Minimum thermal conductivity considerations in aerogel thin films

We demonstrate the use time domain thermoreflectance (TDTR) to measure the thermal conductivity of the solid silica network of aerogel thin-films. TDTR presents a unique experimental capability for measuring the thermal conductivity of porous media due to the nanosecond time domain aspect of the measurement. In short, TDTR is capable of explicitly measuring the change in temperature with time of the solid portion of porous media independently from the pores or effective media. This makes TDTR ideal for determining the thermal transport through the solid network of the aerogel film. We measure the thermal conductivity of the solid silica networks of an aerogel film that is 10% solid, and the thermal conductivity of the same type of film that has been calcined to remove the terminating methyl groups. We find that for similar densities, the thermal conductivity through the silica in the aerogel thin films is similar to that of bulk aerogels. We theoretically describe the thermal transport in the aerogel films with a modified minimum limit to thermal conductivity that accounts for porosity through a reduction in phonon velocity. Our porous minimum limit agrees well with a wide range of experimental data in addition to sound agreement with differential effective medium theory. This porous minimum limit therefore demonstrates an approach to predict the thermal conductivity of porous disordered materials with no a priori knowledge of the corresponding bulk phase, unlike differential effective medium theory.