▎ 摘　　要

The morphology of graphene sheets overlying a substrate plays an important role in controlling the electronic behaviour of graphene-based electronic devices. Atomistic simulations and energetic analysis are performed to study the morphology of graphene edges on a model substrate. We find that the van der Waals interactions are able to significantly reduce the amplitude, penetration depth and wavelength of edge ripples for a single-layer graphene sheet, but suppression of the ripples is not observed in multilayer graphene sheets with unsaturated edges. We explain this difference using an analytical model that accounts for the energetics of rippling and van der Waals interactions.