Mechanism of the electrochemical hydrogenation of graphene

Domain: physics
Published: 2025-11-28
Editorial outcome: major_revision

Abstract
The electrochemical hydrogenation of graphene induces a robust and reversible conductor-insulator transition, of strong interest in logic-and-memory applications. However, its mechanism remains unknown. Here we show that it proceeds as a reduction reaction in which proton adsorption competes with the formation of H2 molecules via an Eley-Rideal process. Graphene’s electrochemical hydrogenation is up to 106 times faster than alternative hydrogenation methods and is fully reversible via the oxidative desorption of protons. We demonstrate that the proton reduction rate in defect-free graphene can be enhanced by an order of magnitude by the introduction of nanoscale corrugations in its lattice, and that the substitution of protons for deuterons results both in lower potentials for the hydrogenation process and in a more stable compound. Our results pave the way to investigating the chemisorption of ions in 2D materials at high electric fields, opening a new avenue to control these materials’ electronic properties.

Introduction
The hydrogenation of graphene was predicted to turn the material into an insulator1–3, but this has been difficult to achieve experimentally. Graphene was first hydrogenated using accelerated hydrogen atoms or protons in plasmas and heated hydrogen gas sources1,4–9. This yielded samples with notably higher electrical resistivity than pristine graphene, but they were typically not electrically insulating. Normally, only one hydrogenation-dehydrogenation cycle was demonstrated. The mechanism for hydrogenation using accelerated hydrogen atoms has been studied extensively1,3,10–13. Theory and scattering experiments demonstrated that a proton approaching a carbon atom in graphene faces an energy barrier of about ~0.3 eV, which if overcome leads to its adsorption in a ~1 eV deep energy well11,12 (Fig. 1d and Supplementary Fig. 1). The adsorption probability of an incoming proton then depends on its momentum, which determines whether it overcomes the adsorption barrier, or is reflected by the lattice1,3,10–13. On the other hand, recent experiments have demonstrated the hydrogenation of graphene via the electrochemical adsorption of protons14,15. This method triggers a robust conductor–insulator transition in graphene that enables field-effect transistors with orders-of-magnitude on-off current ratios. Moreover, hydrogenation via this method is fully reversible and enables precise and robust control of the conductor–insulator transition, such that one million current switching cycles have been demonstrated14. These stark phenomenological differences suggest that the mechanisms behind the two methods could be different. In this work, we investigate the mechanism for the electrochemical hydrogenation of graphene. We reveal that it proceeds via a proton reduction mechanism that is up to 10⁶ times faster than previous hydrogenation methods and that it can be tuned by isotope substitution and nanoscale lattice corrugations.

Results
Experimental devices
The devices for this work consisted of mechanically exfoliated graphene supported on SiO2 or hexagonal boron nitride substrates. The devices were then coated with a non-aqueous proton conducting electrolyte with a wide (>4 V) electrochemical stability window (bis(trifluoromethane)sulfonimide, HTFSI, dissolved in polyethylene glycol, PEG14,15) and connected into the electrical circuit as shown schematically in Fig. 1c and Supplementary Fig. 2. For measurements, a voltage was applied to graphene with a PdHx electrode, which drives an electrochemical current on the surface of graphene. The potential of graphene, VG, is monitored vs a PdHx pseudo-reference electrode. An additional in-plane source-drain voltage, VSD, was applied to graphene to measure its in-plane electronic conductivity as a function of VG and electronic and electrochemical currents were measured simultaneously. The electronic response of graphene during the hydrogenation process is well established and is used here as a reference for the electrochemical signal of the process. This allows referencing the electrochemical response of the devices directly to the Fermi energy of electrons in graphene (their electrochemical potential).

Electronic response
Figure 1b shows that the in-plane electronic conductance as a function of VG displays a local minimum, the so-called charge neutrality point (NP), which separates the hole- and electron-doped branches of the response. For negative potentials vs NP, where graphene is doped with electrons, we observe a conductor–insulator transition when the Fermi energy of electrons is about µe ≈ 1.1 eV vs NP. This transition is accompanied by a sharp D band in graphene’s Raman spectrum, indicating the presence of adatoms in graphene (Fig. 1a, left inset). Previous work has established that this conductor–insulator transition is due to the electrochemical hydrogenation of graphene14,15, which results in a density of adsorbed protons of ~1014 cm−2. This insulating state could be reversed by applying VG ≈ 0 V vs NP, such that graphene recovered its electronic conductivity, and the D band disappeared completely. This allows estimating the Fermi energy for the dehydrogenation transition as µe ≈ 0 eV vs NP (Estimation of Fermi energy in “Methods” section).

Electrochemical response
Figure 1a shows that the electrochemical response was dominated by two peaks whose position matched the potentials for the hydrogenation and dehydrogenation processes in the electronic response. The peak at positive potentials was the smaller of the two and could be readily attributed to the oxidative desorption of protons from graphene. However, the peak at negative potentials had an area ~5 times larger than the oxidation peak and consisted of an exponential decay truncated at the insulating transition. Measurements of this reduction current at slow scan rates revealed that it accelerated exponentially with applied bias as 200 mV dec−1 (Fig. 1a right inset, Tafel slope analysis in “Methods” section), a value similar to that observed in graphite electrodes during the hydrogen evolution reaction16. These findings therefore show that the reduction peak cannot be attributed only to the hydrogenation of graphene, since in such a case, both oxidation and reduction peaks would be similar. We must conclude that the reduction current is the result of a more complex electrochemical process, which can be attributed to H2 evolution via either an Eley–Rideal or Langmuir–Hinshelwood process17,18. In the Eley–Rideal mechanism, an adsorbed hydrogen atom spontaneously combines with an incoming proton and an electron to form H2 (Supplementary Fig. 3). In the Langmuir–Hinshelwood process, two adsorbed hydrogen atoms combine to form H2, but this involves a notable energy barrier (Supplementary Fig. 4). On this basis, we attribute the competing process to an Eley–Rideal mechanism, which proceeds spontaneously. Note that the reduction process would have normally continued beyond the hydrogenation potential, similar to the hydrogen evolution reaction. However, hydrogenation turns graphene into an insulator, yielding the truncated peak observed.

To gain more insights into the reduction reaction, which includes both proton adsorption and the competing process, we measured the rate of proton adsorption directly, isolating it from all competing processes. To that end, we fixed VG and measured the in-plane electronic response of graphene as a function of time with sub-millisecond resolution, as shown in Fig. 1e and Supplementary Fig. 5. Since the hydrogenation process stops14,15 when the proton concentration on graphene reaches ~1014 cm−2, the time τ at which this transition is reached allows estimating the rate of proton adsorption directly as r ≈ 1014 cm−2 τ−1. Figure 1e shows that for potentials around −1.5 V vs NP, the rate was r ~ 1 s−1 nm−2. For reference, we recall that accelerated hydrogen atom experiments report9,19 an adsorption rate r ~ 10−3 s−1 nm−2, whereas ultra-sensitive gas microcontainer experiments20,21 report r ~ 10−8 s−1 nm−2. Hence, even at low potentials, the electrochemical hydrogenation proceeds orders of magnitude faster than other methods. Notwithstanding, the rate in our experiments accelerated exponentially with bias, such that for −2.5 V vs NP, it reached r ~ 103 s−1 nm−2, which is 106 times faster than in experiments with accelerated hydrogen atoms. From these data, we also find that r accelerates exponentially with the applied bias as ≈ 195 mV dec−1, which is the same acceleration (Tafel slope) found for the whole reduction process (Fig. 1a). This suggests that proton adsorption is the limiting step of the reduction process. At even larger potentials, τ saturated at a value of about 10 times the resistor-capacitor (RC) constant of the circuit, which suggests that charging the electrochemical double layer becomes the limiting factor for the process at high bias (Device fabrication in “Methods” section).

Isotope effect
To confirm that proton adsorption is the limiting step of the reduction process, we measured our devices using electrolytes in which protons were substituted for deuterons, nuclei of hydrogen’s heavier isotope deuterium. The deuterated electrolyte was synthesised, producing an electrolyte with the same conductivity as in its proton form22 (Supplementary Fig. 6, 7). Figure 2, bottom panel, shows that deuterated samples also displayed a conductor–insulator transition, and that their Raman spectra were the same as for hydrogenated graphene (Fig. 2, top inset), demonstrating a deuterium concentration of ~1014 cm−2 on graphene. However, graphene’s deuteration took place at less negative potentials compared to its hydrogenation. This finding was confirmed with in situ Raman measurements (Supplementary Fig. 8) and is consistent with previous experiments of graphene’s deuteration using accelerated atoms, which found that the deuteration of graphene proceeded faster than its hydrogenation19. To quantify this isotope effect, we studied it in the limit of low adsorbed proton/deuteron density, which can be accessed in the potential range at which graphene’s electronic conductivity started to decrease (Fig. 2, bottom inset). This revealed that the onset of the deuteration transition occurred for a Fermi energy several tens of meV lower than with the proton electrolyte.

Figure 2, top panel, shows that both electrochemical peaks shifted to the positions of the deuteration and de-deuteration transitions. We also found that their relative sizes changed. The oxidation peak had roughly the same area for samples measured with proton and deuteron electrolytes, but the reduction peak had half the area for samples measured with deuteron electrolyte. Since both types of samples achieve the same concentration of adsorbed protons/deuterons (~1014 cm−2), the smaller reduction peak demonstrates that the competing (Eley–Rideal) process is suppressed for the deuteron reduction process. This shows that the hydrogenation process is faster when the competing process is suppressed, which confirms that proton/deuteron adsorption is the limiting step in the reduction process. From a theory perspective, the isotope effect can be traced back to differences in the zero-point energy of the carbon-hydrogen and carbon-deuterium bonds, which lead to a zero-point energy ≈ 45 meV lower for deuterons than for protons19,23. This makes deuterons harder to remove from graphene, in agreement with our observations. Hence, taken together, our experimental findings demonstrate that hydrogenation takes place as part of a reduction process that involves proton adsorption as the limiting step and that the adsorption process competes with the formation of H2 via an Eley–Rideal process. From the perspective of applications, the isotope substitution experiments show that the deuteration of graphene has the advantage of yielding an insulating transition at lower potentials than the hydrogenation process and results in an even more stable insulating state.

Electrochemical potentials
Our results establish the mechanism of the hydrogenation process and its relation to the electronic response of the devices. However, the electrochemical potential for the hydrogenation found experimentally, µe ≈ 1 eV, would initially appear to differ from the DFT calculations, which report a small energy barrier (~0.3 eV) for this process (Fig. 1d). To reconcile these observations, we note that the DFT calculations assume protons to be in vacuum, whereas protons in the experiments at zero bias are in equilibrium with their adsorption and desorption in the PdHx electrode24. Moreover, the experiments measure changes in electrochemical potential during the process, rather than in energy. To account for these differences, we calculated the Gibbs energy of a proton during the hydrogenation process, in the neutrality point (NP) scale, using the formula25–27: ΔG = UH − Uref + ΔZPE − TΔS − ΔNP. In the formula, UH is the proton adsorption energy in vacuum calculated by DFT; Uref is the energy of protons in the PdHx electrode in the standard hydrogen scale25,28, ΔZPE and ΔS are the differences in zero-point energy and entropy between the proton in the adsorbed state and the reference, respectively; and ΔNP is the position of graphene’s neutrality point in the standard hydrogen electrode scale. When all these contributions are included, the DFT calculation translates into an electrochemical potential of ≈ 1.4 eV vs NP for the hydrogenation and ≈ 0.1 eV vs NP for the dehydrogenation (Analytical theory in Methods). This analysis, therefore, reconciles the DFT calculations with the Fermi energy extracted experimentally within an error of only a couple of hundred meV.

Control of processes via graphene’s morphology
Previous works suggest that changing graphene’s morphology at the nanoscale could alter its electrochemical properties, even in the absence of defects such as vacancies, adatoms or substitutions21,29–31, but this has not been investigated for the electrochemical hydrogenation of graphene. To investigate this possibility, we fabricated two new types of devices. In the first one, graphene was supported on hexagonal boron nitride, rather than on silicon oxide, which yields atomically flat graphene21,32 (Fig. 3a). In the second type, we increased the roughness of graphene at the nanoscale by subjecting our standard graphene devices to thermal cycling between extreme temperatures, resulting in corrugated graphene. Typically, we heated the devices to 400 °C, then rapidly cooled them to liquid nitrogen temperatures (−196 °C) within seconds and repeated this treatment 3–4 times. Graphene’s negative thermal expansion coefficient33 results in a strong mismatch in thermal expansion with the substrate. This increases graphene’s mean square roughness by a factor of ~2 (Fig. 3a, Supplementary Fig. 9 and Corrugated graphene in “Methods” section), and probably even more than the AFM measurements show, since tip convolution effects in scanning probe techniques are known to underestimate the aspect ratio of nanoscale features34. Crucially, this thermal treatment did not introduce any cracks or microscopic defects, as evidenced both in the AFM images and from the lack of a D band in the Raman spectra of the samples (Fig. 3b).

Figure 3c shows that the electrochemical current in the different samples displayed strong differences. Corrugated graphene exhibited the lowest onset potential for the reduction process, followed by graphene-on-SiO2, and finally graphene-on-hBN (inset, Fig. 3c). As a result, the reduction current in corrugated graphene reached values approximately 20 times higher than those in graphene-on-SiO2 devices. In situ Raman measurements confirmed that the hydrogenation of the corrugated samples was also accompanied by a sharp D band (Supplementary Fig. 10). Our DFT calculations indicate that this occurs because corrugations effectively eliminate the energy barrier for proton adsorption in convex regions of the flake, in agreement with previous work13,21,29,30 (Supplementary Fig. 1). This facilitates proton adsorption and thus results in a larger reduction current via an Eley–Rideal process. In contrast, the reduction current was suppressed for graphene-on-hBN devices, which arises because its atomic flatness increases the proton adsorption barrier. Unexpectedly, we found that despite the lower onset potential for proton adsorption in corrugated graphene, the insulation transition occurred at similar potentials across all samples. This shows that achieving a proton coverage of ~10¹⁴ cm⁻² required comparable potentials in all cases. We attribute this to regions within the corrugated graphene that resist hydrogenation, preventing the entire sample from reaching full proton coverage. Our DFT calculations support this interpretation, showing that while proton adsorption barriers are lower in convex areas, they remain the same as in flat graphene in concave regions. These concave areas likely maintain electronic conductivity, and as a result, the conductor–insulator transition of the entire flake is governed by proton adsorption into these regions.

Methods
Device fabrication
Source and drain electrodes (Au/Cr) were patterned using photolithography and electron beam evaporation on Si/SiO2 substrates. Mechanically exfoliated monolayer graphene crystals with a rectangular shape were transferred onto the substrates to form a conducting channel between the source and drain electrodes. An SU-8 epoxy washer with a 15-μm diameter hole covered the source and drain electrodes, leaving a mid-section of the graphene flake exposed (Supplementary Fig. 2). This allows the whole mid-section of the flake to be hydrogenated, which is necessary to observe the insulating transition. The electrolyte used was 0.18 M bis(trifluoromethane)sulfonimide (HTFSI or DTFSI) dissolved in poly(ethylene glycol) (average molecular weight Mn of 600), which was drop-cast on the device inside a glove box containing an inert gas atmosphere. We characterised the conductivity of both HTFSI and DTFSI electrolyte by measuring the conductance of devices consisting of SiNx substrates with a circular hole of different diameters. This allows us to extract the electrolyte conductivity, κ, from the measured conductance, G, using the equation39: G = 4πκr. This reveals κ ≈ 1.062 × 10−4 S cm−1 for HTFSI, consistent with other studies40–42 and a ≈ 35% lower conductivity in the DTFSI electrolyte. Together with the capacitance of the electrolyte we characterised in previous work, C ≈ 20 µF cm−2, we estimate the RC time constant of our microelectrode devices as ≈ 0.6 ms. Palladium hydride or palladium deuteride foils (~0.5 cm2) fabricated following the recipe in ref. 43 were used both as gate and pseudo-reference electrodes. The reaction taking place in the gate and reference electrode is proton adsorption into the metal xH+ + xe− + Pd → PdHx24,44,45. The device was placed inside a chamber filled with 100% hydrogen gas for electrical measurements.

Electrical and electrochemical measurements
For electrochemical measurements, we used a Keithley 2636B source meter and swept the potential at a rate of 10 mV s−1 using programmes that allow controlling the potential of graphene vs the pseudo-reference electrode, VG. We found that VG is effectively the same as the applied potential, within a scatter of <4 mV, similar to a previous work15,46. Reference experiments with an Ivium pocketSTAT2 potentiostat gave the same results. A second Keithley source meter was used both to apply source-drain bias (VSD) and to measure the electronic current. The electrochemical response is normalised by the active area of the devices.

In the manuscript, we have adopted the convention that negative (positive) potentials vs NP dope graphene with electrons (holes). In the setup, protons flow from the gate electrode to graphene during the reduction process (starting at about −1.5 V vs NP), yielding a negative current. Conversely, protons flow from graphene to the gate electrode during the oxidation process (at about 0 vs NP) and yield a positive current.

For measurements of the time dependence of the conductor–insulator transition, graphene was connected to the voltage divider circuit shown in Supplementary Fig. 5, similar to a previous work14. Graphene was connected to a 1 MΩ series resistor, and the total voltage was set to 1 V. The gate electrode was connected to an alternating voltage source using a waveform generator that oscillated between a hydrogenating potential, typically set between −1.5 V and −3.3 V vs NP, and a dehydrogenating potential of +1.2 V vs NP. An oscilloscope or a Keithley 2182A Nanovoltmeter was used to record the output voltage across the graphene channel. The conducting and insulting phases are evident from the low and high plateaus of the output voltage. The time constant was defined as the time it took the response to rise from 10% to 90% of these plateaus.

Tafel slope analysis
The acceleration of an electrochemical process with applied bias is characterised by its Tafel slope. This parameter is defined as39 b = ln(10)kT/αe, with kT the thermal energy, e the elementary charge constant and α ∈ [0, 1] a coefficient that models the symmetry of the energy barrier of the reaction. From the measured b ≈ 200 mV dec−1, we deduce α ≈ 0.3. This coefficient implies39 that the proton reduction reaction is harder than reversing it via the oxidative removal of protons from graphene, consistent with our measurements and energy analysis of these processes.

Raman spectroscopy
The Raman spectra of devices fabricated on glass substrates were measured as a function of applied bias using a WITec Alpha300R Raman spectrometer equipped with a laser operating at 514.5 nm. For each bias, the measurement was performed with a 50× objective, 600 l mm−1 grating, accumulating time of 75 s over 4 cycles, and the laser power was 0.5 mW. The raw spectra include an electrolyte background alongside the graphene signal. Since this background is independent of applied voltage, it is removed using the data processing software’s (Origin) background subtraction tool. Raman spectra of devices not in contact with electrolyte (Fig. 3) were performed on a Renishaw inVia spectrometer equipped with a laser operating at 532 nm using a 100× objective, 1800 l mm−1 grating, accumulating time of 15 s over 3 cycles with the laser power of 1 mW.

