Thermal Expansion in Graphene and Graphane: Role of Anharmonic and Harmonic Effects

As the practical application of graphene nears realization, knowledge of effects of temperature on mechanical properties of graphene becomes important. In this study we use empirical potentials and density-functional perturbation theory (DFPT) to determine the thermal expansion of free-standing graphene, graphene on substrates, and its hydrogenated derivative graphane. Comparisons of MD simulations with calculations using the quasi- harmonic approximation using an empirical potential show that anharmonic effects are negligible at temperatures below 2200K. In contrast to the DFPT calculations using the quasi-harmonic approximation, MD results show that free-standing graphene has a positive thermal expansion coefficient above 600K. For graphene on a substrate our DFPT results agree with those of Jiang et. al [1] and show that the substrate suppresses the negative thermal expansion coefficient with increasing strength of the substrate- graphene interaction. We also investigate the thermal expansion of the thermodynamically stable conformers of graphane using DFPT.\\[4pt] [1] J. W. Jiang, J. S. Wang, B. Li, Phys. Rev. B 80, 205429 (2009).