Designing Phononic Band Gaps With Sticky Potentials

Abstract

Spectral gaps in the vibrational modes of disordered solids are key design elements in the synthesis and control of phononic meta-materials that exhibit a plethora of novel elastic and mechanical properties. However, reliably producing these gaps often require a high degree of network specificity through complex control optimization procedures. In this work, we present as an additional tool to the existing repertoire, a numerical scheme that rapidly generates sizeable spectral gaps in absence of any fine tuning of the network structure or elastic parameters. These gaps occur even in disordered polydisperse systems consisting of relatively few particles (N ~ 102 − 103). Our proposed procedure exploits sticky potentials that have recently been shown to suppress the formation of soft modes, thus effectively recovering the linear elastic regime where band structures appear, at much shorter length scales than in conventional models of disordered solids. Our approach is relevant to design and realization of gapped spectra in a variety of physical setups ranging from colloidal suspensions to 3D-printed elastic networks.

Unifying description of the vibrational anomalies of amorphous materials

“…We resort to numerical simulations to investigate vibrational properties and attenuation rate of model amorphous materials, focusing on systems of particles interacting via an LJ-like potential V (r, x c ). Here, x c is a parameter x c setting the extension of the attractive well [37], which vanishes at x c σ, controlling the relaxation dynamics [38] and the mechanical response [37,[39][40][41]. We follow the model of Ref.…”

Unifying Description of the Vibrational Anomalies of Amorphous Materials

“…Here, x c is a parameter setting the extension of the attractive well [39], which vanishes at x c σ. This parameter influences the relaxation dynamics [40] and the mechanical response [36,37,39,41]. We follow the model of Ref.…”