Diameter dependence of carbon nanotube thermal conductivity and extension to the graphene limit

Using an exact numerical solution of the phonon Boltzmann equation, we demonstrate a nontrivial evolution with diameter of the intrinsic lattice thermal conductivity, κ, of a wide range of achiral and chiral single-walled carbon nanotubes (SWCNTs) into that of graphene, κ_graphene. We find that κ< κ_graphene for all but the smallest diameter SWCNTs and that κ 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.