Diffusion behaviors of energy and momentum for 1D single-walled carbon nanotubes

Abstract

The single-walled carbon nanotube (CNT) is a quasi-1D material with ultra high thermal conductivity. It is known that the heat conduction is closely related with the energy diffusion and the information of heat conduction can be obtained by examining the energy diffusion behavior. The correlated energy distribution CE(i,t) calculated in diffusion process gives the whole spatial distribution of energy spreading at every correlation time which is much better than the traditional heat conduction method where only a number of thermal conductivity is provided. In previous study the anomalous super-diffusion of energy has been reported for CNT via a non-equilibrium diffusion method. Here we apply the more sophisticate equilibrium diffusion method to investigate the energy diffusion behavior in CNT with much longer length up to m with much higher accuracy. At room temperature, the super-diffusion of energy described by the mean square displacement of energy is found to be not far away from ballistic diffusion which is consistent with the experimentally measured ultra high thermal conductivity for CNT. With the equilibrium diffusion method, the diffusion of momentum has also been performed for CNT and ballistic diffusion is found which can be viewed as a support for anomalous super energy diffusion. The momentum diffusion can also give accurate information of sound velocity which is determined as m s−1 at room temperature. In particular, the very weak temperature coefficient of sound velocity can be obtained as m (. The normalized temperature coefficient of sound velocity can be related with the normalized temperature coefficient of Raman frequency shifts experimentally measured as . The obtained value via the momentum diffusion method is consistent with the experimental measurements.