The data show that the hydrogenation transition was accompanied by the appearance of a strong D band, a sharp increase of the G peak intensity and the smearing of the 2D peak. This demonstrates high disorder in graphene47. The density of adsorbed hydrogen atoms in hydrogenated graphene was estimated from the intensity ratio of the D and G bands47, ID/IG, and the integrated-area ratio of AD/AG. From the found ID/IG ≈ 1, AD/AG ≈ 2.03 and the fact that the 2D band is smeared, a density of H atoms of ≈ 1 × 1014 cm−2, was estimated, in agreement with previous reports14,15. Note that ID/IG ≈ 1, AD/AG ≈ 2.03 can translate both into a distance between H atoms of LD ≈ 1 nm or LD ≈ 10–15 nm47,48. This is a consequence of the bell-shaped ID/IG vs LD dependence47,48. To decide which one applies, it is necessary to look for additional signatures of disorder in the spectra. In our spectra, the 2D band is smeared, a signature of highly disordered systems, and thus consistent with LD ≈ 1 nm, or a defect concentration of ≈ 1 × 1014 cm−2. The Raman spectra of pristine graphene were recovered by dehydrogenating the sample, as demonstrated previously14,15.

Our measurements with deuterium electrolyte resulted in a similar response (Supplementary Fig. 8), except the potential at which the D band appeared was lower, in agreement with the transport experiments.

Deuterated electrolyte synthesis
Lithium bis(trifluoromethane)sulfonimide (LiTFSI, 99%) and Dideuterosulfuric acid (D2SO4, 96–98 wt. % in D2O, 99.5 atom% D) were purchased from Sigma–Aldrich and used as received without further purification. All manipulations of air- and moisture-sensitive compounds were carried out under an atmosphere of dry nitrogen using standard Schlenk techniques.

Deuterated bis(trifluoromethanesulfonyl)imide (DTFSI) was synthesised by dissolving 5 g (26.75 mmol) LiTFSI in 5 mL D2SO4 and heating the mixture to 75 °C in a sublimator under a nitrogen atmosphere. The formed product was sublimed and collected under reduced pressure over a curved glass tube in a liquid nitrogen bath. Note that the melting and decomposition of LiTFSI proceed at 234 °C and 340–415 °C, respectively49; whereas the boiling point of D2SO4 is 290 °C; and the melting and boiling points of Lithium sulfate are 859 °C and 1,377 °C, respectively. Hence, only the product DTFSI can be sublimated in this process.

To characterise the electrolyte, NMR spectra of the product (DTFSI) were obtained on a Bruker Avance III Prodigy instrument (500 MHz for 19F NMR, 151 MHz for 13C NMR and 400 MHz for 7Li NMR). Samples were prepared by dissolving the solid powder (~10 mg) in DMSO-d6 (1 mL). Chemical shifts (δ) were described in parts per million (ppm) from high to low frequency and referenced to the residual solvent resonance. The residual signal from the chemical shift of DMSO-d6 at 39.52 ppm was used as an internal reference for 13C NMR50. Supplementary Fig. 7 shows that the 19F NMR spectrum of DTFSI displayed one set of singlet characteristic fluorine peak, demonstrating only one fluorine environment; the 13C NMR spectrum of DTFSI had only one quartet signal, demonstrating only one carbon environment. The 19F NMR and 13C NMR data illustrate that there was only one set of (CF3SO2)2N- anions in the DTFSI product. To rule out the existence of Li in the DTFSI, we also measured the 7Li NMR spectra of LiTFSI and DTFSI. A strong singlet lithium peak at a chemical shift of −1.05 ppm was observed in the 7Li NMR spectrum for LiTFSI, whereas no peaks were observed for the DTFSI, demonstrating the absence of Li in the DTFSI sample, further confirming the purity of the product.

Proton transport in the HTFSI/PdHx system
Protons in our devices originate from trifluoromethanesulfonimide (HTFSI), a superacid (pKa ≈ −10), and are present either as free H+ or as PEG-coordinated complexes51,52. Proton conduction occurs primarily via a Grotthuss-type mechanism, enabled by transient hydrogen bonding with PEG oxygen groups51,52. This is consistent with our conductivity measurements in Supplementary Fig. 6, which revealed a clear isotope effect. At the counter electrode, protons interact with palladium, forming Pd hydride (PdHx). The Pd–H system exhibits two phases: a hydrogen-poor α-phase and a hydrogen-rich β-phase, whose distribution depends on hydrogen concentration, temperature, and pressure44,45. In acidic aqueous media under H2 atmosphere, hydrogen-saturated Pd electrodes equilibrate at ≈ 0 V vs SHE through the Volmer step (H+ + e− + * → H*), whereas pristine Pd shows ~90 mV vs SHE, which very gradually decreases as hydrogen is electrochemically absorbed. Electrodes with intermediate hydrogen loading exhibit potentials between 0 and 90 mV. In our devices, the PdHx displays a zero current potential of ≈ 61 mV vs SHE.

These redox equilibria persist in non-aqueous electrolytes, albeit with slower kinetics due to reduced proton mobility and altered solvation environments53. The potentials for proton adsorption and desorption can also shift by approximately 100 mV relative to their values in aqueous eletroltyes53. Nonetheless, the underlying mechanism and equilibrium positions remain comparable to those in the aqueous case. In our devices, the electronic response of graphene provides direct access to the absolute potential scale, effectively circumventing these small uncertainties.

Analytical theory
To calculate the electrochemical potential of the protons during the hydrogenation process, we need numerical values for the different entries in the formula25
ΔG = UH − Uref + ΔZPE − TΔS − ΔNP (1)

The first term UH ≈ -0.7 eV to −1.08 eV is the energy of a proton adsorbed on graphene vs vacuum, calculated by DFT12. The second term, Uref, is the energy of a proton adsorbed on the reference electrode vs SHE, given by Uref = ½ UH2 − UPdH, with −UH2 = 4.47 eV the binding energy of a hydrogen molecule25 and −UPdH = 60 meV the energy of electrons in the PdHx pseudo-reference electrode during the adsorption process in the SHE scale. The third term, ΔZPE, is the difference in zero-point energy between the proton adsorbed on graphene, ZPE C–H, and the reference, ZPE H2. Hence25 ΔZPE = ZPE C-H − ½ ZPE H2 ≈ 0.17 eV − ½ × 0.27 eV = 0.035 eV. The fourth term, TΔS, is dominated by the contribution from the gas phase, so it is given by25 TΔS ≈ ½ TΔS H2 ≈ −0.205 eV. The fifth term, ΔNP, is the position of the neutrality point in the SHE. To calculate it, we note that 0 vs SHE corresponds to ε0 abs ≈ 4.44 eV in the so-called absolute scale39, in which the energy of electrons is referred against their energy in vacuum. The energy necessary to remove an electron from the neutrality point in graphene into the vacuum is54 FG ≈ 4.5 eV. Hence, ΔNP = ε0 abs − FG ≈ −50 meV. This yields ΔG ≈ 1.4 eV vs NP, which is in reasonable agreement with the experiment. The dehydrogenation potential is estimated with this formula from the energy necessary for the proton to escape the adsorption well (~1.3 eV).

Isotope substitution experiments
Using formula (1), we calculated ΔGH − ΔGD = (UH − UD) − (UrefH − UrefD) + (ΔZPEH − ΔZPED) − (TΔSH − TΔSD), where sub- and super-indexes denote protons (H) and deuterons (D). This expression can be simplified by noting that ΔZPEH − ΔZPED = (ZPE C–H − ZPE C-D) − (ZPE H2 − ZPE D2) and that (ZPE H2 − ZPE D2) = −(UH − UD). Moreover, UrefH = UrefD, because this is the energy calculated by DFT. Neglecting changes in the entropy of hydrogen and deuterium molecules, we obtain the formula:
ΔGH − ΔGD ≈ ZPE C–H − ZPE C–D (2)

To obtain the ZPE for the carbon-proton bond, we note that the vibrational energy is given by hν, with h the Planck constant and ν the vibrational frequency of the bond. From the known ν = 2738 cm−1 of this bond, we obtain its ZPE as hν/2 = 0.17 eV. For deuterons, we obtain hν/2 = 0.124 eV. This then yields an isotope effect of ΔGH − ΔGD ≈ 45 meV.

To measure the isotope effect experimentally, it is necessary to measure the proton/deuteron adsorption in the linear regime of the process55. This is difficult for the hydrogenation process because this process only takes place at high applied biases and is only measurable when a relatively large number of protons are adsorbed on the surface of graphene. To address this challenge, we extracted the Fermi energy for the potential at which the electronic conductivity of the samples starts to decrease. Data from 12 different samples show that this energy was ≈ 0.87 eV vs NP for protons and ≈ 0.82 eV vs NP for deuterons. However, given the large experimental uncertainty in extracting this parameter, we can only estimate that the onset potential of the deuteration transition is several tens of meV lower for deuterons.

Estimation of Fermi energy and carrier mobility
The (gate) potential applied to graphene is related to the charge carrier density n as56,57: VG − VNP = neC−1 + ħvF e−1(πn)1/2, where C is the capacitance of the electrolyte, vF ≈ 1 × 106 ms−1 the Fermi velocity in graphene, and ħ the reduced Planck constant. Since μe = ħvF πn, this yields the relation between potential and Fermi energy: VG − VNP = eC−1 π−1 μe2 (ħvF)−2 + e−1 μe. In previous work15, we have estimated the capacitance of the electrolyte used in this work experimentally as C ≈ 20 µF cm−2, which enables a direct numerical estimate of μe. Note that this description is valid only if the system is conducting and outside a band gap57. For this reason, we cannot specify μe after the hydrogenation transition, as indicated by breaks in the top axes in Figs. 1–3. In principle, this precludes estimating μe for the dehydrogenation transition. However, from the position of the NP before the hydrogenation transition and given the high reproducibility of the dehydrogenation potential vs the NP, we tentatively estimate the Fermi energy for the dehydrogenation as μe ≈ 0 eV vs NP.

We also estimated the carrier mobility in our samples using the protocols reported previously. The carrier concentration in graphene, n, is:
n = sqrt(n0^2 + n(VG*)^2) (3)
where n0 is the residual charge at the NP and n(VG*) are the induced carrier concentration as a function of the applied gate voltage, VG vs the neutrality point. The relation between gate voltage and induced carriers is:
VG* = e−1 C n(VG*) + ħvF e−1 πn(VG*) (4)
where e and ℏ are the elementary charge and reduced Planck constant, respectively. vF is the Fermi velocity, of 1 × 106 ms−1 and C = 20 µF cm–2 is the electrolyte capacitance, as shown in our previous work. The total resistance, RTotal, is then written as:
RTotal = RC + LG / (W G e μe n) (5)
where RC is the contact resistance and LG and WG refer to the gated channel length and width, respectively, and μe is the mobility to be extracted. The extracted mobilities for graphene-on-SiO2 and corrugated graphene devices are in the range of 2000–6000 cm²/V·s, in good agreement with the literature for similar samples, which display mobility between 1000 and 10,000 cm²/V·s58. For Gr-on hBN devices, the mobility values are ~15,000–30,000 cm²/V·s, also in agreement with previous studies32.

DFT calculations of proton adsorption
Density functional theory (DFT) calculations were carried out using the plane-wave-based DFT method as implemented in the Vienna ab Initio Simulation Package (VASP)59. DFT calculations with a dispersion correction method (DFT-D3) were performed to account for van der Waals interactions, using Grimme’s method to correct for long-range interactions60. Spin-polarisation was included in the simulations. The generalised gradient approximation with the Perdew-Burke-Ernzerhof functional (GGA-PBE) was used to calculate the total energy61. Electron-ion interactions were described using the projector augmented wave (PAW) method62. An energy cutoff of 500 eV was set for the plane-wave basis. The convergence criteria were set to 10−6 eV and 0.01 eV Å−1 for the electronic self-consistent iteration and the forces on each atom, respectively. The Brillouin zone was sampled using Monkhorst-Pack mesh k-points with a reciprocal space resolution of 2π × 0.04 Å−1. The computational box used to model graphene had an orthorhombic shape with periodic boundary conditions in all three directions.

The graphene layer consisted of a supercell with 7 × 4 unit cells with a total number of 112 carbon atoms. A periodic length of z = 20 Å was considered along the z-direction perpendicular to the graphene plane, with the graphene being located at the centre in the z-direction to avoid self-interactions with periodic images. To evaluate the effect of curvature on the hydrogenation processes, graphene structures with different concavities were generated. Corrugations were modelled by fixing the out-of-plane positions of carbon atoms so that the crystal forms a Gaussian profile of height h (Supplementary Fig. 1). The atoms were allowed to relax in-plane.

Supplementary Fig. 1 shows the energy profiles for the proton as a function of the aspect ratio of the corrugated graphene structures. We find that for convex structures, the energy barrier for the incoming proton is lower and the adsorption well is deeper with respect to flat graphene, whereas for concave structures, the energy profiles are effectively unchanged, in agreement with previous calculations29,30.

Eley–Rideal process
The potential energy surface (PES) for the formation of H2 on flat graphene via an Eley–Rideal process was calculated with DFT using the same parameters described above. In this process, an incoming proton (H) approaches a proton adsorbed on graphene (Hb). The incoming proton follows the trajectory perpendicular to the basal plane directly on top of the adsorbed proton. In the calculation, the protons were fixed at specific coordinates in the trajectory and then both protons, the carbon atom with the adsorbed proton and its 1st neighbours were allowed to relax in the z-direction (the direction of the protons). 160 points of the PES were calculated as a function of the distances of the two H atoms from the surface, and 2D splines were used to have continuous representations of the functions. Supplementary Fig. 3 shows the PES for the process and the minimum energy path within it. These calculations show that the formation of H2 on graphene via an Eley–Rideal mechanism is a spontaneous process, in agreement with previous work17,18.

Langmuir–Hinshelwood process
The formation of H2 on graphene via a Langmuir–Hinshelwood process was calculated using climbing image nudge elastic band (CI-NEB) DFT using the parameters described above. In this process, two protons adsorbed on graphene recombine to form a H2 molecule. These two protons can adsorb in different relative positions, known as para and ortho dimers. Supplementary Fig. 4 shows that for both configurations, the formation of H2 involves a large ~1–2 eV energy barrier, which makes this mechanism energetically unfavourable compared to the Eley–Rideal process.

