Abstract
The thermal conductivity of an individual single-walled carbon nanotube is calculated with the analysis of all possible combining and splitting umklapp scattering processes based on complete phonon dispersion relations. The relaxation rate for the transverse acoustic phonons that undergo the combination umpklapp process is found to increase with many singularities as temperature rises. The calculated mean free path suggests that the combining (splitting) umklapp process is predominant in the low (high) frequency regime. The phonons with a very high frequency contribute little to thermal conduction due to the splitting umklapp process. The calculated thermal conductivity for (10,10) carbon nanotube is $474\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕\mathrm{m}\phantom{\rule{0.2em}{0ex}}\mathrm{K}$ at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.
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