Abstract
We present an analytical expression for the thermal conductivity in nanostructures which takes into account all phonon properties: the number of modes, the group velocity, the relaxation time due to the Umklapp process and the boundary surface scattering and their variation with the wave vector directions. Phonon properties can be determined from the known dispersion curves and the bulk thermal conductivity. For the example of a cube made of solid argon, the variations of the thermal conductivity with the system size obtained using the analytical model and nonequilibrium molecular dynamics (NEMD) are in good agreement. The model is also used to calculate the thermal conductivity of a single graphite sheet and carbon nanotubes as a function of their characteristic lengths. The variations of the thermal conductivity with size are compared with the theoretical predictions for one and two dimensional systems. Good agreement is obtained for the single graphite sheet, but not for carbon nanotubes, which reveals the limitation of the analytical model.
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