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Based on first-principles calculations and full iterative solution of thelinearized Boltzmann-Peierls transport equation for phonons within three-phononscattering framework, we characterize the lattice thermal conductivities$\kappa$ of strained and unstrained graphene. We find $\kappa$ converges to5450 W/m-K for infinite unstrained graphene, while $\kappa$ diverges forstrained graphene with increasing system size at room temperature. Thedifferent $\kappa$ behaviors for these systems are further validatedmathematically through phonon lifetime analysis. Flexural acoustic phonons arethe dominant heat carriers in both unstrained and strained graphene within thetemperature considered. Ultralong mean free paths of flexural phononscontribute to finite size effects on $\kappa$ for samples as large as 8 cm atroom temperature. The calculated size-dependent and temperature-dependent$\kappa$ for finite samples agree well with experimental data, demonstratingthe ability of the present approach to predict $\kappa$ of larger graphenesample. Tensile strain hardens the flexural modes and increases theirlifetimes, causing interesting dependence of $\kappa$ on sample size and straindue to the competition between boundary scattering and intrinsic phonon-phononscattering. These findings shed light on the nature of thermal transport intwo-dimensional materials and may guide predicting and engineering $\kappa$ ofgraphene by varying strain and size.

Thermal conductivity of graphene mediated by strain and size