Competing Effects of Strain and Curvature on Proton Transport through Corrugated Graphene

Proton transport through graphene is strongly affected by nanoscale morphology, yet the atomic pathway responsible for enhanced permeation near corrugations remains unclear. Here, using first-principles calculations, we resolve proton permeation pathways through individual hexagonal carbon rings in mechanically distorted graphene. We find that a single corrugation creates a heterogeneous permeation landscape in which different carbon rings exhibit substantially different barriers depending on their local strain and curvature, and the most highly curved region is not necessarily the most permeable. Analysis of the permeation energies shows that corrugation partially relieves local in-plane compression relative to planar graphene under the same imposed compression, thereby lowering the transition-state energy, while the remaining barrier variation among rings within the corrugation arises predominantly from the curvature-dependent stabilization of the adsorbed initial state. In addition, concave curvature produces particularly strong initial-state stabilization because the local orbital orientation enhances the interaction with the adsorbed proton. Consequently, weakly curved carbon rings can exhibit permeation barriers that are lower than those of more highly curved regions. These results show that proton transport through corrugated graphene is governed by the local balance between the transition-state accessibility associated with lattice deformation and curvature-induced stabilization of the adsorbed state.