Generalized two-temperature model for coupled phonons

The design of graphene-based composite with high thermal conductivity requires a comprehensive understanding of phonon coupling in graphene. We extended the two-temperature model to coupled phonons driven by the gradients of temperature fields. These equations identify some new physical quantities, the phonon-phonon coupling factor and length, to characterize the phonon coupling quantitatively. Besides, our proposed coupling length has an obvious dependence on system size. These studies would provide a brand new strategy in enhancing thermal conductivity of graphene-based composites and deepen our understanding of phonon transport in the emerging two-dimensional materials.