Multiscale Acoustic Properties of Nanoporous Materials: From Microscopic Dynamics to Mechanics and Wave Propagation

Abstract

Despite significant progress in deciphering the mechanical properties of nanoporous materials, the intimately related phenomenon of acoustic wave propagation in such solids remains largely unexplored at this vanishing length scale (i.e., the molecular scale). Here, we report a multiscale approach to estimate the acoustic properties of zeolites─a prototypical class of nanoporous materials─by combining molecular dynamics simulations and a rigorous upscaling approach using continuum mechanics. Two different zeolites are considered, i.e., RHO and JST zeolites; while they share a simple yet different crystallographic structure, the latter shows auxeticity. First, microscopic simulations are used to calculate the speed of sound from the phonon spectrum as obtained using molecular displacement and velocity data. As an alternate route, macroscopic mechanical constants of the materials are also determined to confirm the inferred acoustic velocities by solving the Kelvin–Christoffel equation. These mechanical constants are obtained either using the strain fluctuations in a simulation performed at equilibrium or from the slope of the stress–strain curve assessed using simple mechanical tests. Second, we propose a nano-to-macro modeling strategy in which the inputs for the continuum-level upscaled model are the specific outcomes from the molecular calculations (e.g., speeds of sound, mechanical parameters). This strategy allows determining the acoustic properties of an empty double porosity material formed by adding an extra scale of porosity to a nanoporous skeleton. Such an extra scale of porosity can represent larger pores, voids in between consolidated nanoporous grains, and/or possible large defects or microfractures in the nanoporous skeleton whose effects can be probed by acoustic waves. This work paves the way for further studies in the field of nanoscale acoustics─especially in the context of applications involving nanoporous materials.