Proton transfer across single-layer graphene proceeds with large computed energy barriers and is therefore thought to be unfavourable at room temperature unless nanoscale holes or dopants are introduced, or a potential bias is applied. Here we subject single-layer graphene supported on fused silica to cycles of high and low pH, and show that protons transfer reversibly from the aqueous phase through the graphene to the other side where they undergo acid–base chemistry with the silica hydroxyl groups. After ruling out diffusion through macroscopic pinholes, the protons are found to transfer through rare, naturally occurring atomic defects. Computer simulations reveal low energy barriers of 0.61–0.75 eV for aqueous proton transfer across hydroxyl-terminated atomic defects that participate in a Grotthuss-type relay, while pyrylium-like ether terminations shut down proton exchange. Unfavourable energy barriers to helium and hydrogen transfer indicate the process is selective for aqueous protons.

Potential-dependent activation energies are calculated quantum mechanically, using a local reaction center model, for the hydrogen reduction−oxidation reaction over platinum by the Volmer−Heyrovsky mechanism, Pt−H + H+ + e-(U) ↔ Pt + H2 (i), modeled by Pt−H···H+(OH2)(OH2)2 + e-(U) ↔ Pt···H−H···OH2(OH2)2 (ii). A contribution from the electrolyte to the potential of the reaction centers in ii is included in the ab initio Hamiltonian. The reversible potential predicted for i based on model ii is 0.04 V, close to the standard hydrogen electrode value of 0 V, and the predicted activation energy at the predicted reversible potential is 0.076 eV, close to the literature value of 0.12 eV for the apparent activation energy. The theoretical results validate the possibility of the Volmer−Heyrovsky mechanism being followed on platinum.

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Quantum mechanically determined electrode potential dependent activation energies for hydronium ion discharge over Pt-H (Heyrovsky reaction) and the reverse reaction have been used to predict Tafel plots. The calculated Tafel plot for H 2 oxidation is similar in shape to an experimental plot from the literature for a Pt(100) electrode and will overlap it when an appropriate preexponential factor is chosen in the Arrhenius expression. This provides strong theoretical support for the first electron-transfer step being rate limiting during H 2 oxidation over the potential range 0 to 0.15 V, and the second electron-transfer step being rate limiting during H 2 evolution over this electrode. The exchange current density is determined from the calculated oxidation and reduction currents and is found to overestimate experiment primarily because the predicted activation energy at the reversible potential underestimates the experimental value. This study illustrates that curvature in nonlinear Tafel plots may stem from the potential dependence of the activation energies or transfer coefficients as well as diffusion and concentration gradient effects. The observed current density and its increase, leveling off, and then decrease at potentials greater than the activation energy-controlled region are attributed to removal of under potential deposited H, passing through the double layer region, and then site blocking by water and its oxidation product OH(ads).

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