarized in Fig. 3b. The Г of specific 2D crystals shows a similar slope
2 P
regardless of layer numbers, but the thinner layers have the larger Г . Figure 3c plots the fitted E
P A
of graphene and MoS with different layer numbers. 2L and 3L graphene have the same value of
2
~1.7 eV, and 1L, 2L and 3L MoS have the same value of ~1.0 eV, i.e., 2D crystals with varying
2
layer numbers have the comparable E during H permeation.
A 2
This layer-number independent behaviour can be explained by a sequential permeation
mechanism. Firstly, regarding the initial dissociation of H , theoretical simulations indicate that
2
the dissociation energy depends primarily on the interlayer spacing and remains unchanged with
increasing layer number (Supplementary Fig. 17). Subsequently, the permeating protons undergo
thermally activated and hop through the lattice layer-by-layer. After surmounting the energy barrier
for single-layer hopping, the kinetic energy loss of the proton can be instantly replenished by the
external heat transfer. This continuous thermal compensation maintains a constant effective kinetic
energy for protons to permeate sequential layers, resulting in the total E that is independent of the
A
permeated layer number.

The observed variation of Г with layer numbers should only results from the pre-exponential
P
factor A. To explore this further, we plot Г as a function of MoS layer number at 400 and 500 °C
P 2
(Fig. 3d). The Г follows an exponential attenuation with increasing layer number N, described by
P
Г ∝ exp(-αN), where  is a material-specific coefficient35. Considering that E is independent of
P A
N, thus the pre-exponential factor can be also described as A = A‧exp(-αN), with the term exp(-N)
representing the effective saturation density of permeating protons for a given thickness. For MoS ,
2
the fitted values of  and A are 1.8 and 4.0×1024 s-1m-2, and those are 1.2 and 1.0×1025 s-1m-2 for
graphene, respectively. Based on this relationship, the estimated Г for 2L graphene and 1L MoS
P 2
at 300 K are ~8×10-6 and ~107 s-1m-2, respectively. These tiny values explain why nearly no H
2
permeation can be detected in 2L graphene and 1L MoS
2
at RT within the limited time13. Although
Г for 1L graphene could not be directly measured, using known of 1.7 eV as E yields an
P A
estimated value of ~3×10-5 s-1m-2, which is approximately 16 orders of magnitude lower than the
rate previously measured from graphene microcontainer13.

Regulation of H permeation
2
Certain metal NPs have been reported to lower the energy barrier of proton permeating graphene
(E ). To investigate this, we transferred platinum (Pt), palladium (Pd) and chromium (Cr) NPs onto
p
H bubbles, as shown in Fig. 4a and Supplementary Fig. 18. Uniformly distributed metal NPs are
2
covered on the graphene bubbles (Supplementary Fig. 19a–c), and the graphene domes are
confirmed to be defect-free after covering Pt NPs and subsequent post-annealing (Supplementary
Fig. 19d). None of the metal NPs contact with encapsulated H directly.
2
H permeating 2L graphene covered with these metal NPs still follows the Arrhenius law, but
2
the fitted E differ significantly depending on the NP type (Fig. 4b). Highly catalytic Pt and Pd
A
NPs enhance the permeation rate Г at relatively lower temperatures. For 2L graphene, Pt produces
P
the most pronounced E reduction of ~0.9 eV, followed by Pd of reduced ~0.5 eV, while Cr shows
A
negligible influence (as summarized in Fig. 4d). Pt also exhibits high efficiency in reducing the
proton permeation barrier E for 1L graphene18, suggesting a similar catalytic mechanism. This is
p
further supported by experimental phenomena that pre-coated Pt NPs suppress H bubble
2
formation, reduce bubble size and density (Supplementary Fig. 20), and local laser irradiation can
realize the H permeation through graphene domes while coating Pt (Supplementary Fig. 21).
2
However, Pt shows no significant reduction for 3L graphene, which may result from the
aggregation and deactivation of Pt NPs at higher temperatures annealing (>900 °C)36,37.

Furthermore, we continue to cover Pt NPs on MoS bubbles with different dome thicknesses
2
(Fig. 4c and Supplementary Fig. 22). The covered Pt efficiently reduces E for MoS across
A 2
different layer number. The Pt on 3L MoS cause a measurable E reduction, and the reduced E
2 A A
values for 1L – 3L MoS is 0.4 ± 0.2 eV (Fig. 4d).
2
Briefly, the complete H
2
permeations are concluded to involve three consecutive steps: (1)
catalytically dissociation of H
2
into protons at the inner surface with the barrier energy of E
1
; (2)
proton permeating the 2D lattice with the barrier energy of E ; (3) hydrogen evolution reaction
p
(HER) at the outer surface with the barrier energy of E . The total E should be constituted by
3 A
these three steps, i.e., E = E + E + E . Considering the fact of long-distance non-direct contact
A 1 p 3
of NPs, as well as reduced E exhibits no correlation with the permeated layer numbers, like Pt
A
NPs on 1L – 3L MoS , the NPs should primarily affect the steps (2) and (3). The enhanced Г and
2 P
reduced E after covering metal NPs are consistent with their well-documented HER catalytic
A
performance hierarchy (Pt > Pd > Cr)38,39.

Subsequently, we modulate H permeation by altering the outside atmosphere (Fig. 5a), using
2
2L graphene dome as the PEM. When the outer environment is high vacuum, the E remains nearly
A
unchanged (Fig. 5b and Supplementary Fig. 23a), with only a slightly reduction in Г , indicating
P
that H permeation is insensitive to the pressure difference. In contrast, when pure oxygen (O ) is
2 2
introduced as the outside atmosphere, the Г at the Arrhenius expression clearly divides into two
P
distinct temperature regions separated by the transition temperature of ~500 °C (Fig. 5b and
Supplementary Fig. 23b)35. Compared to the HER pathway of proton recombining into H (2H+ +
2
2e- → H ), O provides an additional four-electron oxygen reduction reaction (ORR) pathway (4H+
2 2
+ O + 4e- → 2H O)38,40. The ORR with O can increase the Г by two order of magnitude and
2 2 2 P
lower the E to 1.0 ± 0.1 eV, primarily by accelerating the surface recombination rate and reducing
A
the barrier E . Throughout the entire ORR, no defects are observed in the 2L graphene domes
3
(Supplementary Fig. 23b). Even when replacing the conductive graphene by the insulating hBN,
despite of their different electrical properties, O still promote the permeation, yielding two distinct
2
pathways with corresponding E of 0.5 ± 0.2 eV and 1.0 ± 0.2 eV, respectively (Fig. 5c and
A
Supplementary Fig. 24). In contrast, permeation under H atmosphere presents a higher fitted E
2 A
of 1.4 ± 0.3 eV. These results demonstrates that an inert 2D crystal can be rendered catalytically
active through modulation of the external chemical environment.

Subsequently, we introduce Pt NPs in combination with the outside atmosphere of O , and Г
2 P
can be further increased by approximately two orders of magnitude (Fig. 5d and Supplementary
Fig. 23c). Under the synergistic effect of Pt NPs and ORR, Г of 2L graphene can achieve ~1017 s-
P
1m-2 above 470 °C, with its subsequent stabilization suggesting the onset of a saturation permeation
state. In comparison, Г of 1L MoS is estimated to achieve similar permeability as low as 120 °C.
P 2
The exceptional catalytic properties of traditionally inert materials prompt a re-evaluation of the
catalytic potential of 2D crystals. These results confirm that 2D crystal films can be used as the
functional membranes for hydrogen catalysis and proton separation41,42.

Methods
Preparation of H and D bubbles in 2D crystals
2 2
According to our previous study23, the protons in H plasma permeate through the lattices of 2D
2
crystals, and the permeated protons re-combine into the molecular H in the vdW interlayers and
2
gradually aggregate into the H bubble, which reported in 2D crystal flakes (graphite, hBN, MoS
2 2
and MoSe ) with 10–150 nm thickness are exfoliated on SiO /Si or sapphire through traditional
2 2
micromechanical cleavage method. Intercalation of H and D molecules as nanoreactors inside
2 2
2D crystals are performed in a customized inductively coupled plasma chemical vapour deposition
(ICP-CVD) system. Before the ICP treatment, the chamber is degassed by pre-heating at 400 °C
under vacuum (<10-5 Pa) for 30 min to remove the adhesive residues on the 2D crystal surface.
Subsequently, the ICP is excited with the power of 10–100 W under 5 Pa with pure H or D .
2 2
The proton permeation duration is normally 1–20 min at 800, 650, 300 and 300 °C for graphite, hBN,
MoS and MoSe , respectively. The as-prepared bubble domes for graphene, hBN, MoS and
2 2 2
MoSe are mostly 2L, 2L, 1L and 1L, respectively.
2

Extending the existence of HD
The hBN flakes containing pre-existing H bubbles are reloaded into the ICP-CVD system and
2
heated to 650 °C. Subsequently, the D
2
plasma is ignited at 10–100 W under 5 Pa for 1–3 min.
Finally, due to the observable HD characteristic signal, Raman spectra acquired with 25 mW and
1000 s integration confirm the presence of HD.

Extending the layer number of H and D bubble domes in 2D crystals
2 2
H and D bubble domes with other layer numbers are prepared through transferring CVD grown
2 2
2D material films on the as-prepared bubbles. The wafer-scale 1L and 2L MoS films are grown
2
by the two-step vapour deposition method43, and 1L graphene films are grown by the proton-
assisted CVD method44. After CVD growth, the as-grown MoS and graphene films are spin-
2
coated with 800 nm thick PMMA (996k MW, 6 wt% in anisole, 2000 rpm for 1 min) and then
delaminated from the substrate in an aqueous solution. After cleaning in DI water, the PMMA/2D
film directly paste onto 2D crystal flakes with H bubbles in a dry environment, and these
2
transferred PMMA/2D film/2D flakes are baked at 150 °C for 30 min in N -filled glovebox.
2
Subsequently, the protective PMMA is removed by acetone and IPA. Then, the transferred 2D
film/2D flakes are further annealed for 30 min at 350 °C under high vacuum (<10-5 Pa) for
graphene, and annealed for 40 min at 300 °C under atmospheric pressure for MoS . Finally, the
2
H bubbles with 3L dome for graphene, 2L and 3L domes for MoS are prepared.
2 2

Covering Pt, Pd or Cr NPs
Firstly, ~2 nm thick Pt, Pd and Cr films (purity >99.99%) are sputtered on SiO /Si substrates at
2
room temperature, and then they are annealed further annealed under high vacuum (<10-5 Pa) at
450 °C for 30 min to aggregate metal films into individual NPs. Subsequently, the metal NPs with
similar size are transferred onto 2D crystal flakes with H or D bubbles through the standard wet
2 2
transfer method. The covering PMMA films during transfer are removed by acetone and IPA.

Covering Nafion PEM or PMMA films
A Nafion solution (5 wt%, 1100 equiv.) or PMMA (996k MW, 6 wt% in anisole) are spin-coated
on MoS flakes with H bubbles. The thicknesses of Nafion and PMMA films are controlled by
2 2
the spin rate and duration, and the used thicknesses of Nafion PEM and PMMA are 320 nm and
340 nm, respectively. To achieve the highest conductivity of proton, the as-prepared Nafion PEM
are placed in a water-saturated environment at 130 °C for 180 min to cross-link the Nafion.
The PMMA are baked at 150 °C for 30 min under atmospheric condition. These baking treatments do
not affect the H bubbles in MoS flakes.
2

Local laser heating
Localized heating is performed on H bubbles in 2D crystal flakes using a WITec/alpha 300R
2
confocal microscope with 532-nm laser of which radius is 500 nm when a 100× objective lens is
employed. The 532-nm laser with power of 0.5–1 mW for different durations is utilized for MoS
2
with H bubbles.
2

Thermal annealing under various external atmospheres
All thermal annealing treatments under different external atmospheres are conducted in a 2-inch
horizontal tube furnace. Firstly, we load the 2D-flakes/substrate into the tube, followed by
pumping to vacuum (<1 Pa). To minimize residual H O and O , the tube is then purged with Ar or
2 2
H and brought back to atmospheric pressure. Secondly, a high-purity atmosphere is created by
2
introducing H or O /Ar mixture, enabling controlled heat treatment of the 2D-flakes with H or
2 2 2
D bubbles.
2

Directional electric fields to identify the permeating species and pathway
The parallel electric field is generated using a customized copper electrodes with a fixed 3 cm
interelectrode distance and an applied voltage of 1500 V (yielding the electric field strength of 50
kV/m). The electric field direction (parallel or perpendicular to graphite layers) is controlled by
adjusting the spatial orientation of electrodes relative to the sample. All comparative experiments
are conducted in a tube furnace with identical parameters: pressure of <10 Pa, constant temperature
of 500 °C for 30 min.

Proton permeability of PMMA and Nafion
About 340 nm-thick PMMA and 320 nm-thick Nafion membranes are prepared by spin-coating,
with the Nafion membrane undergoing the pre-treatment in a 130 °C high-humidity environment
to promote cross-linking prior to transfer. Both membranes are subsequently transferred onto flat
substrates with a 1 mm diameter aperture using standard wet transfer techniques and annealed at
130 °C to achieve complete and stable surface coverage. Proton conductivity measurements are
performed by mounting the membranes in electrochemical cell filled with 0.1 M HCl electrolyte,
where current–voltage (I–V) characteristics are recorded using Pt electrodes connected to a
Keithley 2450 source meter.

Theoretical dissociation energy of H in graphene layer space
2
Both geometric optimization and electronic property calculations are performed using density
functional theory (DFT) as implemented in VASP45-47. The Perdew-Burke-Ernzerhof (PBE)
approach is employed to describe the exchange-correlation function48,49, while the projector-
augmented wave (PAW) method50,51 accounted for core-valence electron interactions. To ensure
accuracy during structural relaxation, a plane-wave basis set with a kinetic energy cut-off of 450
eV is applied, along with a total energy convergence tolerance of 10-5 eV and a force convergence
tolerance of 0.02 eV/Å. The vdW interactions were treated using the DFT-D3 method52. The
dynamic barriers are calculated via constrained ab initio molecular dynamics (AIMD) simulations
and the slow-growth sampling method (SG-AIMD)53,54. AIMD simulations are conducted at 300
K with a time step of 0.5 fs, keeping the graphene layers fixed. A vacuum layer of approximately
15 Å is consistently maintained to avoid interactions between periodic images. The reaction free
energies are evaluated using the constant-potential hybrid solvation dynamics model (CP-HS-DM),
as developed by Liu et al55-58.

Characterizations
Optical microscope. All the optical images are captured by the optical microscope (Nikon Eclipse
LV100ND).

Raman and PL. Raman spectra are acquired using a WITec/alpha 300R confocal microscope
using a 100× objective lens under ambient conditions. Unless specially noted, the wavelength for
the excitation laser is 532 nm with the power below 1 mW/μm2 to avoid heating. The laser power
for detecting H and HD molecules inside hBN bubbles is 25 mW for 1000 s due to their weak
2
signals.

AFM. AFM measurements are carried out by Bruker Dimension Fastscan system under an
atmospheric environment. The measurements are set at PeakForce tapping mode due to the highest
accuracy to distinguish the changes of formed nanoreactors.

Calculation of the permeation rate of H .
2
The thermal annealing is performed for all the H or D bubbles in 2D crystal flakes. The
2 2
annealing parameters include the temperature, annealing duration and atmosphere, which are
emphasized at the corresponding statement. The H or D bubble sizes are ex situ measured through
2 2
optical microscope and AFM.

