Understanding the dynamics of rings in the melt in terms of annealed tree model

TL;DR

This paper analyzes the dynamics of long polymer rings in a melt using an annealed tree model, providing scaling laws and comparing results with experimental and simulation data, and discussing implications for chromatin behavior.

Contribution

It generalizes the topological obstacle model with Flory theory, linking ring dynamics to annealed branched polymers and self-avoiding walk statistics.

Findings

Scaling of relaxation time with ring length

Diffusion coefficient behavior in ring melts

Agreement with experimental and simulation data within error bars

Abstract

Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the recently developed Flory theory of unentangled rings which maps every ring on an annealed branched polymer and establishes that the backbone associated with each ring follows self-avoiding rather than Gaussian random walk statistics. We find the scaling of ring relaxation time and diffusion coefficient with ring length, as well as time dependence of stress relaxation modulus, zero shear viscosity and mean square averaged displacements of both individual monomers and ring's mass center. Our results agree within error bars with all available experimental and simulations data of the ring melt, although the quality of the data so far is insufficient to make a definitive judgment for or against the annealed tree theory. In the end we review briefly the relation between our findings and experimental data on chromatin dynamics.