Analytical model of the acoustic response of nanogranular films adhering to a substrate

A one-dimensional (1D) mechanical model for nanogranular films, based on a structural interface, is presented.\r\nThe analytical dispersion relation for the frequency and lifetimes of the acoustics breathing modes\r\nis obtained in terms of the interface layer thickness and porosity. The model is successfully benchmarked\r\nboth against three-dimensional finite element method simulations and experimental photoacoustic data on a\r\nparadigmatic system available from the literature. A simpler 1D model, based on an homogenized interface,\r\nis also presented and its limitations and pitfalls discussed at the light of the more sophisticated pillar model.\r\nThe pillar model captures the relevant physics responsible for acoustic dissipation at a disordered interface.\r\nFurthermore, the present findings furnish to the experimentalist an easy-to-adopt, benchmarked analytical tool\r\nto extract the interface layer physical parameters upon fitting of the acoustic data. The model is scale invariant\r\nand may be deployed, other than the case of granular materials, where a patched interface is involved.