Acousticlike excitations in topologically disordered media at mesocale/nanoscale present anomalous features with respect to the Debye's theory. The so-called Rayleigh scattering manifests in a strong increase of the attenuation of the acousticlike excitations and a softening of the phase velocity with respect to its continuum limit value. Mean field models developed in the random media theory framework can successfully predict the occurrence, at the proper length scale, of Rayleigh scattering. The overall attenuation in the Rayleigh region is, however, underestimated. In the framework of random media theory we developed an analytical model, which permits a quantitative description of the acousticlike excitations in topological glasses in the whole first pseudo-Brillouin zone. The underestimation of the Rayleigh scattering is avoided and, importantly, the model allows to account also for the polarization properties of the acousticlike excitations. In a three-dimensional medium an acoustic wave is characterized by its phase velocity, intensity, and polarization. Rayleigh scattering emphasizes how the topological disorder affects the first two properties. The topological disorder is, however, expected to influence also the third one. In common with the Rayleigh scattering, hallmarks possibly related to the mixing of polarizations have been traced in different classes of amorphous solids at nanoscale. The quantitative theoretical approach developed permits to demonstrate how the mixing of polarizations generates a distinctive feature in the dynamic structure factor of amorphous solids. The modeling capability of the proposed mean field theory is tested on glassy 1-octyl-3-methylimidazolium chloride, whose spatial distribution of the elastic moduli is well assessed and can be experimentally characterized. Contrast between theoretical and experimental features for the selected glass reveals an excellent agreement. The mean field approach we present retains a certain degree of generality and can be possibly extended to different stochastic media or different wave fields.

• Received 31 May 2017
• Revised 15 November 2020
• Accepted 17 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.214309