Relaxation properties of single layer graphene sheets on copper substrates

The relaxation properties of three kinds of single layer graphene (SLG) sheets with different aspect ratios on copper substrates are investigated through the molecular dynamics (MD) method. The adaptive intermolecular reactive empirical bond order (AIREBO) potential, the embedded-atom method (EAM) potential and the Lennard-Jones (L-J) potential are utilized to describe the C-C covalent bonds, the Cu-Cu atomic interactions in copper substrate and the C-Cu atomic interactions between graphene film and copper substrate, repectively. According to MD simulation results, we compared fluctuation degree, kinetic energy and stability position of graphene films at 0.01K and 300K. It's found that there are some degree of fluctuations occurred at the edges and inner region of graphene sheets and the fluctuations at the edges are much greater than the inner region. Observation of the relaxation process shows that the single layer graphene is not a perfect planar structure. Moreover, the simulation results indicate that the ambient temperature and the aspect ratio have dramatic influences on the surface fluctuation degree of graphene sheet. After a sufficient relaxation of graphene, the distance between single layer graphene and copper substrate close to 3.274 Angstrom, where the L-J potential for the C-Cu atomic interaction becomes zero.