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Synthetic polymers are a foundational technology that has profoundly changed modern life. In many cases, the properties of polymeric materials are determined by the behaviour of the ends of polymer chains in the liquid, glassy, and crystalline states [1]. Ring polymers, on the other hand, have no ends, and recent work suggests that the unique topology of these molecules may enable the realization of unprecedented properties and functions, with novel applications in the design of advanced functional materials [2]. Not only is the study of ring polymer dynamics a fundamental problem in polymer physics, it is also proving to be fundamental to understanding the longstanding problem of genome folding. How does DNA pack so densely in the cell nucleus without being catastrophically entangled, while at the same time segregating into distinct territories [3]? Moreover, how do ring polymers move and relax in concentrated polymer solutions in the absence of chain ends? Our Workshop aims to provide answers to these key questions in ring polymer physics, with particular emphasis on the development of new theoretical models and simulation methods to understand the properties of ring polymers.
Despite intense investigation since the 1980s [4], we have not yet achieved a full understanding of ring polymer dynamics. Progress has been severely hampered by the near impossibility of preparing pure samples of synthetic ring polymers, since they invariably contain differing fractions of linear polymers, along with concatenated structures that arise during synthesis [5]. Thanks to major breakthroughs in the synthesis of cyclic molecules [6], development of purification processes based on liquid chromatography at the critical condition [7,8], and the capacity to produce large quantities of stable ring DNA that are not concatenated [9], it has been possible recently to carry out meticulous studies of ring polymer dynamics. Over the last decade, fundamental insight into the behaviour of ring polymers has been gained by combining systematic experiments at the molecular and bulk scale [8,10-16], with advanced numerical simulations that enable the analysis and interpretation of experimental data [17-22].

The central finding of these studies is that the unique topology of rings leads to their static and dynamic behaviour being fundamentally different compared to linear chains in the various concentration regimes when they are in solution, and in the melt state. For instance, rings exhibit a different scaling of size with molecular weight and are more compact [11]. Dynamically, ring chains diffuse much faster in a background melt of circular chains [9]. The linear viscoelastic response of ring melts is qualitatively different than linear chains because they do not relax by reptation. Interestingly, stress relaxation in ring polymer melts occurs as a power law, with no rubber-like plateau [8]. In terms of shear rheology, ring melts exhibit lower shear viscosities, much weaker shear thinning response, and a weaker molecular weight dependence [13]. Recent experiments with the filament stretching rheometer indicate that the extensional response of ring melts is markedly different from linear chains, with a dramatic increase in viscosity at low shear rates [16]. In dilute solutions, there are significant differences in the scaling of relaxation times, and a shift in the onset of coil-stretch transition in planar elongational flows [12.14]. Simulations suggest that hydrodynamic interactions induce an open loop configuration because of the reduced degrees of freedom in a ring [14,19]. In ring-linear blends, it is thought that linear chains penetrate open ring conformations, in a phenomenon termed as ‘threading’ [20,21,23,24]. Threadings are believed to dominate ring relaxation in entangled solutions and significantly affect dynamics. By taking advantage of the slow diffusion of rings in ring-linear blends, small fractions of ring molecules in linear melts have been used as sensitive probes to study the dynamics of entangled polymer systems [11]. Recently, Schroeder and co-workers showed that DNA-based rings show large fluctuations in steady-state polymer extension in a background of semi-dilute linear polymers, which is thought to arise by transient threading in flow [15].

Despite recent progress, a molecular-level understanding of ring polymer dynamics is lacking. The challenge is to understand how the topology of rings affects non-equilibrium dynamics, in both solutions and melts. As one example, developing methods to identify ring-ring or linear-ring threading would enable a clear understanding of their microscopic origin. In the context of theory and simulations, the capacity to examine large systems of many rings based on simple coarse-grained models, and studying melts of very large rings remains a challenge. Conformational changes of rings in melts during the unravelling process in extensional flows need to be addressed, along with the role of linear contaminants.

By assembling a team of world-class researchers who have been responsible for nearly all the important advances in the field of ring polymer dynamics in the last decade, we aim to bring focussed attention to the quantitative understanding of ring polymer dynamics. Discussing the relevant questions together will lead to a comparison of observations, a sharing of procedures, and foster new collaborations among a multidisciplinary group of scientists and engineers working on an important contemporary problem.