Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915249152589824 |
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| author | Marcato, Davide Giacometti, Achille Maritan, Amos Rosa, Angelo |
| author_facet | Marcato, Davide Giacometti, Achille Maritan, Amos Rosa, Angelo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_01590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior Marcato, Davide Giacometti, Achille Maritan, Amos Rosa, Angelo Soft Condensed Matter 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. |
| title | Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2407.01590 |