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A facile way to generate compatibilized blends of immiscible polymers is through reactive blending of end-functionalized homopolymers. The reaction may be reversible or irreversible depending on the end-groups and is affected by the immiscibility and transport of the reactant homopolymers and the compatibilizing copolymer product. Here we describe a phase-field framework to model the combined dynamics of reaction kinetics, diffusion, and multi-component thermodynamics on the evolution of the microstructure and reaction rate in reactive blending. A density functional with no fitting parameters, which is obtained by adapting a framework of Uneyama and Doi and qualitatively agrees with self-consistent field theory, is used in a diffusive dynamics model. For a symmetric mixture of equal-length reactive polymers mixed in equal proportions, we find that depending on the Flory χ parameter, the microstructure of an irreversibly reacting blend progresses through a rich evolution of morphologies, including from two-phase coexistence to a homogeneous mixture, or a two-phase to three-phase coexistence transitioning to a homogeneous blend or a lamellar copolymer. The emergence of a three-phase region at high χ leads to a previously unreported reaction rate scaling. For a reversible reaction, we find that the equilibrium composition is a function of both the equilibrium constant for the reaction and the χ parameter. We demonstrate that phase-field models are an effective way to understand the complex interplay of thermodynamic and kinetic effects in a reacting polymer blend.
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This content will become publicly available on October 14, 2026
A theory for diffusion-controlled reactions within nonequilibrium steady states
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the rate of the reaction. Stochastic thermodynamics analysis reveals how work constrains the enhancement of rates relative to their equilibrium values. An analytically solvable ion pairing model under a strong electric field illustrates and validates our approach and theory. These findings provide deeper insights into diffusion-controlled reaction dynamics beyond equilibrium.
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- Award ID(s):
- 2102314
- PAR ID:
- 10647063
- Publisher / Repository:
- Journal of Chemical Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 163
- Issue:
- 14
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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