The application of empirical potentials for calculation of elastic properties of graphene

The elastic properties of a flat graphene layer calculated using the classical empirical Tersoff, Brenner, AIREBO, PPBE-G, and LCBOP potentials have been compared. It is shown that, although the popular Brenner and AIREBO potentials have been developed formally taking into account the elastic properties of graphene, they give significant discrepancies in the values of Young's modulus and Poisson's ratio. Among the potentials under consideration, the LCBOP potential yields the values of these parameters that are closest to experimental data and results of ab initio calculations in the limit of zero elongation. For the quantitative simulation of mechanical phenomena in graphene-based systems, the potential parameters should be fitted to reproduce elastic properties of graphene completely taking into account system deformations and dependences of these constants on the elongation.