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

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.

17 pages, 11 figures

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• Understanding the dynamics of rings in the melt in terms of annealed tree model
• Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes
• A study of the morphology, dynamics, and folding pathways of ring polymers with supramolecular topological constraints using molecular simulation and nonlinear manifold learning
• Conformational properties of complex polymers: rosette versus star-like structures
• Chirality modifies the interaction between knots
• Rings in Random Environments: Sensing Disorder Through Topology
• Ring polymers in crowded environment: conformational properties
• Density effects in entangled solutions of linear and ring polymers
• Scaling behavior of topologically constrained polymer rings in a melt
• Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent