Ring Polymers in Entangled Solutions: Complex Structure and Heterogeneous Dynamics

Understanding how topological constraints affect the structure and dynamics of polymers in solution is a historical challenge in polymer physics: in particular, it still represents the goal of all modern studies aiming at understanding the behavior of concentrated solutions of ring polymers. Ring polymers represent in fact some of the most puzzling objects in polymer physics: at odds with their linear counterparts they do not swell assuming ideal conformations, but they fold into compact, space-filling conformations. At the same time though, rings maintain a considerable degree of mutual interpenetration in the form of \threading", which is at the basis of their surprisingly rich mechanical and rheological behavior. In this Thesis, I investigate general and universal properties of ring polymers emerging in concentrated solutions. Notably, I discuss the scaling behavior of structural and dynamical quantities of single rings being surrounded by neighboring polymers exerting volume interactions on each other. Then, I consider important connection between \threadings" in close-by rings and their consequent slowing down. For the systems under analysis, I employ extensive Molecular Dynamics computer simulations in order to provide a detailed description concerning the equilibrium and dynamical properties of ring polymers in solutions of different densities. For systematic comparison, we also discuss the same properties for their linear counterparts.