Thermomechanical properties of graphene: valence force field model   approach
  Using the valence force field model of Perebeinos and Tersoff [Phys. Rev. B {\bf79}, 241409(R) (2009)], different energy modes of suspended graphene subjected to tensile or compressive strain are studied. By carrying out Monte Carlo simulations it is found that: i) only for small strains ($|\varepsilon| \lessapprox 0.02$) the total energy is symmetrical in the strain, while it behaves completely different beyond this threshold; ii) the important energy contributions in stretching experiments are stretching, angle bending, out-of-plane term and a term that provides repulsion against $\pi-\pi$ misalignment; iii) in compressing experiments the two latter terms increase rapidly and beyond the buckling transition stretching and bending energies are found to be constant; iv) from stretching-compressing simulations we calculated the Young modulus at room temperature 350$\pm3.15$\,N/m, which is in good agreement with experimental results (340$\pm50$\,N/m) and with ab-initio results [322-353]\,N/m; v) molar heat capacity is estimated to be 24.64\,J/mol$^{-1}$K$^{-1}$ which is comparable with the Dulong-Petit value, i.e. 24.94\,J/mol$^{-1}$K$^{-1}$ and is almost independent of the strain; vi) non-linear scaling properties are obtained from height-height correlations at finite temperature; vii) the used valence force field model results in a temperature independent bending modulus for graphene, and viii) the Gruneisen parameter is estimated to be 0.64. 
A. Lajevardipour, M. Neek-Amal and F. M. Peeters
cond-mat.mtrl-sci