Abstract
The frequency domain perfectly matched layer (FDPML) approach is used to study phonon transport in a series of large 2D domains with randomly embedded nanoparticles over a wide range of nanoparticle loadings and wavelengths. The effect of nanoparticle packing density on the mean free path and localization length is characterized. We observe that, in the Mie scattering regime, the independent scattering approximation is valid up to volume fractions exceeding 10% and often higher depending on scattering parameter, indicating that the mean free path can usually be calculated much less expensively using the number density and the scattering cross section of a single scatterer. We also study localization lengths and their dependence on particle loading. For heavy nanoparticles embedded in a lighter material, using the FDPML approach, we only observe localization at volume fractions >30% and only for short wavelength modes where vibrational frequencies exceed those available in the embedded nanoparticles. Using modal analysis, we show that localization in nanoparticle laden materials is primarily due to energetic confinement rather than Anderson localization. We then show that, by using light particles in a heavy matrix, the fraction of confined modes can be substantially increased.
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