Phonon Conductivity of Nanoparticles Embedded in Dielectric Material

Abstract

A theory of the thermal conductivity has been developed for nanomaterials made by embedding nanoparticles in a host dielectric material. The phonon dispersion relation has been calculated using the transfer matrix method in the long-range approximation, where the phonon wavelength is larger than the size of the nanoparticle. We found that these nanomaterials have two phonon branches known as ω þ k -phonon and ω À k -phonon branches. For both phonon branches, the density of states and the phonon velocity are calculated. The thermal conductivity is evaluated with the Kubo formalism and the Green's function method for both ω þ k -phonon and ω À k -phonon branches. It is also found that the density of states, phonon velocity and thermal conductivity for both phonon branches depend on the size of the nanoparticles, spacing between nanoparticles, and the phonon refractive index of the nanoparticles and the host material. In the long wave approximation, expressions of the phonon conductivity, the density of states and the phonon velocity have very simple forms which can be used by experimentalists to explain their experiments or plan new experiments. We have also applied our theory to explain the experimental thermal conductivity data of silica-resin, alumina-resin, AlN-resin and CaO-polyethylene nanomaterials. A good agreement between theory and experiments is achieved. Our results furthermore illustrate that one can fabricate new types of nanomaterials with high and low thermal conductivity by adjusting the refractive index contrast between nanoparticles and the host material. These are very novel and interesting properties and they can be used to fabricate new types of thermal devices.