The thermal conductivity of carbon nanotubes is dependent on the temperature and the large phonon mean free paths. On the graph of thermal conductivity vs temperature, the slope of the line at low temperatures can be modelled using the heat capacity, sound velocity, and relaxation time of the tube.

Thermal Conductivity

There seems to be some disagreement into the exact nature of the thermal conductivity of carbon nanotubes, although most agree that thermal conductivity seems to change depending on temperature, and possible also on current and vacancy concentration. In 1999, J. Hone, M. Whitney, and A. Zettle [15] found that the thermal conductivity was temperature dependent, and was almost a linear relationship. They suggested that the conductivity was linear in temperature from 7 K to 25 K. From 25 K to 40 K, the line increases in slope, and it arises monotonically with temperature to above room temperature. They proposed a model to explain the low temperature behavior, which is:
k_zz = C_z²
Where k_zz is the slope of the line on the graph, C is the heat capacity, is the sound velocity (Hone et al. used 1, 2, and 0.8 x 10⁶cm/s), and is the relaxation time, which is approximately 10^-11 s. They also found that the thermal conductivity for a single rope at room temperature could vary between 1800 - 6000 W/m-K.

Also that year, Che, Cagin, and Goddard [6] numerically calculated the thermal conductivity of a (10, 10) nanotube to approach 2980 W/m-K as the current applied to it is increased (see figure at right.) In 2000, Berber, Kwon, and Tomānek [16] determined the thermal conductivity of carbon nanotubes and its dependence on temperature. They confirmed the suggestion of Hone et al. in 1999 by suggesting an unusually high value of 6,600 W/m-k for the thermal conductivity at room temperature. They theorized that these high values would be due to the large phonon mean free paths, which would concur with Hone's model suggested above. Both groups stated that these values for thermal conductivity are comparable to diamond or a layer of graphite. However, Berber et al. suggested that the graphs of the temperature dependence of thermal conductivity looked much less linear than previously proposed by Hone et al. Instead of a near-linear graph with a positive slope, their graph showed a positive slope from low temperatures up to 100K, where it peaks around 37,000 W/m-K. Then, the thermal conductivity drops dramatically down to around 3000 W/m-k when the temperature approaches 400 K.