The total permeation rate was obtained by summing the contributions from all bubbles within
an individual, exfoliated flake. By combining the spherical cap volume (V) and the inside pressure
(P) of H bubbles, according to the ideal gas law PV = Nk T, k is the Boltzmann constant, the
2 B B
total amount of permeated H molecules (ΔN) can be accumulated by the discrete bubbles and
2
written as,
ΔN= 1/k T * Σ Δ(PV )
B n n (2)
Based on our previous study23, the internal pressure of H bubbles is a constant value of 0.3 MPa
2
(P = 0.3 MPa) for the simplified calculation. Therefore, the hydrogen permeation rate (Γ ) is
P
described as,
Γ = ΔN / (S * t) (3)
P
where S is the projected area of the measured H bubbles and t is the heat treatment time.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors demonstrate an intriguing behavior of hydrogen gas permeation through defect-free atomically-thin membranes. Although the report is more phenomenologically, I believe there is fundamentally important mechanisms underneath. Therefore, I highly recommend its publication to the community that may attract more attentions and promote the discovery of new physics.\nTo my knowledge, catalytic dissociation of hydrogen gas via 2D surfaces at relatively high temperatures (here, up to 900 °C) was not reported previously. More importantly, at this temperature, whether and how proton permeates through multilayer 2D materials remain an interesting open question. In addition, the authors further demonstrate an exit effect of permeation by changing the membrane surfaces that are in contact with either metal catalysts and/or atmosphere gases. Interestingly, these changes seem can remotely influence the permeation process that are separated by defect-free 2D materials.\nPersonally, I think those phenomenon are interestingly enough for publication at this stage. Nevertheless, I still recommend the authors to exclude the possibility of proton permeation through the interlayer spacing. What is the explanation of the faster permeation of D2 in Fig. S5?\nDid the author try gas permeation using hBN bubbles? And what is the activation energy. Important information can be obtained by such experiment.\nHow the metal nanoparticles being deposited onto the graphene surface? Could they introduce any defects? The metal nanoparticles also seem unevenly distributed all over the surface, say in Fig. S7. Do they appear to be on the bubbles?\nMinor suggestions:\n1. It is important to add the methods of controlling the number of bubble wall layers, as well as for identifying the number of layers.\n2. Page 3, Fig. 1d: the scale of the x-axis (from 25 to 400) appears to be incorrect.\n3. Page 5, Fig. 2a: the structural model of the first MoS2 layer appears to be discontinuous (with broken bonds?).\n4. Page 15: undefined variables in the equations.\n5. Spelling typos, such as '… analyze the date (data?)' in the author's contribution.", "reviewer_2": "This manuscript presents a study on hydrogen permeation through defect-free 2D materials, with a focus on graphene. The authors provide experimental evidence that hydrogen can permeate pristine graphene at elevated temperatures in the form of protons. The work is systematic, well-supported by multiple characterization techniques, and offers valuable insights into the catalytic dissociation-permeation mechanism. However, several issues require clarification and additional evidence before the manuscript can be considered for publication.\n1. The authors claim their work \"overturns the conventional wisdom about the gas permeation barrier for graphene.\" However, this conventional wisdom was already challenged by Sun et al., Nature 579, 229–232 (2020) (Ref 13), which first reported room-temperature H₂ permeation through defect-free graphene. The current manuscript should differentiate its contributions from this foundational study.\n2. The systematic investigation of high-temperature regimes, layer-number independence of E_A, and the role of metal NPs/atmosphere, which significantly expands upon the initial discovery. The introduction and discussion sections should be revised to frame the work as a mechanistic deepening and generalization of the phenomenon first reported by Sun et al., rather than a standalone discovery.\n3. While the three-step mechanism is clearly proposed, direct evidence for the catalytic dissociation of H₂ into protons on pristine graphene remains indirect. If would be better if the authors provide more direct spectroscopic or simulation evidence to support this first step.\n4. The mechanism by which Pt and Pd NPs reduce the energy barrier is attributed to steps 2&3, but direct evidence is lacking.\n5. The finding that E_A is independent of layer number is intriguing but counterintuitive. The authors should discuss possible physical or chemical reasons for this behavior more thoroughly, perhaps with support from theoretical calculations or modeling.", "reviewer_3": "The paper by Xu, et al. reports experimental measurements on a potential scenario of graphene helps with hydrogen dissociation into protons. The topic is interesting which has been proposed and tested both experimentally and theoretically in recent years. However, the referee cannot see the main conclusions claimed in the present manuscript being well supported by experimental results. The referee would not recommend publication due to the following comments:\nThe authors did not provide necessary experimental details in terms of how to introduce hydrogen into the bubbles. The surfaces are contamination-free is also scientifically wrong, since all surfaces exposing or being prepared in air contains hydrocarbon, which may lead to the fact that gases in the bubble are not pure hydrogen but certain hydrocarbons. See many papers reporting the mechanical properties of bubbles and characterizations using HRTEM for the hydrocarbon adhered on 2D materials’ surfaces.\nFollowing this comment, no experimental proof for the trapped gases being hydrogen was provided, which is required or the whole study would be built on a wrong or improper assumption.\nFig. 1c shows indeed gradual shrinkage of the bubble but this only occurred at higher than 700C, whereas below this threshold temperature, nothing happened. That, is, the claim ‘their volumes progressively decreases’ is misleading. The constant h/R again is suspicious of sort of thermal induced mechanical evolution of 2D bubbles rather than permeation. Or otherwise, h/R would evolve, say at least h would changes while keeping R more or less constant.\n‘No interlayer H2 migrations are observed’: Did the authors check the areal density of bubbles before and after annealing to different T? Please provide.\nIt could be quite surprising to find hydrogen or protons transport across graphene thicker than monolayer and MoS2 of any thicknesses, which contradicts the previous reports. Authors are suggested to provide detailed explanation.\nThe authors compared PMMA and PEM. The referee here has two comments. On one hand, PMMA could be highly permeable to protons especially in liquids, unless being cross-linked under exposure to high-dose electrons. On the other, these comparisons are so weak that cannot (I am afraid) lead to the conclusion that it was protons that permeate 2D layers. Still no direct evidence is provided.\nPrevious theory on graphene including those on carbon nanotubes suggested that it was convex rather than concave curvatures that enhanced hydrogen dissociation whereas the concave curvatures facilitated desorption. Additionally, a strong tensile strength (the bubble was always tensed with constant h/R) did not help with hydrogen dissociation into ‘protons’. These theoretical suggestions contradicts the authors’ setup and results, which should be clarified.\nThe same activation energy for different layers already provided a strong indication that the reduced volume of bubbles was not due to hydrogen/proton permeating 2D layers but due to other possibilities such as interlayer spacing leakage or creation of gas-leak defects. For spacing leakage, authors should check the areal density of bubbles before and after rather than simply claim neighboring bubbles were not affected. The creation of defects could partly reconcile the conflict results of H2/proton permeate MoS2 by the authors and others. Furthermore, although the authors claim no D peak was observed for tested graphene samples in Raman (S8), 1) Raman cannot sense defect density of lower than say 10%; 2) G’ and 2D’ peaks emerge highly indicative of defects.\nOn the other hand, because the authors found prefactor scales as a function of exp(-N), a more plausible explanation would be the tested species transported layer by layer (for MoS2, the transport would be through high-T induced defects-MoS2 has high-density S vacancies on the surface and also, high catalytic activity). This suggests the tested bubbles that were seemingly sealed by 2L graphene (for example) were essentially composed of bubbles on bubbles and separated by each 1L of graphene. This scenario would reconcile in part the conflict results of H2/proton permeate 2L or thicker graphene by the authors and others.\nWhatever cases are, the authors should provide more experimental evidence and explanation, which are rather weak or lack in the present form.", "reviewer_4": "Report\nThe manuscript by Jie Xu et al. regards the permeability of two-dimensional crystals to hydrogen. In their manuscript, the authors show that hydrogen permeability is a catalysis-driven process leading to the dissociation of molecular hydrogen at the crystal surface. The topic is relevant for fundamental and practical aspects related to the physics and chemistry of atomically thin gas membranes.\nThe experiments performed are numerous, generally well conducted and interesting and the set of data reported and related analysis are potentially valuable. The literature quoted is appropriate and complete. Therefore, this manuscript would deserve publication in Nature Communications.\nYet, the manuscript needs important changes. The English requires some corrections. In some instances, the description of the results is not organised in a clear manner, e.g., different materials are considered in diverse experiments that may create confusion. The optical data require a more accurate discussion. The figures are sometimes not explicative and the last part of the work should be rewritten or reorganised. Indeed, the role of the external gas atmosphere in the molecular hydrogen dissociation is a most relevant aspect that requires a clearer presentation and a more detailed discussion of the data.\nSpecific comments follow.\nAbstract. The last lines of the abstract claim that the results reported “establish graphene a catalytic membrane for hydrogen-based technologies, including fuel cells and high-purity hydrogen extraction”. However, this claim is not further demonstrated nor discussed in the manuscript. The conclusions of the present work should somehow address this technological aspect in a more explicit manner. In addition, similar findings are found in MoSe2, MoS2 and h-BN. Why only graphene is given relevance in the title and abstract?\nPage 2, line 19. Honestly, I don’t quite understand point (2): What else can be the dissociation species of H2 if not protons?\nPage 3, lines 3-5. The process employed to let H2 bubbles form beneath the sample surface would need more details instead of relegating it to few lines in the Methods section. Indeed, the method used by the authors is distinctively different from that employed to create domes in transition metal dichalcogenides and h-BN by a Kaufmann source (refs 24-29) and is instead similar to that used for creating bubbles in h-BN (ref. 30). In particular, the authors should make it clear whether protons or ionised H2 molecules penetrate through the first top layers. I know that this is referenced to previous work by the authors, but given the pivotal role of this process a more explicit mention should be made in the main text.\nPage 4, line 4. Why h/R ~ 0.125 indicates that H2 permeate all the dome layers of graphene? What does this sentence mean? I’m not saying that it is wrong, simply I cannot understand it (and likely the readers as well).\nPage 4, lines 7 and 8. The Raman data should be discussed more explicitly. Why the presence/absence of D peak is relevant? Personally, I know why. However, another reader may not. Please, provide at least a reference and/or say in the extended data what each Raman peak corresponds to. The authors state that “no interlayer H2 migrations are observed. There are no obvious damage or wrinkles observed on the regions where the H2 bubble disappears by AFM”. While I agree on this statement, yet this aspect would require some more discussion or AFM images taken/shown on a smaller scale length to really make the reader appreciate the absence of damages or wrinkles. This is a crucial aspect of the present work and it deserves more attention.\nExtended data Fig. 1. The figure is nice and shows important results, but it is quite confusing: for three different samples, three different sets of data are shown.\n2L graphene: optical and AFM images after 900 °C annealing and Raman vs annealing temperature\n3L graphene: optical and AFM images before annealing and Raman vs annealing temperature\n2L h-BN: AFM images before and after annealing and AFM profile analysis.\nThis makes the readers’ (and referees’) life hard. If the authors wish, they can leave this figure as it is, but I’d encourage them to make an extra effort to render the figure more rational, if possible.\nExtended data Fig. 2. The Raman and photoluminescence (PL) data should be described properly. What are the different Raman peaks (say which Raman peaks are due to the strained bubbles and which ones are due to the bulk material beneath)? Likewise, the PL data are shown without any comment. Are the PL data affected by strain? If the authors feel they cannot explain the PL data, it’d be better to remove them.\nPage 4, lines 13-15. The deuterium treatment was performed after the creation of H2 bubbles. Is it quite puzzling that D+ ionises H2 and form HD. Could it be the case that H contamination was present in the D bottle? In addition, the authors should specify that deuterium treatment was performed on h-BN. Was deuterium treatment performed on h-BN, only? This is just a curiosity, I don’t mean that the authors should perform deuterium treatments on the other materials.\nPage 5, line 15. Frankly, I’d not say that the power is very weak: 1 mW should result in a power density of about 100 kW/cm2. As a matter of fact, this quite high power density is fully consistent with the observation that temperatures in excess of 700 °C are necessary to observe H2 dissociation.\nThe experiment described in Fig. 2 and related text is elegant and insightful. I have some questions. Why MoS2 was chosen? Were similar findings observed for graphite and h-BN, too? This point gives me the opportunity to move a general criticism to this work. Often, the authors move from one material to another that creates some confusion and might leave some room for doubts about the general validity of the reported observations.\nReferring to Figure 2d, I do not understand the profile shown. It looks like the bubble is 10 nm tall. Are the authors sure that they are not measuring just the PMMA material and no bubble is left beneath? The same apply to extended data Figure 4. My impression that no H2 gas is present any more due to the bubble explosion. Can the authors elucidate this point?\nPage 5, line 22. Please, specify the PMMA/PEM thickness.\nPage 14. Regarding the calculation of the permeation rate. Is this an ensemble measurement? What the summation index indicates? A summation over different bubbles?\nPage 7, lines 27 and 28. There should be a mistake in exp(-N), since this formula seemingly makes no sense.\nFigure 4b. I’d suggest to include the NP-free data, too, so that a clear comparison can be done.\nThe experiment with metallic NPs is very interesting. Have the authors ever considered to use NPs before H treatment? Could the formation of H2 bubbles be promoted by the presence on metal NPs?\nPage 9, lines 4-6. The authors state that “it is still puzzled that Pt shows no significant reduction for 3L graphene, which may result from the aggregation and deactivation of Pt NPs at higher temperatures”. Frankly, I find this observation quite sensible and not puzzling at all. Indeed, if the metal NPs are further from the gas-bubble interface, there should be a reduced H2 dissociation. On the contrary, I find it puzzling the absence of a clear reduction of EA with increasing crystal thickness in MoS2.