15. Thermal Vibration of Carbon Nanostructures

The chapter presents the study on thermal vibration of nanostructures, such as carbon nanotube (CNT) and graphene, as well as the basic finding for the relation between the temperature and the root-of-mean-square (RMS) amplitude of the thermal vibration of the carbon nanostructures. In this study, the molecular dynamics (MD) based on modified Langevin dynamics, which accounts for quantum statistics by introducing a quantum heat bath, is used to simulate the thermal vibration of carbon nanostructures. The simulations show that the RMS amplitude of the thermal vibration of the carbon nanostructures obtained from the semi-quantum MD is lower than that obtained from the classical MD, especially for very low temperature and high-order vibration modes. The RMS amplitudes of the thermal vibrations of the single-walled CNT (SWCNT) and graphene obtained from the semi-quantum MD coincide well with those from the models of Timoshenko beam and Kirchhoff plate with quantum effects. These results indicate that quantum effects are important for the thermal vibration of the SWCNT and graphene in the case of high-order vibration modes, small size, and low temperature. Furthermore, the thermal vibration of a simply supported SWCNT subject to thermal stress is investigated by using the models of planar and non-planar nonlinear beams, respectively. The whirling motion with energy transfer between flexural motions is found in the SWCNT when the geometric nonlinearity is significant. The energies of different vibration modes are not equal even over a time scale of tens of nanoseconds, which is much larger than the period of fundamental natural vibration of the SWCNT at equilibrium state. The energies of different modes become equal when the time scale increases to the range of microseconds.