Simulation of Graphene Mechanics

Abstract

Graphene is a one atom thick layer of carbon atoms arranged in hexagonal lattice in two-dimensions. The discovery of graphene has provoked a revolution in nanotechnology, as the structural, thermal, and electronic properties of graphene make it a very useful component for a large variety of devices. In my PhD, we have developed a new semi-empirical potential for graphene, using density functional theory (DFT) calculations for determining the various parameters, which for the first time includes a term for out-of-plane deformations. We have demonstrated the usefulness of this potential in studies of different kind of intrinsic defects (Stone-Wales defect, separating dislocations and grain boundaries). Our simulations show that the stress caused by these defects can be relieved by buckling, which extends to hundreds of nanometers. A detailed study of the formation energies of defects surprisingly revealed that the value for the formation energy depends on the type of boundary conditions. Therefore it is necessary to specify the boundary conditions for the energy of the lattice defects in buckled two-dimensional crystals to be uniquely defined. We have also theoretically described that the vibrational density of states (VDOS) can be used in probing the crystallinity of graphene samples. The low-energy modes in the VDOS are very sensitive to the buckling in the sample. The novel potential can be effectively combined with an interlayer interaction, allowing the simulation of bilayer graphene and the study of the effect of twist angle on the structure and buckling. Our study reveals that the size of mismatched vortices in twisted bilayer graphene becomes constant when the twist angle becomes very small (θ<1°). We have also described the universal shape behaviour of a graphene gas bubble irrespective of its size. We show that for small gas bubbles (~10 nm), the van der Waals pressure is in the order of 1 GPa which can have direct consequence on the properties of the trapped materials.