Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers

Abstract

Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and, yet, they display a large number of topological constraints. To understand their role, here we systematically probe the response of solutions of rings at various densities to "random pinning" perturbations. We show that these perturbations trigger non-Gaussian and heterogeneous dynamics, eventually leading to nonergodic and glassy behavior. We then derive universal scaling relations for the values of solution density and polymer length marking the onset of vitrification in unperturbed solutions. Finally, we directly connect the heterogeneous dynamics of the rings with their spatial organization and mutual interpenetration. Our results suggest that deviations from the typical behavior observed in systems of linear polymers may originate from architecture-specific (threading) topological constraints.

Active topological glass

“…Tiny displacements and their non-Gaussian distribution characterize a local constraint (cage) exploration which is another hallmark of glassy systems 45 . Interestingly, for long lag times the tails of the distribution are just simply exponential as in the equilibrium topological glass induced by pinning perturbations 5 . We attribute these 'fat' tails to a constraint release and a short relocation of the hot segments of an individual chain (Supplementary Movie 1).…”

“…To describe the dynamics, we track in time the mean squared displacements of the rings centers of mass hg 3 ðt; t 0 Þi (see Eq. (5) in Methods and note that the mean is taken over the rings only because the dynamics is not stationary in general). Figure 2b The mean radius of gyration hR g i obtained as an average over all rings at a given time t after the onset of activity (Eq.…”

“…Such a topological glass has been conjectured for the system of long, unknotted, and nonconcatenated polymer rings in dense equilibrium solutions 4,5 . The rings cannot cross each other, but are known to thread-one ring piercing through an eye of another ring, which temporarily topologically constraints the motion of the two rings.…”

“…Then, for sufficiently long rings and high density a glassy behavior can be extrapolated to f ! 0 4,5 . Unfortunately, the conjectured critical length, 90 entanglement lengths, of unpinned rings is currently beyond the reach of experiments and, although the pinning deepens our theoretical understanding of the glass transition [7][8][9] , creating it experimentally to drive the topological glass transition would be challenging.…”

Topological free volume and quasi-glassy dynamics in the melt of ring polymers

“…The main source of difficulty arises from the inevitable constraint that a topological state on inter-ring concatenation and intra-ring knotting has to be rigorously conserved at any later stage unless the bond breakage occurs. Recent experiments and simulations have raised several puzzles in dynamics of dense solution of non-concatenated rings [3][4][5], hinting some analogy to the glass transition [6,7]. The conceived state, dubbed as topological glass, however seems to be very different from ordinary glass in that the large scale dynamical anomaly entails essentially no motional restriction at the scale of constituents (monomers).…”