Liu Rumeng, Wang Lifeng
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, P. R. China.
Phys Chem Chem Phys. 2015 Feb 21;17(7):5194-201. doi: 10.1039/c4cp05495d.
Quantum effects should be considered in the thermal vibrations of carbon nanotubes (CNTs). To this end, molecular dynamics based on modified Langevin dynamics, which accounts for quantum statistics by introducing a quantum heat bath, is used to simulate the thermal vibration of a cantilevered single-walled CNT (SWCNT). A nonlocal elastic Timoshenko beam model with quantum effects (TBQN), which can take the effect of microstructure into consideration, has been established to explain the resulting power spectral density of the SWCNT. The root of mean squared (RMS) amplitude of the thermal vibration of the SWCNT obtained from semiquantum molecular dynamics (SQMD) is lower than that obtained from classical molecular dynamics, especially at very low temperature and high-order modes. The natural frequencies of the SWCNT obtained from the Timoshenko beam model are closer to those obtained from molecular dynamics if the nonlocal effect is taken into consideration. However, the nonlocal Timoshenko beam model with the law of energy equipartition (TBCN) can only predict the RMS amplitude of the SWCNT obtained from classical molecular dynamics without considering quantum effects. The RMS amplitude of the SWCNT obtained from SQMD and that obtained from TBQN coincide very well. These results indicate that quantum effects are important for the thermal vibration of the SWCNT in the case of high-order modes, short length and low temperature.
在碳纳米管（CNT）的热振动中应考虑量子效应。为此，基于修正朗之万动力学的分子动力学通过引入量子热浴来考虑量子统计，用于模拟悬臂单壁碳纳米管（SWCNT）的热振动。为了解释所得SWCNT的功率谱密度，建立了一种能够考虑微观结构效应的具有量子效应的非局部弹性铁木辛柯梁模型（TBQN）。从半量子分子动力学（SQMD）获得的SWCNT热振动的均方根（RMS）振幅低于从经典分子动力学获得的结果，特别是在非常低的温度和高阶模式下。如果考虑非局部效应，从铁木辛柯梁模型获得的SWCNT的固有频率更接近从分子动力学获得的结果。然而，具有能量均分定律的非局部铁木辛柯梁模型（TBCN）只能预测不考虑量子效应时从经典分子动力学获得的SWCNT的RMS振幅。从SQMD获得的SWCNT的RMS振幅与从TBQN获得的结果非常吻合。这些结果表明，在高阶模式、短长度和低温情况下，量子效应对于SWCNT的热振动很重要。