Corrugated graphene
Mechanically exfoliated graphene flakes were transferred onto Si/SiO2 substrates with source-drain electrodes, as described above. To corrugate the flakes, the samples were first annealed in a tube furnace in a He atmosphere at 400 °C for a couple of minutes, following the recipe from a previous work34. The samples were then pulled out of the furnace and placed into liquid nitrogen for rapid cooling. This annealing process was repeated three times. To characterise the roughness of the samples, we performed ambient atomic force microscopy (AFM) using a Dimension FastScan in peak force mode. For further confirmation, additional before/after thermal cycling images were obtained with a separate AFM system (Oxford Instruments Asylum Research Cypher-S) using Budget Sensors Tap300Al-G probes. Both pre- and post-thermal cycling roughness measurements were acquired in AC mode, and all data was processed using the Gwyddion63 SPM and NanoScope data analysis package. Supplementary Fig. 9 shows height statistics collected for both types of samples. These revealed that the thermal treatment increased the roughness of the samples from ≈ 0.1 nm to ≈ 0.17 nm. The changes in the roughness of the samples can be expected to be larger, since tip convolution effects in scanning probe techniques tend to underestimate the aspect ratio of nanoscale features.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Referee report for: Mechanism of the electrochemical hydrogenation of graphene\nIn this manuscript, Y.-C. Soong and co-authors discussed the mechanism of the electrochemical hydrogenation of graphene\nwith the acid electrolyte (HTFSI) dissolved in PEG. They found differences in oxidation and reduction currents during cyclic\nvoltammetry and demonstrated that the hydrogenation proceeds as a reduction reaction in which proton adsorption\ncompetes with a process attributable to the formation of H2 molecules. The work is really interesting and important. I have a\nfew questions that trigger my curiosity.\n1. The circuit design involves several electrodes (Figure 1b and Supplementary Figure 2a). Are those all PdHx electrodes?\nAre there relationships between them, is there an electrochemical current running between them or could one electrode\ninfluence the other during the measurements (see attached figure)? It seems to me that there are now two reference\nelectrodes and a bias is applied between the two. Are the gate and the reference electrode biased with respect to each\nother? In other words, if an electrochemical reaction occurs at the graphene surface and that the graphene is used as a\nGFET, how to disentangle the two contributions (i.e., electrochemistry and field effect)?\n2. Could the authors discuss the mechanism of proton migration in the electrolyte (Grotthuss mechanism, or vehicle\nmechanism). Supplementary Figure 6 shows that the conductivity of proton (in HTFSI) is smaller than that of deuteron (in\nDTFSI). However, it is known that the mobility of proton should be greater than that of deuteron because the mass difference.\n3. In the manuscript, the graphene located in the SU8 washer opening is getting hydrogenated. Figure S2 suggests that the\ngraphene flake is smaller than the opening in the SU8. Are the graphene samples studied here bigger or smaller than the\nopening in the SU8 washer?\nSeparately, the authors should discuss whether the graphene below the SU8 is also getting hydrogenated. Could the\nauthors verify this by using Raman, for example by establishing a Raman map of the hydrogenation sites (within the\nresolution that Raman provides). What would be the LD between the hydrogenation sites (under the assumption LD could\nbe calculated)?\n4. The authors quantified how fast the hydrogenation occurs for a single device (e.g., the one reported in 1d). Have the\nauthors performed experiments on more devices? How do the results vary across devices? Could the author comment on\nthe number of devices they used for each experiment? Could the author provide an error analysis? I have a similar question\nabout error analysis for the Fermi energy calculation in Figure 2 and for the hydrogenation onset potentials of corrugated\ngraphene, graphene on hBN, and graphene on SiO2 in Figure 3c? What is the mean and standard deviation for the\nhydrogenation peak currents and the electron currents?\n5. The electrochemical reactions occurring on PdHx are also key to the mechanisms of graphene hydrogenation. In previous\nwork (reference1), PdHx is used as a reference electrode together with a working electrode and a counter electrode (a 3-\nelectrode electrochemical system). Is PdHx here the working, reference or counter electrode? And, as an electrode, what are\nthe specific reaction equations that occur on PdHx when gaining and losing electrons?\n6. Raman of hydrogenated graphene. In this work, hydrogenated graphene shows a D peak and a G peak with a ratio of 1:1.\nHowever, in previous reports on hydrogenated graphene2,3 Raman showed a D’ peak next to the G peak, and the intensity\nratio of D/G varied with the degree of hydrogenation. Did the authors also observed a D' peak? Is there an intermediate\nhydrogenation state when the D/G ratio is not 1:1?\n7. Figure 3c shows the electronic current of graphene on hBN, on SiO2 and for corrugated graphene. Could the authors also\nshow the Dirac plots where the source drain current is plotted against VG (i.e., plot the electronic current vs VG-VNP over\nthe entire voltage range starting from -2.2V to above +1V)? Highly corrugated graphene should exhibit minimal electron/hole\nmobility. Now the authors plot the source-drain current only in the region of VG-VNP < -1V in Figure 3c.\n8. Could the electrolyte get underneath the graphene through the cracks (if any) and intercalation via the edges? If the\nelectrolyte get underneath the graphene, are there any protons transporting through graphene to the electrolyte below it?\nWould graphene get hydrogenated underneath the SU8? In the reference4, the authors used a similar circuit design but\nmeasured the proton current across graphene rather than the hydrogenation current; see Fig. 1a when Vb = 0 and Fig. 1b in\nreference4). Are the results from ref 4 and those reported here consistent? Could protons also transport through graphene in\nthis work? (i.e. in reference4, both graphene and the bottom channel electrodes share the same ground when Vb = 0,\nsimilarly to this work).\n9. The cleanness of graphene electrodes in electrochemical experiments is very important. I believe that the best practice\nwould be to grow graphene in situ in the electrochemical measurement glassware and after growth to incubate it with\nelectrolytes without any transfer. Could the author comments on the influence of any residues that may appear from the\ndevice fabrication and the possible impact of these residues on the electrochemistry?\nReferences:\n1. Smith, G., Zalitis, C. M. & Kucernak, A. R. J. Thin solid state reference electrodes for use in solid polymer electrolytes.\nElectrochem commun 43, 43–46 (2014).\n2. Li, S. et al. Large transport gap modulation in graphene via electric-field-controlled reversible hydrogenation. Nat Electron\n4, 254–260 (2021).\n3. Elias, D. C. et al. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for Graphane. Science (1979)\n323, 610–613 (2009).\n4. Tong, J. et al. Control of proton transport and hydrogenation in double-gated graphene. Nature 630, 619–624 (2024).", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_3": "The manuscript by Y.-C. Soong et al reports a study of the electrochemical hydrogenation of graphene and the\nconsequences of this process on the transport properties of the material. The work roots in a previous publication in Nature\n630, 619 (2024) by the same research groups. In the present article, the authors aim at providing further insights into the\nhydrogenation process by considering the effect of the replacement of hydrogen with deuterium and of the graphene\nroughness.\nIn general, the article appears rather narrow in terms of broad interest and devoted mainly to those readers with a specific\ntechnical expertise. The main results of the work, as well as their significance, are not always clear and several parts of the\nmanuscript are not well described. In particular, the importance and role of the theoretical support is not easily\nunderstandable.\nMore specific criticisms and remarks follow.\nIn the “main” section on page 1 “has been since been established” should be corrected.\nThe description of the experimental set-up (e.g., suppl. Fig. 2 and Fig. 1b) seems rather incomplete. For instance, the PdHx\nelectrodes are not indicated (is the topmost electrode in Fig. 1b?). In addition, the electrochemical current, its flow, sign, and\nsignificance are not adequately introduced.\nThe theoretical explanation provided at end of page 2and beginning of page 3 is very hard to follow both by its content and\nby its necessity. The presentation of the results could proceed without that part that contributes making the article a bit\nconfusing.\nAre the data shown in Fig. 1a the same as those already presented in Nature 630, 619 (2024)? Or do they differ in some\ndetail?\nThe red and blue arrows in Figure 1c are meant to be consistent with each other. However, the figure misses this purpose.\nThe starting point of the process should be clearly indicated for both the electronic and electrochemical current, as well as\nthe different phases of process occurring concomitantly should be adequately indicated by the arrows. In the figure caption,\nin the sentence “Black arrows mark the proton reduction process its oxidative desorption” an “and” is missing.\nThe caption of Fig. 1c is very confusing. It starts from the description of the bottom panel, then goes to the description of the\n“top-axis” but it doesn’t describe the top panel, then it describes the “Inset” (there are many insets, it has to be specified\nwhich one it is described) and finally it describes the top panel and the top insets. The fact that the bottom inset is described\nafter the “top-axis” is very confusing, the caption should be re-organized.\nThe inset with the Raman data is seemingly compressed vertically, and the labels are written with very small characters.\nBeing small and compressed, the labels cannot be read clearly.\nThe “exponential rise truncated at the insulating transition” mentioned at page 4 should rather be an exponential decay since\nthe insulating transition occurs at low current values.\nIn general, the description of Fig. 1c is not sufficiently detailed and/or clear despite it is a pivotal result of the present work.\nThe Raman results (Fig. 1 and Supplementary Fig. 8) are not so clear and are not discussed in detail. Why are the spectra of\nthe pristine sample (or de-hydrogenated/deuterated) characterized by a much lower signal to noise ratio? Furthermore, why\ndoes the G peak show a much lower intensity than the 2D peak (up to disappearing almost completely, as shown in\nSupplementary Fig. 8) in the pristine samples at variance with the hydrogenated/deuterated ones? And why is there such a\nhuge variation in the peak width for both the G and 2D modes? In Supplementary Fig. 8, around 1300 cm^{-1}, there are\nsome “negative” spikes whose intensity is comparable to that of the G peak. What are they due to? It looks like the signal is\nvery low and the spectra were not integrated much. Why instead are the data in Fig. 3b much better (i.e., with a much higher\nsignal to noise ratio)? Fig 3c is very small, but it seems that the width of the G peak is not as narrow as in the other figures\nand it is maybe consistent with the width of the G peak shown for the hydrogenated/deuterated samples in Figs. 1 and 2.\nThe right panel in Supplementary Fig. 8 shows a sudden change in the Raman spectrum, from the absence of the D band to\nits presence. What happens in between? Can the hydrogenation/deuteration process be monitored? And how precise is the\ninformation which one can get from the Raman spectrum? On page 4, it is said that a deuterium concentration of ~10^{14}\ncm^{-2} is deduced by the Raman spectrum. How precise is this concentration value?\nGenerally, information on the integration time and total intensity of the data should be provided (whenever normalized\nspectra are shown, it would be useful to say how large would the intensity factor be for hydrogenated/deuterated and pristine\nsamples).\nNot enough information on the Raman measurements is provided (laser wavelength, information o the setup and detectors,\netc.).\nIn Fig.2, it would be better to re-use for protons the same colors used in Fig. 1, e.g., red. This would also make the Figure\nclearer (the grey lines are not so well visible).\nThe effects of the morphology on the electronic/electrochemical currents seems the most interesting result of this work. The\nway it is presented is though misleading. On one hand, the reader gets the impression that corrugated graphene is\nbeneficial, but from our understanding it is instead detrimental because a larger electrochemical current is required. On the\nother hand, corrugated graphene shows a higher electronic current that seems to point to a beneficial effect. This part of the\nwork should be better explained as to remove this seemingly inconsistency.\nIn conclusion, the manuscript requires important revisions, and, in particular, it is not of adequate general interest for Nature\nCommunications, but it is more suitable for a specialised journal.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "Response to comments from Reviewer #1\nReferee report for: Mechanism of the electrochemical hydrogenation of graphene\nIn this manuscript, Y.-C. Soong and co-authors discussed the mechanism of the electrochemical\nhydrogenation of graphene with the acid electrolyte (HTFSI) dissolved in PEG. They found\ndifferences in oxidation and reduction currents during cyclic\nvoltammetry and demonstrated that\nthe hydrogenation proceeds as a reduction reaction in which proton adsorption\ncompetes with a\nprocess attributable to the formation of H2 molecules. The work is really interesting and\nimportant. I have a few questions that trigger my curiosity.\nWe are very grateful with the Reviewer for this encouraging assessment of our work. We have done\nour best to clarify the points raised, which we believe have improved the clarity of the manuscript.\n1. The circuit design involves several electrodes (Figure 1b and Supplementary Figure 2a). Are\nthose all PdHx electrodes? Are there relationships between them, is there an electrochemical\ncurrent running between them or could one electrode influence the other during the\nmeasurements (see attached figure)? It seems to me that there are now two reference electrodes\nand a bias is applied between the two. Are the gate and the reference electrode biased with\nrespect to each other? In other words, if an electrochemical reaction occurs at the graphene\nsurface and that the graphene is used as a GFET, how to disentangle the two contributions (i.e.,\nelectrochemistry and field effect)?\nThe setup schematics in Fig. 1 and Fig. S2 were not drawn clearly, which we believe is the source\nof the confusion. We have redrawn them in the revised manuscript.\nIn brief, the devices are connected to two PdHx electrodes. One functions as gate electrode and\nthe other as a reference electrode. The current flowing into the reference electrode is zero and\nthere is no voltage applied between these two electrodes. The setup is similar to that reported in\nref. 15 and by Y. He et al, Nat. Materials 2019, 22, 1098-1104. The voltage V is the potential of\nG\ngraphene vs the reference electrode. We found that this potential is effectively the same as the\napplied gate potential, within an error of <4 mV, similar to our findings in ref. 15 (Extended Data\nFig. 2 in that reference). Nevertheless, we decided to keep the reference electrode, as most\nelectrochemical data is reported this way. We added this discussion to the section ‘Electrical and\nelectrochemical measurements’ in Methods section, page 8.\n2. Could the authors discuss the mechanism of proton migration in the electrolyte (Grotthuss\nmechanism, or vehicle mechanism). Supplementary Figure 6 shows that the conductivity of\nproton (in HTFSI) is smaller than that of deuteron (in DTFSI). However, it is known that the mobility\nof proton should be greater than that of deuteron because the mass difference.\nWe observed the same electrolyte conductivity with HTFSI and DTFSI electrolytes within our\nexperimental resolution, which is hardly surprising. The conductivity of deuterons in aqueous\nelectrolytes is typically ~10% smaller than for protons (e.g. H. Arcis, et al. Phys Chem B 2022,\n126, 8791-8803), and the same can be expected for DTFSI. This relatively small difference is\nwithin our typical device-to-device variability for control devices without graphene. We have\nclarified this point in the caption in Fig. S6.\nRegarding the proton transport mechanism in the electrolyte, there is much less literature for\nHTFSI than for aqueous electrolytes. However, most references we found suggest that proton\ntransport is primarily via a Grotthuss mechanism (A. A. Moses & C. Arntsen Phys Chem Chem\nPhys 2023, 25, 2142 & M. L. Hoarfrost et al. J. Phys Chem B 2012, 116, 8201-8209).\n3. In the manuscript, the graphene located in the SU8 washer opening is getting hydrogenated.\ngraphene samples studied here bigger or smaller than the opening in the SU8 washer?\nSeparately, the authors should discuss whether the graphene below the SU8 is also getting\nhydrogenated. Could the authors verify this by using Raman, for example by establishing a Raman\nmap of the hydrogenation sites (within the resolution that Raman provides). What would be the\nLD between the hydrogenation sites (under the assumption LD could be calculated)?\nThe graphene flakes are slightly smaller than the opening in the SU8 mask. This is because\nobserving the insulating transition requires all electronic conduction paths along the graphene\nflake to be closed. This in turn requires a full section of the flake to be hydrogenated. This will not\nbe possible if the flake is larger than the SU8 opening because the areas covered with SU8 are not\nhydrogenated. This is consistent with previous control experiments in which the areas covered by\nthe SU8 are probed electronically and are found to be not hydrogenated (e.g. Fig. 2 in ref. 14 in the\nmanuscript). We have included this discussion in the section ‘Device fabrication’ in Methods,\npage 7.\nRegarding the Raman, from the ratio of intensity of the D to G bands in hydrogenated samples,\nI /I ≈ 1, we can estimate that the distance between H atoms in graphene is L ≈ 1 nm. This\nD G D\ncorresponds to a concentration of H atoms of ≈ 1 x 1014 cm-2. Estimates of defect density using\nthe Raman spectra are accurate within order of magnitude (Luchese et al Carbon 2010, 48, 1592-\n1597 and Jorio et al, Physica Status Solidi B 2010, 247, 2980-2982). However, the electronic\ntransport measurements find that the hydrogenation transition takes place for a charge carrier\ndensity of ≈ 1 x 1014 cm-2 (the Fermi energy extracted from these measurements can be readily\nconverted into charge density) in agreement with the Raman experiments. Hence, the\nconcentration of H atoms in the hydrogenated phase can be estimated with a fair degree of\naccuracy. We have included an expanded discussion of the Raman experiments in the Methods\nsection, page 8.\n4. The authors quantified how fast the hydrogenation occurs for a single device (e.g., the one\nreported in 1d). Have the authors performed experiments on more devices? How do the results\nvary across devices? Could the author comment on the number of devices they used for each\nexperiment? Could the author provide an error analysis? I have a similar question about error\nanalysis for the Fermi energy calculation in Figure 2 and for the hydrogenation onset potentials of\ncorrugated graphene, graphene on hBN, and graphene on SiO2 in Figure 3c? What is the mean\nand standard deviation for the hydrogenation peak currents and the electron currents?\nAll experiments in this work were carried out with at least 3 and up to 8 devices per experiment.\nWe found small variability from device to device. Below we specify the statistics for the different\nquantities requested and the sample number for each of the experiments. This information is now\nin Supplementary Table 1 and in the text.\n(a) Hydrogenation potentials in Fig. 3c\nGr-on-SiO , -1.75 ± 0.08 V 8 devices\nGr on BN, -1.99 ± 0.02 V 4 devices\n(b) Hydrogenation peak currents in Figure 3c (normalised by exposed flake area)\nGr on SiO , 0.19 ± 0.05 mA cm-2 8 devices\nGr on BN, 0.23 ± 0.02 mA cm-2 4 devices\n(c) Maximum electronic current in Figure 3c (normalised by the minimum width of the\nexposed flake section)\nGr on BN, 45 ± 7.4 mA m-1 4 devices\n(d) Fig. 1e in the revised manuscript shows the reaction rate as a function of applied potential\nfrom three different devices. The scatter is ~10%.\n(e) Statistic for the Fermi energy calculation in Figure 2. Onset potential for deuteration is\n0.82 ± 0.015 eV and 0.84 ± 0.005 eV for hydrogenation. 8 devices for hydrogenation and 4\nfor deuteration experiments.