Structure, thermodynamics and dynamics of confined and supercooled liquids
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Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. In this dissertation, we explore the connections between self-diffusivity, density, available space, and excess entropy in two non-trivial problems in liquid state theory, confined and supercooled liquids. We present exact simulation data for the relationship between self-diffusivity and excess entropy for a wide range of simple of simple fluids (i.e. hard-sphere, Lennard-Jones and square-well) confined to pores with a variety of different sizes and fluid-wall interations. Our main finding is that, at a given temperature, self-diffusivity of the confined fluids collapses onto the bulk behavior when plotted versus excess entropy. In other words, the only information required to "predict" the implications of confinement for the single-particle dynamics is the bulk fluid behavior at a given temperature and the excess entropy of the confined fluid. This should prove practically useful given that the bulk behavior is well known for these fluid systems, and the excess entropy of the confined fluids can be readily estimated from classical density functional theory. We also show that the self-diffusivity of the confined fluids approximately collapses onto the data for the corresponding bulk fluid when plotted versus the average packing fraction (which is based on total, rather than center accessible volume). For continuous interaction potentials such as Lennard-Jones, calculation of effective packing fraction requires knowledge of both the number density of the fluid and a temperature-dependent Boltzmann diameter associated with the repulsive part of the interparticle interactions. We suggest a way to calculate this effective diameter, which to a very good approximation, collapse the temperature- and density-dependent data for the self-diffusivity of the bulk Lennard-Jones fluid onto hard-sphere fluid data plotted versus the fluid's effective packing fraction. Finally, we found that the self-diffusivities of several model systems in their supercooled state also scale exponentially not only with the excess entropy, but also with the two-body contribution to the excess entropy obtained from the pair correlation function of the fluid. The latter observation is particularly interesting because it provides direct evidence of a quantitative link between the dynamics and the average structural order of supercooled liquids. Whether such a connection could indeed be discovered is part of a long-standing question in the study of liquids.