Effect of Pore Size on Reduction of the Lattice Thermal Conductivity of Nano to Micro-Scale Porous Materials

We studied the effect of thermal phonon scattering on reduction of the lattice thermal conductivity (LTC) of porous materials with spherical pores and inclusions of different diameter from nano to micro-scales. By use of a model based on the gamma distribution of pore sizes we calculated effective phonon mean free paths for scattering at randomly distributed pore boundaries and obtained a general relationship by use of the "gray medium" approximation for the LTC of the material. We then determined the LTC of several phases in the presence of inclusions of different size scales embedded within a single host material and obtained a simple analytical expression for the effective LTC of a three-phase composite with nano and micro-scale randomly distributed inclusions. We show that the presence of hollow pores and (or) inclusions with all-scale hierarchical disorder leads to a substantial reduction in the LTC of the composite. Results from our model are compared with experimental data.