\nThe experiments involving a different external atmosphere are very intriguing. However, I urge the authors to reformulate this part (from line 15 to line 30 at page 9 and from line 1 to line 2 at page 10) of the manuscript. Both text and Figure 4d are very confusing and hard to follow. The caption of Figure 4d is unacceptable: there is no account and explanation whatsoever of the data and lines shown. I’d prepare a new figure 5 (possibly including the data shown in extended data Fig. 8 and 9; the authors can best decide on this point) entirely devoted to this nice experiment and describe the results in a plain and clear manner by specifying what all lines in the figure are. In particular, a clear comparison between the data obtained in standard annealing experiments (namely, no O2) and in annealing experiments under O2 presence should be made. Similarly, extended data Fig. 8 and 9 are a bit confusing, since the figures compare images taken after annealing at different temperatures and different gas atmospheres. I know that the bubble deflation occurs at different temperature values, but the authors should try to compare images as close as possible in terms of annealing temperatures and experimental conditions. This is particularly true for h-BN in extended data Fig. 9.\nFinally, a critical discussion of the implications of the experiments with regards to applicative prospects for catalysis and fuel cell is lacking, despite this aspect was mentioned in the abstract. The authors should discuss this point, also briefly.\nIn summary, the manuscript sometimes lacks of clarity. The data presentation and related figures are confusing in some instance. Nevertheless, the topic is of high current interest and the results obtained are accurate, relevant and worth being published in Nat. Commun."}, "author_response": "Point-by-point response letter (NCOMMS-25-81449-T)\nPoint-by-point responses to the Reviewers’ comments (NCOMMS-25-81449-T)\nReferee #1 (Remarks to the Author):\nIn this manuscript, the authors demonstrate an intriguing behavior of hydrogen gas permeation\nthrough defect-free atomically-thin membranes. Although the report is more phenomenologically, I\nbelieve there is fundamentally important mechanisms underneath. Therefore, I highly recommend its\npublication to the community that may attract more attentions and promote the discovery of new\nphysics.\nTo my knowledge, catalytic dissociation of hydrogen gas via 2D surfaces at relatively high\ntemperatures (here, up to 900 °C) was not reported previously. More importantly, at this temperature,\nwhether and how proton permeates through multilayer 2D materials remain an interesting open\nquestion. In addition, the authors further demonstrate an exit effect of permeation by changing the\nmembrane surfaces that are in contact with either metal catalysts and/or atmosphere gases.\nInterestingly, these changes seem can remotely influence the permeation process that are separated by\ndefect-free 2D materials.\nPersonally, I think those phenomenon are interestingly enough for publication at this stage.\nReply: We thank the Referee #1 for his/her positive comments, strong support and favourable\nrecommendation for our work.\n(1) Nevertheless, I still recommend the authors to exclude the possibility of proton permeation through\nthe interlayer spacing.\nReply: Thanks for your kind suggestion. As for the possibility of proton permeation through the\ninterlayer spacing, we have conclusively excluded this mechanism based on the experimental evidence\nbelow:\na) Monitoring of areal density changes\nBy monitoring the areal density evolution of H bubbles during permeation, no observable\n2\nappearance of proton permeating through vdW interlayers. If such permeations occur, it should result\nin the following observable phenomena: (i) detectable bubble displacement; (ii) emerging new bubbles;\n(iii) enlarging bubbles. However, there are no these expected signatures. Fig. R1a-b demonstrate that\nthe areal density of H bubbles in graphite is reduced from 0.008 μm-2 to 0.006 μm-2 after 850 °C\n2\nannealing, where no new bubbles are emerged, no bubbles are migrated or enlarged, and the\nvolumes for almost all bubbles are decreased. The morphological evolution remains consistent even\nfor the graphite with much higher H bubble density (Fig. R1c-d). The areal density is reduced from\n2\n0.040 μm-2 to 0.027 μm-2 where no bubble migration is observed.\nFig. R1. Areal density evolution of H bubbles. a, b, Optical images for as-prepared H bubbles in 2L\n2 2\ngraphene and the same graphite after thermal annealing at 850 °C under pure H atmosphere. c, d, Optical\n2\nimages for as-prepared H bubbles in 2L graphene and the same graphite after thermal annealing at\n2\n600 °C under pure O atmosphere.\n2\nb) Directional electric field modulation\nTo verify whether the proton transporting across vdW interlayer, we have supplemented to apply a\nparallel electric field (50 kV/m) to the graphite layers with 2L-Gra bubbles and perform the annealing\nat 500 °C. If protons decomposed by H\n2\nprimarily transport across interlayer channels, this electric\nfield should significantly accelerate their interlayer migration. However, Figure R2a-e show no\nsignificant change in either the size or the location of H bubbles under the applied parallel electric\n2\nfield. This demonstrates that protons cannot be effectively driven along interlayer channels, and the\nvdW interlayer is neither the primary nor an efficient pathway for proton permeation.\nWe have further applied a perpendicular electric field (50 kV/m) perpendicular to the graphite flakes\nwith 2L-Gra bubbles and perform the same annealing at 500 °C. In stark contrast to the parallel electric\nfield, the perpendicular electric field significantly enhances the permeation rate (Fig. R2f-j). Based on\nthe direction of electric field (Fig. R2h, inset), we propose that electrons accumulate on the H\n2\nbubble\ndomes, which assists the proton permeation. This result clearly demonstrates two conclusions: (i) The\ndissociation species of H are electrically charged (should be protons), since their permeation is\n2\nstrongly affected by the electric field; (ii) Enhanced permeation occurs only when the field is aligned\nperpendicular to the graphite layers, indicating that the protons must traverse an energy barrier normal\nto the basal plane (i.e., through the lattice) rather than transporting along in-plane interlayer pathways.\nFig. R2. Regulation by directional electric field. a, Optical image of as-prepared 2L-Gra bubble on\nSiO /Si. b, Corresponding AFM image of 2L-Gra bubble labelled in a. c, Optical image of 2L-Gra bubble\n2\nafter 30-min annealing at 500 °C under parallel electric field (50 kV/m). The inset illustrates the schematic\nof applying parallel electric field. d, Corresponding AFM image of 2L-Gra bubble in labelled in c. e,\nComparison of ex situ AFM height profiles for the same bubble, extracted along the dashed lines in b and\nd. f, Optical image of as-prepared 2L-Gra bubble on SiO /Si. g, Corresponding AFM image of 2L-Gra\n2\nbubble labelled in f. h, Optical image of 2L-Gra bubble after 30-min annealing at 500°C under\nperpendicular electric field (50 kV/m). The inset illustrates the schematic of applying perpendicular electric\nfield. i, Corresponding AFM image of 2L-Gra bubble labelled in h. j, Comparison of ex situ AFM height\nprofiles for the same bubble, extracted along the dashed lines in g and i.\nTaken together, the supplemented experiments involving areal density evolution and electric field\nmodulation collectively demonstrate that proton permeation occurs through perpendicular permeation\nof the graphite lattice.\nIn the revised manuscript, we have added the relevant experimental details in the Methods\n“Directional electric fields to identify the permeating species and pathway”, and we have already\nadded Fig. R1 and Fig. R2 into the Supplementary Fig. 7 and 8, and revised the statement below:\nPage 5, line 15: “Furthermore, the areal density evolutions of H bubbles are monitored, indicating\n2\nno observable evidence of proton transporting through the vdW interlayers (Supplementary Fig. 7).\nThen, we further apply the electric field with different direction to regulate the proton permeation, and\nfind the parallel electric field have no effect on the H permeation (Supplementary Fig. 8a–e). However,\n2\nthe perpendicular electric field can markedly reduce the H permeation temperature and enhance the\n2\npermeation rate (Supplementary Fig. 8f–j). All these experimental results together confirm that the\npermeating species are charged and migrates through the 2D materials lattice rather than along the\nvdW interlayer space.”\n(2) What is the explanation of the faster permeation of D\n2\nin Fig. S5?\nReply: Thank you for your insightful question. The difference in permeation rates between H and D\n2 2\ncan be explained within the Arrhenius equation Γ\nP\n= A‧exp(-E\nA\n/k\nB\nT). Here, k\nB\nis the Boltzmann\nconstant, T is the permeation temperature, E is the activation energy. The pre‑exponential factor A\nA\nencompasses other factors, such as the number of graphene layers, molecular thermal velocity, and the\ninteraction between the molecules and the graphene surface.\nAt lower temperatures, the exponential term exp(-E /k T) dominates, and the observed permeation\nA B\nis primarily governed by the activation energy E . As temperature rises, the influence of the\nA\npre‑exponential factor A becomes increasingly significant. Our measured values are A = 1.5×1026 s-\nD\n1m-2 and A = 1.0×1024 s-1m-2, with A being two orders of magnitude higher than A . The critical\nH D H\ntemperature at which these two factors balance corresponds to the intersection point of the H and D\n2 2\ncurves, approximately 580 °C.\nWe propose that this large difference between A and A is attributed to the mass‑dependent kinetic\nD H\nenhancement of deuterium under confined, high‑temperature conditions. At elevated\ntemperatures, spatial confinement promotes more frequent and energetic intermolecular collisions.\nDue to its larger mass, D gains greater momentum or kinetic energy from both thermal motion and\n2\ncollision processes than H . This leads to a stronger interaction with the graphene lattice, thereby\n2\nincreasing the probability of dissociation and permeation, which is reflected in the larger pre-\nexponential factor A.\nNotably, while the above kinetic model consistently explains our experiments, the detailed\nmechanism behind the pronounced mass‑dependent enhancement in the pre‑exponential factor,\nespecially under confinement and at high temperature, presents a promising direction for further\ninvestigation. Clarifying this scenario is an important goal of ongoing work, and we hope that these\nexperimental findings will also stimulate further theoretical interest in this research area.\n(3) Did the author try gas permeation using hBN bubbles? And what is the activation energy. Important\ninformation can be obtained by such experiment.\nReply: Thank for your professional comment.\nWe have conducted gas permeation experiments using hBN bubbles under different atmospheres.\nFor 2L hBN bubbles, H permeation shows a critical temperature of about 600 °C under external H\n2 2\nenvironment (Fig. R3a). Numerical fitting yields an E of 1.40 ± 0.30 eV (Fig. R3c).\nA\nWhen the external atmosphere is changed to pure O\n2\n(Fig. R3b). The Arrhenius plot also shows two\ndistinct slopes, which is similar as the behaviour of H bubbles in graphite, corresponding to two\n2\ndifferent activation energies (0.5 ± 0.2 eV and 1.0 ± 0.2 eV, respectively) within specific temperature\nranges (Fig. R3c).\nIn the revised manuscript, we have already added Fig. R3c into the Fig. 5c, and added Fig. R3a-b\ninto Supplementary Fig. 24, and revised the statement below:\nPage 11, line 15: “… two distinct pathways with corresponding E of 0.5 ± 0.2 eV and 1.0 ± 0.2 eV,\nA\nrespectively (Fig. 5c and Supplementary Fig. 24). In contrast, permeation under H atmosphere\n2\npresents a higher fitted E of 1.4 ± 0.3 eV. These results demonstrates that an inert 2D crystal can be\nA\nrendered catalytically active through modulation of the external chemical environment.”\nFig. R3. H permeating hBN under different atmospheres. a, Morphological evolution of H bubbles in\n2 2\n2L hBN by annealing under H atmosphere at different T. The height and diameter of bubbles show\n2\ndecrease from 600 °C. b, Morphological evolution of H bubbles in 2L hBN by annealing under O\n2 2\natmosphere at different T. The height and diameter of bubbles show obviously decrease from 500 °C. c,\nГ of 2L hBN domes under in H and O external atmosphere, respectively. Error bars represent at least\nP 2 2\nthree different samples, and dash lines are fitting to the Arrhenius dependence with T.\n(4) How the metal nanoparticles being deposited onto the graphene surface? Could they introduce any\ndefects? The metal nanoparticles also seem unevenly distributed all over the surface, say in Fig. S7.\nDo they appear to be on the bubbles?\nReply: Thanks for your professional comment.\nAll the metal nanoparticles (NPs) are deposited onto the 2D material flakes via a mild wet transfer\nmethod. This approach is specifically chosen to avoid the possible bubble defects that can be induced\nby thermal evaporating or magnetron sputtering metal films. The standard procedure is as follows:\nmetal NPs are coated onto SiO /Si using thermal evaporation or sputter. The PMMA film is then spin-\n2\ncoated onto the NPs and detached from SiO /Si after immersed in KOH aqueous solution. The PMMA\n2\nfilm with NPs is subsequently cleaned by DI water, and then pasted onto the 2D flakes with as-prepared\nbubbles. Following 120 °C drying, the PMMA is removed by acetone, resulting in the bubbles\ndecorated with metal NPs uniformly.\nFigure R4a shows an optical image of graphene bubbles decorated with uniformly covered Pt NPs,\nwhere a scratch is shown for reference. Figure R4b presents an AFM image of 2L-Gra bubble covered\nby Pt NPs, confirming their uniformly distributed across the bubble domes. Zoom-in AFM image (Fig.\nR4c) reveal that most NPs have the diameters around 20 nm with heights between 3 ‒ 5 nm, indicating\nhomogeneous dispersion. Figure R4d plots the Raman spectra of Pt-decorated 2L-Gra bubbles before\nand after thermal annealing. The as-prepared graphene bubble domes show no defect-related D peaks,\nconfirming that the transfer process of NPs introduces no detectable defects. Remarkably, even after\ncompletely reducing bubbles by thermal annealing (750 °C), the same dome region still remains free\nof defect signatures.\nFig. R4. Uniformity of coated Pt NPs on H bubbles. a, Optical image of 2L-Gra bubble decorated with\n2\ntransferred Pt NPs. b, AFM image of 2L-Gra bubble decorated with transferred Pt NPs. c, Zoom-in AFM\nimage showing the homogenous distribution of Pt NPs, indicating the dimensions for NPs are ~20 nm in\ndiameter and 3 ‒ 5 nm in height. d, Raman evolutions of H bubbles in 2L-Gra decorated with Pt NPs after\n2\nannealing in H atmosphere at different temperature. The Raman spectra of Pt-decorated 2L-Gra bubbles\n2\nafter thermal annealing still shows no defect-related D peaks, confirming that the transfer process of NPs\nand thermal treatment introduce no detectable defects.\nRegarding the non-uniform regions observed in previous Fig. S7 (revised Supplementary Fig. 22),\nthese are primarily residual fragments caused by the rupture during producing MoS bubbles, rather\n2\nthan the inhomogeneous distribution of metal NPs. As clarified in Fig. R4, the NPs are only 3 – 5 nm\nin size, which makes them difficult to distinguish by optical microscopy. In fact, the transferred NPs\nare uniformly distributed by AFM.\nIn the revised manuscript, we have already added Fig. R4 into the Supplementary Fig. 19, and\nrevised the statement below:\nPage 9, line 11: “Uniformly distributed metal NPs are covered on the graphene bubbles\n(Supplementary Fig. 19a–c), and the graphene domes are confirmed to be defect-free after covering\nPt NPs and subsequent post-annealing (Supplementary Fig. 19d).”\nMinor suggestions:\n(5) It is important to add the methods of controlling the number of bubble wall layers, as well as for\nidentifying the number of layers.\nReply: Thanks for your suggestions.\nThe control and determination of bubble layer numbers have been investigated in our previous study\n(Gao L. B. et al., Nano Lett. 23, 8203, 2023). Briefly, layer number control is primarily achieved by\nadjusting the plasma power and temperature, and the thickness of the bubbles is characterized mainly\nby measuring the step heights of burst bubbles using AFM.\nAs redrawn in Fig. C1, we analyse the burst bubbles that formed due to the rapid growth. Figure\nC1a-b present AFM images and corresponding height profiles of three representative burst bubbles\nwith different permeation depths. Each step is measured to be ~0.35 nm, matching the monolayer\nthickness of graphene, and the measured dome thicknesses correspond to 1, 2, and 3 layers. A statistical\nanalysis of numerous burst bubbles in graphite and MoS reveals distinct thickness distributions (Fig.\nIn contrast, the bubbles in MoS predominantly have 1L domes. These variations are attributed to\n2\ndifferences in the electronic structure and internal interactions of the respective 2D crystals.\nAdditionally, the layer thickness of graphene domes can be controlled by adjusting the plasma power\n(Fig. C1d), a phenomenon similarly observed in other 2D crystals.