Thermal Vibration Of Carbon Nano-structures

Thermal vibration plays an important role in the dynamics of nanostructures.The quantum effects,boundary effects and van der Waals(vd W)interaction have significant influence on the thermal vibration of nanostructures.The objective of the dissertation is to investigate the dynamics behaviors of nanostructures induced by thermal noise.Carbon nanotubes(CNTs)and graphene have attracted lots of researches for their novel electronic properties and superior mechanical strength.In this dissertation,the nonlinear thermal vibration behavior of a single-walled CNT(SWCNT),thermal vibration of CNTs and graphene at low temperatures are studied by the continuum mechanics and molecular dynamics(MD)method.The dissertation begins with a brief survey on dynamics problems in nanostructures in Chapter 1.There follows the main body of the dissertation,from chapters 2 to 8.The dissertation ends with some concluding remarks in Chapter 9.The results and the main contributions of the dissertation are as following.Chapter 2 presents a brief introduction of MD method and temperature control methods.The critical lengths of an oscillator that based on double-walled carbon nanotubes(DWCNTs)are studied by MD method.The influences of chirality and temperature for the critical lengths are investigated by MD simulations.Chapter 3 presents the study on the nonlinear thermal vibration behavior of a SWCNT by using MD simulation and a nonlinear,nonplanar beam model.Whirling motion with energy transfer between flexural motions is found in the free vibration of the SWCNT excited by the thermal motion of atoms when the geometric nonlinearity is significant.A nonlinear,nonplanar beam model considering the coupling in two vertical vibrational directions is presented to explain the whirling motion of the SWCNT.Energy in different vibrational modes is 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 energy of different modes becomes equal when the time scale increases to the microsecond range.Chapter 4 focuses on the quantum effects in the thermal vibrations of CNTs.An MD method 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 SWCNT.A nonlocal elastic Timoshenko beam model with quantum effects(TBQN),which can take the effect of microstructure into consideration,is 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 by the semiquantum molecular dynamics(SQMD)is lower than that obtained by the classical MD(CMD),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 MD 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 CMD without considering quantum effects.The RMS amplitude of the SWCNT obtained from the SQMD and that obtained from the 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.Chapter 5 investigates thermal vibration of a rectangular single-layered graphene sheet(RSLGS)with initial stress by SQMD method.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 CMD.The RSLGS vibrates with the same frequencies via both the SQMD simulation and the CMD simulation.The RMS amplitude obtained via the CMD is larger 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 with each other 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.Chapter 6 presents the study on the vibration of DWCNTs by using different beam models of continuum mechanics and the MD simulations.The models of the double Euler beam(DEB)and the double Timoshenko beam(DTB),with the energy of vd W interaction between layers taken into consideration,are applied to predict the natural frequencies of DWCNTs with one ends fixed.For the relatively long DWCNTs,the results obtained by the DEB model and the DTB model are very close,and the MD simulations show that these two models can predict the natural frequencies well.However,for the vibration of the relatively short DWCNTs,the difference between the DEB model and the DTB model becomes obvious,and the DTB model offers much better predictions than the DEB model.Chapter 7 established the equivalent plate model with quantum effects of a double-layered graphene to study thermal vibration of the double-layered graphene at low temperature.The initial stress of the graphene is also taken into consideration.The natural frequency and the RMS amplitude of the double-layered graphene with different initial stress in different temperatures are calculated.The natural frequency of the in-phase vibration is the same as the natural frequency of a single-layered graphene.The natural frequency of the anti-phase vibration is higher than the in-phase vibration frequency.The RMS amplitude obtained by the plate model considering quantum effects is smaller than that obtained by the plate model together with the law of energy equipartition.The different of these two models becomes more obvious at the lower temperature.The natural frequency will increase with increasing of the initial stress,while the RMS amplitude will decrease.The initial stress has more significant influence for the in-phase vibration than the anti-phase vibration.Chapter 8 studied the effect of zero-point energy for the thermal vibration of the double-layered graphene.If the zero-point energy is taken into consideration to the mean modal energy,the RMS amplitude obtained by the plate model considering quantum effects is larger than that obtained by the plate model together with the law of energy equipartition.The difference is obvious when the temperature is very low.Besides,the RMS amplitude of the graphene is not zero at the temperature of 0K.