Thermal Transport Due to Phonons in Random Nano-particulate Media in the Multiple and Dependent (Correlated) Elastic Scattering Regime

Effects of multiple and dependent or correlated elastic scattering of phonons due to nanoparticles on thermal transport in random nano-particulate media (random phononic crystals) 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. Multiple and dependent scattering effects become important when the interparticle distance is comparable to the wavelength of phonons. 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 nanoparticles. Modification of these parameters affects the equilibrium phonon intensity and the thermal conductivity of phonons.