Thermal Transport Due to Phonons in Nano-Particulate Media in the Multiple and Dependent Elastic Scattering Regime

Effects of multiple and dependent elastic scattering of phonons due to nano particles on thermal transport due to phonons in nano particulate media are investigated in this paper under various approximations. Multiple scattering means that the scattered wave from one particle is incident on another particle to be scattered again. Dependent scattering means far-field interference of the scattered waves due to phase difference, which is ignored in the independent scattering regime. Results show that multiple scattering primarily affects the velocity and density of states of phonons and dependent scattering primarily affects the mean free path of phonons. Effects of both multiple and dependent scattering increases with increasing volume fraction of the elastic scatterers. Modification of these parameters affects the equilibrium phonon intensity and the thermal conductivity of phonons. Finally a new simplified model called dependent effective field approximation is introduced in this paper. This model accurately captures the effects of both multiple and dependent scattering.