On the Contribution of Dispersion Forces to the Linear and Point Energies of Graphene

For two-dimensional structures, the linear and point energies are physical parameters of the same significance as the surface and linear energies, respectively, for three-dimensional bodies. The theory presented in this communication enables one to calculate the contribution of dispersion forces to the local cohesion energy, local linear energy, and point energy of graphene from its microscopic parameters, namely, the lattice spacing, two-dimensional atomic density, and pair interaction potential. The local values are calculated on the basis of the Irving–Kirkwood pressure tensor inside of a plane-parallel empty two-dimensional slit with a finite size extension between two rectangular pieces of graphene lying in the same plane. The calculation is performed for the absolute zero of temperature (when the energy is equivalent to the free energy). The structure of graphene is assumed to be rigid, which entails ignorance of the effect of relaxation upon the separation of the two graphene pieces. The calculation result depends on the direction of graphene boundary line. The line normal to the σ-bonds has been selected for the calculations, with this line corresponding to the natural boundary of graphene. The linear and point energies of graphene are calculated within the model of rigid spheres with dispersion forces and the Lennard—Jones model. It has been found that, near a corner of a rectangular graphene piece, the linear energy becomes a value variable within five distances between atoms in the lattice, thereby making it possible to evaluate the contribution of the dispersion forces to the point energy of graphene.