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.