Unified study of viscoelasticity and sound damping in hard and soft amorphous solids

Abstract Amorphous solids are diverse materials that can take on various forms such as structural glasses, granular materials, foams, emulsions, and biological systems. Recent research has made significant progress in understanding non-phonon vibrations universally present in amorphous materials, which have been observed as excess vibrational states over the Debye law, known as boson peak, as well as quasi-localized vibrations. These vibrational states are crucial to explaining material properties of a wide range of amorphous materials, from ``hard" solids like structural glasses to ``soft" solids like foams and emulsions. However, we still lack a theoretical framework that can comprehensively explain them in a unified manner. Here, we propose a unified theory for viscoelasticity and sound damping which are significantly different between hard and soft amorphous solids but are ultimately determined by non-Debye scaling laws of the non-phonon vibrations. Our theory can explain acoustic properties of structural glasses, which have been measured experimentally with light, inelastic X-ray, and neutron scattering techniques, on one hand, and mechanical properties of foams and emulsions, which have been measured by various macrorheology and microrheology techniques, on the other. We thus provide a comprehensive explanation for these experimental measurements of two distinct types of amorphous solids.