Deep-learning-potential molecular dynamics simulations predict that graphanol — graphane in which the hydrogen atoms are replaced by hydroxyl groups — conducts protons rapidly in the complete absence of water, with single-sided graphanol predicted at 313–1567 mS/cm over 300–800 K (activation energy about 99 meV) and double-sided graphanol (DSG) predicted to combine that fast proton transport with lower thermal fluctuations and proton self-diffusivity at 800 K similar to the single-sided material, conductivities far above hydrated Nafion and most anhydrous proton conductors. These predictions exist only in silico: no one has synthesized both-faces hydroxylated graphane in membrane form, and no anhydrous proton-conductivity measurement exists for any hydroxylated-graphene material. The synthesis and experimental validation of DSG as an anhydrous proton exchange membrane remain open.

Background

Proton exchange membrane (PEM) fuel cells convert hydrogen and oxygen into electricity, and the membrane that separates the electrodes must transport protons while blocking gases. The dominant membrane material, Nafion, conducts protons only when hydrated, so conventional fuel cells must be kept wet and relatively cool. High-temperature, low-humidity operation would improve catalyst tolerance and simplify water management, which motivates materials that conduct protons anhydrously, that is, without water; existing anhydrous conductors (polybenzimidazole–phosphoric acid systems, ionic-liquid polymers, solid acids) have limitations in stability, cost, or conductivity. Graphane is graphene in which every carbon bears a hydrogen atom, converting the sheet from sp2 to sp3 bonding. Graphanol (also called hydroxygraphane) is the derivative in which those hydrogens are replaced by hydroxyl (–OH) groups, so the sheet carries a dense, regular lattice of hydroxyls; single-sided graphanol (SSG) is functionalized on one face and double-sided graphanol (DSG) on both; in the DSG structure used in the simulations the hydroxyls alternate between the two faces, giving one hydroxyl per carbon (C:O:H ≈ 1:1:1), so each face carries its own triangular hydroxyl lattice over half the carbon sites. In such a lattice a proton can move by the Grotthuss mechanism — hopping along chains of hydrogen bonds from one hydroxyl to the next, with occasional hydroxyl rotation re-forming the chains — so no humidification is needed. Evaluating this by density functional theory (DFT) directly is infeasible at the required length and time scales, so Achar, Bernasconi, Alvarez and Johnson (2023) trained a deep-learning potential (DP), an interatomic potential fitted to DFT data with near-DFT accuracy at a small fraction of the cost, using active learning, and ran DP-based molecular dynamics. For SSG they predicted anhydrous proton conductivity of 313–1567 mS/cm between 300 and 800 K with an activation energy of 99±1399 \pm 13 meV (99±999 \pm 9 meV averaged over the two system sizes simulated), obtained from the Nernst–Einstein relation using an assumed mobile-proton concentration of c=0.0028 mol/cm3c = 0.0028\ \mathrm{mol/cm^3} — one excess proton in a 24-carbon cell divided by an assumed membrane volume — and showed that conductivity survives up to about 50% missing hydroxyls because proton hopping on the triangular hydroxyl lattice percolates above a site-occupation threshold of 0.5, meaning that nearly half of the OH groups on that lattice may be replaced by H — so a practical membrane does not require perfect stoichiometry. For DSG they found proton self-diffusivity at 800 K comparable to SSG, with smaller thermal fluctuations, and reported that the structural differences between DSG and SSG do not impact proton transport; the DSG paper reports phonon properties, thermal fluctuations and self-diffusivity but no DSG conductivity value. The predicted single-sided conductivities exceed essentially all measured anhydrous (and most hydrated) proton conductors. The experimental basis for the material itself, however, is thin: hydroboration of graphene oxide (Poh, Sofer, Šimek, Tomandl and Pumera, 2015) yields disordered, partially hydroxylated material near composition (C1O0.78H0.75)n(\mathrm{C}_1\mathrm{O}_{0.78}\mathrm{H}_{0.75})_n; the only ordered two-dimensional alcohol, graphenol (Lim et al., 2020), has just one hydroxyl per six carbons and is epitaxially bound to a Cu(111) substrate; and double-sided covalent functionalization of free-standing graphene has been demonstrated only for hydrogen (Betti et al., 2022). None of these materials is double-sided graphanol, and none has had its proton conductivity measured. The 2023 DSG paper therefore closes by stating that DSG is a promising membrane material deserving of synthetic efforts, and the present problem is exactly that experiment: fabricate the material and test the prediction.

Problem Statement

Synthesize double-sided graphanol — a graphene-derived sheet whose both faces carry covalently bound hydroxyl groups, ideally one hydroxyl per carbon alternating between the two faces (near-stoichiometric C:O:H ≈ 1:1:1, the DSG structure used in the simulations), with the hydroxyl coverage characterized separately on each face and each face retaining at least about 50% of its hydroxyl sites (no more than about half of that face's OH groups replaced by H), the triangular-hydroxyl-lattice site-percolation threshold that the single-sided graphanol simulations identify as sufficient for conduction; no defect simulations were reported for DSG itself, and a specimen whose hydroxylation is concentrated on one face does not meet this target, however much its overall OH-per-carbon ratio compares with 0.5 — in a form that can serve as a membrane, and experimentally determine whether it conducts protons anhydrously as predicted. Specifically: (1) develop and execute a synthesis/fabrication route yielding a free-standing or supported both-faces hydroxylated graphane material or film, with structural and compositional characterization establishing the hydroxylation pattern, the hydroxyl coverage on each face, and the two-sidedness, and reporting the specimen form (free-standing or supported, layer number) together with evidence that the measured conduction is dominated by the both-faces hydroxylated graphanol layer rather than by substrate, interfacial or interlayer paths; (2) measure its proton conductivity under rigorously anhydrous conditions as a function of temperature (covering the range where predictions exist, from room temperature to several hundred degrees Celsius), including the activation energy, and report the mobile-proton (doping) concentration and the membrane thickness/volume normalization to which the measured conductivity refers; and (3) compare the measured conductivity and activation energy with the deep-learning-potential predictions for graphanol (313–1567 mS/cm over 300–800 K with an activation energy of about 99 meV, 99±1399 \pm 13 meV for the 24-carbon system and 99±999 \pm 9 meV averaged over system sizes, obtained via the Nernst–Einstein relation with an assumed proton concentration c=0.0028 mol/cm3c = 0.0028\ \mathrm{mol/cm^3}) and with the published DSG result that proton self-diffusivity at 800 K in DSG is similar to that in single-sided graphanol with lower thermal fluctuations, making the comparison at matched proton-concentration and thickness/volume normalization or stating the rescaling used. A well-characterized demonstration that the predicted anhydrous conduction is absent would equally resolve the question by refuting the simulations.

References

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