Temperature-dependent bending rigidity of graphene

Both previous theoretical and experimental work showed that the bending rigidity of a liquid membrane decreases with increasing temperature. We demonstrate that the elastic energy forms for a solid membrane and a liquid membrane are identical under equal-biaxial stretching, implying the bending rigidity of a solid membrane should decrease with increasing temperature. We perform molecular dynamics simulations to study how thermal fluctuation affects the bending rigidity of graphene, and find that the bending rigidity decreases exponentially with increasing temperature. This is in contrast with recent atomistic Monte Carlo simulation result that the bending rigidity of graphene increases with increasing temperature.