Temperature dependence of the thermal conductivity in chiral carbon nanotubes

Abstract

The thermal conductivity of a chiral carbon nanotube (CCNT) is calculated using a tractable analytical approach. This is based on solving the Boltzmann kinetic equation with energy dispersion relation obtained in the tight binding approximation. The results obtained are numerically analysed. Unusually high electron thermal conductivity χ e z is observed along the tubular axis. The dependence of χ e z against temperature T was plotted for varying Δ z and a given Δ s ( Δ z and Δ s are the overlapping integrals (exchange energy) for the jumps along the tubular axis and the base helix, respectively). It is noted that χ e z shows a peaking behaviour before falling off at higher temperature. As Δ z varies from 0.010 eV to 0.048 eV for a given Δ s = 0.0150 eV , the peak values of χ e z shift from 40 000 W / m K at 100 K to 55 000 W / m K at about 300 K. Interestingly our results at 104 K which is 41 000 W / m K and occurred at Δ z = 0.023 eV compares very well with that reported for a 99.9% isotopically enriched 12C diamond crystal. Another interesting result obtained is the fact that the circumferential electron thermal conductivity χ e c appears to be very small. The ratio of χ e z to χ e c is of the order of 2.