Lattice thermal conductivity and phonon properties of polycrystalline graphene

Using spectral energy density method, we predict the phonon scattering mean lifetimes of polycrystalline graphene (PC-G) having polycrystallinity only along $\rm{x}$-axis with seven different misorientation (tilt) angles at room temperature. Contrary to other studies on PC-G samples, our results indicate strong dependence of the thermal conductivity (TC) on the tilt angles. We also show that the square of the group velocity components along $\rm{x}$ and $\rm{y}$ axes and the phonon lifetimes are uncorrelated and the phonon density of states are almost the same for all samples with different tilt angles. Further, a distribution of the group velocity component along $\rm{x}$ or $\rm{y}$ axis as function of normal frequency is found to be exponentially decaying whereas that of phonon lifetime showed piecewise constant function behavior with respect to frequency. We provide parameters for these distribution functions and suggest another measure of the TC based on these distributions. Finally, we perform a size-dependent analysis for two tilt angles, $21.78^\circ$ and $32.20^\circ$, and find that bulk TC components decrease by around 34% to 62% in comparison to the bulk TC values of the pristine graphene. Our analysis reveals intriguing insights into the interplay between grain orientation, phonon scattering and thermal conductivity in graphene.