Thermomechanics of monolayer graphene: Rippling, thermal expansion and elasticity

Thermomechanical properties of monolayer graphene with thermal fluctuation are studied by both statistical mechanics analysis and molecular dynamics (MD) simulations. While the statistical mechanics analysis in the present study is limited by a harmonic approximation, significant anharmonic effects are revealed by MD simulations. The amplitude of out-ofplane thermal fluctuation is calculated for graphene membranes under both zero stress and zero strain conditions. It is found that the fluctuation amplitude follows a power-law scaling with respect to the linear dimension of the membrane, but the roughness exponents are different for the two conditions due to anharmonic interactions between bending and stretching modes. Such thermal fluctuation or rippling is found to be responsible for the effectively negative in-plane thermal expansion of graphene at relatively low temperatures, while a transition to positive thermal expansion is predicted as the anharmonic interactions suppress the rippling effect at high temperatures. Subject to equi-biaxial tension, the amplitude of thermal rippling decreases nonlinearly, and the in-plane stress-strain relation of graphene becomes nonlinear even at infinitesimal strain, in contrast with classical theory of linear elasticity. It is found that the tangent biaxial modulus of graphene depends on strain non-monotonically, decreases with increasing temperature, and depends on membrane size. Both statistical mechanics and MD simulations suggest considerable entropic contribution to the thermomechanical properties of graphene, and as a result thermal rippling is intricately coupled with thermal expansion and thermoelasticity for monolayer graphene membranes. & 2014 Elsevier Ltd. All rights reserved.