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We introduce a lattice framework that incorporates elements of Flory–Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory–Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory–Huggins–Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil–globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers.
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Exact analytical solution of the Flory–Huggins model and extensions to multicomponent systems
The Flory–Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at equilibrium have not been determined analytically, and numerical techniques are required that restrict the theory’s ease of application. In this work, we derive an implicit analytical solution to the Flory–Huggins theory of one polymer in a solvent by applying a procedure that we call the implicit substitution method. While the solutions are implicit and in the form of composite variables, they can be mapped explicitly to a phase diagram in composition space. We apply the same formalism to multicomponent polymeric systems, where we find analytical solutions for polydisperse mixtures of polymers of one type. Finally, while complete analytical solutions are not possible for arbitrary mixtures, we propose computationally efficient strategies to map out coexistence curves for systems with many components of different polymer types.
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- PAR ID:
- 10585836
- Publisher / Repository:
- J. Chemical Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 161
- Issue:
- 4
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1063/5.0215923
