# Calculation of thermal conductivity of ideal and defective CNT

A reverse nonequilibrium molecular dynamics method [1] was implemented in our MD-kMC code in order to calculate temperature gradient along the simulated sample at fixed heat flux. Thermal conductivity is then easily calculated using differential form of Fourier’s law of thermal conduction.

Thermal conductivity of the single-walled carbon nanotubes (5,5) with different length in the range 50-500 nm was calculated using Brenner interatomic potential in its simplified form [2] and compared with the results of work [3]. When CNT length (L) is much less than phonon mean free path (about 750 nm at 300 K) CNT thermal conductance does not depend on tube length and thermal conductivity is proportional to L (ballistic regime). At large L thermal conductivity does not depend on L (diffusive regime). Obtained in simulations dependence of thermal conductivity on the tube length indicates the gradual transition from strongly ballistic to diffusive-ballistic regime. Calculations of thermal conductivity of longer structures are hampered by the demand of huge amount of computational resources and time and are in progress now.

Dependence of thermal conductivity on vacancy concentration for CNT with fixed length was calculated using NEMD method. This problem was already addressed in the literature [4] so we just need to compare our results with those obtained earlier. Thermal conductivity of 10 nm CNT (8,0) with randomly distributed vacancies with concentration in the range 0-2% was calculated. It was found that thermal conductivity decreases about 4 times for 1% vacancy concentration due to the acoustic phonon scattering. Comparison of our results with results of work [4] revealed that in spite of differences in calculation method (direct NEMD method in work of Kondo) the absolute values of thermal conductivity are very close.

1. F. Muller-Plathe, J. Chem. Phys. 106 (1997) 6082-6085

2. Y. Yamaguchi, S. Maruyama, Chem. Phys. Lett. 286 (1998) 336-342

3. J. Shiomi, S. Maruyama, JJAP 47, 4 (2008) 2005-2009

4. N. Kondo, T. Yamamoto, K. Watanabe, e-J. Suf. Sci. Nanotech. Vol. 4 (2006) 239-243