\n5. The electrochemical reactions occurring on PdHx are also key to the mechanisms of graphene\nhydrogenation. In previous work (reference1), PdHx is used as a reference electrode together with\na working electrode and a counter electrode (a 3-electrode electrochemical system). Is PdHx\nhere the working, reference or counter electrode? And, as an electrode, what are the specific\nreaction equations that occur on PdHx when gaining and losing electrons?\nOur setup is equivalent to a three-electrode electrochemical cell in which both counter and\nreference electrodes are PdHx. The reaction taking place in the counter and reference electrode\nis proton adsorption into the metal: H+ + e- + Pd → PdHx (e.g. M. Grden, et al. Electrochimica Acta\n2008, 53, 7583-7598). This is an important property of Pd that is exploited when using this metal\nas either pseudo reference electrode or to reduce contact resistance in nano-electronic devices\nworking with protons (e.g. A. J. Tan, et al. Nature Materials 2019, 18, 35-41 or C. Zhong et al.\nNature Communications 2011, 2:476). This discussion has been added to the section ‘Device\nfabrication’ in Methods, page 7.\n6. Raman of hydrogenated graphene. In this work, hydrogenated graphene shows a D peak and a\nG peak with a ratio of 1:1. However, in previous reports on hydrogenated graphene2,3 Raman\nshowed a D’ peak next to the G peak, and the intensity ratio of D/G varied with the degree of\nhydrogenation. Did the authors also observed a D' peak? Is there an intermediate hydrogenation\nstate when the D/G ratio is not 1:1?\na b\n-1.5 V\nI D /I G = 1.08 D G -1.0 V\nA /A = 2.03 0 V\nD G D G\n0.7 V\n) .u ) .u 0 V 1 2D\n.a .a\n(\ny\n(\ny\n2\ntis tis\nn n 3\ne e\ntn tn\nI D' I 4\n5\n1100 1300 1500 1700 1300 1950 2600\nRaman shift (cm-1) Raman shift (cm-1)\nFig. R1.1. (a) Analysis of Raman spectra of hydrogenated samples. Data points, experimental\nobservation. Red, green and blue curves are fitted Lorentzian for D, G and D’ bands, respectively.\nBlack curve, Sum of D, G and D’ bands. I /I and A /A are the intensity and integrated-area ratios\nD G D G\nfor the D and G bands, respectively. (b) Raman spectra of samples during a typical\ndehydrogenation cycle. Numbers 1-5 mark the sequence of measurements. Starting from -1.5 V\nvs NP (spectrum #1), the 2D band is initially smeared. At -1V, the G band starts becoming less\nprominent. At 0V, the 2D band becomes sharp, but the D band is still apparent. At 0.7 V, the\n3\nspectrum of pristine graphene is recovered, but the device is doped due to the applied voltage,\nyielding a relatively less sharp 2D band. Finally (spectrum #5), the voltage is swept back to 0V vs\nNP, yielding the spectra of pristine, undoped graphene. These findings are very similar to those in\nFig. 1, ref. 14.\nFig. R1.1a shows analysis of a typical Raman spectra for hydrogenated graphene samples. This\nshows that D’ band is convoluted with the large G band.\nRegarding the second question, we did not observe intermediate phases during the\nhydrogenation of graphene in the Raman spectra. We observe the sudden appearance of a sharp\nD and G band. This is consistent with the electronic measurements, which show a sharp\nconductor insulator transition. Even at moderate bias (e.g. -1.5 vs NP), graphene becomes\nhydrogenated in a couple of seconds (as shown in Fig. 1e).\nThis finding is also consistent with ref. 14. The authors of that work observed intermediate\nhydrogenated states, but only during the de-hydrogenation process. We also observe this. Fig.\nR1.1b shows that the Raman spectra evolve from the highly disordered phase to pristine\ngraphene more gradually.\n7. Figure 3c shows the electronic current of graphene on hBN, on SiO2 and for corrugated\ngraphene. Could the authors also show the Dirac plots where the source drain current is plotted\nagainst VG (i.e., plot the electronic current vs VG-VNP over the entire voltage range starting from\n-2.2V to above +1V)? Highly corrugated graphene should exhibit minimal electron/hole\nmobility. Now the authors plot the source-drain current only in the region of VG-VNP < -1V in Figure 3c.\nFig. R1.2 shows the electronic response over the full voltage range for the devices in Fig. 3,\nnormalised by the width of the graphene flake. The figure shows that there are no significant\ndifferences in the electronic current between the different devices (corrugated or supported on\nhBN and SiO2) within the expected device-to-device scatter reported in point #4, when\nnormalised by flake dimensions. This is consistent with previous works. Note that while highly\ncorrugated graphene should display a high density of electron hole puddles and charge\nlocalisation (e.g. e.g. J. Martin, et al. Nature Physics 2008, 4, 144-148 and ref. 34), it is not\nexpected to display minimal electron/hole mobility at room temperature. This is because the\nlength scale of corrugations is larger than the Fermi wavelength of charge carriers in graphene for\nthe Fermi level in our devices. To observe the effect\nof charge localisation in electronic transport\n60\nmeasurements, it is necessary to go to Fermi energy\n50 levels of the order ~1010 – 1011 cm-2 (e.g. J. Martin et\n1)\n-m al), which are inaccessible at ambient conditions.\nA∙\n40\nm\n(\ntn\ne 30\nrru\nFig. R1.2. Electronic current from the graphene-on-\nc\nc in 20 Gr-SiO 2 silicon oxide (blue), graphene-on-hBN (green) and\no rtc\ne lE\nG\na\r\nt\n-\ne\nh\nd\nB N\nGr\nc\nin\no\nt\nr\nh\nru\ne\ng\nm\nat\na\ne\ni\nd\nn t\ng\ne\nr\nx\na\nt\np\n.\nh\nT\ne\nh\nn\ne\ne\nd\n(iff\nre\ne\nd\nre\n)\nn\nsa\nc\nm\ne i\np\nn\nl e\ne\ns\nle\ns\nc\nh\ntr\no\no\nw\nn\nn\nic\ni\nc\nn\nu\nF\nr\ni\nr\ng\ne\n.\nn\n3\nt\nbetween data sets is comparable to device-device\n0\nvariation within the same type of device (see point\n−2 −1 0 1\n#4).\nV - V (V)\nG NP\n8. Could the electrolyte get underneath the graphene through the cracks (if any) and intercalation\nvia the edges? If the electrolyte get underneath the graphene, are there any protons transporting\n4\nthrough graphene to the electrolyte below it? Would graphene get hydrogenated underneath the\nSU8? In the reference4, the authors used a similar circuit design but\nmeasured the proton current\nacross graphene rather than the hydrogenation current; see Fig. 1a when Vb = 0 and Fig. 1b in\nreference4). Are the results from ref 4 and those reported here consistent? Could protons also\ntransport through graphene in this work? (i.e. in reference4, both graphene and the bottom\nchannel electrodes share the same ground when Vb = 0, similarly to this work).\nWe did not observe electrolyte intercalation between graphene and the substrate, consistent with\nthe strong van der Waals forces between 2D crystals and oxide surfaces (e.g. S. Koenig, et al\nNature Nanotechnology 2011, 6, 543-546).\nRegarding comparison with our previous work, in Tong et al we worked with suspended graphene\ndevices. In that case, the electrochemical signal was dominated by proton transport through\ngraphene, which yields large currents of the order of 10 mA cm-2, even for zero back gate voltage.\nIn contrast, the present devices are supported on substrates (e.g. SiO ) and display very small\n2\nelectrochemical currents of the order of 0.1 mA cm-2. The shape of the I-V response is also\ncompletely different in the two works. In Tong et al. there is a continuous rise of current with\napplied voltage, whereas in the present work the current is negligible except at the hydrogenation\nand dehydrogenation potentials. Both works are consistent. In the present work there is no proton\ntransport through graphene because transferred protons have no way of closing the\nelectrochemical circuit. Conversely, our understanding is that the hydrogenation current is also\npresent in ref. 15. but, because it is so small compared to the huge proton transport signal, it is\nnot discernible in the experiments.\n9. The cleanness of graphene electrodes in electrochemical experiments is very important. I\nbelieve that the best practice would be to grow graphene in situ in the electrochemical\nmeasurement glassware and after growth to incubate it with electrolytes without any transfer.\nCould the author comments on the influence of any residues that may appear from the\ndevice fabrication and the possible impact of these residues on the electrochemistry?\nGrowing graphene via CVD in the target substrate can produce high quality samples. However,\none can never rule out the presence of defects, such as vacancies or grain boundaries in CVD\ngraphene, which can have significant impact on electrochemical process and thus complicates\nthe interpretation of the data. To avoid this problem, most groups studying fundamental\nphenomena in graphene work with mechanically exfoliated crystals, which are defect free. To\nensure the cleanliness of the exfoliated crystals, we use transfer recipes that have been\noptimised through many years and are widely reported in the literature. This yields very clean\nsamples that can be studied in high precision electronic transport experiments or, as we showed\nrecently, in electrochemical measurements with nanoscale spatial resolution and fA current\nresolution (e.g. O. J. Wahab, et al. Nature 620, 782-786, 2023, ref. 31 in manuscript).\nReferences:\n1. Smith, G., Zalitis, C. M. & Kucernak, A. R. J. Thin solid state reference electrodes for use in solid\npolymer electrolytes. Electrochem commun 43, 43–46 (2014).\n2. Li, S. et al. Large transport gap modulation in graphene via electric-field-controlled\nreversible hydrogenation. Nat Electron 4, 254–260 (2021).\n3. Elias, D. C. et al. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for\nGraphane. Science (1979) 323, 610–613 (2009).\n4. Tong, J. et al. Control of proton transport and hydrogenation in double-gated\ngraphene. Nature 630, 619–624 (2024).\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscript\nWe thank the Reviewer for taking the time to look at our manuscript.\nResponse to comments from Reviewer #3\nThe manuscript by Y.-C. Soong et al reports a study of the electrochemical hydrogenation of\ngraphene and the consequences of this process on the transport properties of the material. The\nwork roots in a previous publication in Nature 630, 619 (2024) by the same research groups. In\nthe present article, the authors aim at providing further insights into the hydrogenation process\nby considering the effect of the replacement of hydrogen with deuterium and of the graphene\nroughness.\nIn general, the article appears rather narrow in terms of broad interest and devoted mainly to\nthose readers with a specific technical expertise. The main results of the work, as well as their\nsignificance, are not always clear and several parts of the manuscript are not well described. In\nparticular, the importance and role of the theoretical support is not easily understandable.\nMore specific criticisms and remarks follow.\nThe electrochemical hydrogenation of graphene has been recently shown to drive a robust and\nreversible conductor-insulator transition, which is of strong interest in computing applications\nbased on ionic-electronic processes. However, the mechanism for this new process remains\nunknown. Glaring gaps in knowledge remain, such as why this reaction happens at the potentials\nobserved, or even what is the reaction rate of this process as a function of potential. This is a\nproblem, because processes that are not understood cannot be fully controlled in applications.\nOur work reports the electrochemical fingerprint of the hydrogenation reaction for the first time\n(Fig. 1a). This allowed us to elucidate the mechanism for this process and answered these open\nquestions. It also addresses the fundamental question of how a proton adsorbs\nelectrochemically to a pristine sheet of carbon atoms These findings are of general importance\nto communities working on electrochemistry, solid-liquid interfaces an ion-based computing;\nand their importance was highlighted by Reviewer #1.\nWe have carefully addressed all the points raised by the Reviewer, which we believe have\nimproved the clarity of our manuscript.\nIn the “main” section on page 1 “has been since been established” should be corrected.\nWe have rephrased this statement.\nThe description of the experimental set-up (e.g., suppl. Fig. 2 and Fig. 1b) seems rather\nincomplete. For instance, the PdHx electrodes are not indicated (is the topmost electrode in Fig.\n1b?). In addition, the electrochemical current, its flow, sign, and significance are not adequately\nintroduced.\nWe have clarified the schematic for the experimental setup in Fig. 1 and Fig. S2. Regarding the\nelectrochemical current, protons flow from the gate electrode to graphene during the reduction\nprocess (starting at about -1.5 vs NP), yielding a negative current. Conversely, protons flow from\ngraphene to the gate electrode during the oxidation process (at about 0 vs NP) and yield a positive\ncurrent. The significance of these currents is discussed in detail in the section ‘Electrochemical\nresponse’ in the main text.\nMethods, end of first paragraph, page 8.\nThe theoretical explanation provided at end of page 2and beginning of page 3 is very hard to follow\nboth by its content and by its necessity. The presentation of the results could proceed without\nthat part that contributes making the article a bit confusing.\nFollowing the Reviewer comment, we have moved the theory further down in the main text to a\nnew section titled ‘Electrochemical potentials’ and simplified the discussion as much as\npossible. However, we respectfully disagree with the Reviewer on the point that this theory is not\nnecessary. Understanding why the electrochemical hydrogenation of graphene takes place at the\npotential observed is essential to reconcile the experimental observations with DFT predictions.\nDFT predicts a low energy barrier of ~0.3 eV, which differs markedly with the experiments because\nthese observe this process when graphene’s Fermi level is about ~1 eV. This difference has been\nnow reconciled using standard thermodynamic theory that calculates the Gibbs energy of the\nprocess based on the previous DFT calculations. This is an approach routinely used to analyse\nelectrochemical data.\nAre the data shown in Fig. 1a the same as those already presented in Nature 630, 619 (2024)? Or\ndo they differ in some detail?\nThe electrochemical data in Fig. 1 is different to that in Tong et al. (Nature 2024) in qualitative\nshape, magnitude, the device structure it comes from and the underlying electrochemical\nprocess. In Tong et al, we studied suspended graphene devices. The electrochemical signal is\ndominated by proton transport through graphene, which yields currents that continuously rise\nwith voltage and are of the order of 10 mA cm-2. In contrast, the present work studies graphene\nsupported on substrates, which do not allow for proton transport through graphene. In this case,\nthe electrochemical response is dominated by the hydrogenation reaction on the graphene\nsurface, yielding currents that are only significant at the hydrogenation and dehydrogenation\ntransitions. Even then, the currents are only of the order of 0.1 mA cm-2. Hence, the\nelectrochemical response of the devices in this work are fundamentally different to those in Tong\net al. Crucially, the new data in this manuscript reports the electrochemical fingerprint of the\nhydrogenation reaction, which had not been reported before and without which it is not possible\nto elucidate its mechanism.\nThe electronic current in both works is naturally the same and is presented here only to reference\nthe processes behind the peaks in the electrochemical response. Following the Reviewer\ncomment, this has been stressed in the main text, at the beginning of the section ‘Electronic\nresponse’.\nThe red and blue arrows in Figure 1c are meant to be consistent with each other. However, the\nfigure misses this purpose. The starting point of the process should be clearly indicated for both\nthe electronic and electrochemical current, as well as the different phases of process occurring\nconcomitantly should be adequately indicated by the arrows. In the figure caption, in the\nsentence “Black arrows mark the proton reduction process its oxidative desorption” an “and” is\nmissing.\nFollowing the Reviewer comment, we have added numbers in both electronic and\nelectrochemical curves to make the comparison clearer. This was a helpful suggestion.\nThe caption of Fig. 1c is very confusing. It starts from the description of the bottom panel, then\n7\ngoes to the description of the “top-axis” but it doesn’t describe the top panel, then it describes\nthe “Inset” (there are many insets, it has to be specified which one it is described) and finally it\ndescribes the top panel and the top insets. The fact that the bottom inset is described after the\n“top-axis” is very confusing, the caption should be re-organized.\nWe have relabelled the different panels in the graph and have reorganised the caption for clarity.\nThe inset with the Raman data is seemingly compressed vertically, and the labels are written with\nvery small characters. Being small and compressed, the labels cannot be read clearly.\nThe “exponential rise truncated at the insulating transition” mentioned at page 4 should rather be\nan exponential decay since the insulating transition occurs at low current values.\nIn general, the description of Fig. 1c is not sufficiently detailed and/or clear despite it is a pivotal\nresult of the present work.\nWe have made the Raman graph as big as possible given the space constraints. The phrase\n‘exponential rise’ has been changed to ‘exponential decay’.\nThe Raman results (Fig. 1 and Supplementary Fig. 8) are not so clear and are not discussed in\ndetail. Why are the spectra of the pristine sample (or de-hydrogenated/deuterated) characterized\nby a much lower signal to noise ratio? Furthermore, why does the G peak show a much lower\nintensity than the 2D peak (up to disappearing almost completely, as shown in Supplementary\nFig. 8) in the pristine samples at variance with the hydrogenated/deuterated ones? And why is\nthere such a huge variation in the peak width for both the G and 2D modes? In Supplementary\nFig. 8, around 1300 cm^{-1}, there are some “negative” spikes whose intensity is comparable to\nthat of the G peak. What are they due to? It looks like the signal is very low and the spectra were\nnot integrated much. Why instead are the data in Fig. 3b much better (i.e., with a much higher\nsignal to noise ratio)? Fig 3c is very small, but it seems that the width of the G peak is not as narrow\nas in the other figures and it is maybe consistent with the width of the G peak shown for the\nhydrogenated/deuterated samples in Figs. 1 and 2.\nThe Raman spectra of the devices are already discussed in refs. 14&15 and are used here only as\na reference to confirm that the hydrogenation process is taking place. Nevertheless, following the\nReviewer comment, we have expanded the discussion of these data in the manuscript.\nThe 2D band intensity is low because the concentration of protons is so high that graphene is now\nin the highly disordered/amorphous phase. In this regime, the ratio of integrated-area ratio of the\nD and G bands (A /A ) is known to be greater than one (e.g. Luchese et al Carbon 2010, 48, 1592-\nD G\n1597 and Jorio et al, Physica Status Solidi B 2010, 247, 2980-2982). This is consistent with our\nfindings, which reveal a peak intensity ratio of I /I ≈ 1.08 and integrated-area ratio of A /A ≈ 2.03,\nD G D G\nas shown in Fig. R1.1 (see response to point #6 from Reviewer #1, page 3). Note also that I /I ≈\nD G\n1, A /A ≈ 2.03 can translate both into a distance between H atoms of L ≈ 1 nm or L ≈ 10-15 nm.\nD G D D\nThis is a consequence of the bell-shape of the I /I vs L dependence (e.g. Fig. 4 in Luchese et al).\nD G D\nTo decide which one applies, it is necessary to look for additional signatures of disorder in the\nspectra. In our spectra, the 2D band is smeared, a signature of highly disordered systems, and\nthus consistent with L ≈ 1 nm.\nD\nRegarding the question of why the G band intensity in pristine samples is much lower than for the\n2D band, we point out that this is what is expected for pristine graphene. The ratio of 2D to G band\nis normally around 2-4 times (e.g. Physical review letters, 2006, 97: 187401; Physical Review B,\n2010, 82: 125429).\nRegarding the signal-to-noise ratio, ref. 14&15 already showed that the transition to highly\ndisordered/amorphous graphene during the hydrogenation process is accompanied by an\n8\nincrease in intensity of the overall Raman spectrum. This is very noticeable in the Raman data in\nFig. 1 and Fig. S2 because the electrolyte yields a significant background. This background\nobscures the spectra of pristine graphene (this is the source of the ‘negative’ spikes in the spectra)\nbut does not obscure the more intense signal from hydrogenated graphene. This background is\nnot an issue for the data in Fig. 3c because those samples are not in contact with the electrolyte.\nThis has been clarified in the corresponding figure captions in the manuscript. These latter\nspectra characterise the starting samples prior to hydrogenating them, to demonstrate that they\nare defect free. Following the Reviewer comment, we have included this discussion in Raman\nspectroscopy in Methods.