MD Simulation of Phonon Transport in Single-Walled Carbon Nanotubes

We have simulated the heat conduction characteristics of finite length single walled carbon nanotubes (SWNTs) with the molecular dynamics method [1-3] with Tersoff-Brenner bond order potential. Temperature at each end of a SWNT was controlled by the phantom technique, and the thermal conductivity was calculated with Fourier’s law from the measured temperature gradient and the energy budgets in phantom molecules. Hence, without the use of periodic boundary conditions in the nanotube axis direction, thermal conductivity of finite length nanotube was calculated. The thermal conductivity was diverging [2,3] with the powerlaw characteristics with nanotube length at least up to the 0.4 μm long nanotube for (5, 5). This feature can be compared with the theoretical 1 dimensional heat conduction calculations. The temperature dependency of measured thermal conductivity behaved as 1/T in high temperature range. The limitation of classical molecular dynamics in low temperature calculation was also discussed [3]. As the first step for exploration the basic heat conduction mechanism, phonon density of states and phonon dispersion relations were directly extracted from the molecular dynamics trajectories as in Fig. 1. The phonon dispersion relations and density of states were calculated from each components of displacement vector (r, θ, z) or velocity components (vr, vθ, vz). It can be seen that all 36 distinguishable branches of dispersion relations are reproduced in Fig. 1. The dispersion relations calculated from eigen values and eigen vectors of dynamical matrix made with the force-constant tensor scaled from 2 D graphite [4] is also shown in Fig.