Statistics and Geometrical Picture of Ring Polymer Melts and Solutions

TL;DR

This paper develops a phenomenological geometrical theory for noncatenated ring polymer melts, explaining key structural features and topological effects, and providing insights into entanglement in polymer systems.

Contribution

It introduces a new geometrical model incorporating noncatenation constraints via effective excluded volume, capturing essential features of ring polymer melts.

Findings

Size and coordination number of rings match experimental observations

Topological length scale varies with molecular weight and stiffness

Provides a geometrical interpretation of entanglement in polymers

Abstract

We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts (Phys. Rev. Lett. 106, 167802 (2011)). A basic assumption lies in the implementation of the noncatenation constraint via the effective excluded-volume effect, from which a geometrical picture of melts emerges. The result captures many of the salient features observed so far, including (i) the overall spacial size of rings, (ii) the coordinate number, i.e., the number of rings surrounding a given ring, (iii) the topological length scale as a function of the molecular weight and (iv) the effect of the chain stiffness and concentration. We also suggest a geometrical interpretation of the topological length scale, which may shed some light on the entanglement concept in polymeric systems.