\nThe right panel in Supplementary Fig. 8 shows a sudden change in the Raman spectrum, from the\nabsence of the D band to its presence. What happens in between? Can the\nhydrogenation/deuteration process be monitored? And how precise is the information which one\ncan get from the Raman spectrum? On page 4, it is said that a deuterium concentration of\n~10^{14} cm^{-2} is deduced by the Raman spectrum. How precise is this concentration value?\nThe hydrogenation process has already been monitored with Raman in this work and in refs.\n14&15 and the transition was shown to be sudden – as expected from the sharp conductor-\ninsulator transition. We now show that even fixing a relatively low potential of ≈1.5 vs NP would\nlead to hydrogenation of the sample within a couple of seconds, as shown in Fig. 1e. However,\nthe dehydrogenation is a more gradual process, as already shown in ref. 14 and as we show in Fig.\nR1.1, in response to question 6 from Reviewer #1 (page 3).\nRegarding the accuracy of the H (D) concentration in hydrogenated (deuterated) samples, these\nestimates are accurate within order of magnitude (e.g. Luchese et al Carbon 2010, 48, 1592-\n1597). However, the electronic transport measurements reveal that the hydrogenation transition\ntakes place for a charge carrier density of ≈ 1 x 1014 cm-2 (the Fermi energy extracted from these\nmeasurements can be readily converted into charge density) in agreement with the Raman\nexperiments. Hence, the concentration of H atoms in the hydrogenated phase can be estimated\nwith a fair degree of accuracy.\nGenerally, information on the integration time and total intensity of the data should be provided\n(whenever normalized spectra are shown, it would be useful to say how large would the intensity\nfactor be for hydrogenated/deuterated and pristine samples).\nNot enough information on the Raman measurements is provided (laser wavelength, information\no the setup and detectors, etc.).\nWe have specified the various parameters used in the Raman experiments in the methods\nsection.\nIn Fig.2, it would be better to re-use for protons the same colors used in Fig. 1, e.g., red. This would\nalso make the Figure clearer (the grey lines are not so well visible).\nWe have made this change.\nThe effects of the morphology on the electronic/electrochemical currents seems the most\ninteresting result of this work. The way it is presented is though misleading. On one hand, the\nreader gets the impression that corrugated graphene is beneficial, but from our understanding it\nis instead detrimental because a larger electrochemical current is required. On the other hand,\ncorrugated graphene shows a higher electronic current that seems to point to a beneficial effect.\nThis part of the work should be better explained as to remove this seemingly inconsistency.\nThis reveals that the electronic current is the same for all three types of devices within\nexperimental scatter (see point 4 from Reviewer #1) and thus that corrugations do not result in\nhigher electronic current.\nCorrugations do have a significant effect on the electrochemical hydrogenation process. The\nelectrochemical current of the devices is strongly enhanced, and the onset of the process is\nabout -1 V vs NP for corrugated samples, compared to about -1.5 V vs NP for flat graphene. Our\nDFT calculations show that this arises because convex areas within the corrugations have a lower\nenergy barrier for proton adsorption, which leads to a large reduction current via an Eley-Rideal\nprocess. This reduction process stops when the insulating transition takes place, which happens\nat potentials comparable to those observed in flat graphene (graphene-on-hbn). Our DFT\ncalculations suggest that this arises because corrugated samples contain both convex and\nconcave areas – and the latter do not favour hydrogenation. This results in the preferential\naccumulation of protons in convex areas, leaving concave ones free from hydrogen atoms. This\ndelays the overall insulating transition, which requires all electrically conductive pathways in the\nflake to be closed.\nIn summary, corrugations locally enhance the proton adsorption rate, but the conductor-\ninsulator transition of the whole flake is dominated by the concave areas in the flake, whose\nhydrogenation becomes the limiting step in the transition.\nIn conclusion, the manuscript requires important revisions, and, in particular, it is not of\nadequate general interest for Nature Communications, but it is more suitable for a specialised\njournal.\nWe have done our best to address all the points raised by the Reviewer, which we believe have\nimproved the clarity of our manuscript. We would also like to emphasise the relevance of our\nwork, which addresses the fundamental question of how protons adsorb to graphene\nelectrochemically and which, as pointed out by Reviewer #1, is of great relevance and interest.\nWe hope that in light of these revisions and extended discussions, the Reviewer might consider\nrecommending our manuscript for publication.\nResponse to comments from Reviewer #4\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscript\nWe thank the Reviewer for taking the time to revise our manuscript.\nWe thank the authors for their responses. We still have several questions after the authors have\nrevised their manuscript.\nWe thank the Reviewer for taking the time to do a careful review of our manuscript. We have made\nour best to answer all questions raised.\n1) Thanks to the authors for redrawing the circuit, which makes it clearer. The authors used a\nsource meter (Keithley 2636B source meter, two-wire measurement) and a voltmeter (Keithley\n2182A Nanovoltmeter) instead of using a potentiostat to perform CV scans. We believe that this\nplatform, particularly the reference electrode, cannot provide feedback control for the\ncurrent loop. The circuits in the references 1,2 seem to also use a source meter with a voltmeter.\nWe therefore still question whether the use of a potentiostat would yield different results than\nusing two separate Keithley instruments for determining hydrogenation overpotentials. In\nelectrochemistry we use potentiostat as standard equipment.\nOur setup can be programmed to function as a potentiostat, as mentioned in the Methods\nsection. More information can be found on the manufacturer's manual\nhttps://www.tek.com/en/documents/application-note/keithley-instrumentation-\nelectrochemical-test-methods-and-applications.\nTo confirm this capability, Fig. R1.1 shows\nmeasurements of the classic K Fe(CN) redox\n3 6\n20\nreaction vs Ag/AgCl reference electrode with our\nsetup. The advantage of our setup is its high\n10\nadaptability, which enables performing both\n)A 0 electronic and electrochemical measurements\nµ\n(\ntn\nsimultaneously.\ne rru -10\nC\nFig. R1.1. Cyclic voltammogram of Pt wire working\n-20 electrode immersed in a 10 mM K Fe(CN)\n3 6\naqueous solution with 1.0 M KCl supporting\n-30\nelectrolyte. Reference electrode Ag/AgCl (3M\nNaCl). Scan rate 20mV/s. The figure shows a\n0.0 0.1 0.2 0.3 0.4 0.5\nseparation between reduction and oxidation\nPotential (V vs. Ag/AgCl)\npeaks (ΔEp) of 77 mV, as expected.\n2) In their response to point 2 the authors mention that the conductivity of deuterons in aqueous\nelectrolytes is ~10% smaller than for protons (Arcis et). According to the CRC Handbook of\nElectrochemistry and Physics 3 (page 5-77), the conductivity of H+ is 1.4 times that of D+ in water\nat 25°C.\nWe are aware of the 1.4 factor. However, this value applies to aqueous electrolytes and may differ\nfor HTFSI and DTFSI in PEG. In our response we used the symbol “~” and the 10% value to reflect\nthis uncertainty. The important point is that the difference in conductivity between H+ and D+ is\nexpected to be relatively small.\n3) Separately, in Figure S6, the authors could not measure a significant difference of conductivity\nbetween H+ and D+ in HTFSI and DTFSI for SiNx substrates with a hole without graphene, and\nattributed this result to device-to-device variations (see point 2, where a difference of 1.4 is\nreported for bulk conductivities of H+ and D+). Therefore, we question whether PdHx and PdDx\nare reliable in detecting proton or deuteron currents.\nPdHx/PdDx electrodes have been shown to be effective to measure proton/deuteron currents\n(e.g. C. Zhong, et al. Nat. Comms. 2011, 2:476). However, we completely agree with the Reviewer\nthat the contact resistance of these electrodes will depend on hydrogen loading. This could\nindeed contribute to the ~10% error observed in our open-hole measurements (without\ngraphene).\nHowever, our data indicate that if contact resistance variations exist, they have a negligible\nimpact on experiments with graphene. This is evident from the low device-to-device variability in\nboth the potential of the hydrogenation transition and the peak currents in the electrochemical\nsignal.\nThis robustness was expected. In our experiments, the working electrode (graphene) is highly\nresistive, with currents orders of magnitude lower than in open-hole devices. Additionally, the\ngraphene electrode is micrometer-sized, while the counter electrode (PdHx) is centimeter-sized.\nIn this regime, cell resistance is dominated by the microelectrode (e.g., ref. 40 in the text).\nAs a\nresult, any small variations in contact resistance due to different PdHx electrodes should have\nminimal impact on device performance, as confirmed by our observations.\n4) In our initial question we asked which electrochemical reactions occur on PdHx. We asked this\nquestion because we believe that the electrochemical reactions occuring at the reference\nelectrode are key to determine the overpotential of hydrogenation on graphene. We asked the\nfollowing question: “what are the specific reaction equations that occur on PdHx when gaining\nand losing electrons?” In their revised manuscript, the authors mention that “Pd + H++ e- -> PdHx”\nis happening. What if the reaction would be “Pd + xH+ + xe-   PdHx. Separately, if PdHx is saturated\nwith H, atomic hydrogen or hydrides can no longer be inserted into the electrode. The literature\nreport on an upper limit to the electrochemical insertion of H into Pd, which could be considered\nhere for the discussion.5 Possible reactions include 6:(see pdf)\n〖PdH〗_X+X H^++X e^-→Pd+X H_2 (2)\n〖PdH〗_X→Pd+X H^++X e^- (3)\nH_2 □(□(→┴(Pd/〖PdH〗_X ) )) 2 H^++2 e^- (4)\nUnfortunately, we cannot determine definitively which of these reactions is taking place, and any\ncharacterisation we could perform is unlikely to resolve the question conclusively. However, we\npoint out that these suggested reactions primarily take place in hydrogen-saturated PdHx\nelectrodes or nanoscale Pd, which is likely not the case here. More important, as noted in the\nreferences suggested by the Reviewer and several others (e.g., ref. 6 from the Reviewer; C.\nGabrielli et al., J. Electrochem. Soc. 2004, 151, A1937; K. Hubkowska et al., Electrochim. Acta\n2010, 56, 235-242), the onset potential for these reactions typically differs by 100–200 mV. This\nwould result in a one-off shift of the same magnitude in the potential of our devices versus SHE,\nwhich is acceptable for the purposes of this work. Note as well that the difference in potential for\nthe insulating transition triggered with proton- and deuteron-conducting electrolytes is 300 mV\nand thus larger than the uncertainty in question.\nIndependent of all this, a key advantage of measuring both the electronic and electrochemical\nresponses of our devices simultaneously is the ability to reference the potential of the\nelectrochemical processes against the NP in graphene. This provides access to the absolute\nscale, which is independent of the reference electrode and remains constant across all devices\nand processes because it depends solely on the band structure of graphene. This method thus\nprovides a direct way to characterize these processes that bypasses the uncertainties that may\nbe associated with non-aqueous reference electrodes. We believe that this is an important novel\naspect of our work, which could be applied to other processes. Following the Reviewer’s\ncomment, we have stressed the importance of the electronic response of graphene as an\nindependent reference in page 2, second paragraph, line two before last.\n5) Overall and over the time of the measurement, the composition of the reference electrode may\nchange and therefore such reference electrode may not be used to determine the overpotential\nof hydrogenation on graphene. In order determine whether the reference electrode composition\nchanges (or not), the authors could use XRD or XPS before and after the measurement.\nThe PdHx electrodes are stable over time in our experiments. This is evidenced from the fact that\nthe position of graphene’s neutrality point does not change over time in our measurements. It is\nalso evident from the low variability of the hydrogenation potential between different samples.\nAs\ndiscussed in point 3, this stability is expected from the huge difference in size between the\nworking and counter electrode.\n6) In the lower panel of figure 3C, corrugated graphene shows a higher current compare to\ngraphene on hBN and graphene on SiO2; the authors carried out an error analysis and\nconcluded that differences in currents are attributed to device-to-device variations (now the\nauthor normalized the electronic current to the width of the graphene). We expect corrugated\ngraphene to have lower charge carrier mobilities than less corrugated graphene. What if the\nauthors would calculate and compare the carrier mobility for the different samples instead of\nthe current 7,8 ; and establish whether corrugated graphene has a better affinity for H+ (see also\npoint 5).\nOur work studies the conductor-insulator transition induced by hydrogen adsorption. The\nmobility of electrons is unnecessary to understand this phenomenon. Nevertheless, regarding\nthe question of whether corrugations are expected to change graphene’s mobility, we note that\nat low temperatures, one indeed expects corrugated samples to have lower mobility. However, at\nambient conditions this is not expected. Theoretically, mobility at these temperatures is primarily\nlimited by phonon scattering (in the absence of defects), and corrugations are not expected to\nalter the already strong scattering at this temperature. For a broader discussion on this subject,\nsee S. Das Sarma et al., Rev. Mod. Phys. 2011, 83, 407-470. For an explicit calculation of this\neffect at room temperature see, for example, in R. Shah & M. G. Mohiuddin, Proc. World Cong.\nEng. 2011, Vol II (https://www.iaeng.org/publication/WCE2011/WCE2011_pp1357-1362.pdf).\nAdditionally, we point out that extracting carrier mobility – especially subtle effects that could\narise from lattice corrugations – requires Hall effect measurements. Estimates based on two\nprobe resistance measurements cannot provide conclusive insights into this question.\n7) Corrugated graphene should have much lower overpotential of hydrogenation comparing to\ngraphene on SiO2 and hBN. However, corrugated graphene was measured to have the similar\noverpotential as for graphene on SiO2 and hBN (the potential at the peak of hydrogenation\ncurrent in upper panel of Figure 3c). Similarly, corrugated graphene should have much lower\noverpotential at the insulating transition compared to graphene on SiO2 and hBN. However,\ncorrugated graphene was measured to have the maximum overpotential (the potential at the\nzero current transition in lower panel of Figure 3c) compare to graphene on SiO2 and hBN. The\nauthors explain these results as \"concave areas relatively free of protons […] leaves\nelectronically conductive paths\". However, this reason is unclear. Drawing a schematic diagram of\nelectronically conductive paths in the concave and convex areas may be relevant. In addition, if\nthe concave areas with conductive paths exist, why does corrugated graphene undergo the same\ninsulating transition as graphene on SiO2 and hBN?\nTo clarify this observation, it is important to note that the electrochemical process driving the\nhydrogenation (insulating) transition is proton adsorption, which competes with desorption via\nan Eley-Rideal process. The insulating transition occurs when, as a result of this process, a high\nproton coverage of ~10¹⁴ cm⁻² is reached.\nAs the Reviewer correctly expects, corrugated graphene indeed exhibits a significantly lower\nonset potential for the electrochemical process. To illustrate this more clearly, we provide the\nelectrochemical response in Fig. 3, zoomed in on the current range where the reaction begins\n(Fig. R1.2). This figure shows that the reaction onset is indeed lowest for corrugated graphene,\nfollowed by graphene-on-SiO₂, and finally graphene-on-hBN.\n0.0\nla c 2 -m\n) G\nG Co\nr\n-\n-\nr\nS\nh ru B\niO\ng N a\n2\nted Gr\nF\ngr\ni\na\ng\np\n.\nh\nR\ne\n1\n.n\n2 .\nsa\nE\nm\nle\np\nc\nl\nt\ne\nro\ns\nch\nzo\ne\no\nm\nm\nic\ne\na\nd\ni\nr\nn\ne s\nf\np\nro\no\nm\nns e\nF ig\no\n.f\n3\nd iff\nat\ne r\nt\ne\nh\nn\ne\nt\nim\ne A\ncurrent level where the proton adsorption onset.\nh\nc\nm\n(\n−0.1\no\nr tc\ntn\ne The unexpected finding is that, while the onset for\ne lE r r u proton adsorption is lower in corrugated graphene\nc\n−0.2\n−2.0 −1.5 −1.0 compared to graphene-on-hBN or graphene-on-SiO 2 ,\nV vs V all samples require similar potentials to achieve\nG NP\ncoverage of ~1014 cm-2. We attribute this to the\nexistence of areas in corrugated graphene that resist hydrogenation, thus preventing the sample\nas a whole to achieve proton coverage of ~1014 cm-2. Our DFT calculations suggest that such areas\nare probably those with concave corrugations, where proton adsorption requires similar\npotentials to those of flat graphene (Supplementary Fig. 1). This would explain why full coverage\nis achieved only at potentials comparable to those observed in graphene-on-hBN or graphene-\non-SiO₂.\nWhile we could provide schematics of this interpretation, we believe they would not add\nsignificant clarity. A definitive answer to this question would require techniques capable of\nmeasuring proton coverage with high spatial resolution (e.g., STM), However, this is beyond the\nscope of this work. In response to the Reviewer’s comment, we have edited the discussion in the\nmain text of the manuscript, last paragraph before conclusion (pages 6&7), to clarify these points.\nWe have also added Fig. R1.2 as inset in Fig. 3.\n8) The size of the washer compared to the size of graphene is very important for the fully insulation\ntransition. So, we asked before, “Are the graphene samples studied here bigger or smaller than\nthe opening in the SU8 washer?” The authors point out that the graphene flake must be smaller\nthan the opening of the SU8 washer, which is important for the insulating transition. We strongly\nagree with this point of view. However, in a previous paper by the same research group 1, the\ngraphene flake seems larger than the opening in the SU8 washer, and an insulating transition is\nalso observed. Are there here any contradictions between the two situations/articles?\nThe washers in both this work and ref. 1 are either larger or of the same size of the flake. The device\nshown in Extended Data Fig. 1 of ref. 1 was a device in which the size of the flake matched that of\nthe washer. There are no contradictions between the two works.\nReferences\n1. Tong, J. et al. Control of proton transport and hydrogenation in double-gated graphene.\nNature 630, 619–624 (2024).\n2. Cai, J. et al. Wien effect in interfacial water dissociation through proton-permeable\ngraphene electrodes. Nat Commun 13, 5776 (2022).\n3. CRC Handbook of Chemistry and Physics. (CRC Press, 2014). doi:10.1201/b17118.\n4. Lozada-Hidalgo, M. et al. Sieving hydrogen isotopes through two-dimensional crystals.\nScience (1979) 351, 68–70 (2016).\n5. Benck, J. D., Jackson, A., Young, D., Rettenwander, D. & Chiang, Y.-M. Producing High\nConcentrations of Hydrogen in Palladium via Electrochemical Insertion from Aqueous and\nSolid Electrolytes. Chemistry of Materials 31, 4234–4245 (2019).\n6. Moumaneix, L., Rautakorpi, A. & Kallio, T. Controlling the Reactivity and Interactions\nbetween Hydrogen and Palladium Nanoparticles via Management of the Particle\nDiameter. ChemElectroChem 10, (2023).\n7. Zhang, Z., Xu, H., Zhong, H. & Peng, L.-M. Direct extraction of carrier mobility in graphene\nfield-effect transistor using current-voltage and capacitance-voltage measurements. Appl\nPhys Lett 101, (2012).\n8. Zhong, H., Zhang, Z., Xu, H., Qiu, C. & Peng, L.-M. Comparison of mobility extraction\nmethods based on field-effect measurements for graphene. AIP Adv 5, 057136 (2015).\nResponse to comments from Reviewer #2\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank the Reviewer for taking the time to carefully read and comment our manuscript.\nResponse to comments from Reviewer #3\nThe authors replied to the previous concerns and the manuscript has improved, yet some\naspects regarding Raman measurements remain not fully clarified, such as the quality of the\nspectra. In particular, while it has now been clarified that the spectra of the pristine samples are\naffected by the presence of a electrolyte background signal, this should not impede to have a\nbetter signal-to-noise ratio. In the methods section, it is mentioned that for Raman\nmeasurements, \"accumulating time of 75s over 4 cycles\" were used. Were both the pristine and\nhydrogenated sample spectra taken under these same conditions?