\nFig. C1. Permeation depth of protons into 2D crystal multilayers. a, Typical AFM images of the busted\nbubbles with different layer numbers in graphite. b, Corresponding height profiles of the busted bubbles,\neach step is ~0.35 nm thick. c, Statistics of the layer number of H bubble domes in graphite and MoS\n2 2\nflakes after proton permeation. The data is taken from hundreds of busted bubbles, graphite prefers 2L\nbubbles, MoS prefers 1L bubbles. d, Statistics of the layer number of bubble domes in graphite treated\n2\nby the different plasma powers. The layer number of bubble domes strongly depends on the kinetic\nenergies of protons.\nIn the revised manuscript, we have revised the section on the bubble preparation and characterization.\nPage 3, line 21: “Based on our previous work, protons from a hydrogen plasma permeate the 2D\ncrystals lattices at elevated temperature, subsequently recombining into molecular H within the\n2\ninterlayer region, where they gradually accumulate. A substantial amount of H are confined within\n2\nthe van der Waals interlayers of 2D material to form H bubbles, with a defined layer number of 2D\n2\nmaterial as the bubble domes, the domes thickness can be confirmed by burst bubbles.”\n(6) Page 3, Fig. 1d: the scale of the x-axis (from 25 to 400) appears to be incorrect.\nReply: Thanks for your kind reminder. The scale of the x-axis in main Fig.1d has been corrected.\n(7) Page 5, Fig. 2a: the structural model of the first MoS layer appears to be discontinuous (with\n2\nbroken bonds?).\nReply: Thanks for your kind reminder. This is a typo, and it has been corrected in the revised\nmanuscript.\n(8) Page 15: undefined variables in the equations.\nReply: Thanks for your reminder.\nThis undefined variable k is the Boltzmann constant. We have also supplemented the following\nB\ndescriptions in Page 16, line 12: “k is the Boltzmann constant.”\nB\n(9) Spelling typos, such as ‘… analyze the date (data?)’ in the author’s contribution.\nReply: Thanks for your kind reminder.\nWe have also corrected the typos, can corrected it as follows,\nPage 20, line 6: “...analyse the data and wrote the manuscript.”\nReferee #2 (Remarks to the Author):\nThis manuscript presents a study on hydrogen permeation through defect-free 2D materials, with a\nfocus on graphene. The authors provide experimental evidence that hydrogen can permeate pristine\ngraphene at elevated temperatures in the form of protons. The work is systematic, well-supported by\nmultiple characterization techniques, and offers valuable insights into the catalytic dissociation-\npermeation mechanism. However, several issues require clarification and additional evidence before\nthe manuscript can be considered for publication.\nReply: We thank the Referee #2 for his/her positive comments, strong support and favourable\nrecommendation for our work.\n(1) The authors claim their work “overturns the conventional wisdom about the gas permeation barrier\nfor graphene.” However, this conventional wisdom was already challenged by Sun et al., Nature 579,\n229–232 (2020) (Ref 13), which first reported room-temperature H permeation through defect-free\n2\ngraphene. The current manuscript should differentiate its contributions from this foundational study.\nReply: Thanks for your kinder reminder and we appreciate your valuable comment.\nRegarding the pioneering study (Geim A. K. et al., Nature 579, 229–232, 2020), they have\nconfirmed H could permeate through defect-free 1L graphene lattice even at room temperature, and\n2\nfurther suggest that the atomic hydrogen is supposed to the dissociation species of H that permeating\n2\ngraphene (Geim A. K. et al., PNAS 120, e2300481120, 2023).\nOur study shows that H can permeate 2L graphene, 1L MoS and hBN at elevated temperatures and\n2 2\nproviding new insights into the permeation mechanisms that dissociation species of H permeating\n2\ngraphene is proton. Besides, we also quantify the associated activation energies, and explore the\nbroader implications among different 2D materials, thereby extending the understanding of this\nphenomenon beyond the initial discovery.\nTo better differentiate our work to Geim’s results, we have made significant revisions in the abstract\nsection, as follows,\nPage 1, line 18: “While defect-free 2D crystals such as graphene have long been considered\nimpermeable to all gases, recent studies show that pristine monolayer graphene permits room-\ntemperature hydrogen permeation. However, the identity of the permeating species and its\ngeneralizability to other 2D materials remain unclear.”\nPage 1, line 28: “These findings reveal a catalysis-driven proton permeation mechanism, and\nfundamentally deepen the understanding of hydrogen permeation through 2D crystals.”\n(2) The systematic investigation of high-temperature regimes, layer-number independence of E ,\nA\nand\nthe role of metal NPs/atmosphere, which significantly expands upon the initial discovery. The\nintroduction and discussion sections should be revised to frame the work as a mechanistic deepening\nand generalization of the phenomenon first reported by Sun et al., rather than a standalone discovery.\nReply: We sincerely thank the reviewer for this constructive suggestion.\nWe have carefully revised the introduction and discussion sections to explicitly frame our findings\nas a mechanistic extension and generalization of the gas permeation phenomenon firstly reported by\nSun et al., rather than as an independent discovery.\nWe have made significant revisions in the introducing section, as follows:\nPage 2, line 18: “Building on this initial report of RT H permeation13, a deeper understanding of\n2\nthe inherent catalytic-permeation properties of defect-free graphene and related 2D crystals is\nessential.” Ref 13 is (Sun et al., Nature 579, 229–232, 2020).\nPage 2, line 23: “Resolving these aspects is essential for a deeper mechanistic understanding and\nfor generalizing the observed behaviour, with potential implications for applications such as\nhigh‑temperature proton‑conducting fuel cells and catalytic membrane reactors in hydrogen‑based\nprocesses.”\n(3) While the three-step mechanism is clearly proposed, direct evidence for the catalytic dissociation\nof H into protons on pristine graphene remains indirect. If would be better if the authors provide more\n2\ndirect spectroscopic or simulation evidence to support this first step.\nReply: We sincerely appreciate your insightful comment.\nActually, we are always seeking a suitable method to detect protons directly. Unfortunately, we fully\nacknowledge that acquiring direct spectroscopic or computational evidence for this step remains\nparticularly challenging, mainly because experimental techniques for directly detecting trace protons\nare difficult at high temperature. Our experiments are conducted at high temperatures, and the proposed\nproton-formation pathway inherently involves charge‑transfer processes, both factors pose significant\nchallenges for real‑time spectroscopic characterization or theoretical simulation now.\nTo address this concern, we also design more experiments by externally applying electric fields in\ndifferent directions (parallel vs. perpendicular) to monitor the changes of the dissociated hydrogen\nspecies. The experimental conclusions are summarized below:\n· Applying parallel electric field at 500 °C, the H permeation shows negligible affected,\n2\nindicating the dissociation species does not transport across the vdW interlayer (Fig. R2a-e).\n· Applying perpendicular electric field at 500 °C, the H\n2\npermeations are significantly affected,\nwhich is consistent with the charged species (protons, H+) (Fig. R2f-j).\nThe direction-dependent field effect strongly implies that the dissociated hydrogen species are\ncharged, as neutral species (H or H ) should not exhibit such anisotropic behaviour. We believe the\n2\nnew experimental results can further provide practical alternative evidence that the dissociated species\nof H through 2D materials is proton.\n“Directional electric fields to identify the permeating species and pathway”, and we have already\nadded Fig. R2 into the Supplementary Fig. 8, and revised the statement below:\nPage 5, line 16: “Then, we further apply the electric field with different direction to regulate the\nproton permeation, and find the parallel electric field have no effect on the H permeation\n2\n(Supplementary Fig. 8a–e). However, the perpendicular electric field can markedly reduce the H\n2\npermeation temperature and enhance the permeation rate (Supplementary Fig. 8f–j). All these\nexperimental results together confirm that the permeating species are charged and migrates through\nthe 2D materials lattice rather than along the vdW interlayer space.”\nFig. R2. Regulation by directional electric field. a, Optical image of as-prepared 2L-Gra bubble on\nSiO /Si. b, Corresponding AFM image of 2L-Gra bubble labelled in a. c, Optical image of 2L-Gra bubble\n2\nafter 30-min annealing at 500 °C under parallel electric field (50 kV/m). The inset illustrates the schematic\nof applying parallel electric field. d, Corresponding AFM image of 2L-Gra bubble in labelled in c. e,\nComparison of ex situ AFM height profiles for the same bubble, extracted along the dashed lines in b and\nd. f, Optical image of as-prepared 2L-Gra bubble on SiO /Si. g, Corresponding AFM image of 2L-Gra\n2\nbubble labelled in f. h, Optical image of 2L-Gra bubble after 30-min annealing at 500°C under\nperpendicular electric field (50 kV/m). The inset illustrates the schematic of applying perpendicular electric\nfield. i, Corresponding AFM image of 2L-Gra bubble labelled in h. j, Comparison of ex situ AFM height\nprofiles for the same bubble, extracted along the dashed lines in g and i.\n(4) The mechanism by which Pt and Pd NPs reduce the energy barrier is attributed to steps 2&3, but\ndirect evidence is lacking.\nReply: Thank you for raising this important innovation point.\nAlthough the lack of direct experimental evidences for steps 2 (proton permeation) and 3 (proton\nrecombination), we would like to clarify that the proposed mechanism is grounded by the integrative\nanalysis of published literatures and our experimental observations.\nPrior studies have definitively shown that noble metals such as Pt and Pd can effectively reduce the\nenergy barriers associated with proton permeation even without direct contact with protons (Step\n2) (Geim A. K. et al., Nature 516, 227-230, 2014) and proton recombination (Step 3) (Jaramillo T.\nF. et al., Science 355, eaad4998, 2017). These published literatures provide a foundation for the\ninfluence of metal NPs on these two critical steps.\nIn our experimental, the total E is constituted by these three steps, i.e., E = E + E + E . On one\nA A 1 p 3\nhand, Pt and Pd NPs are coated on the outer surface of the bubble domes. Crucially, the NPs are not in\ndirect contact with the H\n2\nmolecules inside the bubble. This positioning allows them to interact with\nprotons during permeation from the interior to the exterior (Step 2, E ), and to directly catalyse the\np\nproton recombination reaction (Step 3, E ). Moreover, if Pt and Pd NPs attributed to the step 1, E\n3 1\nshould be associated with the materials domes thickness. However, the reduced activation energy (E )\nA\nexhibits no correlation with the permeated layer numbers, like Pt NPs on MoS bubbles (main Fig. 4d),\n2\nwhere E is not correlated with metal NPs. The absence of variation for different permeation\n1\ndistances rules out a significant role in Step 1 (initial dissociation, E ).\nsized bubbles remains difficult and merits targeted investigations in the future. Nevertheless, the\nconsistent reduction of E under the conditions of spatial separated Pt and Pd NPs, leads us to conclude\nA\nthat steps 2 and 3 are the most plausible pathways through which the NPs exert their effect.\nPage 10, line 13, we state that: “Considering the fact of long-distance non-direct contact of NPs, as\nwell as reduced E exhibits no correlation with the permeated layer numbers, like Pt NPs on 1L – 3L\nA\nMoS , the NPs should primarily affect the steps (2) and (3).”\n2\n(5) The finding that E is independent of layer number is intriguing but counterintuitive. The authors\nA\nshould discuss possible physical or chemical reasons for this behaviour more thoroughly, perhaps with\nsupport from theoretical calculations or modelling.\nReply: We appreciate the reviewer’s insightful attention.\nWe agree that this finding merit deeper mechanistic discussion, and provide the following additional\nclarifications:\na) Theoretical challenge in modelling the high‑temperature proton dynamics\nThrough in-depth discussions with the theorists, we realize that the theoretical simulation of\ngraphene‑catalysed dissociation of H molecules into positively charged species (i.e., protons) at high\n2\ntemperature, along with the subsequent permeation through crystalline lattices, poses a major\nchallenge for commonly used theoretical and computational methods. These processes involve\nnon‑equilibrium thermal effects and dynamic barrier‑crossing events, which are difficult to capture\nusing the standard static or low‑temperature approximations.\nb) Theoretical simulation of layer number-independent dissociation energy\nAs an alternative, we substitute to perform the theoretical calculations of the activation energy\nrequired for H dissociation in the graphite vdW interlayers. As shown in Fig. R5, the dissociation\n2\nenergy is mainly correlated to the interlayer spacing and are not affected by the upper and bottom layer\nnumbers.\nWith the interlayer spacing of 3.5 Å, the activation energy required for spontaneous H dissociation\n2\nbetween graphene layers is 1.71 eV (Fig. R5a–b). When the interlayer spacing exceeds 5 Å, the H\n2\ndissociation energies keep around 4.2 eV. When H molecules are confined within graphene bubbles,\n2\nwhere the dome height far exceeds 5 Å, the activation energy for H dissociation here is high. When\n2\nthe interlayer spacing is fixed at 3.5 Å, theoretical calculations reveal that the upper or bottom layer\nnumber of graphene has negligible influence on the dissociation energy (Fig. R5c–d). This may make\nup the absence of the theoretical mechanism of constant E for different layer number in 2D crystals.\nA\nFig. R5. Theoretical simulation of dissociating H in different graphite vdW interlayers. a, Schematic\n2\nof dissociating H in graphite vdW interlayer. b, Relationship between dissociation energy and reaction\n2\ncoordinate at different vdW interlayer spacings. At the interlayer spacing of 3.5 Å, the energy required for\nspontaneous H dissociation between graphene layers is 1.71 eV. When the interlayer spacing exceeds 5\n2\nÅ, the H dissociation energy plateaus is around 4.2 eV. When H molecules are confined within graphene\n2 2\ndomes, where the dome height far exceeds 5 Å, so the highest energy barrier for H dissociation appears\n2\nhere. c, Schematic of H between 2L and 3L graphene interlayers with interlayer spacing of 3.5 Å. d,\nÅ. The dissociation energy is mainly related to the interlayer spacing and has no relation to the layer\nnumbers of graphene domes.\nc) Proposed layer-by-layer hopping mechanism with kinetic energy compensation\nWe therefore reasonably propose a possible mechanism whereby protons permeating the 2D crystal\nlattices through a layer-by-layer hopping process. Upon crossing the energy barrier of monolayer and\nprovisionally staying the vdW interlayer space, the tiny kinetic energy loss of protons can be rapidly\ncompensated by external thermal fluctuations at high temperature or perpendicular electric field\nby electrons injection. Since each layer has an identical energy barrier (E ) and the energy loss can\np\nbe dynamically compensated, the total E remains independent of the permeated layer numbers.\nA\nHowever, the layer number still affects the permeation rate, the thicker the 2D layers, the slower the\npermeation rate, which are experimentally confirmed.\nIn the revised manuscript, we have added the theoretical details in the Methods “Theoretical\ndissociation energy of H in graphene layer space”, and already added Fig. R5 into the Supplementary\nPage 8, line 7: “This layer-number independent behaviour can be explained by a sequential\npermeation mechanism. Firstly, regarding the initial dissociation of H , theoretical simulations\n2\nindicate that the dissociation energy depends primarily on the interlayer spacing and remains\nunchanged with increasing layer number (Supplementary Fig. 17).”\nReferee #3 (Remarks to the Author):\nThe paper by Xu, et al. reports experimental measurements on a potential scenario of graphene helps\nwith hydrogen dissociation into protons. The topic is interesting which has been proposed and tested\nboth experimentally and theoretically in recent years. However, the referee cannot see the main\nconclusions claimed in the present manuscript being well supported by experimental results. The\nreferee would not recommend publication due to the following comments:\nReply: We fully thank Referee #3 for the strong concern on this research area and support for this\nstudy.\nAs your comments, protons can permeate in 2D crystals and form H bubbles (WS : Polimeni A.\n2 2\net al., Adv. Mater. 31, 1903795, 2019; hBN: Wang H. M. et al., Nat. Commun. 