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