Equilibrium and transport properties of ring polymers

We are presenting a proposal with the goal of investigating key properties of dilute and concentrated solutions of ring (cyclic) polymers. Our aim is to shed light onto how the interplay between rigidity, charge, solvent quality and topology determines equilibrium and transport properties of these macromolecules. Starting from a well-established and tested model for flexible ring polymers in athermal solvent conditions [A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter 6, 2435 (2010)], we will modify its microscopic structure to introduce the following modifications: tunable rigidity between the bonds by means of a suitable three-body interaction, solvent quality by means of attractive monomer-monomer interactions, and electric charge through appropriate Coulomb interactions. We will derive effective interactions between the centers of mass of the modified ring polymers to explore the influence of the above-mentioned factors on the shape of the rings, on the realistic possibility of cluster formation upon introduction of rigidity, and of the equilibrium dynamics in the case of varying solvent quality. In all cases, the influence of the topology, manifested through the presence of knots that cause permanent entanglements, will be analyzed. Ring polymers will also be considered in confined geometries, to examine their adsorption properties in comparison to those of linear chains, and to investigate the possibility of surface-induced knot localization. Finally, the out-of-equilibrium behavior of rings will be investigated, both under steady-shear and under Poiseuille flow, with the goal of exploring the influence of knots on the translocation probabilities along narrow channels. The methods of the project cover a broad spectrum of simulation techniques (Monte Carlo, Molecular and Brownian Dynamics, Multiparticle Collisional Dynamics) as well as Density Functional Theory and scaling theory of polymers.

The project has focused it attention on the investigation of the properties of cyclic polymers, i.e., macromolecular chains without free ends, resulting from the connection of the two free ends of the chain with one another. The general topic is of high scientific, technological and biological ineterst on a number of grounds: first of all, the simple operation of connecting the two ends of a polymer with one another results into a strong and irreversible topological constraint, namely the introduction of the no-concatenation condition, which effectively acts as an additional repulsion between rings. This has far-reaching consequences into the forms and shapes that rings assume at high concentration, including their organization into well- defined territories, as opposed to open chains that feature extended configurations with multiple overlaps. From the technological point of view, ring polymer solutions and melts differ markedly in their flow properties from their linear counterparts, since they lack the classical mechanism of entanglements, which dominate the flow properties of chains, featuring instead crumpled configurations with multiple threadings. Finally, biomacromolecules, such as mitochondrial DNA or viral RNA, are often found in cyclical or knotted forms, and this drastically affects their reproduction properties or the machanisms of their ejections from the viral capsids. The project advanced our understanding of ring polymers and on the stability of knots on the same both in bulk and in geometric confienement at equilibrium, and it also brought about new insights into the ways in which rings are transported and sheared, elucidating the interplay beteen topology and hydrodynamics. Introduging rigidity into the polymer backbones (a property inherent, e.g., to DNA molecules), it has been discovered that, contrary to naive expectations, a knot on a ring under tension would not localize in the most flexible region of the molecule. Instead, there is a domain of optimal rigidity to find the knot, caused by a subtle interplay between curvature of the knot ans stretching of the strands in the brading region. This finding has consequences in understanding the location of knots along the backbine of DNA-molecules, which indeed display a rigidity that depends on the base-pair sequence. Another major discovery made in the realm of this project was the emergence of a novel macroscopic phase of matter in solutions of rigid ring polymers, which has been termed a cluster glass. Here, the rings self-organize in an amorphous scaffold of territories or clusters made of many rings, which remain arrested or frozen for extremely long times, creating thereby a rigid macroscopic state known as a glass. Contrary to usual glasse, however, individual rings can hop from one cluster to the other, causing thereby a decoupling between self- and collective relaxations in the system. The third major novel finding in this project concerns, finally, properties of ring polymers (knot-free as well as knotted ones) under transport or shear. Here we found that a unique combination of hydrodynamic interactions (back flow) and topology (closed form of the rings) causes the rings under shear to form stretched, open configurations, as opposed to the slender, rodlike configurations assumed by linear chains. This opens the way for fast and efficient filtering techniques based on modern microfluidic devices.