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arXiv · 2407.01590

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

Davide Marcato·Achille Giacometti·Amos Maritan·Angelo Rosa
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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.

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Davide Marcato, Achille Giacometti, Amos Maritan, Angelo Rosa. 2024-12-18. Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior. https://doi.org/10.1103/physrevmaterials.8.125601

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