3. Thermal Conductivity of Particulate Nanocomposites

The modeling of the thermal conductivity of composites made up of metallic and non-metallic micro/nanoparticles embedded in a solid matrix is discussed in detail, at both the dilute and non-dilute limits of particle concentrations. By modifying both the thermal conductivity of the matrix and particles, to take into account the strong scattering of the energy carriers with the surface of the nanoparticles, it is shown that the particle size effect shows up on the thermal conductivity of nanocomposites through: (1) the collision cross-section per unit volume of the particles and, (2) the mean distance that the energy carriers can travel inside the particles. The effect of the electron–phonon interactions within metallic particles shows up through the reduction of the thermal conductivity of these particles with respect to its values obtained under the Fourier law approach. The thermal conductivity of composites with metallic particles depend strongly on (1) the relative size of the particles with respect to the intrinsic coupling length, and (2) the ratio between the electron and phonon thermal conductivities. The obtained results have shown that the size dependence of the composite thermal conductivity appears not only through the interfacial thermal resistance but also by means of the electron–phonon coupling. Furthermore, at the non-dilute limit, the interaction among the particles is taken into account through a crowding factor, which is determined by the effective volume of the particles. The proposed crowding factor model is able to capture accurately the effect of the interactions among the particles for concentrations up to the maximum packing fraction of the particles. The predictions of the obtained analytical models are in good agreement with available experimental and numerical data and they can be applied to guide the design and improve the thermal performance of composite materials.