The Effect of Nanoparticles on the Thermal Conductivity of Crystalline Thin Films at Low Temperatures

This study is concerned with the prediction of the effective thermal conductivity of nanocomposite thin films consisting of nanoparticles randomly distributed in a solid matrix. Crystalline sodium chloride with embedded monodisperse silver nanoparticles is investigated as a case study for thin films where phonons are the main heat carriers. To the best of our knowledge, the equation for phonon radiative transfer is solved for the first time with an exact scattering transport cross-section of the nanoparticles as a function of frequency which was obtained from the literature. The one-dimensional equation for phonon radiative transfer based on the isotropic scaling approximation is solved on a spectral basis using the discrete ordinates method to predict the temperature profile and the heat flux across the nanocomposite thin films. The thermal conductivity is retrieved at temperatures where the effects of Umklapp and Normal processes can be neglected and scattering by the particles on phonon transport dominates. The method of solution and closure laws were validated with experimental data of thermal conductivity for bulk samples at 2.53, 5.94, and 10.56 K. The effects of the film thickness (1 μm to 2.5 cm), nanoparticle diameter (5 nm to 100 nm) and volume fraction (0.0001 to 0.2) on the thermal conductivity of the nanocomposite thin film are investigated. The results indicate that the thermal conductivity decreases with decreasing particle radius as well as with increasing particle concentration. Finally, a dimensionless analysis revealed a power law relationship between the dimensionless thermal conductivity and a dimensionless length of the order of the acoustic thickness of the medium. These results can be used to design nanocomposite thin films for various low temperature thermal applications by choosing optimal nanoparticle radius and volume fraction, and film thickness.