Using an exact numerical solution of the phonon Boltzmann equation, we demonstrate a nontrivial evolution with diameter of the intrinsic lattice thermal conductivity, $\kappa$, of a wide range of achiral and chiral single-walled carbon nanotubes (SWCNTs) into that of graphene, ${\kappa }_{graphene}$. We find that $\kappa <{\kappa }_{graphene}$ for all but the smallest diameter SWCNTs and that $\kappa$ exhibits a minimum for modest diameters. This behavior results because the inherent curvature in SWCNTs violates a selection rule in graphene arising from its reflection symmetry, which strongly restricts phonon-phonon scattering in that system.

• Received 18 July 2010

DOI:https://doi.org/10.1103/PhysRevB.82.161402