Graphene nano-flakes on Cu low-index surfaces by density functional theory and molecular dynamics simulations

This chapter reviews structural, electronic, and diffusion properties of graphene nano-flakes growing on Cu low-index surfaces obtained by ab initio and large-scale classical molecular dynamics simulations. Previous experimental and theoretical data revealed the preference of the flake's zig-zag edges with the Cu [110] surface directions. This observation was explained through density functional theory calculations that yielded Cu 3d–C 2p bonding hybridizations between the nano-flakes’ zig-zag edges and the Cu [110] low-index surfaces' directions that reduce the lattice mismatch. The molecular dynamics simulations also found the energy preference of the CN (N = 24–560) nano-flakes' zig-zag edge along the [110] surface direction predicting lower binding energy for the rectangular, rectangular tetragonal, and hexagonal nano-flakes on Cu(110), Cu(001), and Cu(111) surfaces, respectively. Finally, the transfer and rotation diffusion mechanism found for C44 and C560 on Cu(110) substrate the zig-zag flake alignment parallel to the Cu(110) channel.