Thermal expansion of free-standing graphene: benchmarking semi-empirical potentials

The thermodynamical properties of free-standing graphene have been investigated under constant zero pressure as a function of temperature using Monte Carlo simulations. A variety of atomistic models have been used, including the simple three-body Stillinger potential and a series of bond-order many-body potentials based on the Tersoff-Brenner seminal models, with recent reparametrizations dedicated to graphene, extensions to medium-range or long-range dispersion corrections. In addition, we have also tested a tight-binding potential in the fourth-moment approximation. The simulations reveal significant discrepancies in the in-plane lattice parameter and the thermal expansion coefficient, which despite showing monotonically increasing variations with temperature, can be positive, negative or change sign at moderate temperature depending on the potential. Comparison with existing experimental and theoretical data obtained from complementary approaches indicates that empirical potentials limited to nearest-neighbour interactions give rather dispersed results, and that van der Waals corrections generally tend to flatten the variations of the in-plane lattice constant, in contradiction with experiment. Only the medium-range corrected potentials of Los and Fasolino, as well as the tight-binding model in the fourth-moment approximation, are reasonably close to the reference results near room temperature. Our results suggest that classical potentials should be used with caution for thermal properties.