Theoretical investigations of the role of excluded volume, topological constraints, and attractive forces in the slow dynamics of soft matter systems

Soft matter physics has been continuously growing over the last 50 years due to its implications in physics, biology, chemistry, and materials science. One interest in the field arises from the viscoelastic nature of such materials; depending on the length and time scales studied the material can be more akin to a liquid (viscous) or a solid (elastic). Viscoelasticity is a seemingly generic phenomena, observed in many systems such as atomic, molecular, colloidal, and polymeric liquids, glasses and gels. Broadly there are three common microscopic mechanisms that describe such behavior: (i) excluded volume constraints and caging, (ii) topological or connectivity constraints, and (iii) attractive forces and physical bonding. The goal of this thesis is to develop microscopic force based theories to understand the slow dynamics of various soft matter systems. The starting point for all such theories is the generalized Langevin equation, which is characterized by the force-force time correlation function. By developing a self-consistent theory for the force correlations in terms of the packing structure of the fluid we are able to predict a dramatic slowing down of collective dynamics and the possible transition to activated "hopping" motions. With these guiding principles, we studied the role of excluded volume, topology and attractions in atomic, molecular, colloidal, and polymeric liquids. This thesis can be roughly divided into two parts: (i) studies of excluded volume and attractive forces in spherical particle liquids, and (ii) the role of connectivity and topological constraints in polymeric liquids. The former studies are primarily discussed in Chapters 3 and 4, where we answer questions about the interplay of repulsive and attractive forces in the single and two particle slow dynamics. The latter studies are discussed in Chapters 5 - 8, which discuss the emergence of and consequences of entanglements in dense polymer liquids, melts, and nanocomposites. In all cases repeated comparisons with recent simulations and experiments are in good agreement with the theoretical predictions. These results pave the way for future statistical mechanical developments