Thermal vibration of a single-layered graphene with initial stress predicted by semiquantum molecular dynamics

Abstract

Thermal vibration of a rectangular single-layered graphene sheet (RSLGS) with initial stress is investigated by a semiquantum molecular dynamics (SQMD) method on the basis of modified Langevin dynamics. The quantum effect in the thermal vibration of RSLGS is accounted by introducing a quantum thermal bath. The spectrum of the thermal vibration of RSLGSs is obtained both by SQMD and classical molecular dynamics (CMD). The RSLGS vibrates with the same frequencies via both the SQMD simulation and the CMD simulation. The root of mean squared (rms) amplitude obtained via the CMD is greater than that obtained via the SQMD. The energy in high order mode is frozen at very low temperature if quantum effect is taken into consideration. An elastic plate model with initial stress considering quantum effects is established to describe the thermal vibration of the RSLGS. The rms amplitude of RSLGS calculated by plate model with the law of energy equipartition and that obtained from the CMD coincide very well. The plate model considering the quantum effects provides accurate prediction of the rms amplitude of the RSLGS obtained from the SQMD. These results indicate that quantum effects cannot be neglected in the thermal vibration of the RSLGS at low temperature case.