Adhesive contact between a graphene sheet and a nano-scale corrugated surface

Adhesive contacts between graphene sheets and corrugated surfaces are investigated. It is found that the final configuration between the graphene sheet and the substrate depends not only on the surface roughness of the substrate, but also on the length of graphene. A continuous transition, rather than a recent observation of 'snap-through' transition, is exhibited in our study. For a graphene sheet with a fixed length, it is easy to fully conform to the substrate of small roughness. Otherwise, the graphene sheet will remain flat on top of the corrugated substrate due to the unsatisfied bending energy or partially conform to the substrate due to the resistance of large interface friction. In order to reduce the effect of interface friction on the adhesive configuration, a new method, i.e. tilting the graphene sheet with a proper angle, is proposed. The tilting angle will significantly influence the final conformation of the adhesive interface. Some interesting types of behaviour are observed, such as rolling graphene, a double layer of graphene and fully adhesive contact, which is physically determined by the competition of thermal fluctuation and interfacial van der Waals interaction.