Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology

TL;DR

This study investigates how solution density and ring topology influence the equilibrium and kinetic properties of ring polymers, revealing that while equilibrium metrics are weakly affected, kinetics are strongly modulated by entanglement, especially at low densities.

Contribution

It introduces a novel approach by fixing ring length and varying density and topology to study entanglement effects on ring polymers' properties.

Findings

Equilibrium properties are weakly affected by density increases.

Kinetics change significantly with concentration, up to tenfold.

Topology influences the slowest diffusion process of the knotted region.

Abstract

The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed solution density. Here, we use a different approach to investigate numerically the equilibrium and kinetic properties of solutions of model ring polymers. Specifically, the ring contour length is maintained fixed, while the interplay of inter- and intra-chain entanglement is modulated by varying both solution density (from infinite dilution up to \approx 40 % volume occupancy) and ring topology (by considering unknotted and trefoil-knotted chains). The equilibrium metric properties of rings with either topology are found to be only weakly affected by the increase of solution density. Even at the highest density, the average ring size, shape anisotropy and length of the knotted region differ at most by 40% from those of isolated rings. Conversely, kinetics are strongly affected by the degree of inter-chain entanglement: for both unknots and trefoils the characteristic times of ring size relaxation, reorientation and diffusion change by one order of magnitude across the considered range of concentrations. Yet, significant topology-dependent differences in kinetics are observed only for very dilute solutions (much below the ring overlap threshold). For knotted rings, the slowest kinetic process is found to correspond to the diffusion of the knotted region along the ring backbone.