\nWe thank the Reviewer for taking the time to review our manuscript. We believe the comments\nhave improved it.\nRegarding the question, both the pristine and hydrogenated sample spectra were measured with\nthe same conditions. Unfortunately, we did not manage to enhance the resolution of the spectra\nfor pristine graphene in the presence of the electrolyte. Changing different parameters such as\nlaser power (0.4 mW to 1 mW), accumulating time (10-100 s) and cycles (1-5), did not make a\nnotable difference. However, the key spectral feature that characterises the process is the I /I\nD G\nratio. This feature is clearly discernible in the acquired spectra, rendering further enhancement\nunnecessary for the purposes of this work.\nIn the caption of figure 1, it is said \"Raman spectra of pristine and hydrogenated samples. The\nbackground signal from the electrolyte was subtracted; the latter spectrum was divided by 5 for\nclarity\". From this, it seems that there is only a factor of 5 in the intensity of the spectra, while the\nsignal-to-noise-ratio seems to be lower than that by looking at the spectra. Furthermore, the\nspectra in Fig. 3b look better than those in Fig. 1 and Supplementary Fig. 8. Is this discrepancy\ndue to different accumulation times or to something else?\nTo clarify this point, Fig. R2.1 shows the Raman spectra for the different samples taken under the\nsame conditions, without normalisation factor (factor of 5). It shows why dividing the spectra of\nhydrogenated graphene by a factor of 5 is helpful for presentation purposes.\nFig. R2.1. Raman spectra of hydrogenated graphene\nD G\n(blue data) and pristine graphene (red) in contact\nwith the electrolyte. No normalisation constant was\n2D applied to the data. For reference, we show the\n) H-Gr with electrolyte\n.u\nspectra of pristine graphene prior to exposing it to\n.a\n(\ny\nthe electrolyte (black).\ntis\nn Gr with electrolyte\ne Regarding the lower noise of the Raman data in Fig.\ntn\nI 3b compared to Fig. 1, we point out that, as\nmentioned in our previous response, these samples\nGr without electrolyte\nwere not exposed to the electrolyte. As for the data\npresented in Supplementary Fig. 8, its signal-to-\n1500 2000 2500\nnoise ratio is comparable to that of Fig. 1. It may\nRaman shift (cm-1)\nappear clearer because it is displayed in a larger\npanel. However, as previously noted, space constraints in the inset of Fig. 1 prevent displaying\nthe figure any larger.\nAs for Figure 1, we know that the data of Figure 1 are different to those shown in 2024 Nature\npaper. In our previous report, we were referring to Fig. 1a (now Fig. 1d) showing the Energy vs\ndistance plot. This plot shows the same data plotted in Extended Data Fig. 8 (zero electric field).\nWe are sorry we were not clear enough.\nThank you for clarifying this point. The energy vs. distance plot in Fig. 1d is a classical calculation\nthat appears in numerous papers, including refs. 11-15 and Extended Data Fig. 8 in Tong et al.\nHowever, we believe it is important to include this plot in the main text of our work, as it plays an\nimportant role in the discussion. This is especially relevant given that our manuscript is intended\nfor a broad audience, which may not be familiar with the hydrogenation of graphene.\nThis said, while we believe that the manuscript was improved, we still feel that this work would\nbe more suitable for a specialised journal.\nWe thank the Reviewer for their comments, which we believe have improved our manuscript.\nRegarding the suitability of our work for this journal, we respectfully disagree, but we will not\nrevisit this point further, as this was addressed in the previous response.\nResponse to comments from Reviewer #4\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank the Reviewer for taking the time to review our manuscript.\nResponse to comments of Reviewer #1\nBelow are my detailed comments and suggestions, which may be helpful for revising the\nmanuscript:\nWe thank the Reviewer for their careful evaluation of our manuscript, as well as for their\ncontinued support for our work throughout the revision process. In response to the latest\ncomments, we have added several new experiments and expanded key discussions. We believe\nthese additions address all the points raised and further strengthen the clarity of the manuscript.\n1. Circuit reproducibility and experimental setup\nWe thank the authors for elaborating on their circuit and introducing a discussion on using the\nKeithley 2636B as a potentiostat. However, the current explanation remains ambiguous. It would\nsignificantly improve clarity and reproducibility if the authors could provide a schematic diagram\nshowing how the Keithley 2636B sourcemeter and the 2182A nanovoltmeter are connected to the\ngraphene and PdHx electrodes. This would assist future researchers in reproducing the setup\naccurately. Still, I would not be surprised that doing similar experiments with a potentiostat would\nyield different onset potentials for hydrogenations and dehydrogenations and therefore\nresults/interpretations/conclusions.\nAdditionally, could the authors clarify whether the Keithley 2636B sourcemeter was operated in\n2-wire or 4-wire mode? As the manufacturer’s manual notes, the sourcemeter functions as a\npotentiostat only in 4-wire mode, where the Sense LO provides feedback to Force LO. If used in\n2-wire mode, this feedback loop is not valid, which would compromise the reliability of the\nmeasured potentials at the reference electrode.\nsee Figure 2 of this manual on the website of Tek:\na b\n0.00\nKeithley\nI H e cr o F I H e s n e S\nA\nA V V w o L e s n e S w o L e cr o F\n2-m\nc A m ( tn e rru\nc\n)\n-0.05\nRef la\nc im-0.10 Electrochemical station\ne Keithley\nh\nc\no\nrtc\ne\nlE\nGraphene\n-0.15\nCounter electrode\n-1.8 -1.3 -0.8 -0.3 0.2 0.7\nV vs. PdHx (V)\nFig. R1. a, Sample-to-Keithley connection diagram. b, Electrochemical current-voltage response\nof a sample measured with the Keithley setup and an Ivium pocketSTAT2 potentiostat.\nThe Keithley was operated in 4-wire mode for all measurements. We have added a detailed wiring\ndiagram in the revised manuscript (Figure S2). The mention of sourcemeter and nanovoltmeter\nwas an oversight, carried over from (Tong, J et al., Nature. 2024, 630, 619-624). In that study the\nelectrolytic current involved proton transport without electron transfer, so no potentiostatic\n1\ncontrol was needed—in any case, gate/reference potentials differed by less than 4 mV in that\nstudy (Extended Data Fig. 2 in Tong, J et al., Nature. 2024, 630, 619-624).\nTo ensure full clarity, and to directly address the Reviewer's concern, we have now also performed\ncyclic voltammetry measurements of graphene hydrogenation using an Ivium pocketSTAT2\npotentiostat. As shown in Fig. R1, these measurements reproduce the same redox features and\npotentials observed in our previous data, confirming the consistency and reliability of our\napproach. The only minor difference is that the Keithley setup offers better resolution at the\nlowest current levels (~1 pA), which are near the detection limit of the Ivium system. We thank\nthe Reviewer for drawing our attention to this point. We hope this work will help popularising the\nuse of sourcemeters as highly versatile instruments for electrochemical measurements.\n2. Use a potentiostat to perform CV on graphene hydrogenation\nWhile we appreciate the CV measurements provided for the Pt electrode in a K₃Fe(CN)₆ solution\n(Fig R1.1 of the rebuttal), this alone, without a counter electrode does not validate the\nelectrochemical circuit used in the manuscript. If the authors aim to demonstrate the validity of\ntheir custom circuit, they could consider performing measurements using a commercial\npotentiostat on graphene hydrogenation with PdHx electrodes and compare the results obtained\nwith their setup using the two Keithleys.\nIn the CV measurements with K₃Fe(CN)₆ in the previous round of comments, the counter\nelectrode was a graphite rod, validating the electrochemical circuit. However, we now\nunderstand the insistence on this point. Following the reviewer comment, we measured the\nhydrogenation of graphene using an Ivium potentiostat as described above.\nTaken together, our results confirm that our setup reproduces both classical electrochemical\nexperiments and the new hydrogenation reaction in graphene. We trust that, together with the\nschematics provided, these new experiments resolve the reviewer’s concern in full.\n3. Ambiguity in proton and deuteron transport\nThe manuscript should clarify the differences observed between H+ and D+ transport in free pore\nmeasurements in the context of mobility similarities/differences in HTFSI/PEG systems or\nwhether those differences may arise from the electrode–electrolyte contact resistance. A more\ndetailed discussion or additional control experiments would help clarify the interpretation of the\ndata.\nFigure R2. Conductance of devices with circular apertures\netched in a silicon nitride substrate; HTFSI/DTFSI\nelectrolyte on both sides; and two PdHx/PdDx electrodes.\n0.15 Each data point is a different device. Solid lines, best linear\n)S HTFSI fit to data.\nµ\n(\ne\nc n0.10\na\ntc We have performed additional measurements using SiNx\nu\nd\nn substrates with holes of different radii, r. This allows us to\no\nC0.05 DTFSI\nextract the electrolyte conductivity, κ, from the measured\nconductance, G, using the equation: G = 4πκ r (Bard, A. J. &\n0.00 Faulkner, L. R., Wiley. 2001). This reveals κ ≈1.062x10-4 S\n0 2 4 6 8 10 12 14 16\nAperture diameter (µm) cm-1 for HTFSI, consistent with other studies (e.g. Yang, Z.,\net al., J. Membr. Sci. 2008, 313, 91-96; Yu, L., et al., J. Phys.\nChem. B. 2012, 116, 6553-6560; Yoshizawa, M. & H. Ohno., Chem. Commun. 2004, 1828-1829).\nMore importantly, with this expanded dataset, we are now able to resolve a ≈35% lower\nconductivity in the DTFSI electrolyte.\nconductivity and as such, we believe this data set is an additional novelty ingredient of our work.\nWe have added this discussion in the Methods section, page 7 and Fig. R2 is the new Fig. S6.\n4. PdHx electrode characterization and proton transport in HTFSI/PEG\nThe PdHx electrode is used for detecting hydronium ion currents, as demonstrated in prior\nliterature involving hydrated media (e.g., maleic–chitosan, ref 1). However, PEG is not hydrated.\nThere must be some difference between hydronium ion and HTFSI when those interact with PdHx.\nThe manuscript should carefully discuss how proton exits in HTFSI and how they react with PdHx\nelectrodes.\nFollowing the Reviewer comment, we have added a new section to the manuscript in which we\ndiscuss proton transport in HTSFI as well as proton interaction with PdHx electrodes. Below, we\nsummarise the key points.\nProton transport in PEG/HTFSI. Protons originate from HTFSI, a superacid (pKa ≈ –10), and exist\nas either free H⁺ or PEG-coordinated complexes. Proton transport is thought to take place\nprimarily via a Grotthuss-type mechanism enabled by transient hydrogen bonding with its ether\noxygens (Moses, A. A. & Arntsen, C., Phys. Chem. Chem. Phys. 2023, 25, 2142-2152; Burankova,\nT. et al., J. Phys. Chem. B. 2015 119, 10643-10651). This is consistent with our conductivity\nmeasurements with open hole devices that demonstrate a notable isotope effect (see point #3\nabove).\nProton interaction with PdHx in aqueous electrolytes. Some of the first investigations of\npalladium (Pd) and hydrogen interactions were the classical experiments by Flannagan\n(Flanagan, T. B. & Lewis, F. A., J. Chem. Phys. 1958, 29, 1417-1418), which demonstrated hydrogen\nabsorption in Pd films exposed to pressurised H₂ gas. Under these conditions, Pd forms two\ndistinct hydride phases: the low-hydrogen content α-phase and the hydrogen-rich β-phase. In\nbulk Pd, these phases often coexist, and their distribution depends on hydrogen pressure,\ntemperature, and the electrode's morphology, as described by the material’s phase diagram\n(Flanagan, T. B. & Lewis, F. A., J. Chem. Phys. 1958, 29, 1417-1418).\nFig. R3. Potential of PdHx\n63\nelectrode vs SHE in 1M HCl\n)E\nH in H 2 atmosphere as a\nS\n.s 62 function of time. Potential at\nv\nV\nzero current is recorded in a\nm\n(\nla\n61 three-electrode cell with\nitn PdHx working electrode and\ne to60 Pd counter electrode and\nP\nAg/AgCl (3M) reference\n0 1 2 3 4 5 electrode.\nTime (hr)\nFlannagan also examined the equilibrium between PdHx and acidic solutions in H environment.\nreaching exactly 0 V when fully saturated. This reflects equilibrium between surface-adsorbed\nhydrogen and protons in solution via the Volmer step: H⁺ + e⁻ + * → H*. Hence, hydrogen-saturated\nPd electrodes behave like Pt in acidic solutions. Conversely, pristine Pd initially shows a potential\nof ≈90 mV vs SHE, which gradually decreases to 0 V over tens of hours as the electrode becomes\nelectrochemically hydrogenated (Flanagan, T. B. & Lewis, F. A., J. Chem. Phys. 1958, 29, 1417-\n1418). Electrodes with intermediate hydrogen content exhibit potentials between 0 and 90 mV vs\nSHE, indicating coexistence of α and β phases. We characterised our electrodes in this way. Fig.\nintermediate H loading.\nProton interaction with PdHx in non-aqueous solvents. In non-aqueous solvents, the same\nequilibrium principles apply at the Pd/electrolyte interface. Hubkowska, K., et al., J. Solid State\nElectrochem. 2024, 28, 1159-1169 shows that these reactions proceed more slowly than in\naqueous media and the IV characteristics of the electrode can shift slightly compared to aqueous\nelectrolytes. Thus, the underlying redox mechanism at PdHx remains the same, except with\nslower kinetics and slightly different potentials. Our devices bypass the minor uncertainties\nassociated with reference electrodes in non-aqueous by offering direct access to the absolute\npotential scale via the graphene neutrality point. As demonstrated by the statistical analysis in\nTable S1, the hydrogenation potential vs the neutrality point is highly reproducible and is in\nagreement with the previous independent study of this process (Li, S. et al. Nat Electron., 2021,\n4, 254-260). This discussion has been added in a new section, ‘Proton transport in the\nHTSFI/PdHx system’ in Methods, page 9.\nMoreover, it is unclear how the authors prepared the PdHx electrode. In previous studies, the\nPdHx electrode were saturated with hydrogen (ref 1–3). If saturation occurred, the ability of PdHx\nto absorb further protons would be limited. Could the author describe more in details how they\nprepared the PdHx electrodes.\nWe prepared PdHx following the protocol described and used in Murphy, D. W. et al. Chem.\nMater., 1993, 5, 767-769. In both works, palladium is immersed in a sodium borohydride solution\novernight while stirring and thoroughly rinsed with deionised water. We have added this reference\nto the manuscript in the Methods section.\nAdditionally, the electrochemical equation on page 7 appears unbalanced. A more rigorous form\nwould be: xH+ + xe- + Pd → PdHx . This should be corrected for clarity and chemical accuracy.\nWe agree with the Reviewer and have written the reaction as suggested.\n5. Mobility estimation and interpretation of insulating behavior\nThe authors do not use two-end (source and drain) field-effect-based mobility analysis, despite\nits widespread adoption in similar studies (Ref 4–8). If there is a known inconsistency in applying\nthis method to the present system, it should be discussed explicitly. Avoiding this issue weakens\nthe interpretation of the observed insulating transition, which is based on carrier conduction but\nlacks support of quantitative carrier mobility and carrier concentration.\nFollowing the Reviewer’s suggestion, we have estimated the electronic mobility in our samples\nusing the model in Lv, H. et al. Appl. Phys. Lett., 2013, 103, 193102. The carrier concentration in\ngraphene, 𝑛, is:\n𝑛 = √𝑛2+𝑛(𝑉∗)2 (1)\nwhere 𝑛 and 𝑛(𝑉∗) is the induced carrier concentration as a function of the applied gate voltage,\n0 𝐺\n𝑉 vs the neutrality point. The relation between gate voltage and induced carriers is:\nG\n𝑉∗ = 𝑒 ∙𝑛(𝑉∗)+ ℏ∙𝑣F∙√𝜋𝑛(𝑉 G ∗) (2)\nG 𝐶E G 𝑒\nwhere 𝑒 and ℏ are the elementary charge and reduced Planck constant, respectively. 𝑣 is the\nF\nFermi velocity, of 1.15×106 m s-1 and 𝐶 = 20 µF cm–2 is the electrolyte capacitance, as shown in\nE\nour previous work.\nThe total resistance, 𝑅 , is then written as:\n𝑇𝑜𝑡𝑎𝑙\n𝑅 = 𝑅 +\n𝐿G\n∙\n1\n(3)\nTotal C\n𝑊G 𝑒∙𝜇∙𝑛\n4\nwhere 𝑅 is the contact resistance and 𝐿 and 𝑊 refer to the gated channel length and width,\nC G G\nrespectively and 𝜇 is the mobility to be extracted.\nFig. R4. Total resistance as a function\nGr-SiO Corrugated Gr\n8\non SiO (left) and corrugated graphene\n2\n)\nΩ (right).\nk ( 6\nla\nto\nT\nR We have estimated carrier mobilities in\n4\nour samples with this model, as listed\n2 in Table R1 below. The extracted\n−1 0 1 −1 0 1 mobilities are in the range of 2,000 -\nV - V (V) V - V (V) 6,000 cm²/V·s, in good agreement with\nG NP G NP\nthe literature (K. S. Novoselov et al.,\nScience, 2004, 306,666-669) for similar samples (~1,000 to 10,000 cm²/V·s). The estimates also\nsuggest a small ~2× lower carrier mobility for corrugated graphene compared to graphene-on-\nSiO devices. This information has been included in the revised manuscript, Methods section,\n2\npage 11.\nTable R1. Estimated carrier mobility in graphene samples\nElectron Contact Residue carrier\nHole mobility Number of\nmobility resistance concentration\n10 3 cm 2 / V·s 10 3 cm 2 / V·s kΩ 1011 cm −2 samples\nGraphene-\n3.800 ± 0.8 5.9 ± 0.7 2.2 ± 0.3 8.0 ± 1.1 8\non-SiO2\nCorrugated\n1.9 ± 0.5 2.8 ± 0.5 2.0 ± 0.3 6.9 ± 1.4 4\ngraphene\n6. Role of curvature in hydrogenation\nThe authors emphasize that curvature (convex and concave regions) affects graphene\nhydrogenation, yet they don’t provide direct visual or experimental support for this claim.\nIncluding schematics or Raman mapping (e.g., spatial or time/potential-resolved analysis of D-\nband changes) could help clarify whether such morphological effects exist and how they\ninfluence reactivity.\nMorphological effects on the hydrogenation of graphene have previously been reported in studies\nusing plasma as the hydrogen source. For example, Goler, S. et al., J. Phys. Chem. C. 2013, 117,\n11506-11513 performed STM measurements on plasma-hydrogenated graphene with local\ncorrugations induced by the underlying SiC substrate. The authors\nvisually demonstrated that hydrogen adsorption occurs\npreferentially in convex regions of the sample (e.g., Fig. R5). Away\nfrom these convex regions no hydrogen adsorption was detected.\nThese findings are supported by DFT calculations, including those\nwe present in Fig. S1, which predict a lower energy barrier for\nchemisorption on convex areas of the sample.\nFig. R5. STM measurements of plasma hydrogenated graphene on\nSiC substrates obtained from Goler, S. et al., J. Phys. Chem. C.\n2013, 117, 11506-11513. Scale bar, 2 nm.\nD G\nfurther support this point, we have performed potential-\n-2.1 V resolved Raman spectroscopy measurements that\n-1.7 V\n-1 V\ndirectly monitor the hydrogenation process, as\n).u suggested by the Reviewer. These spectra show a clear\n.a (\ny\n2D onset of the D band at the potentials corresponding to\ntis\nthe hydrogenation of the sample. These new data are\nn\ne\ntn\nI included as Fig. S10 in the revised manuscript.\nFig. R6. Raman spectra of corrugated graphene samples\nduring a hydrogenation cycle. The signatures of the\n1300 1950 2600 hydrogenation appear at about -2.1 V vs NP.\nRaman shift (cm-1)\n7. Novelty\nFig 3c shows a largely enhanced dehydrogenation current for corrugated graphene. This is the\nimpressive part of the results. However, mechanistically, the hydrogenation of graphene has been\nreported in multiple prior studies (e.g., Refs.9–15). Several mechanistic discussions are also\navailable in literature (e.g., Refs.16,17). It is still not clear from the manuscript and data what is\nthe mechanism of hydrogenation and dehydrogenation.\nWould the author measure similar high electrochemical currents in dry Nafion/PdHx systems\n(ref3)? Again I am not sure the electrochemistry is right in HTFSI (see above). Here also, I wonder\nwhether switching to using a potentiostat would yield different results? However, I acknowledge\nthat from Fig 3c top panel, the results are impressive.\nWe thank the Reviewer for their encouraging assessment of our results. This work builds on over\na decade of investigations into proton–graphene\ninteractions across a range of device configurations.\n2-m )\n0\nc\nA\nFig. R7. Electrochemical and electronic response of\nm\n(\ntn\ne rru\n-14\n0\ng\ne\nr\nn\na\nv\np\nir\nh\no\ne\nn\nn\nm\ne\ne n\nd\nt\ne\n.\nvi\nI\nc\nn\ne\ns et\ng\ns\na t\ns\ne\nh\nd\no w\nw it\nt\nh\nh\nN a\nth\ne\nfi\no n\nd e\nu\nn\nic\nd\ne\ne\nd\nr\nd\nd\no\nry\nn\nA\no\nr\nt\nc\nla -28\n-100 survive the first hydrogenation cycle.