On the role of topological constraints in melts of ring polymers: from structure to dynamics

Ring polymers display several noteworthy properties arising from their non-linear topology, which are absent in linear chain systems. Rings are of great interest in materials science as they offer opportunities for creating new soft materials that harness topological constraints to achieve unconventional features. Moreover, they have significant implications in biology, as they connect to the physical behavior of chromosomes within cell nuclei. In this Thesis, we investigate their physics, in particular from the point of view of topological constraints, by using large-scale computer simulations. First, we focus on melts of non-concatenated and unknotted ring polymers; in this case, theoretical models predict that the permanent topological constraints force the rings to double-fold onto compact and segregated tree-like objects. Yet, recent numerical investigations have shown that rings overlap and thread each other. We show how to reconcile these two pictures and provide new measurements that support the tree-like structure of the rings. At the same time, we provide evidence attesting to the fundamental role of threadings in the dynamics of melts of rings, which are not predicted by current theories. In the second part of the Thesis, inspired by the recent experimental synthesis of DNA-based topological networks, we develop a computational model with which we explore how to fine-tune the topology of self-assembled polymer networks through several experimentally controllable parameters. We also consider the impact of geometric confinement on network synthesis, which we find can be exploited to bias the synthesis towards polymer networks that are softer under mechanical stress. Then, we also show how entanglements in polymer melts arise from the topological interactions in the system. Finally, inspired by recent efforts to account for the active processes shaping both the structure and dynamics of biological filaments, we study how the role of entanglements is influenced in melts of active linear chains. We find that both the statics and dynamics of the chains are affected by the activity of the chains. Significantly, in contrast to passive systems, we do not find any sign of reptation in the chains' relaxation dynamics, which we interpret as the result of intra-chain entanglements becoming less detrimental to the relaxation of active chains.