Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

TL;DR

This paper develops an analytic Flory-Huggins theory for mixtures of hard spheres and larger flexible polymers with excluded volume interactions, revealing how their phase behavior and critical densities depend on polymer size and interaction strength.

Contribution

It introduces a comprehensive analytic model for sphere-polymer mixtures covering from ideal to strongly excluded volume polymers, highlighting their immiscibility and critical point properties.

Findings

Critical monomer density decreases with polymer length as 1/√N.

Sphere density at critical point approaches a constant for large polymers.

Mixtures with excluded volume interactions are less miscible than ideal polymer mixtures.

Abstract

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.