10, 2815, 2019; graphite,\nGao L. B. et al., Nano Lett. 23, 8203, 2023), H can also be catalytically dissociated and permeate 1L\n2\ngraphene and hBN at room temperature (Geim A. K. et al., Nature 579, 229-232, 2020; Geim A. K. et\nal., PNAS 120, e2300481120, 2023), but it is not clear which species are H dissociated into.\npropose and experimentally can confirm the dissociated H species is proton, which is catalytically\n2\ndissociated on the surface of 2D crystals.\nMoreover, we have substantially expanded the revised manuscript to provide clearer background,\nmore detailed explanations of the original data, and additional experimental and theoretical\nsimulations. We believe these revisions effectively address your concerns and offer more robust\nsupport for our key innovation point.\nWe sincerely hope the revised manuscript can meet your expectations and welcome your further\ncomments.\n(1) The authors did not provide necessary experimental details in terms of how to introduce hydrogen\ninto the bubbles. The surfaces are contamination-free is also scientifically wrong, since all surfaces\nexposing or being prepared in air contains hydrocarbon, which may lead to the fact that gases in the\nbubble are not pure hydrogen but certain hydrocarbons. See many papers reporting the mechanical\nproperties of bubbles and characterizations using HRTEM for the hydrocarbon adhered on 2D\nmaterials’ surfaces.\nFollowing this comment, no experimental proof for the trapped gases being hydrogen was provided,\nwhich is required or the whole study would be built on a wrong or improper assumption.\nReply: Thank for your comments.\nWe agree that achieving high-purity hydrogen bubbles is the cornerstone of this study, and we\napologize for any lack of clarity in describing the method. This study is based on our previous results\n(Gao L. B. et al., Nano Lett. 23, 8203, 2023), where we describe how H molecules are intercalated in\n2\nthe 2D vdW interlayers to form non-destructive bubbles.\nBriefly, we develop a proton-assisted method (weak H plasma at elevated temperature) to permeate\n2\nthrough the 2D crystal lattices, and permeated protons re-combine into the molecular H in the\n2\ninterlayer and gradually aggregate into H bubbles (Fig. C2a).\n2\nvacuum and high-temperature annealing to remove the residual surface contaminants as thoroughly as\npossible. Followed by the introducing H gas and exciting plasma, protons are generated. With\n2\nprolonging protons injection, the H bubbles gradually grow larger (Fig. C2b–d). This method differs\n2\nfundamentally from mechanically transferred or stacking-based bubbles, which may introduce\nhydrocarbons inside.\nRaman spectroscopy further confirm that the graphene domes remain defect-free throughout this\nprocess (Fig. C2e). As established in published papers (Geim A. K. et al., Nature 516, 227, 2014; Geim\nA. K. et al., Nature 579, 229, 2020; et al.), defect-free graphene is impermeable to all molecules except\nhydrogen. Thus, even if there are adsorbates onside bubbles, they cannot permeate the lattice and mix\nwith the gases inside bubble. We do not detect any Raman signals associated with hydrocarbons.\nFurthermore, we directly measure the characteristic Raman peaks of molecular H (H+-assisted)\n2\nand D (D+-assisted) inside the bubbles (Fig. C2f), providing the clear experimental evidence of the\n2\ninside gas composition.\nNotably, the preparations of H bubbles in hBN and WS using permeating protons have also been\n2 2\nreported in other research groups (hBN: Wang H. M. et al., Nat. Commun. 10, 2815, 2019; WS :\nTo clarify the mechanism of H bubbles formation and enhance readability, we have also\n2\nsupplemented the related introductions in revised manuscript, as follows,\nPage 3, line 21: “Based on our previous work, protons from a hydrogen plasma permeate the 2D\ncrystals lattices at elevated temperature, subsequently recombining into molecular H within the\n2\ninterlayer region, where they gradually accumulate.”\nFig. C2. Formation of H -filled bubbles in 2D crystals. a, Schematic of H filled bubbles formed in the\n2 2\ninterlayers of graphite. Hydrogens permeate the lattices in the form of protons, resulting in the progressive\naccumulation of H in the interlayers. b, Typical AFM images of graphite after proton permeation for\n2\ndifferent times, from left to right are the ex situ measurements of the as-exfoliated surface, proton\npermeation for 40 s, and an additional 80 s. The density and size of H bubbles both increase as the\n2\ntreatment prolongs. c, Height evolution of a bubble growing as the proton permeation prolongs; the\ncorresponding bubble is labelled by green dash circles. d, Raman characteristic of bubbles with different\nheight, and no defects and hydrocarbons associate peaks are found. e, Raman characteristic peaks of H\n2\nand D molecules filled in the bubble. g, H bubbles in hBN formed by permeated protons. h, H bubbles\n2 2 2\nin WS formed by permeated protons. (Fig. C2a-e are redrawn from Nano Lett. 23, 8203, 2023; Fig. C2g\n2\nis redrawn from Nat. Commun. 10, 2815, 2019; Fig. C2h is redrawn from Adv. Mater. 31, 1903795, 2019)\n(2) Fig. 1c shows indeed gradual shrinkage of the bubble but this only occurred at higher than 700 C,\nwhereas below this threshold temperature, nothing happened. That is, the claim ‘their volumes progressively decreases’ is misleading. The constant h/R again is suspicious of sort of thermal induced\nmechanical evolution of 2D bubbles rather than permeation. Or otherwise, h/R would evolve, say at\nleast h would changes while keeping R more or less constant.\nReply: Thank for your constructive and professional comment.\nAs rightly noted, the bubble volumes decrease beyond a threshold temperature. Accordingly, we\nhave revised the previous description.\nPage 4, line 11: From “their volumes progressively decrease as the temperature increases until the\nbubble disappears entirely” into “their volumes progressively decreases once the temperature exceeds\na threshold value, until the bubbles disappear entirely”.\nMoreover, as addressed in the response to Comment (1), the H bubbles are unambiguously formed\n2\nby the permeation and subsequent recombination of protons into molecular H within the interlayer\n2\nspace, followed by gradual aggregation, rather than by thermally induced mechanical evolution.\nAdditionally, the constant ratio of height to radius (h/R) is determined by the elastic properties and\ninterfacial adhesion of the 2D crystals. We have statistically analysed the aspect ratios of the H bubbles\n2\nin 2L graphene, 1L hBN and 1L MoS with different heights. The average ratios of h /R in graphite,\n2 max\nhBN and MoS are 0.125, 0.14 and 0.18, respectively (Fig. C3, redrawn from Nano Lett. 23, 8203,\n2\n2023).\nFig. C3. H -filled bubbles in 2D crystals. a, Comparison of the cross-sectional profiles of 2L graphene,\n2\n1L hBN, and 1L MoS bubbles with the same diameter. b, Statistical aspect ratio of the H bubbles in 2L\n2 2\ngraphene, 1L hBN, and 1L MoS with different heights. The average ratios of h /R in graphite, hBN, and\n2 max\nMoS are 0.125, 0.14, and 0.18, respectively. Inset is a schematic of the true proportional bubble shape\n2\n(h /R = 0.125) with the calculated average strain of ~1.04%.\nmax\n(3) ‘No interlayer H migrations are observed’: Did the authors check the areal density of bubbles\n2\nbefore and after annealing to different T? Please provide.\nReply: Thank for your constructive and professional comment.\nBy monitoring the areal density evolution of H bubbles during permeation, no observable\n2\nappearance of proton permeating through vdW interlayers. If such permeations occur, it should result\nin the following observable phenomena: (i) detectable bubble displacement; (ii) emerging new bubbles;\n(iii) enlarging bubbles. However, there are no these expected signatures. Fig. R1a-b demonstrate that\nthe areal density of H bubbles in graphite is reduced from 0.008 μm-2 to 0.006 μm-2 after 850 °C\n2\nannealing, where no new bubbles are emerged, no bubbles are migrated or enlarged, and the\nvolumes for almost all bubbles are decreased. The morphological evolution remains consistent even\nfor the graphite with much higher H bubble density (Fig. R1c-d). The areal density is reduced from\n2\n0.040 μm-2 to 0.027 μm-2 where no bubble migration is observed.\nIn the revised manuscript, we have already added Fig. R1 as the Supplementary Fig. 7, and revised\nthe statement in the main content, as follows,\nPage 5, line 15: “Furthermore, the areal density evolutions of H bubbles are monitored, indicating\n2\nno observable evidence of proton transporting through the vdW interlayers (Supplementary Fig. 7).”\nFig. R1. Areal density evolution of H bubbles. a, b, Optical images for as-prepared H bubbles in 2L\n2 2\ngraphene and the same graphite after thermal annealing at 850 °C under pure H atmosphere. c, d, Optical\n2\nimages for as-prepared H bubbles in 2L graphene and the same graphite after thermal annealing at\n2\n600 °C under pure O atmosphere.\n2\n(4) It could be quite surprising to find hydrogen or protons transport across graphene thicker than\nmonolayer and MoS of any thicknesses, which contradicts the previous reports. Authors are suggested\n2\nto provide detailed explanation.\nReply: We appreciate your insightful comments.\nThe experimental phenomena of hydrogen/proton transporting across thicker graphene and MoS\n2\nlayers are indeed inconsistent with published results. This apparent discrepancy also underscores the\nkey innovation point of our study. It can be explained by the following aspects:\n(i) Prior experimental researches are predominantly conducted at near room-temperature, where\nthe kinetic energy is insufficient to overcome the energy barrier for protons permeating through\nmultilayers (Geim A. K. et al., Nature 516, 227-230, 2014; Geim A. K. et al., Nature 579, 229-\n232, 2020; et al.). In contrast, our studies are performed at elevated temperatures, where kinetic\nenergy are enough to enable the permeation across thicker layers. This aligns with the\nArrhenius-type behaviour expected for thermally activated actions.\n(ii) Our study also indicates that the activation energy for permeation remains largely independent\nof layer number for both graphene and MoS . This suggests that the permeation process through\n2\nsuccessive layers shares a similar energy barrier, and that proton energy can be effectively\ncompensated at high-temperature or under perpendicular electric field. Consequently,\nincreasing layer thickness can only reduce the absolute permeation rate, and it cannot\nfundamentally prevent proton permeations.\n(5) The authors compared PMMA and PEM. The referee here has two comments. On one hand, PMMA\ncould be highly permeable to protons especially in liquids, unless being cross-linked under exposure\nto high-dose electrons. On the other, these comparisons are so weak that cannot (I am afraid) lead to\nthe conclusion that it was protons that permeate 2D layers. Still no direct evidence is provided.\nReply: Thank for your constructive and professional comment.\nWe have supplemented more systematic experiments to address these concerns.\na) Proton permeability of PMMA and Nafion membranes\nWe perform the comparative studies to directly assess the intrinsic proton permeability of PMMA\nand Nafion. Firstly, the ~340 nm-thick PMMA film and ~320 nm-thick Nafion membranes (the same\nto Fig. 2) are prepared and transferred onto the flat substrates with a 1-mm-diameter aperture, followed\nby annealing at 130 °C to ensure complete and stable contact. Then, they are separately mounted in a\ncustomized electrochemical cell (Fig. R6a) using 0.1 M HCl as electrolyte and Pt foils as electrodes.\nStandard I–V scanning shows that the PMMA membrane exhibits a nearly undetectable current of <10-\nvoltage of ~0.1 V (Fig. R6b-c). This difference of proton permeability confirms the extremely low\nproton permeability for the used PMMA films, which can be used as the effective proton-blocking\nbarrier.\nIn the revised manuscript, we have added the experimental details in the Methods “Proton\npermeability of PMMA and Nafion”, and already added Fig. R6 as the Supplementary Fig. 13, and\nrevised the statement as follows,\nPage 6, line 13: “… where protons can permeate PEM but PMMA cannot (Supplementary Fig. 13)”\nFig. R6. Proton permeability of PMMA and Nafion membranes. a, Schematic of the proton permeability\nmeasurement for the different membranes. b, I–V characteristics of the 340 nm-thick PMMA membrane.\nc, I–V characteristics of the 320 nm-thick Nafion membrane.\nb) Probing the charged feature of the permeating species\nTo address this concern, we also design more experiments by externally applying electric fields in\ndifferent directions (parallel vs. perpendicular) to monitor the changes of the dissociated hydrogen\nspecies. The experimental conclusions are summarized below:\n· Applying parallel electric field at 500 °C, the H permeation shows negligible affected,\n2\nindicating the dissociation species does not transport across the vdW interlayer (Fig. R2a-e).\n· Applying perpendicular electric field at 500 °C, the H\n2\npermeations are significantly affected,\nwhich is consistent with the charged species (protons, H+) (Fig. R2f-j).\nThe direction-dependent field effect strongly implies that the dissociated hydrogen species are\ncharged, as neutral species (H or H ) should not exhibit such anisotropic behaviour. We believe the\n2\nnew experimental results can further provide practical alternative evidence that the dissociated species\nof H through 2D materials is proton.\n“Directional electric fields to identify the permeating species and pathway”, and we have already\nadded Fig. R2 into the Supplementary Fig. 8, and revised the statement below:\nPage 5, line 16: “Then, we further apply the electric field with different direction to regulate the\nproton permeation, and find the parallel electric field have no effect on the H permeation\n2\n(Supplementary Fig. 8a–e). However, the perpendicular electric field can markedly reduce the H\n2\npermeation temperature and enhance the permeation rate (Supplementary Fig. 8f–j). All these\nexperimental results together confirm that the permeating species are charged and migrates through\nthe 2D materials lattice rather than along the vdW interlayer space.”\nFig. R2. Regulation by directional electric field. a, Optical image of as-prepared 2L-Gra bubble on\nSiO /Si. b, Corresponding AFM image of 2L-Gra bubble labelled in a. c, Optical image of 2L-Gra bubble\n2\nafter 30-min annealing at 500 °C under parallel electric field (50 kV/m). The inset illustrates the schematic\nof applying parallel electric field. d, Corresponding AFM image of 2L-Gra bubble in labelled in c. e,\nComparison of ex situ AFM height profiles for the same bubble, extracted along the dashed lines in b and\nd. f, Optical image of as-prepared 2L-Gra bubble on SiO /Si. g, Corresponding AFM image of 2L-Gra\n2\nbubble labelled in f. h, Optical image of 2L-Gra bubble after 30-min annealing at 500°C under\nperpendicular electric field (50 kV/m). The inset illustrates the schematic of applying perpendicular electric\nfield. i, Corresponding AFM image of 2L-Gra bubble labelled in h. j, Comparison of ex situ AFM height\nprofiles for the same bubble, extracted along the dashed lines in g and i.\n(6) Previous theory on graphene including those on carbon nanotubes suggested that it was convex\nrather than concave curvatures that enhanced hydrogen dissociation whereas the concave curvatures\nfacilitated desorption. Additionally, a strong tensile strength (the bubble was always tensed with\nconstant h/R) did not help with hydrogen dissociation into ‘protons’. These theoretical suggestions\ncontradicts the authors’ setup and results, which should be clarified.\nReply: Thank for your constructive and professional comment.\nWe appreciate the opportunity to clarify how our experimental observations relate to the established\ntheoretical works on curvature-dependent hydrogen dissociation.\nFirstly, it has been experimentally demonstrated that graphene can dissociate and permeate H\n2\neven\nwhen the H is located on the concave side. The phenomenon is firstly reported by the gas-sealed drum\n2\n(Fig. C4a-b; Geim A. K. et al., Nature 579, 229-232, 2020), there is a pressure difference inducing\nstrain in graphene membrane, and the efficient permeation is observed from the concave to the convex\nside, indicating that the H dissociation remains feasible under certain strained, concave structures.\ncalculated strain in graphene domes is only ~1%. Furthermore, theoretical calculations indicate that\nthe non-flatness (ripples) of graphene can facilitate the H dissociation and permeation (Fig. C4c-d;\nretains nanoscale ripples or local convex features, which can provide favourable sites for H\n2\ndissociation even within the overall concave geometry.\nFig. C4. H permeation from concave to convex sides of graphene. a, b, H permeating graphene\n2 2\ndrum, where H is sealed at the concave side of graphene. c, d, Theoretical calculations of H permeation\n2 2\nfrom graphene assisted by the non-flatness (ripples) at the nanoscale. (a and b are redrawn from Geim A.