Stochastically driven vibrations of single-layered graphene sheets

Abstract

Thermal vibration of single-layered graphene sheets (SLGSs) is investigated using plate model together with the law of equi-partition of energy and the molecular dynamics (MD) method based on the condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field. The in-plane stiffness and Poisson ratio of SLGSs are calculated by stretching SLGSs. The effective thickness of SLGSs is obtained by the MD simulations for the thermal vibration of SLGSs through the natural frequency. The root-mean-squared (RMS) amplitudes for SLGSs of differing temperatures and boundary conditions are calculated by the MD, and are compared with the results calculated by the thin plate model together with the law of equi-partition of energy. At the center of SLGSs, the thin plate theory can predict the MD results reasonably well. For the difference of bonding structure of the edge atoms, the deviation between the MD results and plate theory becomes more readily apparent near the edges of SLGSs.