In this work, we perform molecular dynamics (MD) simulations together with phonon spectral analysis to predict the thermal conductivity of both suspended and supported graphene. We quantitatively address the relative importance of different types of phonon in thermal transport and explain why thermal conductivity is significantly reduced in supported graphene compared to that in suspended graphene. Within the framework of equilibrium MD, we perform spectral energy density analysis to obtain the phonon mean free path of each individual phonon mode. The contribution of each mode to thermal conductivity is then calculated and summed to obtain the lattice thermal conductivity in the temperature range 300–650 K. Our predicted values and temperature dependence for both suspended and supported graphene agree with experimental data well. In contrast to prior studies, our results suggest that the contribution from out-of-plane acoustic (ZA) branch to thermal conductivity is around 25–30% in suspended graphene at room temperature. The thermal conductivity of supported graphene is predicted to be largely reduced, which is consistent with experimental observations. Such reduction is shown to be due to stronger scattering of all phonon modes rather than only the ZA mode in the presence of the substrate.

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