\nK. et al., Nature 579, 229, 2020; c and d are redrawn from Yuan et al., Phys. Rev. B 108, 045408, 2023).\n(7) The same activation energy for different layers already provided a strong indication that the reduced\nvolume of bubbles was not due to hydrogen/proton permeating 2D layers but due to other possibilities\nsuch as interlayer spacing leakage or creation of gas-leak defects. For spacing leakage, authors should\ncheck the areal density of bubbles before and after rather than simply claim neighboring bubbles were\nnot affected. The creation of defects could partly reconcile the conflict results of H /proton permeate\n2\ntested graphene samples in Raman (S8), 1) Raman cannot sense defect density of lower than say 10%;\n2) G’ and 2D’ peaks emerge highly indicative of defects.\nReply: We appreciate your thoughtful suggestions.\nWe have further conducted additional experiments and analyses to address the concerns on\nmechanisms of bubble reduction systematically, as follows,\na) No interlayer spacing leakage through monitoring of areal density changes\nRefer to the response to Comment (3).\nb) No interlayer spacing leakage through directional electric field modulation\nRefer to the response to Comment (3).\nTaken a) and b) together, the areal density evolution and electric field modulation collectively\ndemonstrate that proton permeation occurs through the atomic lattices of 2D crystals.\nc) About Raman’s sensitivity to graphene defects\nRaman spectroscopy is widely recognized as an extremely sensitive tool for detecting defects in\ngraphene. According to published papers (Ferrari A. C. et al., Nano Lett. 11, 3190, 2011; Jorio A. et\nal., Phys. Rev. B 82, 125429, 2010; Jorio A. et al., Carbon 48, 1592, 2010; et al.), even when two\natomic defects are spaced 24 nm (<40 ppm defect density), the apparent Raman D peak can still be\nclearly observed (Fig. C5a). Generally, the Raman 2D peak in graphene is highly sensitive to the layer\nnumber, stacking order and interlayer coupling, but is not strongly related to atomic defects.\nAdditionally, there are not observable defect-related peaks (D and D’) in the Raman spectra for the\ngraphene bubble domes.\nFig. C5. Raman sensitivity to graphene defects. a, Raman spectra of graphene with different defect\ndensity, where I /I can be used to calibrate the defect density. b, Normalized Raman D, D’, G and 2D\nD G\npeaks for graphene with different defect density. (a is redrawn from Nano Lett. 11, 3190, 2011; b is redrawn\nfrom Phys. Rev. B 82, 125429, 2010)\nMoreover, we think that you may confuse with the two G peaks and two 2D peaks, which seem like\nthe G’ and 2D’ peaks (Fig. R7). In fact, the two G peaks (located at 1542 and 1582 cm-1) and the two\n2D peaks (located at 2610 and 2682 cm-1) are derived from the 3L graphene bubble domes (which has\na tensile strain of ~1%) and the bottom graphite. We do not detect any defect-related D peaks (which\nshould range between 1305 cm-1 and 1350 cm-1).\nFig. R7. H permeating 3L graphene. a, Schematic of H bubble in 3L graphene. b, Optical and AFM\n2 2\nimages after thermal annealing at different temperature. c, Raman evolutions of 3L graphene dome after\nannealing at 800 and 900 °C.\n(8) On the other hand, because the authors found prefactor scales as a function of exp(-N), a more\nplausible explanation would be the tested species transported layer by layer (for MoS , the transport\n2\nwould be through high-T induced defects-MoS has high-density S vacancies on the surface and also,\n2\nhigh catalytic activity). This suggests the tested bubbles that were seemingly sealed by 2L graphene\n(for example) were essentially composed of bubbles on bubbles and separated by each 1L of graphene.\nThis scenario would reconcile in part the conflict results of H /proton permeate 2L or thicker graphene\n2\nby the authors and others.\nReply: We appreciate your insightful observations and professional suggestions.\nWe agree that this layer-number activation energy (E ) merit deeper mechanistic discussion, and\nA\nprovide the following additional clarifications:\na) Theoretical challenge in modelling the high‑temperature proton dynamics\nThrough in-depth discussions with the theorists, we realize that the theoretical simulation of\ngraphene‑catalysed dissociation of H molecules into positively charged species (i.e., protons) at high\n2\ntemperature, along with the subsequent permeation through crystalline lattices, poses a major\nchallenge for commonly used theoretical and computational methods. These processes involve\nnon‑equilibrium thermal effects and dynamic barrier‑crossing events, which are difficult to capture\nusing the standard static or low‑temperature approximations.\nb) Theoretical simulation of layer number-independent dissociation energy\nAs an alternative, we substitute to perform the theoretical calculations of the activation energy\nrequired for H dissociation in the graphite vdW interlayers. As shown in Fig. R5, the dissociation\n2\nenergy is mainly correlated to the interlayer spacing and are not affected by the upper and bottom layer\nnumbers.\nWith the interlayer spacing of 3.5 Å, the activation energy required for spontaneous H dissociation\n2\nbetween graphene layers is 1.71 eV (Fig. R5a–b). When the interlayer spacing exceeds 5 Å, the H\n2\ndissociation energies keep around 4.2 eV. When H molecules are confined within graphene bubbles,\n2\nwhere the dome height far exceeds 5 Å, the activation energy for H dissociation here is high. When\n2\nthe interlayer spacing is fixed at 3.5 Å, theoretical calculations reveal that the upper or bottom layer\nnumber of graphene has negligible influence on the dissociation energy (Fig. R5c–d). This may make\nup the absence of the theoretical mechanism of constant E for different layer number in 2D crystals.\nA\nFig. R5. Theoretical simulation of dissociating H in different graphite vdW interlayers. a, Schematic\n2\nof dissociating H in graphite vdW interlayer. b, Relationship between dissociation energy and reaction\n2\ncoordinate at different vdW interlayer spacings. At the interlayer spacing of 3.5 Å, the energy required for\nspontaneous H dissociation between graphene layers is 1.71 eV. When the interlayer spacing exceeds 5\n2\nÅ, the H dissociation energy plateaus is around 4.2 eV. When H molecules are confined within graphene\n2 2\ndomes, where the dome height far exceeds 5 Å, so the highest energy barrier for H dissociation appears\n2\nhere. c, Schematic of H between 2L and 3L graphene interlayers with interlayer spacing of 3.5 Å. d,\nÅ. The dissociation energy is mainly related to the interlayer spacing and has no relation to the layer\nnumbers of graphene domes.\nIn the revised manuscript, we have added the theoretical details in the Methods “Theoretical\ndissociation energy of H in graphene layer space”, and already added Fig. R5 into the Supplementary\nPage 8, line 7: “This layer-number independent behaviour can be explained by a sequential\npermeation mechanism. Firstly, regarding the initial dissociation of H , theoretical simulations\n2\nindicate that the dissociation energy depends primarily on the interlayer spacing and remains\nunchanged with increasing layer number (Supplementary Fig. 17).”\nc) Proposed layer-by-layer hopping mechanism with kinetic energy compensation\nWe therefore reasonably propose a possible mechanism whereby protons permeating the 2D crystal\nlattices through a layer-by-layer hopping process. Upon crossing the energy barrier of monolayer and\nprovisionally staying the vdW interlayer space, the tiny kinetic energy loss of protons can be rapidly\ncompensated by external thermal fluctuations at high temperature or perpendicular electric field\nby electrons injection. Since each layer has an identical energy barrier (E ) and the energy loss can\np\nbe dynamically compensated, the total E remains independent of the permeated layer numbers.\nA\nHowever, the layer number still affects the permeation rate, the thicker the 2D layers, the slower the\npermeation rate, which are experimentally confirmed.\nd) Layer number determination for bubble domes\nWe measure the burst bubbles whose formation are attributed to rapid growth, as shown in Fig. C1\n(redrawn from our previous result: Gao L. B. et al., Nano Lett. 23, 8203, 2023). The AFM images and\ncorresponding height profiles of three representative burst bubbles indicate different permeation depths.\nEach step is ~0.35 nm height, matching the monolayer thickness of graphite. The measured dome\nthicknesses correspond to 1, 2, and 3 layers. The complete fractures also suggest that the bubbles are\npredominantly situated underneath the few-layer graphene, not intercalated between interlayers.\nFig. C1. Permeation depth of protons into graphite. a, Typical AFM images of the busted bubbles with\ndifferent layer numbers in graphite. b, Corresponding height profiles of the busted bubbles, each step is\n~0.35 nm thick. (All the data are redrawn from our previous result: Nano Lett. 23, 8203, 2023)\n(9) Whatever cases are, the authors should provide more experimental evidence and explanation, which\nare rather weak or lack in the present form.\nReply: We sincerely appreciate the reviewer’s constructive feedbacks and help us improve the\nmanuscript.\nBelow is a brief summary for our corresponding responses:\n1) H purity inside the bubbles (Fig. C2)\n2\n· Clarifying the proton-assisted method to produce H bubbles.\n2\n· Providing Raman characteristic peaks for H and D , but no hydrocarbon inside bubbles.\n2 2\n2) Mechanism of reducing H bubbles (Fig. R1 & R2)\n2\n· Revising the description for the temperature threshold.\n· Monitoring the areal density of bubbles and applying directional electric field.\n3) Conflict with published studies (Fig. R5)\n· Explaining that high temperature provides the necessary kinetic energy for proton permeation.\n· Providing theoretical calculations of the dissociation energy is related to interlayer spacing,\nbut not the layer number.\n4) Evidences for proton permeation (Fig. R2 & R6)\n· Conducting comparative experiments that PMMA blocks protons while Nafion does not.\n· Only perpendicular electric field can affect the permeation behaviours, indicating the\npermeating species are charged (protons).\n5) Reconciliation with theoretical predictions (Fig. C3)\n· Citing published results that show hydrogen permeating from the concave side of graphene.\n· Referencing theories on how nanoscale ripples (present under strain) facilitate the process.\n6) Concerns about bubble defects (Fig. C4 & R7)\n· Citing published papers on Raman sensitivity to confirm our detection level is sufficient.\n· Clarifying that observed two peaks in Raman spectra originate from strain, not defects.\n7) Clarification of bubble structure (Fig. C1)\n· Provided AFM analysis of burst bubbles, showing they are located underneath the multilayer\nstack, not intercalated between individual layers.\nReferee #4 (Remarks to the Author):\nThe manuscript by Jie Xu et al. regards the permeability of two-dimensional crystals to hydrogen.\nIn their manuscript, the authors show that hydrogen permeability is a catalysis-driven process leading\nto the dissociation of molecular hydrogen at the crystal surface. The topic is relevant for fundamental\nand practical aspects related to the physics and chemistry of atomically thin gas membranes.\nThe experiments performed are numerous, generally well conducted and interesting and the set of\ndata reported and related analysis are potentially valuable. The literature quoted is appropriate and\ncomplete. Therefore, this manuscript would deserve publication in Nature Communications.\nYet, the manuscript needs important changes. The English requires some corrections. In some\ninstances, the description of the results is not organised in a clear manner, e.g., different materials are\nconsidered in diverse experiments that may create confusion. The optical data require a more accurate\ndiscussion. The figures are sometimes not explicative and the last part of the work should be rewritten\nor reorganised. Indeed, the role of the external gas atmosphere in the molecular hydrogen dissociation\nis a most relevant aspect that requires a clearer presentation and a more detailed discussion of the data.\nReply: We sincerely appreciate your thoughtful and constructive comments on our manuscript. We\nhave carefully addressed all the raised concerns and have made substantial revisions to improve the\nclarity, organization, and presentation of our work.\nRegarding the English language, the manuscript has been thoroughly polished to ensure grammatical\naccuracy and readability. In addition, we have undertaken key revisions in direct response to your\nsuggestions.\nSpecific comments follow.\n(1) Abstract. The last lines of the abstract claim that the results reported “establish graphene a catalytic\nmembrane for hydrogen-based technologies, including fuel cells and high-purity hydrogen extraction”.\nHowever, this claim is not further demonstrated nor discussed in the manuscript. The conclusions of\nthe present work should somehow address this technological aspect in a more explicit manner.\nReply: Thank for your constructive comments.\nWe agree that the comment that the technological applications is presented as a broad conclusion\nwithout sufficient discussion in the manuscript. We recognize that while these potential applications\nare an exciting and logical extension of our studies, a detailed technological analysis falls beyond the\ncore scope of this research contents.\nTherefore, in the revised version, we have rewritten the concluding statement to more accurately\nreflect the experimental contributions of our study. The last line of the abstract now:\nPage 1, line 28: “These findings reveal a catalysis-driven proton permeation mechanism, and\nfundamentally deepen the understanding of hydrogen permeation through 2D crystals.”\n(2) In addition, similar findings are found in MoSe , MoS and h-BN. Why only graphene is given\n2 2\nrelevance in the title and abstract?\nReply: Thank for your kind reminder.\nWe agree that highlighting only graphene in the previous manuscript title and abstract do not fully\nrepresent our research contents, where the catalytic phenomena include several 2D crystals.\nTo accurately show the broader scope of our study, the title has been revised to “Two-dimensional\ncrystals catalyse hydrogen into protons”. Furthermore, we have updated the abstract to explicitly\ninclude the other studied 2D crystals.\n(3) Page 2, line 19. Honestly, I don’t quite understand point (2): What else can be the dissociation\nspecies of H if not protons?\nThe fact is molecular hydrogen (H ) dissociation is considered to yield either neutral hydrogen\n2\natoms (H) or charged protons (H+). The point (2) aims to highlight that, in the context of permeation\nthrough the 2D crystals, we have specifically identified and verified that the permeating species are\nH+ (proton) rather than H (hydrogen atom). This distinction is the crucial to the proposed catalysis-\ndriven permeation mechanism.\n(4) Page 3, lines 3-5. The process employed to let H bubbles form beneath the sample surface would\n2\nneed more details instead of relegating it to few lines in the Methods section. Indeed, the method used\nby the authors is distinctively different from that employed to create domes in transition metal\ndichalcogenides and h-BN by a Kaufmann source (refs 24-29) and is instead similar to that used for\ncreating bubbles in h-BN (ref. 30). In particular, the authors should make it clear whether protons or\nionised H molecules penetrate through the first top layers. I know that this is referenced to previous\n2\nwork by the authors, but given the pivotal role of this process a more explicit mention should be made\nin the main text.\nReply: Thank for your constructive comments.\nWe have expanded the description of the bubble formation process in the main text. Specifically, we\nnow explicitly state that the species permeating through the topmost 2D crystal layer are protons.\nThis is based on the mechanism established in our previous study (Gao L. B. et al., Nano Lett. 23, 8203-\n8210, 2023). The protons originate from the H plasma, permeate through the atomic lattice, and\n2\nsubsequently recombine into molecular H in the interlayer space, where they gradually accumulate to\n2\nform H bubbles.\nPage 3, line 21: “Based on our previous work, protons from a hydrogen plasma permeate the 2D\ncrystals lattices at elevated temperature, subsequently recombining into molecular H within the\n2\ninterlayer region, where they gradually accumulate.”\n(5) Page 4, line 4. Why h/R ~ 0.125 indicates that H permeate all the dome layers of graphene? What\n2\ndoes this sentence mean? I’m not saying that it is wrong, simply I cannot understand it (and likely the\nreaders as well).\nReply: Thank you for raising this point, which allows us to clarify the prior researches of our statement.\nFig. C3 shows our previous results where the aspect ratio (h/R) of the bubbles is governed by the\nYoung’s modulus of the 2D materials, where the lower modulus generally results in the larger h/R. 1L\nMoS exhibits the lowest Young’s modulus than 2L graphene or 2L h‑BN, so the h/R value of 1L MoS\n2 2\nbubble is measured highest. Similarly, the Young’s moduli of 2L graphene (~2 TPa) and 1L graphene\n(~1 TPa) are also expected to result in different bubble geometries.