Ring polymers in melts and solutions: scaling and crossover

TL;DR

This paper introduces a mean-field theory for ring polymer melts that accounts for topological effects, predicting a crossover from Flory's compact exponent to a dense-packed regime in practical chain lengths.

Contribution

It combines topological volume fraction with van der Waals theory to model many-body effects in dense ring polymer systems, providing new insights into their structural scaling behavior.

Findings

Predicted crossover from $ u=2/5$ to $ u=1/3$ in chain statistics

Most practical systems exhibit the $ u=2/5$ regime

The theory captures topological effects in dense polymer melts

Abstract

We propose a simple mean-field theory for the structure of ring polymer melts. By combining the notion of topological volume fraction and a classical van der Waals theory of fluids, we take into account many body effects of topological origin in dense systems. We predict that although the compact statistics with the Flory exponent $\nu=1/3$ is realized for very long chains, most practical cases fall into the crossover regime with the apparent exponent $\nu = 2/5$ during which the system evolves toward a topological dense-packed limit.