The thermal conductivity of single-walled and multi-walled carbon nanotubes has been investigated as a function of the tube length L, temperature and chiral index using non-equilibrium molecular dynamics simulations. In the ballistic-diffusive regime the thermal conductivity follows a L(alpha) law. The exponent alpha is insensitive to the diameter of the carbon nanotube; alpha approximately 0.77 has been derived for short carbon nanotubes at room temperature. The temperature dependence of the thermal conductivity shows a peak before falling at higher temperatures (>500 K). The phenomenon of thermal rectification in nanotubes has been investigated by gradually changing the atomic mass in the tube-axial direction as well as by loading extra masses on the terminal sites of the tube. A higher thermal conductivity occurs when heat flows from the low-mass to the high-mass region.

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The thermal rectification in nanotubes with a mass gradient is studied by reverse non-equilibrium molecular dynamics simulations. We predict a preferred heat flow from light to heavy atoms which differs from the preferential direction in one-dimensional monoatomic systems. This behavior of nanotubes is explained by anharmonicities caused by transverse motions which are stronger at the low-mass end. The present simulations show an enhanced rectification with increasing tube length, diameter and mass gradient. Implications of the present findings for applied topics are mentioned concisely.

The thermal conductivity of composites of carbon nanotubes and polyamide-6,6 has been investigated using reverse non-equilibrium molecular dynamics simulations in a full atomistic resolution. It is found, in line with experiments, that the composites have thermal conductivities, which are only moderately larger than that of pure polyamide. The composite conductivities are orders of magnitude less than what would be expected from naïve additivity arguments. This means that the intrinsic thermal conductivities of isolated nanotubes, which exceed the best-conducting metals, cannot be harnessed for heat transport, when the nanotubes are embedded in a polymer matrix. The main reason is the high interfacial thermal resistance between the nanotubes and the polymer, which was calculated in addition to the total composite thermal conductivity as well as that of the subsystem. It hinders heat to be transferred from the slow-conducting polymer into the fast-conducting nanotubes and back into the polymer. This interpretation is in line with the majority of recent simulation works. An alternative explanation, namely, the damping of the long-wavelength phonons in nanotubes by the polymer matrix is not supported by the present calculations. These modes provide most of the polymers heat conduction. An additional minor effect is caused by the anisotropic structure of the polymer phase induced by the nearby nanotube surfaces. The thermal conductivity of the polymer matrix increases slightly in the direction parallel to the nanotubes, whereas it decreases perpendicular to it.