\nc\nim -200\ne\nh\nc\no\nrtc\ne\nlE\nGraphene\n-42 -300\nl\n-2.5-2.0-1.5-1.0-0.50.0 0.5 hydrogenation of graphene via plasma is well\nlE\nestablished, as discussed in Refs. 9–15 from the\n)S µ 1x104 Reviewer and the introduction of our manuscript. In\n( e330 5x103\nc n 0 contrast, the electrochemical hydrogenation of\na\ntc -5x103 graphene is a much more recent development, and its\nu\nd n\no\n220 -1x104 -2 -1 0 mechanism is not established. While Ref. 16 from the\nc\nc in Reviewer (Daniels et al) and other studies report\no110\rtc electrochemical and Raman measurements of\ne\nlE\ngraphene in aqueous environments, we note that they\n0\ndid not observe a conductor–insulator transition or\n-2.0 -1.5 -1.0 -0.5 0.0 0.5\nV vs.NP (V) demonstrate the reversibility in the Raman D band—\nboth of which are critical hallmarks of successful\nhydrogenation. In the absence of this evidence, it is premature to conclude that electrochemical\n6\nhydrogenation was achieved in those works. As such the mechanism for this phenomenon\nremains unexplored.\nFollowing the Reviewer’s suggestion, we have now performed the experiments using Nafion in dry\nAr environment. Fig. R7. shows that the conductivity of the devices starts decreasing at around\n1.8 V vs NP. Unfortunately, the devices break before reaching the insulating transition (insets in\nFig. R7). This arises because even in dry Nafion films, water remains essential for proton\nconductivity (Mauritz, K. A. & Moore, R. B., Chem. Rev. 2004, 104, 4535-4586), and the large\napplied potential results in water breakdown.\nThe drop in conductance could perhaps be attributed to the onset of the hydrogenation process.\nThe absence of an insulating transition may arise because water-based electrolytes, being more\nactive (see point #4), also yield a faster Eley-Rideal process. However, the drop in conductance\ncould also arise due to irreversible damage of the graphene electrodes. Since the devices do not\ndisplay a full hydrogenation-dehydrogenation cycle, it is not possible to conclude based on these\ndata.\n1. Zhong, C. et al. A polysaccharide bioprotonic field-effect transistor. Nat Commun 2, 476\n(2011).\n2. Morgan, H., Pethig, R. & Stevens, G. T. A proton-injecting technique for the measurement of\nhydration-dependent protonic conductivity. J Phys E 19, 80–82 (1986).\n3. Hu, S. et al. Proton transport through one-atom-thick crystals. Nature 516, 227–230 (2014).\n4. Lv, H. et al. High carrier mobility in suspended-channel graphene field effect transistors. Appl\nPhys Lett 103, (2013).\n5. Xu, H. et al. Top-Gated Graphene Field-Effect Transistors with High Normalized\nTransconductance and Designable Dirac Point Voltage. ACS Nano 5, 5031–5037 (2011).\n6. Kim, S. et al. Realization of a high mobility dual-gated graphene field-effect transistor with\nAl2O3 dielectric. Appl Phys Lett 94, (2009).\n7. Farmer, D. B. et al. Utilization of a Buffered Dielectric to Achieve High Field-Effect Carrier\nMobility in Graphene Transistors. Nano Lett 9, 4474–4478 (2009).\n8. Liao, L. et al. High- κ oxide nanoribbons as gate dielectrics for high mobility top-gated\ngraphene transistors. Proceedings of the National Academy of Sciences 107, 6711–6715 (2010).\n9. Elias, D. C. et al. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for\nGraphane. Science (1979) 323, 610–613 (2009).\n10. Li, S. et al. Large transport gap modulation in graphene via electric-field-controlled\nreversible hydrogenation. Nat Electron 4, 254–260 (2021).\n11. Tong, J. et al. Control of proton transport and hydrogenation in double-gated graphene.\nNature 630, 619–624 (2024).\n12. Zhao, M., Guo, X.-Y., Ambacher, O., Nebel, C. E. & Hoffmann, R. Electrochemical generation\nof hydrogenated graphene flakes. Carbon N Y 83, 128–135 (2015).\n13. Fei, Y., Fang, S. & Hu, Y. H. Synthesis, properties and potential applications of hydrogenated\ngraphene. Chemical Engineering Journal 397, 125408 (2020).\n14. Hu, Y. et al. Synaptic transistor based on reversible hydrogenation of graphene channel.\nAppl Phys Lett 126, (2025).\n15. Cha, J., Choi, H. & Hong, J. Damage-free hydrogenation of graphene via ion energy control in\nplasma. Applied Physics Express 15, 015002 (2022).\n16. Daniels, K. M. et al. Mechanism of Electrochemical Hydrogenation of Epitaxial Graphene. J\nElectrochem Soc 162, E37–E42 (2015).\n17. Podlivaev, A. I. & Katin, K. P. Competition of hydrogen desorption and migration on graphene\n7\nsurface in alternating electric field: Multiscale molecular dynamics and diffusion study. Appl\nSurf Sci 686, 162125 (2025).\nResponse to comments of Reviewer #2\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank the Reviewer for taking the time to carefully read and comment our manuscript.\n8"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Below are my detailed comments and suggestions, which may be helpful for revising the manuscript:\n1. Circuit reproducibility and experimental setup\nWe thank the authors for elaborating on their circuit and introducing a discussion on using the Keithley 2636B as a\npotentiostat. However, the current explanation remains ambiguous. It would significantly improve clarity and reproducibility if\nthe authors could provide a schematic diagram showing how the Keithley 2636B sourcemeter and the 2182A nanovoltmeter\nare connected to the graphene and PdHx electrodes. This would assist future researchers in reproducing the setup\naccurately. Still, I would not be surprised that doing similar experiments with a potentiostat would yield different onset\npotentials for hydrogenations and dehydrogenations and therefore results/interpretations/conclusions.\nAdditionally, could the authors clarify whether the Keithley 2636B sourcemeter was operated in 2-wire or 4-wire mode? As\nthe manufacturer’s manual notes, the sourcemeter functions as a potentiostat only in 4-wire mode, where the Sense LO\nprovides feedback to Force LO. If used in 2-wire mode, this feedback loop is not valid, which would compromise the\nreliability of the measured potentials at the reference electrode.\nsee Figure 2 of this manual on the website of Tek: https://www.tek.com/en/documents/application-note/keithley-\ninstrumentation-electrochemical-test-methods-and-applications\n2. Use a potentiostat to perform CV on graphene hydrogenation\nWhile we appreciate the CV measurements provided for the Pt electrode in a K₃Fe(CN)₆ solution (Fig R1.1 of the rebuttal),\nthis alone, without a counter electrode does not validate the electrochemical circuit used in the manuscript. If the authors aim\nto demonstrate the validity of their custom circuit, they could consider performing measurements using a commercial\npotentiostat on graphene hydrogenation with PdHx electrodes and compare the results obtained with their setup using the\ntwo Keithleys.\n3. Ambiguity in proton and deuteron transport\nThe manuscript should clarify the differences observed between H+ and D+ transport in free pore measurements in the\ncontext of mobility similarities/differences in HTFSI/PEG systems or whether those differences may arise from the\nelectrode–electrolyte contact resistance. A more detailed discussion or additional control experiments would help clarify the\ninterpretation of the data.\n4. PdHx electrode characterization and proton transport in HTFSI/PEG\nThe PdHx electrode is used for detecting hydronium ion currents, as demonstrated in prior literature involving hydrated\nmedia (e.g., maleic–chitosan, ref 1). However, PEG is not hydrated. There must be some difference between hydronium ion\nand HTFSI when those interact with PdHx. The manuscript should carefully discuss how proton exits in HTFSI and how they\nreact with PdHx electrodes.\nMoreover, it is unclear how the authors prepared the PdHx electrode. In previous studies, the PdHx electrode were saturated\nwith hydrogen (ref 1–3). If saturation occurred, the ability of PdHx to absorb further protons would be limited. Could the\nauthor describe more in details how they prepared the PdHx electrodes.\nAdditionally, the electrochemical equation on page 7 appears unbalanced. A more rigorous form would be: xH+ + xe- + Pd\n→ PdHx . This should be corrected for clarity and chemical accuracy.\n5. Mobility estimation and interpretation of insulating behavior\nThe authors do not use two-end (source and drain) field-effect-based mobility analysis, despite its widespread adoption in\nsimilar studies (Ref 4–8). If there is a known inconsistency in applying this method to the present system, it should be\ndiscussed explicitly. Avoiding this issue weakens the interpretation of the observed insulating transition, which is based on\ncarrier conduction but lacks support of quantitative carrier mobility and carrier concentration.\n6. Role of curvature in hydrogenation\nThe authors emphasize that curvature (convex and concave regions) affects graphene hydrogenation, yet they don’t provide\ndirect visual or experimental support for this claim. Including schematics or Raman mapping (e.g., spatial or time/potential-\nresolved analysis of D-band changes) could help clarify whether such morphological effects exist and how they influence\nreactivity.\n7. Novelty\nFig 3c shows a largely enhanced dehydrogenation current for corrugated graphene. This is the impressive part of the results.\nHowever, mechanistically, the hydrogenation of graphene has been reported in multiple prior studies (e.g., Refs.9–15).\nSeveral mechanistic discussions are also available in literature (e.g., Refs.16,17). It is still not clear from the manuscript and\ndata what is the mechanism of hydrogenation and dehydrogenation.\nWould the author measure similar high electrochemical currents in dry Nafion/PdHx systems (ref3)? Again I am not sure the\nelectrochemistry is right in HTFSI (see above). Here also, I wonder whether switching to using a potentiostat would yield\ndifferent results? However, I acknowledge that from Fig 3c top panel, the results are impressive.\n1. Zhong, C. et al. A polysaccharide bioprotonic field-effect transistor. Nat Commun 2, 476 (2011).\n2. Morgan, H., Pethig, R. & Stevens, G. T. A proton-injecting technique for the measurement of hydration-dependent protonic\nconductivity. J Phys E 19, 80–82 (1986).\n3. Hu, S. et al. Proton transport through one-atom-thick crystals. Nature 516, 227–230 (2014).\n4. Lv, H. et al. High carrier mobility in suspended-channel graphene field effect transistors. Appl Phys Lett 103, (2013).\n5. Xu, H. et al. Top-Gated Graphene Field-Effect Transistors with High Normalized Transconductance and Designable Dirac\nPoint Voltage. ACS Nano 5, 5031–5037 (2011).\n6. Kim, S. et al. Realization of a high mobility dual-gated graphene field-effect transistor with Al2O3 dielectric. Appl Phys Lett\n94, (2009).\n7. Farmer, D. B. et al. Utilization of a Buffered Dielectric to Achieve High Field-Effect Carrier Mobility in Graphene\nTransistors. Nano Lett 9, 4474–4478 (2009).\n8. Liao, L. et al. High- κ oxide nanoribbons as gate dielectrics for high mobility top-gated graphene transistors. Proceedings\nof the National Academy of Sciences 107, 6711–6715 (2010).\n9. Elias, D. C. et al. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for Graphane. Science (1979)\n323, 610–613 (2009).\n10. Li, S. et al. Large transport gap modulation in graphene via electric-field-controlled reversible hydrogenation. Nat\nElectron 4, 254–260 (2021).\n11. Tong, J. et al. Control of proton transport and hydrogenation in double-gated graphene. Nature 630, 619–624 (2024).\n12. Zhao, M., Guo, X.-Y., Ambacher, O., Nebel, C. E. & Hoffmann, R. Electrochemical generation of hydrogenated graphene\nflakes. Carbon N Y 83, 128–135 (2015).\n13. Fei, Y., Fang, S. & Hu, Y. H. Synthesis, properties and potential applications of hydrogenated graphene. Chemical\nEngineering Journal 397, 125408 (2020).\n14. Hu, Y. et al. Synaptic transistor based on reversible hydrogenation of graphene channel. Appl Phys Lett 126, (2025).\n15. Cha, J., Choi, H. & Hong, J. Damage-free hydrogenation of graphene via ion energy control in plasma. Applied Physics\nExpress 15, 015002 (2022).\n16. Daniels, K. M. et al. Mechanism of Electrochemical Hydrogenation of Epitaxial Graphene. J Electrochem Soc 162, E37–\nE42 (2015).\n17. Podlivaev, A. I. & Katin, K. P. Competition of hydrogen desorption and migration on graphene surface in alternating\nelectric field: Multiscale molecular dynamics and diffusion study. Appl Surf Sci 686, 162125 (2025).", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "We thank the Reviewer for their careful evaluation of our manuscript, as well as for their\ncontinued support for our work throughout the revision process. In response to the latest\ncomments, we have added several new experiments and expanded key discussions. We believe\nthese additions address all the points raised and further strengthen the clarity of the manuscript.\n1. Circuit reproducibility and experimental setup\nWe thank the authors for elaborating on their circuit and introducing a discussion on using the\nKeithley 2636B as a potentiostat. However, the current explanation remains ambiguous. It would\nsignificantly improve clarity and reproducibility if the authors could provide a schematic diagram\nshowing how the Keithley 2636B sourcemeter and the 2182A nanovoltmeter are connected to the\ngraphene and PdHx electrodes. This would assist future researchers in reproducing the setup\naccurately. Still, I would not be surprised that doing similar experiments with a potentiostat would\nyield different onset potentials for hydrogenations and dehydrogenations and therefore\nresults/interpretations/conclusions.\nAdditionally, could the authors clarify whether the Keithley 2636B sourcemeter was operated in\n2-wire or 4-wire mode? As the manufacturer’s manual notes, the sourcemeter functions as a\npotentiostat only in 4-wire mode, where the Sense LO provides feedback to Force LO. If used in\n2-wire mode, this feedback loop is not valid, which would compromise the reliability of the\nmeasured potentials at the reference electrode.\nsee Figure 2 of this manual on the website of Tek:\na b\n0.00\nKeithley\nI H e cr o F I H e s n e S\nA\nA V V w o L e s n e S w o L e cr o F\n2-m\nc A m ( tn e rru\nc\n)\n-0.05\nRef la\nc im-0.10 Electrochemical station\ne Keithley\nh\nc\no\nrtc\ne\nlE\nGraphene\n-0.15\nCounter electrode\n-1.8 -1.3 -0.8 -0.3 0.2 0.7\nV vs. PdHx (V)\nFig. R1. a, Sample-to-Keithley connection diagram. b, Electrochemical current-voltage response\nof a sample measured with the Keithley setup and an Ivium pocketSTAT2 potentiostat.\nThe Keithley was operated in 4-wire mode for all measurements. We have added a detailed wiring\ndiagram in the revised manuscript (Figure S2). The mention of sourcemeter and nanovoltmeter\nwas an oversight, carried over from (Tong, J et al., Nature. 2024, 630, 619-624). In that study the\nelectrolytic current involved proton transport without electron transfer, so no potentiostatic\n1\ncontrol was needed—in any case, gate/reference potentials differed by less than 4 mV in that\nstudy (Extended Data Fig. 2 in Tong, J et al., Nature. 2024, 630, 619-624).\nTo ensure full clarity, and to directly address the Reviewer's concern, we have now also performed\ncyclic voltammetry measurements of graphene hydrogenation using an Ivium pocketSTAT2\npotentiostat. As shown in Fig. R1, these measurements reproduce the same redox features and\npotentials observed in our previous data, confirming the consistency and reliability of our\napproach. The only minor difference is that the Keithley setup offers better resolution at the\nlowest current levels (~1 pA), which are near the detection limit of the Ivium system. We thank\nthe Reviewer for drawing our attention to this point. We hope this work will help popularising the\nuse of sourcemeters as highly versatile instruments for electrochemical measurements.\n2. Use a potentiostat to perform CV on graphene hydrogenation\nWhile we appreciate the CV measurements provided for the Pt electrode in a K₃Fe(CN)₆ solution\n(Fig R1.1 of the rebuttal), this alone, without a counter electrode does not validate the\nelectrochemical circuit used in the manuscript. If the authors aim to demonstrate the validity of\ntheir custom circuit, they could consider performing measurements using a commercial\npotentiostat on graphene hydrogenation with PdHx electrodes and compare the results obtained\nwith their setup using the two Keithleys.\nIn the CV measurements with K₃Fe(CN)₆ in the previous round of comments, the counter\nelectrode was a graphite rod, validating the electrochemical circuit. However, we now\nunderstand the insistence on this point. Following the reviewer comment, we measured the\nhydrogenation of graphene using an Ivium potentiostat as described above.\nTaken together, our results confirm that our setup reproduces both classical electrochemical\nexperiments and the new hydrogenation reaction in graphene. We trust that, together with the\nschematics provided, these new experiments resolve the reviewer’s concern in full.\n3. Ambiguity in proton and deuteron transport\nThe manuscript should clarify the differences observed between H+ and D+ transport in free pore\nmeasurements in the context of mobility similarities/differences in HTFSI/PEG systems or\nwhether those differences may arise from the electrode–electrolyte contact resistance. A more\ndetailed discussion or additional control experiments would help clarify the interpretation of the\ndata.\nFigure R2. Conductance of devices with circular apertures\netched in a silicon nitride substrate; HTFSI/DTFSI\nelectrolyte on both sides; and two PdHx/PdDx electrodes.\n0.15 Each data point is a different device. Solid lines, best linear\n)S HTFSI fit to data.\nµ\n(\ne\nc n0.10\na\ntc We have performed additional measurements using SiNx\nu\nd\nn substrates with holes of different radii, r. This allows us to\no\nC0.05 DTFSI\nextract the electrolyte conductivity, κ, from the measured\nconductance, G, using the equation: G = 4πκ r (Bard, A. J. &\n0.00 Faulkner, L. R., Wiley. 2001). This reveals κ ≈1.062x10-4 S\n0 2 4 6 8 10 12 14 16\nAperture diameter (µm) cm-1 for HTFSI, consistent with other studies (e.g. Yang, Z.,\net al., J. Membr. Sci. 2008, 313, 91-96; Yu, L., et al., J. Phys.\nChem. B. 2012, 116, 6553-6560; Yoshizawa, M. & H. Ohno., Chem. Commun. 2004, 1828-1829).\nMore importantly, with this expanded dataset, we are now able to resolve a ≈35% lower\nconductivity in the DTFSI electrolyte.\nconductivity and as such, we believe this data set is an additional novelty ingredient of our work.\nWe have added this discussion in the Methods section, page 7 and Fig. R2 is the new Fig. S6.\n4. PdHx electrode characterization and proton transport in HTFSI/PEG\nThe PdHx electrode is used for detecting hydronium ion currents, as demonstrated in prior\nliterature involving hydrated media (e.g., maleic–chitosan, ref 1). However, PEG is not hydrated.\nThere must be some difference between hydronium ion and HTFSI when those interact with PdHx.\nThe manuscript should carefully discuss how proton exits in HTFSI and how they react with PdHx\nelectrodes.\nFollowing the Reviewer comment, we have added a new section to the manuscript in which we\ndiscuss proton transport in HTSFI as well as proton interaction with PdHx electrodes. Below, we\nsummarise the key points.\nProton transport in PEG/HTFSI. Protons originate from HTFSI, a superacid (pKa ≈ –10), and exist\nas either free H⁺ or PEG-coordinated complexes. Proton transport is thought to take place\nprimarily via a Grotthuss-type mechanism enabled by transient hydrogen bonding with its ether\noxygens (Moses, A. A. & Arntsen, C., Phys. Chem. Chem. Phys. 2023, 25, 2142-2152; Burankova,\nT. et al., J. Phys. Chem. B. 2015 119, 10643-10651). This is consistent with our conductivity\nmeasurements with open hole devices that demonstrate a notable isotope effect (see point #3\nabove).\nProton interaction with PdHx in aqueous electrolytes. Some of the first investigations of\npalladium (Pd) and hydrogen interactions were the classical experiments by Flannagan\n(Flanagan, T. B. & Lewis, F. A., J. Chem. Phys. 1958, 29, 1417-1418), which demonstrated hydrogen\nabsorption in Pd films exposed to pressurised H₂ gas. Under these conditions, Pd forms two\ndistinct hydride phases: the low-hydrogen content α-phase and the hydrogen-rich β-phase. In\nbulk Pd, these phases often coexist, and their distribution depends on hydrogen pressure,\ntemperature, and the electrode's morphology, as described by the material’s phase diagram\n(Flanagan, T. B. & Lewis, F. A., J. Chem. Phys. 1958, 29, 1417-1418).\nFig. R3. Potential of PdHx\n63\nelectrode vs SHE in 1M HCl\n)E\nH in H 2 atmosphere as a\nS\n.s 62 function of time. Potential at\nv\nV\nzero current is recorded in a\nm\n(\nla\n61 three-electrode cell with\nitn PdHx working electrode and\ne to60 Pd counter electrode and\nP\nAg/AgCl (3M) reference\n0 1 2 3 4 5 electrode.\nTime (hr)\nFlannagan also examined the equilibrium between PdHx and acidic solutions in H environment.\nreaching exactly 0 V when fully saturated. This reflects equilibrium between surface-adsorbed\nhydrogen and protons in solution via the Volmer step: H⁺ + e⁻ + * → H*. Hence, hydrogen-saturated\nPd electrodes behave like Pt in acidic solutions. Conversely, pristine Pd initially shows a potential\nof ≈90 mV vs SHE, which gradually decreases to 0 V over tens of hours as the electrode becomes\nelectrochemically hydrogenated (Flanagan, T. B. & Lewis, F. A., J. Chem. Phys. 1958, 29, 1417-\n1418). Electrodes with intermediate hydrogen content exhibit potentials between 0 and 90 mV vs\nSHE, indicating coexistence of α and β phases. We characterised our electrodes in this way. Fig.