Statistical geometry, ordering, and association: Theoretical investigations of the liquid and glassy states

This dissertation describes an investigation of the structure and thermodynamics of model amorphous materials. It comprises two related components. The first focuses on the development of theoretical and computational tools for the structural characterization of disordered systems. The second addresses the thermodynamic implications of the local (hydrogen-bond-induced) ordering of molecules in liquid water.; Disordered packings of equilibrium hard-sphere fluids are studied both analytically and via computer simulation. Two levels of structure are examined: the interparticle correlations and the void geometry. The simulation results demonstrate that the interparticle correlations exhibit a structural precursor to the freezing transition. While no precursor to freezing is indicated by the void geometry, the algorithm introduced for its measurement is shown to provide robust thermodynamic and structural information for conditions where standard methods yield inadequate statistics. A theoretical framework which relates the interparticle correlations, the void statistics, and the density fluctuations in many-body systems is also introduced. The relationships are resolved analytically for two limiting cases: overlapping spheres and the hard-rod fluid.; To quantify the disorder present in simple liquids and solids, a new set of scalar order parameters is presented. These measures facilitate the introduction of a new concept, the ordering phase diagram, which illustrates the placement in order-parameter space of both equilibrium phases and history-dependent non-equilibrium structures. This diagram, which is constructed for the hard-sphere system via simulation, provides insights into the types of disorder exhibited by condensed phases and the nature of the random close-packed state.; Finally, a microscopic model for water is introduced that accounts for the fact that hydrogen bonds are directional and favor the formation of locally open structures. Its thermodynamic behavior is analyzed by a novel perturbation theory that is capable of incorporating many-body interactions. The resulting equation of state reproduces the distinctive thermodynamic behavior of liquid water, including the phase behaviors that can describe supercooled water's anomalies. This theory is extended to describe the thermodynamics of water confined between two planar hydrophobic surfaces. The predictions yield insights into the phase behavior of confined water and the possibility of long-range interactions between hydrophobic entities.