Miscibility Phase Diagram of Ring Polymer Blends: A Topological Effect

TL;DR

This paper develops a mean-field theory to understand how topological constraints in ring polymers influence their phase behavior in blends, predicting enhanced miscibility in ring-linear blends and weak demixing in ring-ring blends.

Contribution

It introduces a novel topological volume concept and scaling formulas to describe the impact of topological constraints on polymer blend phase diagrams.

Findings

Enhanced miscibility in ring-linear polymer blends.

Weak demixing tendency in ring-ring polymer blends.

Topological length acts as a screening factor in effective excluded-volume effects.

Abstract

The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of {\it topological volume}, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analysis put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.