\nintermediate H loading.\nProton interaction with PdHx in non-aqueous solvents. In non-aqueous solvents, the same\nequilibrium principles apply at the Pd/electrolyte interface. Hubkowska, K., et al., J. Solid State\nElectrochem. 2024, 28, 1159-1169 shows that these reactions proceed more slowly than in\naqueous media and the IV characteristics of the electrode can shift slightly compared to aqueous\nelectrolytes. Thus, the underlying redox mechanism at PdHx remains the same, except with\nslower kinetics and slightly different potentials. Our devices bypass the minor uncertainties\nassociated with reference electrodes in non-aqueous by offering direct access to the absolute\npotential scale via the graphene neutrality point. As demonstrated by the statistical analysis in\nTable S1, the hydrogenation potential vs the neutrality point is highly reproducible and is in\nagreement with the previous independent study of this process (Li, S. et al. Nat Electron., 2021,\n4, 254-260). This discussion has been added in a new section, ‘Proton transport in the\nHTSFI/PdHx system’ in Methods, page 9.\nMoreover, it is unclear how the authors prepared the PdHx electrode. In previous studies, the\nPdHx electrode were saturated with hydrogen (ref 1–3). If saturation occurred, the ability of PdHx\nto absorb further protons would be limited. Could the author describe more in details how they\nprepared the PdHx electrodes.\nWe prepared PdHx following the protocol described and used in Murphy, D. W. et al. Chem.\nMater., 1993, 5, 767-769. In both works, palladium is immersed in a sodium borohydride solution\novernight while stirring and thoroughly rinsed with deionised water. We have added this reference\nto the manuscript in the Methods section.\nAdditionally, the electrochemical equation on page 7 appears unbalanced. A more rigorous form\nwould be: xH+ + xe- + Pd → PdHx . This should be corrected for clarity and chemical accuracy.\nWe agree with the Reviewer and have written the reaction as suggested.\n5. Mobility estimation and interpretation of insulating behavior\nThe authors do not use two-end (source and drain) field-effect-based mobility analysis, despite\nits widespread adoption in similar studies (Ref 4–8). If there is a known inconsistency in applying\nthis method to the present system, it should be discussed explicitly. Avoiding this issue weakens\nthe interpretation of the observed insulating transition, which is based on carrier conduction but\nlacks support of quantitative carrier mobility and carrier concentration.\nFollowing the Reviewer’s suggestion, we have estimated the electronic mobility in our samples\nusing the model in Lv, H. et al. Appl. Phys. Lett., 2013, 103, 193102. The carrier concentration in\ngraphene, 𝑛, is:\n𝑛 = √𝑛2+𝑛(𝑉∗)2 (1)\nwhere 𝑛 and 𝑛(𝑉∗) is the induced carrier concentration as a function of the applied gate voltage,\n0 𝐺\n𝑉 vs the neutrality point. The relation between gate voltage and induced carriers is:\nG\n𝑉∗ = 𝑒 ∙𝑛(𝑉∗)+ ℏ∙𝑣F∙√𝜋𝑛(𝑉 G ∗) (2)\nG 𝐶E G 𝑒\nwhere 𝑒 and ℏ are the elementary charge and reduced Planck constant, respectively. 𝑣 is the\nF\nFermi velocity, of 1.15×106 m s-1 and 𝐶 = 20 µF cm–2 is the electrolyte capacitance, as shown in\nE\nour previous work.\nThe total resistance, 𝑅 , is then written as:\n𝑇𝑜𝑡𝑎𝑙\n𝑅 = 𝑅 +\n𝐿G\n∙\n1\n(3)\nTotal C\n𝑊G 𝑒∙𝜇∙𝑛\n4\nwhere 𝑅 is the contact resistance and 𝐿 and 𝑊 refer to the gated channel length and width,\nC G G\nrespectively and 𝜇 is the mobility to be extracted.\nFig. R4. Total resistance as a function\nGr-SiO Corrugated Gr\n8\non SiO (left) and corrugated graphene\n2\n)\nΩ (right).\nk ( 6\nla\nto\nT\nR We have estimated carrier mobilities in\n4\nour samples with this model, as listed\n2 in Table R1 below. The extracted\n−1 0 1 −1 0 1 mobilities are in the range of 2,000 -\nV - V (V) V - V (V) 6,000 cm²/V·s, in good agreement with\nG NP G NP\nthe literature (K. S. Novoselov et al.,\nScience, 2004, 306,666-669) for similar samples (~1,000 to 10,000 cm²/V·s). The estimates also\nsuggest a small ~2× lower carrier mobility for corrugated graphene compared to graphene-on-\nSiO devices. This information has been included in the revised manuscript, Methods section,\n2\npage 11.\nTable R1. Estimated carrier mobility in graphene samples\nElectron Contact Residue carrier\nHole mobility Number of\nmobility resistance concentration\n10 3 cm 2 / V·s 10 3 cm 2 / V·s kΩ 1011 cm −2 samples\nGraphene-\n3.800 ± 0.8 5.9 ± 0.7 2.2 ± 0.3 8.0 ± 1.1 8\non-SiO2\nCorrugated\n1.9 ± 0.5 2.8 ± 0.5 2.0 ± 0.3 6.9 ± 1.4 4\ngraphene\n6. Role of curvature in hydrogenation\nThe authors emphasize that curvature (convex and concave regions) affects graphene\nhydrogenation, yet they don’t provide direct visual or experimental support for this claim.\nIncluding schematics or Raman mapping (e.g., spatial or time/potential-resolved analysis of D-\nband changes) could help clarify whether such morphological effects exist and how they\ninfluence reactivity.\nMorphological effects on the hydrogenation of graphene have previously been reported in studies\nusing plasma as the hydrogen source. For example, Goler, S. et al., J. Phys. Chem. C. 2013, 117,\n11506-11513 performed STM measurements on plasma-hydrogenated graphene with local\ncorrugations induced by the underlying SiC substrate. The authors\nvisually demonstrated that hydrogen adsorption occurs\npreferentially in convex regions of the sample (e.g., Fig. R5). Away\nfrom these convex regions no hydrogen adsorption was detected.\nThese findings are supported by DFT calculations, including those\nwe present in Fig. S1, which predict a lower energy barrier for\nchemisorption on convex areas of the sample.\nFig. R5. STM measurements of plasma hydrogenated graphene on\nSiC substrates obtained from Goler, S. et al., J. Phys. Chem. C.\n2013, 117, 11506-11513. Scale bar, 2 nm.\nD G\nfurther support this point, we have performed potential-\n-2.1 V resolved Raman spectroscopy measurements that\n-1.7 V\n-1 V\ndirectly monitor the hydrogenation process, as\n).u suggested by the Reviewer. These spectra show a clear\n.a (\ny\n2D onset of the D band at the potentials corresponding to\ntis\nthe hydrogenation of the sample. These new data are\nn\ne\ntn\nI included as Fig. S10 in the revised manuscript.\nFig. R6. Raman spectra of corrugated graphene samples\nduring a hydrogenation cycle. The signatures of the\n1300 1950 2600 hydrogenation appear at about -2.1 V vs NP.\nRaman shift (cm-1)\n7. Novelty\nFig 3c shows a largely enhanced dehydrogenation current for corrugated graphene. This is the\nimpressive part of the results. However, mechanistically, the hydrogenation of graphene has been\nreported in multiple prior studies (e.g., Refs.9–15). Several mechanistic discussions are also\navailable in literature (e.g., Refs.16,17). It is still not clear from the manuscript and data what is\nthe mechanism of hydrogenation and dehydrogenation.\nWould the author measure similar high electrochemical currents in dry Nafion/PdHx systems\n(ref3)? Again I am not sure the electrochemistry is right in HTFSI (see above). Here also, I wonder\nwhether switching to using a potentiostat would yield different results? However, I acknowledge\nthat from Fig 3c top panel, the results are impressive.\nWe thank the Reviewer for their encouraging assessment of our results. This work builds on over\na decade of investigations into proton–graphene\ninteractions across a range of device configurations.\n2-m )\n0\nc\nA\nFig. R7. Electrochemical and electronic response of\nm\n(\ntn\ne rru\n-14\n0\ng\ne\nr\nn\na\nv\np\nir\nh\no\ne\nn\nn\nm\ne\ne n\nd\nt\ne\n.\nvi\nI\nc\nn\ne\ns et\ng\ns\na t\ns\ne\nh\nd\no w\nw it\nt\nh\nh\nN a\nth\ne\nfi\no n\nd e\nu\nn\nic\nd\ne\ne\nd\nr\nd\nd\no\nry\nn\nA\no\nr\nt\nc\nla -28\n-100 survive the first hydrogenation cycle.\nc\nim -200\ne\nh\nc\no\nrtc\ne\nlE\nGraphene\n-42 -300\nl\n-2.5-2.0-1.5-1.0-0.50.0 0.5 hydrogenation of graphene via plasma is well\nlE\nestablished, as discussed in Refs. 9–15 from the\n)S µ 1x104 Reviewer and the introduction of our manuscript. In\n( e330 5x103\nc n 0 contrast, the electrochemical hydrogenation of\na\ntc -5x103 graphene is a much more recent development, and its\nu\nd n\no\n220 -1x104 -2 -1 0 mechanism is not established. While Ref. 16 from the\nc\nc in Reviewer (Daniels et al) and other studies report\no110\rtc electrochemical and Raman measurements of\ne\nlE\ngraphene in aqueous environments, we note that they\n0\ndid not observe a conductor–insulator transition or\n-2.0 -1.5 -1.0 -0.5 0.0 0.5\nV vs.NP (V) demonstrate the reversibility in the Raman D band—\nboth of which are critical hallmarks of successful\nhydrogenation. In the absence of this evidence, it is premature to conclude that electrochemical\n6\nhydrogenation was achieved in those works. As such the mechanism for this phenomenon\nremains unexplored.\nFollowing the Reviewer’s suggestion, we have now performed the experiments using Nafion in dry\nAr environment. Fig. R7. shows that the conductivity of the devices starts decreasing at around\n1.8 V vs NP. Unfortunately, the devices break before reaching the insulating transition (insets in\nFig. R7). This arises because even in dry Nafion films, water remains essential for proton\nconductivity (Mauritz, K. A. & Moore, R. B., Chem. Rev. 2004, 104, 4535-4586), and the large\napplied potential results in water breakdown.\nThe drop in conductance could perhaps be attributed to the onset of the hydrogenation process.\nThe absence of an insulating transition may arise because water-based electrolytes, being more\nactive (see point #4), also yield a faster Eley-Rideal process. However, the drop in conductance\ncould also arise due to irreversible damage of the graphene electrodes. Since the devices do not\ndisplay a full hydrogenation-dehydrogenation cycle, it is not possible to conclude based on these\ndata.\n1. Zhong, C. et al. A polysaccharide bioprotonic field-effect transistor. Nat Commun 2, 476\n(2011).\n2. Morgan, H., Pethig, R. & Stevens, G. T. A proton-injecting technique for the measurement of\nhydration-dependent protonic conductivity. J Phys E 19, 80–82 (1986).\n3. Hu, S. et al. Proton transport through one-atom-thick crystals. Nature 516, 227–230 (2014).\n4. Lv, H. et al. High carrier mobility in suspended-channel graphene field effect transistors. Appl\nPhys Lett 103, (2013).\n5. Xu, H. et al. Top-Gated Graphene Field-Effect Transistors with High Normalized\nTransconductance and Designable Dirac Point Voltage. ACS Nano 5, 5031–5037 (2011).\n6. Kim, S. et al. Realization of a high mobility dual-gated graphene field-effect transistor with\nAl2O3 dielectric. Appl Phys Lett 94, (2009).\n7. Farmer, D. B. et al. Utilization of a Buffered Dielectric to Achieve High Field-Effect Carrier\nMobility in Graphene Transistors. Nano Lett 9, 4474–4478 (2009).\n8. Liao, L. et al. High- κ oxide nanoribbons as gate dielectrics for high mobility top-gated\ngraphene transistors. Proceedings of the National Academy of Sciences 107, 6711–6715 (2010).\n9. Elias, D. C. et al. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for\nGraphane. Science (1979) 323, 610–613 (2009).\n10. Li, S. et al. Large transport gap modulation in graphene via electric-field-controlled\nreversible hydrogenation. Nat Electron 4, 254–260 (2021).\n11. Tong, J. et al. Control of proton transport and hydrogenation in double-gated graphene.\nNature 630, 619–624 (2024).\n12. Zhao, M., Guo, X.-Y., Ambacher, O., Nebel, C. E. & Hoffmann, R. Electrochemical generation\nof hydrogenated graphene flakes. Carbon N Y 83, 128–135 (2015).\n13. Fei, Y., Fang, S. & Hu, Y. H. Synthesis, properties and potential applications of hydrogenated\ngraphene. Chemical Engineering Journal 397, 125408 (2020).\n14. Hu, Y. et al. Synaptic transistor based on reversible hydrogenation of graphene channel.\nAppl Phys Lett 126, (2025).\n15. Cha, J., Choi, H. & Hong, J. Damage-free hydrogenation of graphene via ion energy control in\nplasma. Applied Physics Express 15, 015002 (2022).\n16. Daniels, K. M. et al. Mechanism of Electrochemical Hydrogenation of Epitaxial Graphene. J\nElectrochem Soc 162, E37–E42 (2015).\n17. Podlivaev, A. I. & Katin, K. P. Competition of hydrogen desorption and migration on graphene\n7\nsurface in alternating electric field: Multiscale molecular dynamics and diffusion study. Appl\nSurf Sci 686, 162125 (2025).\nResponse to comments of Reviewer #2\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank the Reviewer for taking the time to carefully read and comment our manuscript.\n8"}, {"round": 3, "reviewer_comments": {"reviewer_1": "Thanks for the reply. We appreciate the efforts of the authors to answer our questions and revise their manuscript. We found a few points in the revised files that merit some attention from the authors. After that the manuscript can be published.\n(1) All the electron current data were replaced in the revised manuscript with conductance values. However, the plots have similar absolute values (i.e. conductance vs current). Is this correct (Figure 1b, Figure 2, bottom panel, Figure 3c bottom panel)? Taking into example Figure 1b: the absolute value now of the conductance is the same as the current they reported in the previous version. For that to be correct, length to width ratio of the graphene device should be strictly 1:1? However, in Figure S2b, the shape of the graphene is irregular and the gold electrode is a V-shaped arrangement. Similarly in the bottom panel of Figure 2, in the revised manuscript, the red and blue curves now touches at Vg-Vnp=-1.2V but not in the original manuscript. If the authors applied a scaling factor of 1.13, what is the reason? Or are the devices not at the same scale? For the point on the blue line where the current is 441.4 nA, the corresponding conductance value is 497.6 μS.\nWe have a similar question concerning the lower panel of Figure 3c: the vertical axis value for the Gr-SiO2 sample remain unchanged when switching from current to conductance, while the vertical axis values of Gr-hBN and Corrugated Gr seems scaled by a certain factor? For example, the scaling factor of the Gr-hBN curve is 0.90, while the scaling factor of the Corrugated-Gr curve is 0.50. We do not understand the origin of these scaling factors reported now in the revised manuscript.\n(2) The data point of the original Figure S6 for the 10 μm pore is not shown in the new plot (Figure S6) of the new manuscript. This data point shows that the conductance of DTFSI is 0.19 μS and the conductance of HTFSI is 0.17 μS. Including these data points in the fitting of circular hole etched in the SiNx membrane would yield a larger bulk conductance for H and D.\nWe calculated those 0.19 μS using the intercepts: For DTFSI curve, we read two points :(-3, -0.56), (3, 0.57). The slope is (0.57+0.56)/(3+3)=0.19 (μS)\nSimilarly, for HTFSI curve, we read two points : (-3, -0.49), (3, 0.51). The slope is (0.51+0.49)/(3+3)=0.17 (μS)\n(3) Concerning the hydrogen saturation of the PdHx electrode: According to Murphy, D. W. et al, Chem. Mater., 1993, 5, 767-769, the Pd was immersed in a BH4- solution overnight while stirring. The previous study emphasized that the Pd was saturated with H; however, this article claims that Pd electrode has intermediate H loading. Why did the loading stop at intermediate state? In addition, if a Pd electrode that is already saturated with H, which means that it can only lose protons but cannot gain protons. Can it still be used as a reference electrode or counter electrode here?\n(4) The calculation of the carrier mobility of Gr-BN. We proposed that the authors could calculate the carrier mobility for their three type of samples for comparison. Could the authors provide the value of Gr-BN as well?", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "We thank the Reviewer for their continued support throughout the review process. Answer to the points raised below.\n(1) All the electron current data were replaced in the revised manuscript with conductance values. However, the plots have similar absolute values (i.e. conductance vs current). Is this correct (Figure 1b, Figure 2, bottom panel, Figure 3c bottom panel)? Taking into example Figure 1b: the absolute value now of the conductance is the same as the current they reported in the previous version. For that to be correct, length to width ratio of the graphene device should be strictly 1:1? However, in Figure S2b, the shape of the graphene is irregular and the gold electrode is a V-shaped arrangement. Similarly in the bottom panel of Figure 2, in the revised manuscript, the red and blue curves now touches at Vg-Vnp=-1.2V but not in the original manuscript. If the authors applied a scaling factor of 1.13, what is the reason? Or are the devices not at the same scale? For the point on the blue line where the current is 441.4 nA, the corresponding conductance value is 497.6 μS.\nWe have a similar question concerning the lower panel of Figure 3c: the vertical axis value for the Gr-SiO2 sample remain unchanged when switching from current to conductance, while the vertical axis values of Gr-hBN and Corrugated Gr seems scaled by a certain factor? For example, the scaling factor of the Gr-hBN curve is 0.90, while the scaling factor of the Corrugated-Gr curve is 0.50. We do not understand the origin of these scaling factors reported now in the revised manuscript.\nThe original draft had data in current units (nA) and the applied sd voltage is 1 mV, so the numbers look identical in µS conductance units (1 nA/1 mV = 1 µS). Normalising by length and width of the flakes led to the differences noted by the Reviewer.\nGiven that these are two-probe measurements with flakes of similar, but irregular size, our preference has always been to present the data without any normalisation—as we did in the first version. In the revised manuscript, we present all data as conductance (current/voltage) without normalisation by flake size. We believe that this is the clearest presentation.\n(2) The data point of the original Figure S6 for the 10 μm pore is not shown in the new plot (Figure S6) of the new manuscript. This data point shows that the conductance of DTFSI is 0.19 μS and the conductance of HTFSI is 0.17 μS. Including these data points in the fitting of circular hole etched in the SiNx membrane would yield a larger bulk conductance for H and D.\nWe calculated those 0.19 μS using the intercepts: For DTFSI curve, we read two points :(-3, -0.56), (3, 0.57). The slope is (0.57+0.56)/(3+3)=0.19 (μS)\nSimilarly, for HTFSI curve, we read two points : (-3, -0.49), (3, 0.51). The slope is (0.51+0.49)/(3+3)=0.17 (μS)\nThe devices shown in the original Fig. S6 were fabricated using 10 µm lithography masks, but overexposure during fabrication may have produced apertures larger than the nominal size. At the time, the aperture diameters were not characterised in detail, since our aim was to confirm that no large differences in conductance existed between the electrolytes. In the revised manuscript, all apertures were measured accurately, which allowed us to obtain precise and reproducible conductivity values. Because the exact sizes of the earlier devices are unknown, 1 they had to be excluded from the current dataset. With hindsight, we can see that these devices indeed must have had a larger aperture.\n(3) Concerning the hydrogen saturation of the PdHx electrode: According to Murphy, D. W. et al, Chem. Mater., 1993, 5, 767-769, the Pd was immersed in a BH4- solution overnight while stirring. The previous study emphasized that the Pd was saturated with H; however, this article claims that Pd electrode has intermediate H loading. Why did the loading stop at intermediate state? In addition, if a Pd electrode that is already saturated with H, which means that it can only lose protons but cannot gain protons. Can it still be used as a reference electrode or counter electrode here?\nMurphy et al. used Pd powders, which can easily approach full H loading due to their high surface area. Our experiments used a Pd foil, where hydrogen uptake is slower, leading to intermediate loading. Nevertheless, PdHx with both intermediate and saturated loading are in equilibrium with the electrolyte as shown by Flannagan and our own measurements in the previous round of comments, making them suitable as reference and counter electrodes.\n(4) The calculation of the carrier mobility of Gr-BN. We proposed that the authors could calculate the carrier mobility for their three type of samples for comparison. Could the authors provide the value of Gr-BN as well?\nFor Gr-on-hBN devices, the mobility values are about an order of magnitude larger, in agreement with previous studies.\nElectron Hole Contact Residue carrier\nNumber of\nmobility mobility resistance concentration\n3 2 2 11 −2\nsamples\n10 cm / V·s cm / V·s kΩ E cm\nGraphene-\n3.800 ± 0.8 5.9 ± 0.7 2.2 ± 0.3 8.0 ± 1.1 8\non-SiO2\nCorrugated\n1.9 ± 0.5 2.8 ± 0.5 2.0 ± 0.3 6.9 ± 1.4 4\ngraphene\nGraphene-\n20.0 ± 3.2 28.6 ± 3.8 2.2 ± 0.5 3.6 ± 0.5 4\non-hBN\nResponse to comments from Reviewer #2\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nWe that the Reviewer for taking the time to comment our manuscript. 2"}, {"round": 4, "reviewer_comments": {"reviewer_1": "Thank you for the clarifications and answers. We do not have further comments and like to congratulate the authors for their work.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

Decision letter