Unknotted and unlinked ring polymers in the melt behave very differently than their linear counterparts. The reason behind this difference lies in the closed topology of the rings and on the global topological invariance of the system. In fact, crumpled rings do not fully segregate or expel neighbouring chains from the occupied space, rather, they fold into interpenetrating or “threading” conformations that are akin to interacting lattice animals with long-range (loose) loops. Inter-chain penetrations or threadings have always been assumed to play an important role in solutions of rings, but in general, it is very challenging to provide a quantitative definition of them. As a consequence, the effect of threadings on the dynamics of the rings is even more elusive and for this reason, very poorly understood.
The topological constraints affect the molecular motion and make the ring polymers resemble a glassy material. The glass transition of polymers is of great interest in the industry. Many commercial products of polymers are indeed used in the glassy state. For example, thermoplastics such as polystyrene and poly(methyl methacrylate). Despite its great importance in a lot of daily usages, a detailed theoretical description of the glass transition in polymers is missing. Generally speaking, the topological constraints of entangled polymers make them be excellent glass candidates since the molecular motion can be extremely prohibited, but the mathematics to describe the transition process is inevitably hard.
Here, we studied a novel glass transition in systems made of ring polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We showed that such rings strongly interpenetrate through one another, generating an extensive network of topological constraints that dramatically affect their dynamics. We studied the effect of topological constraints by “randomly pinning” solutions of semi-flexible ring polymers, and probe the dynamic response of the rings for different solution densities and chain lengths.
Davide Michieletto, Negar Nahali, and Angelo Rosa. Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers. PhysRevLett. 119, 197801 (2017)