Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior

TL;DR

This paper develops a mean-field lattice model for polymer solutions with solvent and cosolvent, deriving an exact free energy expression and analyzing phase behavior, providing insights into the fundamental roles of solvent components.

Contribution

It introduces a novel lattice model linking polymer solutions to the $O(n)$-vector spin model, enabling analytical free energy estimation and phase stability analysis.

Findings

Model explains diverse polymer solution behaviors

Highlights the competing roles of solvent and cosolvent

Provides a framework for analyzing phase separation

Abstract

We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the limit $n \to 0$, we derive an exact field-theoretic expression for the partition function of the system. The latter is then evaluated at the saddle point, providing a mean-field estimate of the free energy. The resulting expression, which conforms to the Flory-Huggins type, is then used to analyze the system's stability with respect to phase separation, complemented by a numerical approach based on convex hull evaluation. We demonstrate that this simple lattice model can effectively explain the behavior of a variety of seemingly unrelated polymer systems, which have been predominantly investigated in the past only through numerical simulations. This includes both, single-chain and multi-chain, solutions. Our findings emphasize the fundamental, mutually competing, roles of solvent and cosolvent in polymer systems.