Temperature dependence of thermal conductivity in hybrid nanodispersions

Abstract

We derive first a formula for the overall heat conductivity for dispersions of cuboid nanowires and recall similar formulas derived previously in Behrang et al., Appl. Phys. Lett., 2014, 104, 233111, 104, 063106 and Behrang et al., J. Appl. Phys., 2013, 114, 014305, by using the same method, for several other morphologies (dispersions of nano-size spheres, nano-size spheres of different sizes, nano-wires, rectangular cuboid nano-wires, and nano-spheres and nano-wires). The temperature dependence of the microscopic quantities (like the phonon mean free path) entering the formulas is known from the phonon kinetic theory. The formulas thus provide a setting for investigating the temperature dependence of the overall heat conductivity of dispersions. In general, we see that the interface that is present in hybrid nanodispersions influences significantly the thermal conductivity only in lower temperatures. This then means that the possible benefit of hybrid nanodispersions in fabricating electronic devices diminishes with increasing the temperature.