Theories of slow dynamics: from glassy colloidal suspensions to entangled macromolecular liquids

Motivated by the intriguing slowing down of dynamics in glassy and polymeric fluids, microscopic theories for the dynamical behavior of these systems are explored. Of particular interest is the relative importance of equilibrium structure and topological constraints on system dynamics, and theories studying each effect are constructed and applied in this dissertation. The first part of this thesis treats suspensions of hard-sphere colloids --- the theorist's idealization of a dense liquid --- by connecting two-point equilibrium structure with the emergence of glassy dynamics. An earlier single-particle theory is qualitatively extended to study the dynamically correlated motion of two tagged particles in the fluid. A theory for Gaussian density fluctuations is constructed at the level of two tagged particles in a fluid of identical particles, and this theory is then extended to study highly non-Gaussian activated ``hopping'' events by modeling motion on a dynamic free energy surface. By coarse graining over the initial separation between the tagged particles many aspects of ``dynamic heterogeneity,'' a set of phenomena accompanying the glass transition, can be understood. Connections with diverse alternative theories for describing the glass transition are also made. The second part of this thesis studies polymeric fluids from a quite different perspective. By modeling macromolecules of various geometries as infinitely thin, zero-excluded-volume objects (rods, crosses, random walks) all equilibrium structural information is removed from the problem. Instead, system dynamics are determined by exactly including topological constraints, i.e., by rigorously enforcing macromolecular uncrossability at the two-body level. This advance permits a wide variety of phenomena to be studied. The initial focus is on the equilibrium dynamics of cross- and rod-shaped macromolecules, and the theory is compared with both simulation and experimental results on synthetic and biological polymers. The theory is generalized to treat flexible polymers as random walks of coarse-grained primitive path steps. The non-equilibrium behavior of rods under nonlinear rheological conditions is then studied in depth. We first posit a generalized Maxwell model for the constitutive equations controlling relaxation after an instantaneous step strain, the so-called ``fundamental deformation.'' This model is then generalized to a generic, time-dependent shear deformation, and the consequences for continuous, constant-rate shear flows are studied. Finally, we exploit our ability to describe polymer interactions microscopically to compute the entanglement shear modulus directly from intermolecular contributions; this represents a potentially radical departure from the standard theoretical model of how stresses are stored in dense polymeric media