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

TL;DR

This paper introduces an analytical 1D model for the acoustic response of nanogranular films on substrates, validated against simulations and experiments, providing a practical tool for interface characterization.

Contribution

It presents a novel 1D pillar model capturing interface physics and compares it with a homogenized approach, enhancing understanding of acoustic dissipation in nanogranular films.

Findings

The model accurately predicts acoustic frequencies and lifetimes.

Validation against FEM simulations and experimental data confirms its reliability.

The approach offers a practical method for extracting interface parameters.

Abstract

A 1D mechanical model for nanogranular films, based on a structural interface, is here 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 3D 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.