We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.

The design and engineering of hybrid materials exhibiting tailored phononic band gaps are fundamentally relevant to innovative material technologies in areas ranging from acoustics to thermo-optic devices. Phononic hybridization gaps, originating from the anti-crossing between local resonant and propagating modes, have attracted particular interest because of their relative robustness to structural disorder and the associated benefit to ‘manufacturability’. Although hybridization gap materials are well known, their economic fabrication and efficient control of the gap frequency have remained elusive because of the limited property variability and expensive fabrication methodologies. Here we report a new strategy to realize hybridization gap materials by harnessing the ‘anisotropic elasticity’ across the particle–polymer interface in densely polymer-tethered colloidal particles. Theoretical and Brillouin scattering analysis confirm both the robustness to disorder and the tunability of the resulting hybridization gap and provide guidelines for the economic synthesis of new materials with deliberately controlled gap position and width frequencies.

We report on the occurrence of absolute elastic band gaps in three-dimensional binary systems made up of steel spheres in polyester, and examine how the width of such gaps depends on the geometry of the structure.

We develop a Green's function multiple-scattering formalism for the calculation of the density of states and the local density of states of the elastic field in periodic and nonperiodic structures consisting of nonoverlapping scatterers in a homogeneous host medium. The formalism is based on concepts and techniques developed in relation to the similar problem of electrons in solids. We apply the method to a specific example which demonstrates the existence of virtual bound states of the elastic field localized about a plane of nonoverlapping steel spheres in polyester. These states are manifested as dips in the transmission spectrum of the monolayer. They develop into narrow frequency bands in a phononic crystal built by a succession of such planes