Effect of surface roughness on adhesion of graphene membranes

To integrate graphene in functional devices, it is essential to understand interfacial adhesion between graphene and surrounding materials for mechanical support and encapsulation. In complement with recent efforts aiming to measure the adhesion energy experimentally, we present a theoretical model to predict how the surface roughness may affect the adhesion between graphene membranes and their substrates. It is found that the bending modulus, which increases drastically from monolayer to multilayered graphene, plays an important role in the transition from conformal to non-conformal morphology of the graphene membranes on a corrugated surface. As such, the work of adhesion drops considerably from monolayer to bilayer graphene, in good agreement with recent measurements. Moreover, the theoretical results suggest that tunable adhesion of graphene can be achieved by controlling the surface roughness of the substrate.