We study the structural and thermodynamic properties of bilayer graphene, a prototype two-layer membrane, by means of Monte Carlo simulations based on the empirical bond order potential LCBOPII (long-range carbon bond order potential II). We present the temperature dependence of lattice parameter, bending rigidity, and high-temperature heat capacity as well as the correlation function of out-of-plane atomic displacements. The thermal-expansion coefficient changes sign from negative to positive above $\approx 400\text{K}$, which is lower than previously found for single-layer graphene and close to the experimental value of bulk graphite. The bending rigidity is twice larger than for single layer graphene, making the out-of-plane fluctuations smaller. The crossover from correlated to uncorrelated out-of-plane fluctuations of the two carbon planes occurs for wave vectors shorter than $\approx 3{\text{nm}}^{-1}$.

• Received 1 April 2010

DOI:https://doi.org/10.1103/PhysRevB.81.235439