Relation Between Liquid-Solid Transition And Characteristic Property And Vibrational Modes Of Amorphous Material

Amorphous materials are materials without long-range order, such as glasses, san-dle piles, etc. Glass transition and jamming transition are typical liquid-solid transitions of amorphous materials. During the transition, the system does not show significant structural changes, but it turns into a rigid solid. The control parameters of the tran-sition include the temperature, density, and stress. Various transitions controlled by these parameters have been unified into the same framework of the jamming phase di-agram. Amorphous solids possess special mechanical, thermodynamic, and electronic properties, and are thus widely used in our everyday life and industry. However, due to their complexity, we have limited knowledge about their liquid-solid transition and the underlying physical mechanisms. In this thesis, we study the properties of amor-phous solids from the normal modes of vibration and the effects of anisotropy on the liquid-solid transitions of amorphous materials.At zero temperature, because particles are not in contact, the system is not rigid until it undergoes the jamming transition at the random close packing density. When the temperature is very low, the glass transition happens at a volume fraction lower than the random close packing, so at nonzero temperatures, systems sitting between the glass transition and jamming transition (in the zero temperature limit, it is the regime of hard sphere glasses) are rigid. We obtain the dispersion relation and sound attenuation coeffcient from dynamical structure factors, from which we calculate the Ioffe-Regel frequency. Above the Ioffe-Regel frequency, the phonon mean free path is smaller than its wavelength, so that the phonon is ill defined. In the zero temperature limit, a system undergoes the glass transition and jamming-like transition in sequence un-der compression. The transverse and longitudinal Ioffe-Regel frequencies vanish at the jamming-like transition and glass transition, respectively. Therefore, glasses above the jamming-like transition (denoted as Glass TL) can carry both well-defined transverse and longitudinal phonons, while those between the two transitions (denoted as Glass L) can only carry well-defined longitudinal phonons. Furthermore, we find that the ratio of the shear modulus to the bulk modulus decreases with increasing volume fraction until reaching the minimum at the jamming-like transition. Such a volume fraction de-pendence opposite to the soft sphere glasses above the jamming transition is a direct reflection of the special nature of hard-sphere glasses.In the zero temperature limit, we determine the transitional and orientational glass transition volume fractions of ellipsoidal systems from fitting the diffusion coefficient to the mode-coupling formula. There is a crossover aspect ratio, above which the orien- tational glass transition happens at a lower volume fraction than the translational one. When the aspect ratio is lower than the crossover, the orientational glass transition hap-pens at a higher volume fraction than the translational one. The translational glass tran-sition volume fraction varies non-monotonically as a function of the aspect ratio.