Surface roughness and size effects on the morphology of graphene on a substrate

•The respective effect of surface amplitude and wavelength on graphene morphology is investigated.•The effect of surface roughness on snap-through transition of graphene is discussed.•Size effect on graphene morphology is studied.

We study the morphology and snap-through transitions of multilayer graphene on a corrugated elastic substrate whose surface roughness is determined by surface amplitude and wavelength. Based on the couple stress theory, we develop a theoretical model to understand the size effect on the graphene morphology. It is indicated that the surface amplitude has no effect on the corrugation of graphene, whereas increased surface wavelength results in greater corrugation of the graphene on the substrate. At high surface roughness, a snap-through transition is more likely to happen. Moreover, our results show obvious size effect on the graphene morphology for high surface roughness and compliant substrates. This work offers theoretical insights to control graphene morphology by changing the substrate surface roughness.

Graphical abstractIn the limiting case of freely graphene sliding on substrate, the substrate surface amplitude only influence the critical condition of snap-through transition, the surface wavelength is proved to be a dominated factor to control the morphology of graphene.Figure optionsDownload full-size imageDownload as PowerPoint slide