The Study Of Quantum Effects And Thermodynamic Properties In A Carbon Nanotube

Nanotechnology is the frontiest sciences in the nowadays, especially recently with the development of technique in nanostructial set-up and nano-device manufacture, more and more people is interested in research on nanomateral. Carbon nanotube is novel in nanomateral., there exists widespread applied prospect because of particular property. For example, it can be used as field emission source, modifier electrode and catalyst carrier, used for compositing molecular device, made from conductive and antistatic lastics.Based on which people is more interested in the property of optics, electricity and mechanics, Our work focus on research on thermodynamics of Carbon nanotube under low temperature. In this thesis, Continuum elasticity theory and Green's function are applied in studying the thermodynamic properties in a Carbon nanotube, which is weakly coupled to a semi-infinite Carbon substrate. The research benefits on understanding the observed phenomena, and provides theoretical guidance on fabricating nanoscale devices.Firstly, Continuum elasticity theory can be used for solving all normalized eigenmodes and dispersion relations in the isolated nanotube and substrate under the free boundary conditions. Secondly, we discuss the phonon spectrum in coupled nanotube according to perturbative theory in Green's function, the retarded Green's function for nanotube can be obtained by calculating the Eucidean time-orderd Green's function, then, we can work out phonon spectrum by Fourier transforming and Dyson equation solving. Furthermore, we solve out the thermodynamic properties of the system by numerical calculation. We find that the phonon spectrum can be expanded continuous spectrum from discrete one.