\nCritically, the h/R values of bubbles in 2L graphene remains unchanged during the bubble growing\nup, indicating that the permeating hydrogen species have completely permeated the two layers, rather\nthan being confined to the interlayer space.\nFig. C3. Bubbles in the 2D crystals. a, Comparison of the typical AFM cross-sectional profiles of 2L\ngraphene, 2L hBN and 1L MoS bubbles with the same diameter. b, Statistical aspect ratio of the H\n2 2\nbubbles in 2L graphene, 2L hBN and 1L MoS with different heights. The average ratios of h /R in\n2 max\ngraphite, hBN and MoS are 0.125, 0.14 and 0.18, respectively. (Redrawn from Nano Lett. 23, 8203-8210,\n2\n2023)\n(6) Page 4, lines 7 and 8. The Raman data should be discussed more explicitly. Why the\npresence/absence of D peak is relevant? Personally, I know why. However, another reader may not.\nPlease, provide at least a reference and/or say in the extended data what each Raman peak corresponds\nto.\nReply: Thank you for this helpful suggestion. We agree that a clearer explanation of the Raman data,\nparticularly the significance of the D peak, will benefit more readers.\nWe explicitly state the origin of the main Raman peaks: G peak at ~1580 cm-1 is related to in-plane\nvibrations of sp2 carbon atoms and the 2D peak at ~2680 cm-1 (for 532 nm laser) is a second-order,\ndouble-resonance mode that is sensitive to layer number and stacking order. Most importantly, we\nclarify that the D peak at ~1350 cm-1 is a disorder-induced feature, activated by defects, edges, or\ncovalent functionalization (such as hydrogenation). Based on this, we discuss the relevance of the\nabsence of a D peak in Fig. R8 (Supplementary Fig. 1). We have also added corresponding references\n(Ref. Phys. Rev. Lett. 97, 187401, 2006; Science 323, 610-613, 2009; Nano Lett. 11, 3190-3196, 2011)\nin the Supplementary Information.\nFig. R8. Additional morphology of H permeating 2L graphene. a, Schematic of H bubble in 2L\n2 2\ngraphene. b, Optical and AFM images after 10-min annealing at different temperature. c, Raman\nevolutions of 2L graphene dome after consecutive annealing from 25 to 900 °C. Raman spectroscopic\nanalysis of the graphene bubble dome reveals crucial structural insights.\nMoreover, there are two G peaks located at 1542 and 1582 cm-1, and two 2D peaks located at 2610\nand 2682 cm-1, which are derived from the 2L or 3L graphene bubble domes (which has a tensile strain\nof ~1%) and the bottom graphite. We have already labelled all the origins of G and 2D peaks in all the\nSupplementary figures (Fig. 1, 3, 14, 15, 17), like Fig. R7 (Supplementary Fig. 3).\nFig. R7. H permeating 3L graphene. a, Schematic of H bubble in 3L graphene. b, Optical and AFM\n2 2\nimages after thermal annealing at different temperature. c, Raman evolutions of 3L graphene dome after\nannealing at 800 and 900 °C.\n(7) The authors state that “no interlayer H migrations are observed. There are no obvious damage or\n2\nwrinkles observed on the regions where the H bubble disappears by AFM”. While I agree on this\n2\nstatement, yet this aspect would require some more discussion or AFM images taken/shown on a\nsmaller scale length to really make the reader appreciate the absence of damages or wrinkles. This is\na crucial aspect of the present work and it deserves more attention.\nReply: Thank for your constructive comments.\nWe have conducted additional high-resolution AFM imaging to thoroughly examine the regions\nwhere H bubbles eliminated (Fig. R9). It reveals that the preserved integrity of the region without\n2\ndetectable defects and wrinkles, and only surface fluctuations of ~1 nm in height are observed,\nindicating these permeation processes are non-destructive to graphene lattices.\nFig. R9. Morphological evolution of the H bubble domes. a, AFM image of the as-prepared 2L-Gra\n2\nbubble. b, AFM image of the same bubble region after H permeation. c, Zoom-in AFM image of the same\n2\nbubble disappeared region, corresponding to the circled area in a and b.\nIn the revised manuscript, we have already added Fig. R9 as the Supplementary Fig. 2, and revised\nthe statement below,\nPage 4, line 17: “High-resolution AFM imaging of regions where H bubbles disappeared reveals\n2\nno detectable damage or wrinkles, confirming the structural integrity of the graphene membrane after\nH permeation (Supplementary Fig. 2).”\n2\n(8) Supplementary Fig. 1. The figure is nice and shows important results, but it is quite confusing: for\nthree different samples, three different sets of data are shown.\n2L graphene: optical and AFM images after 900 °C annealing and Raman vs annealing temperature\n3L graphene: optical and AFM images before annealing and Raman vs annealing temperature\n2L h-BN: AFM images before and after annealing and AFM profile analysis.\nThis makes the readers’ (and referees’) life hard. If the authors wish, they can leave this figure as it is,\nbut I’d encourage them to make an extra effort to render the figure more rational, if possible.\nReply: Thank for your constructive comments.\nFollowing your valuable suggestion, the original Extended data figure has been split into three\nseparate Supplementary figures (Fig. 1, 3, and 4), as shown in Fig. R8, 7 and 11, corresponding to:\n· 2L graphene (Fig. R8, Supplementary Fig. 1): optical, AFM images and Raman spectra after\nannealing at different temperature.\n· 3L graphene (Fig. R7, Supplementary Fig. 3): optical, AFM images and Raman spectra after\nannealing at different temperature.\n· 2L hBN (Fig. R10, Supplementary Fig. 4): AFM images before and after annealing and AFM\nanalysis.\nWe appreciate your help again in improving the readability and rigor of our manuscript.\nFig. R8. Additional morphology of H permeating 2L graphene. a, Schematic of H bubble in 2L\n2 2\ngraphene. b, Optical and AFM images after 10-min annealing at different temperature. c, Raman\nevolutions of 2L graphene dome after consecutive annealing from 25 to 900 °C. Raman spectroscopic\nanalysis of the graphene bubble dome reveals crucial structural insights.\nFig. R7. Additional morphology of H permeating 3L graphene. a, Schematic of H bubble in 3L\n2 2\ngraphene. b, Optical and AFM images after thermal annealing at different temperature. c, Raman\nevolutions of 3L graphene dome after annealing at 800 and 900 °C.\nFig. R10. Additional morphology of H permeating 2L hBN. a, Schematic of H bubble in 2L hBN. b,\n2 2\nAFM images after thermal annealing at different temperature. c, Height profiles for the reduced H bubble\n2\nlabelled in b.\n(9) Supplementary Fig. 2. The Raman and photoluminescence (PL) data should be described properly.\nWhat are the different Raman peaks (say which Raman peaks are due to the strained bubbles and which\nones are due to the bulk material beneath)? Likewise, the PL data are shown without any comment.\nAre the PL data affected by strain? If the authors feel they cannot explain the PL data, it’d be better to\nremove them.\nReply: Thank for your constructive comments.\nWe have added Raman spectra of the fresh 2D crystals to Supplementary Fig. 5 as a reference, which\nnow helps distinguish peaks from the strained bubbles and the bulk material beneath, and we have\nremoved the PL data as advised, as shown in Fig. R11.\nFig. R11. Additional morphology of H permeating MoS and MoSe . a, Optical evolution of H bubbles\n2 2 2 2\nin 1L MoS dome by annealing at 400 °C for 5 min. The height and diameter of bubbles show obviously\n2\ndecreased. Raman of bubble dome presents unchanged significantly. b, Optical evolution of H bubbles in\n2\n1L MoSe dome by annealing at 350 °C for 30 min. Raman of bubble dome presents unchanged\n2\nsignificantly.\n(10) Page 4, lines 13-15. The deuterium treatment was performed after the creation of H bubbles.\n2\nin the D bottle? In addition, the authors should specify that deuterium treatment was performed on h-\nBN. Was deuterium treatment performed on h-BN, only? This is just a curiosity, I don’t mean that the\nauthors should perform deuterium treatments on the other materials.\nReply: Thank for your constructive comments.\nFirstly, we would like to emphasize that a crucial prerequisite of this experiment is the continued\ninjection of deuterium (D+) ions into samples where H bubbles have already been formed. The\n2\nformation of HD does not originate from H contamination in the D gas, because there are no any\n2 2\ndetectable H or HD Raman peaks in D bubbles (Fig. C6a).\n2 2\nThe chemosynthesis of HD molecules results from the catalytic process at the inside surface of hBN\nbubble domes. Specifically, H molecules dissociate into hydrogen atoms (H) or protons (H+) at the\n2\nhBN surface, where the incoming D+ ions are combined into HD. This mechanism conclusively\ndemonstrates hBN can catalytically dissociate H , which is the key innovation point of our study.\n2\nBesides, we only use hBN bubbles for the deuterium labelling reaction because the Raman\ncharacteristic peaks of hBN do not affect the detection of H , D and HD. The Raman characteristic\n2 2\npeaks of graphite mostly overlap with those of H (Fig. C6b; Phys. Status Solidi B 248, 2435, 2011).\n2 2\nwhich easily causes H permeation due to the thermal effects.\n2 2\nRaman spectra of graphite, there are neighbouring peaks near the H and D peaks, as labelled by yellow.\n2 2\n(a is redrawn from Nano Lett. 23, 8203, 2023; b is redrawn from PSSB 248, 2435,2011)\nWe have added this sentence and revised the expression in the main content:\nPage 4, line 23: “To directly confirm the catalytic dissociation of H on 2D crystal surfaces, we used\n2 2\nvibrational modes and remain stable under intense laser irradiation. We introduced deuterium ions\n(D⁺) into pre-existing H bubbles at elevated temperature.”\nPage 13, line 15: “Extending the existence of HD\nThe hBN flakes containing pre-existing H bubbles are reloaded into the ICP-CVD system and\n2\nheated to 650 °C. Subsequently, the D plasma is ignited at 10 – 100 W under 5 Pa for 1–3 min. Finally,\n2\ndue to the observable HD characteristic signal, Raman spectra acquired with 25 mW and 1000 s\nintegration confirm the presence of HD.”\n(11) Page 5, lines 14-15. Frankly, I’d not say that the power is very weak: 1 mW should result in a\npower density of about 100 kW/cm2. As a matter of fact, this quite high power density is fully\nconsistent with the observation that temperatures in excess of 700 °C are necessary to observe H\n2\ndissociation.\nReply: Thank you for pointing out the controversial points.\nWe agree your comment and have updated the description in the main content below:\nPage 6, line 5: “The laser power is moderate and does not damage the 2D lattices.”\n(12) The experiment described in Fig. 2 and related text is elegant and insightful. I have some questions.\nWhy MoS was chosen? Were similar findings observed for graphite and h-BN, too? This point gives\n2\nme the opportunity to move a general criticism to this work. Often, the authors move from one material\nto another that creates some confusion and might leave some room for doubts about the general validity\nof the reported observations.\nReply: Thank for your high praise and constructive comment.\nWe find that the direct laser heating is insufficient to achieve the threshold temperature for\ndissociating H catalysis in 2L graphene and 2L hBN. In contrast, 1L MoS can catalytically dissociate\n2 2\nH at a lower temperature. Moreover, when 2L graphene is covered with Pt NPs, the threshold\n2\ntemperature is reduced, and it can also catalytically dissociate H only through laser heating (Fig.\nFig. R12. Height evolution of a bubble in graphite and graphite covered by Pt NPs after the local\nlaser heating. a, Morphologic evolution of H bubbles in 2L graphene domes by laser (532 nm, 1000 s)\n2\nirradiation with different powers, from left to right are ex situ AFM images of irradiation after 5 and 20\nmW/μm2. The height and diameter of bubbles show no obviously reduced. b, Morphological evolution and\nRaman of H bubbles in 2L graphene dome with Pt NPs by local irradiation in O atmosphere at different\n2 2\ntime of 532 nm, from left to right are ex situ optical and AFM images measured at the same regions after\n7 mW/μm2 10 and 100 s. The height and diameter of bubbles show obviously decrease. Raman of bubbles\npresent no D peaks indicating that the lattice of graphene still keeps the structure perfect.\nMoreover, we also want to clarify the difference of 2D crystals selected in our study. The H bubbles\n2\ncan be formed in all the 2D crystals, including graphite, hBN, MoS and MoSe , and H can permeate\n2 2 2\nthem at elevated temperature. While graphene is commonly investigated and used as the primary 2D\ncrystals to report these general phenomena, but it is not suitable for all the experiments, like (i) Raman\ncharacteristic peaks for H , D and HD (main Fig. 1e), using hBN instead; (ii) Laser heating-induced\n2 2\nH permeation (main Fig. 2), using MoS instead.\n2 2\nWe have revised the manuscript to explicitly outline these considerations, ensuring clarity and\navoiding misinterpretations. We have added Fig. R12a as Supplementary Fig. 10 and Fig. R12b as\nSupplementary Fig. 21 and revised the expression below:\nPage 4, line 23: “To directly confirm the catalytic dissociation of H on 2D crystal surfaces, we used\n2 2\nvibrational modes and remain stable under intense laser irradiation.”\nPage 6, line 5: “... this power is insufficient to induce hydrogen permeation of bubbles in graphene\nor hBN (Supplementary Fig. 10).”\nPage 10, line 1: “... and local laser irradiation can realize the H\n2\npermeation through graphene\ndomes while coating Pt (Supplementary Fig. 21).”\n(13) Referring to Figure 2d, I do not understand the profile shown. It looks like the bubble is 10 nm\ntall. Are the authors sure that they are not measuring just the PMMA material and no bubble is left\nbeneath? The same apply to extended data Figure 4. My impression that no H gas is present any more\n2\ndue to the bubble explosion. Can the authors elucidate this point?\nReply: We appreciate the reviewer’s insightful observation.\nTo clarify this, we have conducted additional AFM evolutions. Figure R13a shows the as-prepared\n1L MoS bubble, and Fig. R13b shows the same bubble after being covered with PMMA. Following\n2\nlaser heating, significant bursting occurs in the heated region, while the PMMA-covered area retains\nthe original bubble size (Fig. R13c). After removing PMMA, the laser-heated bubble is eliminated\ncompletely (Fig. R13d), although several tiny sub-bubbles remained. This should be pre-formed tiny\nH bubbles beneath the 1L MoS big bubble, which could be eliminated after further annealing (Fig.\n2 2\nR13e). AFM height profiles indicate that the residual thickness of in Fig. R13c after PMMA removal\nis about 50 nm. Therefore, we think that the residual 10 nm height for burst region in the main Fig. 2d\nmay originate from a deeper, unburst bubble located beneath the 1L-MoS bubble.\n2 2\nprepared 1L-MoS bubble. b, AFM image of the 1L-MoS bubble coated with PMMA. c, AFM image of the\n2 2\n1L-MoS bubble covered by PMMA after laser irradiation. d, AFM image of the 1L-MoS bubble after\n2 2\nremoving PMMA. e, AFM image of the 1L-MoS bubble after further annealing. f, Corresponding height\n2\nprofiles obtained from b‒e labelled by dashed lines. After removing PMMA and before annealing, the as-\nproduced H bubbles nearly disappear, only leaving tiny sub-bubbles. This behaves like pre-formed tiny\n2 2\nWe have added Fig. R13 as Supplementary Fig. 15 and revised the expression below:\nPage 6, line 19: “After removing the PMMA, the originally illuminated bubbles are found to\ncompletely disappear (Supplementary Fig. 15).”\n(14) Page 5, line 22. Please, specify the PMMA/PEM thickness.\nReply: Thank for your comments.\nWe have added the thickness in the following sentence:\nPage 6, line 14: “~340 nm-thick PMMA and ~320 nm-thick Nafion are separately coated on the H\n2\nbubbles in MoS ”\n2\n(15) Page 14. Regarding the calculation of the permeation rate. Is this an ensemble measurement?\nWhat the summation index indicates? A summation over different bubbles?\nReply: Thank you for your constructive comments.\nYes, the calculation includes the statistical measurements over the entire 2D flake. The summation\nindex indicates that we aggregate the contributions from all the bubbles located within an exfoliated\nflake to estimate the total permeation rate. To clarify this, we have added the following sentence to the\nMethods section:\nMethods section, Page 16, line 10: “The total permeation rate was obtained by summing the\ncontributions from all bubbles within an individual, exfoliated flake.”\n(16) Page 7, lines 27 and 28. There should be a mistake in exp(-N), since this formula seemingly makes\nno sense.\nReply: We appreciate the careful reading and professional comment.