Correlation Between Glass Transition And Vibrational And Structural Properties Of Amorphous Solids

The research on the glass transition and jamming transition and their correlations has become a hot and important topic in soft condensed matter physics recently. The progress of the study is essential to the development of the theory of noncrystalline solids. The glass transition occurs when the relaxation time of supercooled liquids ex-ceeds the measurable time window, while the jamming transition happens when a pack-ing of particles interacting via repulsions gains rigidity and turns into an amorphous solid upon compression. Many efforts have been made to improve our understanding of both transitions. However, their nature still remains elusive.In this thesis, we are focused on several important problems of the jamming transi-tion and glass transition. Importantly, we propose a new perspective to study the glass transition.In the study of the jamming transition, we achieve two important results by work-ing on the critical scalings in thermal systems with repulsions near the zero-temperature jamming transition. First, the strong coupling between the isostaticity and the plateau in the density of vibrational states observed in marginally jammed solids at zero tempera-ture near the jamming transition is still valid in low-temperature systems. Second, ther-mal systems with a pressure higher than p, exhibit properties of the zero-temperature jammed solids, where pj is the crossover pressure at which the first peak of the pair correlation function reaches the maximum height at fixed temperature. Interestingly, we observe scaling collapse of multiple thermodynamic and structural quantities by ap-plying the scaling relations at pj and isostaticity, which reveals the criticality of the zero-temperature jamming transition.In the study of the glass transition, our major achievement is the proposal of under-standing the glass transition from the perspective of the structural and vibrational prop-erties of the zero-temperature glasses. We have carried out two projects to validate our proposal. First, we find that the glass transition temperature, dynamical heterogeneity, and glass fragility of core-softened colloids all exhibit non-monotonic pressure depen-dence at high pressures. Our further analysis indicates that the non-monotonic behaviors can be predicted from the structural and vibrational properties of the zero-temperature glasses, such as the structural order and its spatial fluctuation, the quasilocalization of low-frequency modes, and energy barrier height along quasi-localized modes. Second, we have explained the nonperturbative effects of attraction on the dynamics of super-cooled liquids, from the structural and vibrational properties of the zero-temperature glasses. More importantly, we have successfully predicted the density dependence of the glass transition temperature purely from the structural and vibrational quantities of the zero-temperature glasses.