Molecular Dynamics of Heat Conduction through Carbon Nanotube

The heat conduction along a single walled carbon nanotube (SWNT)[1-4] was simulated by the molecular dynamics method with the Tersoff-Brenner bond order potential [5,6]. One of the purposes of this study is to clarify the thermal conductivity of carbon nanotubes, which is speculated to be higher than any other material along the cylindrical axis. Very recently, measurements of thermal conductivity of a 5 μm thick deposited “mat” of SWNTs were reported for randomly oriented [7] or magnetically aligned [8] conditions. Comparing with the temperature dependence of electrical conductance in the same condition, it was concluded that the contribution of electrons to the thermal conductivity is negligible in all temperature range [7,8]. Quickly following those experiments, several preliminary molecular dynamics simulations [9-11] showed very high thermal conductivity such as 6600 W/mK at 300 K [9]. However, the estimated values of thermal conductivity were widely different from one another. Another purpose of this study is the preliminary connection of molecular dynamics techniques to the solid-state heat conduction usually discussed as “phonon transport” in solid physics. In principle, the molecular dynamics simulation should be used to obtain information for phonon transport dynamics [12,13] such as phonon dispersion relation, group velocity, mean free path, boundary scattering rate and the rate of phonon-phonon scattering (Umklapp process). It is also anticipated that by developing the phonon concept to more general form in order to understand the thermal boundary resistance even in the liquid-solid interface [14]. Three SWNT models with different chiralities (5,5), (8,1), and (10,10) were chosen. While (10,10) is the well-known armchair structure [3], (5,5) and (8,1) have the almost similar diameters as C60 and the inexpensive and huge scale production of SWNTs with this diameter is anticipated [15] with the new generation technique using high-pressure and high-temperature CO gas [16]. By applying the phantom heat bath model to each end of a SWNT, the temperature difference was applied. Here, no periodic boundary condition was applied to minimize the “boundary scattering of phonons.” It is often discussed [10] that the cell length of periodic boundary condition should be larger than the “mean free path” of phonon, which is argued to be order of 1 μm [7] though it is really arbitral value depending on the definition. The typical length of the SWNTs were selected to be about 125 Å but longer nanotube up to about 500 Å were calculated for (5,5) tube. With our configuration, thermal conductivity was calculated from the measured temperature gradient and the heat flux obtained by the integration of the additional force by the phantom molecules. The preliminary result showed that the thermal conductivity was about 200 ∼ 300 W/mK and the dependence on the length of the tube was relatively small. The thermal conductivity value for (8,1) chiral tube was measured to be a little smaller than armchair system. The temperature jump near the heating and cooling region was explained by assuming the thermal boundary resistance of about 0.15 nKm/W due to the miss-match of the phantom technique to the structured phonon density distribution. The phonon density of states were measured as the power spectra of velocity fluctuations and compared with the experimental Raman spectra. Finally, the photon dispersion relations were observed as the time-space 2 dimensional Fourier transform of the position of each molecule.