\nThe temperature-dependent Г follow the Arrhenius law: Г =A‧exp(-E / k T). The observed Г\nP P A B P\nfollows the exponential attenuation with increasing layer number (N), as indicated by the dashed fitting\nlines in the main Fig. 3d. However, the activation energy (E ) is independent of the permeated layer\nA\nnumbers (main Fig. 3c, will also discuss in Comment 19). Thus, the different Г for different layer\nP\nnumbers only results from the pre-exponential factor A. Therefore, pre-exponential factor A can be\nalso described as A = A’‧exp(-αN).\nMoreover, our explain also refer to the published literature for proton transport through the\natomically thin micas (Ref. 36: Lozada-Hidalgo M. et al., Nat. Nanotech. 14, 962, 2019, doi:\n10.1038/s41565-019-0536-5), where the permeation rate is also exponentially layer-dependent. They\nobtain the following empirical formula for the proton areal resistivity (conductivity) through mica\nlattice, R = R ‧exp(αN)‧exp(E / k T).\np 0 p B\n(17) Figure 4b. I’d suggest to include the NP-free data, too, so that a clear comparison can be done.\nReply: Thank for your constructive comments.\nWe have already included the NPs-free data in the revised main Fig. 4b for a clear comparison.\n(18) The experiment with metallic NPs is very interesting. Have the authors ever considered to use\nNPs before H treatment? Could the formation of H bubbles be promoted by the presence on metal\nReply: We sincerely appreciate your insightful suggestions.\nWe have supplemented the H bubbles are formed in the graphite with pre-coated Pt NPs using the\n2\nsame proton-assisted process (800 °C), as shown in Fig. R15. The presence of Pt NPs suppresses the\nbubble formation, reducing both bubble size and density. This result aligns with the role of Pt in\nlowering the H permeation energy barrier. At high temperatures, H bubble formation involves\n2 2\nconcurrent processes: protons permeating graphene to form H , while H also out-permeates. Pt NPs\n2 2\ncan reduce the energy barrier for H out-permeation, thereby accelerating its escape at a given\n2\ntemperature. This enhanced the out-permeation rate ultimately suppresses bubble growth and reduces\ntheir density. Furthermore, the Pt NPs are also strongly aggregated at 800 °C, compared with Fig. R4c.\nFig. R14. The formation of H bubbles in graphite with/without pre-coated Pt NPs. a, Optical image\n2\nof 800 °C formed H bubbles in graphite without Pt NPs (inset: AFM topography). b, Optical image of\n2\n800 °C formed H bubbles in graphite with pre-coated Pt NPs (inset: AFM topography).\nPage 9, line 20: “This is further supported by experimental phenomena that pre-coated Pt NPs\nsuppress H bubble formation, reduce bubble size and density (Supplementary Fig. 20),”\n2\n(19) Page 9, lines 4-6. The authors state that “it is still puzzled that Pt shows no significant reduction\nfor 3L graphene, which may result from the aggregation and deactivation of Pt NPs at higher\ntemperatures”. Frankly, I find this observation quite sensible and not puzzling at all. Indeed, if the\nmetal NPs are further from the gas-bubble interface, there should be a reduced H dissociation. On the\n2\ncontrary, I find it puzzling the absence of a clear reduction of E with increasing crystal thickness in\nA\nMoS .\nWe agree that this finding merit deeper mechanistic discussion, and provide the following additional\nclarifications:\na) Theoretical challenge in modelling the high‑temperature proton dynamics\nThrough in-depth discussions with the theorists, we realize that the theoretical simulation of\ngraphene‑catalysed dissociation of H molecules into positively charged species (i.e., protons) at high\n2\ntemperature, along with the subsequent permeation through crystalline lattices, poses a major\nchallenge for commonly used theoretical and computational methods. These processes involve\nnon‑equilibrium thermal effects and dynamic barrier‑crossing events, which are difficult to capture\nusing the standard static or low‑temperature approximations.\nb) Theoretical simulation of layer number-independent dissociation energy\nAs an alternative, we substitute to perform the theoretical calculations of the activation energy\nrequired for H dissociation in the graphite vdW interlayers. As shown in Fig. R5, the dissociation\n2\nenergy is mainly correlated to the interlayer spacing and are not affected by the upper and bottom layer\nnumbers.\nWith the interlayer spacing of 3.5 Å, the activation energy required for spontaneous H dissociation\n2\nbetween graphene layers is 1.71 eV (Fig. R5a–b). When the interlayer spacing exceeds 5 Å, the H\n2\ndissociation energies keep around 4.2 eV. When H molecules are confined within graphene bubbles,\n2\nwhere the dome height far exceeds 5 Å, the activation energy for H dissociation here is high. When\n2\nthe interlayer spacing is fixed at 3.5 Å, theoretical calculations reveal that the upper or bottom layer\nnumber of graphene has negligible influence on the dissociation energy (Fig. R5c–d). This may make\nup the absence of the theoretical mechanism of constant E for different layer number in 2D crystals.\nA\nFig. R5. Theoretical simulation of dissociating H in different graphite vdW interlayers. a, Schematic\n2\nof dissociating H in graphite vdW interlayer. b, Relationship between dissociation energy and reaction\n2\ncoordinate at different vdW interlayer spacings. At the interlayer spacing of 3.5 Å, the energy required for\nspontaneous H dissociation between graphene layers is 1.71 eV. When the interlayer spacing exceeds 5\n2\nÅ, the H dissociation energy plateaus is around 4.2 eV. When H molecules are confined within graphene\n2 2\ndomes, where the dome height far exceeds 5 Å, so the highest energy barrier for H dissociation appears\n2\nhere. c, Schematic of H between 2L and 3L graphene interlayers with interlayer spacing of 3.5 Å. d,\nÅ. The dissociation energy is mainly related to the interlayer spacing and has no relation to the layer\nnumbers of graphene domes.\nc) Proposed layer‑by‑layer hopping mechanism with kinetic energy compensation\nWe therefore reasonably propose a possible mechanism whereby protons permeating the 2D crystal\nlattices through a layer-by-layer hopping process. Upon crossing the energy barrier of monolayer and\nprovisionally staying the vdW interlayer space, the tiny kinetic energy loss of protons can be rapidly\ncompensated by external thermal fluctuations at high temperature or perpendicular electric field\nby electrons injection. Since each layer has an identical energy barrier (E ) and the energy loss can\np\nbe dynamically compensated, the total E remains independent of the permeated layer numbers.\nA\nHowever, the layer number still affects the permeation rate, the thicker the 2D layers, the slower the\npermeation rate, which are experimentally confirmed.\nIn the revised manuscript, we have added the theoretical details in the Methods “Theoretical\ndissociation energy of H in graphene layer space”, and already added Fig. R5 into the Supplementary\nPage 8, line 7: “This layer-number independent behaviour can be explained by a sequential\npermeation mechanism. Firstly, regarding the initial dissociation of H , theoretical simulations\n2\nindicate that the dissociation energy depends primarily on the interlayer spacing and remains\nunchanged with increasing layer number (Supplementary Fig. 17).”\n(20) The experiments involving a different external atmosphere are very intriguing. However, I urge\nthe authors to reformulate this part (from line 15 to line 30 at page 9 and from line 1 to line 2 at page\n10) of the manuscript. Both text and Figure 4d are very confusing and hard to follow. The caption of\nFigure 4d is unacceptable: there is no account and explanation whatsoever of the data and lines shown.\nI’d prepare a new figure 5 (possibly including the data shown in Supplementary Fig. 8 and 9; the\nauthors can best decide on this point) entirely devoted to this nice experiment and describe the results\nin a plain and clear manner by specifying what all lines in the figure are. In particular, a clear\ncomparison between the data obtained in standard annealing experiments (namely, no O ) and in\n2\nannealing experiments under O presence should be made. Similarly, Supplementary Fig. 8 and 9 are\n2\na bit confusing, since the figures compare images taken after annealing at different temperatures and\ndifferent gas atmospheres. I know that the bubble deflation occurs at different temperature values, but\nthe authors should try to compare images as close as possible in terms of annealing temperatures and\nexperimental conditions. This is particularly true for h-BN in Supplementary Fig. 9.\nReply: Thank for your constructive and forward-looking comments.\nIn the revised version, we have thoroughly re-structured this section to improve clarity. Following\nyour suggestion, we have split the original Fig. 4 into two separate figures: the new Fig. 4 focusing on\nthe influence by different metal NPs (Fig. R16), and the new Fig. 5 to analyse the influence under\ndifferent external environments (Fig. R17). The figure captions have also been rewritten to provide a\nclear expression.\nTo facilitate better comparison under the similar external environments, we have included the\nfollowing images: AFM and optical images of H bubbles in 2L graphene after vacuum annealing (Fig.\n2 2\nH bubbles in a Pt NP-coated 2L graphene after O annealing (Fig. R18c, middle). To better monitor\n2 2\nthe bubble evolution, the annealing temperatures and duration are carefully controlled until their\ndisappearance.\nFurthermore, we have also re-organized and clarified the corresponding contents (Pages 10–13), and\nmoved previous Supplementary Fig. 8 and 9 as Supplementary Fig. 23 and 24. The height and diameter\nof bubbles show minor change after 400 °C and obviously decrease at 450 °C.\nWe believe these revisions have significantly enhanced the readability and interpretability of the key\ninnovation points of our study.\nFig. R16. Energy barriers of H permeating 2D crystals with different metal NPs. a, Schematic of H\n2 2\npermeating 2L graphene domes assisted with Pt NPs. b, Г of 2L graphene, both pristine and covered with\nP\nPt, Pd and Cr NPs at different T. Error bars represent at least three different samples, and dash lines are\nfitting to the Arrhenius dependence with E . c, Г of 1–3L MoS decorated with Pt NPs at different T. Error\nA P 2\nbars represent at least three different samples, and dash lines are fitting to the Arrhenius dependence with\nE . d, E reduction of graphene (left) and MoS (right) with different layer numbers after covering with Pt,\nA A 2\nPd and Cr NPs. Pt NPs can hugely reduce E , Pd can slightly reduce E , but Cr cannot.\nA A\nFig. R17. Energy barriers of H permeating 2D crystals under different environments. a, Schematic\n2\nof H permeating 2L graphene domes under outside O atmosphere. b, Г of 2L graphene under H , O\n2 2 P 2 2\nand vacuum external atmosphere. c, Г of 2L hBN under H and O outside atmosphere. d, Г of 2L\nP 2 2 P\ngraphene with Pt NPs under H and O outside atmosphere. Г are significantly affected by the external\n2 2 P\natmospheres. All error bars represent at least three different samples with dozens of H bubbles, and dash\n2\nlines are fitting to the Arrhenius dependence with E .\nA\nFig. R18. H permeating 2L graphene under different atmospheres. a, Morphological evolutions of H\n2 2\nbubbles in 2L graphene by annealing under vaccum. The height and diameter of bubbles show sharply\ndecrease from 800 °C. b, Morphological and Raman evolutions of H bubbles in 2L graphene by annealing\n2\nunder O atmosphere at 500 and 550 °C. The height and diameter of bubbles show sharply decrease from\n2\n550 °C. There is no Raman D peaks as decreasing the bubble, indicating that the graphene lattice still\nkeeps perfect. c, AFM evolution of H bubbles in 2L graphene dome with Pt NPs by annealing in O outside\n2 2\natmosphere at 400 and 450 °C. The height and diameter of bubbles show minor change after 400 °C and\nobviously decrease at 450 °C.\n(21) Finally, a critical discussion of the implications of the experiments with regards to applicative\nprospects for catalysis and fuel cell is lacking, despite this aspect was mentioned in the abstract.\nThe authors should discuss this point, also briefly.\nReply: Thank for your professional comment. This comment is similar to the previous comment (1).\nWhile these potential applications are an exciting extension of our findings, a further analysis falls\nbeyond the core scope of this fundamental study. Therefore, we have refined the concluding statement\nin the revised version, to more accurately highlight the direct experimental contributions of our study.\nIn the revised manuscript, we have already revised the statement below:\nPage 1, line 28 in the abstract: “These findings reveal a catalysis-driven proton permeation\nmechanism, and fundamentally deepen the understanding of hydrogen permeation through 2D\ncrystals.”\nPage 11, line 24: “The exceptional catalytic properties of traditionally inert materials prompt a re-\nevaluation of the catalytic potential of 2D crystals.”\nPage 12, line 6 in the conclusion: “These findings establish a coherent framework for understanding\nH permeation in 2D crystals, provide a foundation for high-efficiency hydrogen separation\n2\nmembranes via catalytic dissociation-permeation, and ultimately reveal how traditionally inert 2D\ncrystals can be catalytically activated for advanced energy applications.”\n(22) In summary, the manuscript sometimes lacks of clarity. The data presentation and related figures\nare confusing in some instance. Nevertheless, the topic is of high current interest and the results\nobtained are accurate, relevant and worth being published in Nat. Commun.\nReply: We sincerely appreciate your high recognition and strong recommendation of our work.\nFollowing your professional suggestions, we have carefully revised the manuscript accordingly. We\nbelieve the revised manuscript now presents our findings with greater clarity and significantly\nimproved quality.\nPoint-by-point responses to the Reviewers’ comments (NCOMMS-25-81449-T)\nReferee #1 (Remarks to the Author):\nThe authors have addressed my previous concerns. I recommend its publication.\nReply: We thank the Referee #1 for his/her positive comments, strong support and favourable\nrecommendation for our work.\nReferee #2 (Remarks to the Author):\nThe author's responses address the reviewer's main concerns. By revising the text to accurately\nposition the work, supplementing it with new experiments to strengthen key claims, using literature\ncitations and logical reasoning to compensate for the lack of some direct evidence, and candidly stating\ncurrent technical and theoretical limitations, the author has significantly enhanced the manuscript's\nrigor and completeness. I think that these responses should meet the requirements for publication.\nReply:We thank the Referee #2 for his/her positive comments, valuable suggestions, and recognition\nof our work.\nReferee #3 (Remarks to the Author):\nThe referee thanks the authors for the detailed replies to the comments and concerns and is satisfied\nwith most of them. Specially, the referee cannot really agree with the claim that an elevated temperature\napplied in this work would help protons, hydrogen or whatever cross the 2D lattice of either multilayer\ngraphene, or three atom-thick MoS , considering that barrier of higher than 1 eV and if only providing\n2\nkinetic energy by heat, kT, requires over 10^4 K. Anyway, I would leave the decision to the editor.\nReply: We fully thank Referee #3 for the strong concern on this research area and support for this\nstudy.\nWe respectfully clarify that the elevated temperature in our work is not primarily intended to\novercome the energy barrier for proton permeation through thermal activation alone, but rather to\nenhance the catalytic dissociation of hydrogen molecules on the material surface. Our experimental\nresults and supporting analyses demonstrate that temperature plays a key role in facilitating this surface\nreaction, thereby enabling the overall permeation process. We appreciate your consideration and leave\nthe final decision to the editor.\nReferee #4 (Remarks to the Author):\nThe authors addressed the points raised by the referees in a very satisfactory manner.\nThe analyses and explanations provided make the manuscript suitable for publication in Nature\nCommunications. In general, this is a very detailed, valuable and interesting work.\nJust few comments:\n1) reply to point (18) does not convince me totally, but this is not a problem.\n2) I would strongly recommend to modify the range scale of the Raman spectra in Supplementary\nFig. 5 rightmost. For a better readability of the data, the frequency axis should run from 300 to 500\ncm^1.\nReply:We sincerely appreciate your thoughtful and constructive comments on our manuscript.\nWe have revised the frequency axis of Raman spectra from 300 to 500 cm-1 to Supplementary Fig.\n5 rightmost, as shown in Fig. R1.\nFig. R1. Additional morphology of H permeating MoS . Raman evolution of H bubbles in 1L MoS\n2 2 2 2\ndome by annealing at different temperatures. Raman of bubble dome presents unchanged\nsignificantly.\n2"}]

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