Self-consistent theory and structural dynamics of equilibrium aperiodic solids



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Essential microscopic aspects of activated transport in liquids, which precedes the glass transition, have evaded explanation for decades. These poorly understood aspects include: the molecular underpinning of the excess, configurational entropy; the transition state configurations for the activated transport; the chemical origin of the fragile vs. strong liquid behavior; and many others. This dissertation puts forth a radically novel way to address these open questions, in which liquids near their glass transition are viewed as structurally degenerate assemblies of strongly interacting, local sources of frozen-in stress. The thermodynamics and activated barriers for rearrangement of this stress field have been mapped onto a Heisenberg model with six-dimensional spins. A meanfield analysis of the spin model has shown glasses can be viewed as frozen-in patterns of shear stress and/or uniform compression/dilation, the two extremes corresponding to the strong and fragile behaviors. A self-consistent elasticity theory of aperiodic, metastable solids emerges in the present analysis; it supersedes the traditional elasticity theory, which fails to self-consistently account for the structural degeneracy stemming from the inherent mismatch between cohesive forces and steric repulsion. The observable elastic constants self-consistently emerge in theory similarly to how the dielectric susceptibility is determined by the properties of molecular dipoles. First simulations of the spin model have been carried out. In addition to direct observations of transition states for the activated transport, several key features of the glass transition are yielded by the spin model, including a strongly non-exponential, non-Arrhenius character of the relaxations and its correlation with the Poisson ratio of the substance.



Amorphous solids, Glass, Supercooled liquids, Structural entropy, Eshelby tensor, Inhomogeneous inhomogeneity, Configurational entropy, Temperature exchange Monte Carlo, Activated transport, Cavity method, Polar liquid