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Coupling between phase separation and geometry on a closed elastic curve: Free energy minimization and dynamics
Hanchun Wang1, Ronojoy Adhikari1, Michael E Cates1
1DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
The Journal of Chemical Physics
|June 17, 2026
Summary
The closure constraint of a deformable filament alters its free energy landscape, creating new stable and metastable states. This study explores these morphologies using analytical and simulation methods for elastic filaments coupled to concentration fields.
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- Elastic filaments coupled to concentration fields are relevant in various physical phenomena.
- Phase separation tendencies and concentration-dependent spontaneous curvature influence filament behavior.
- Previous studies often simplified analysis by avoiding the complexities of closed filament geometry.
Purpose of the Study:
- To investigate the free energy landscape and dynamics of a closed elastic filament interacting with a concentration field.
- To analyze the impact of the closure constraint on filament morphology.
- To explore equilibrium and metastable states beyond the limitations of previous models.
Main Methods:
- Analytical calculations of free energy and dynamics.
- Numerical simulations employing coupled Willmore flow and Cahn-Hilliard gradient flow.
- Global free energy minimization to determine equilibrium morphologies.
Main Results:
- The closure constraint qualitatively alters the free energy landscape compared to rigid or open filaments.
- Multiple domains of stable and metastable states are admitted.
- Numerical exploration reveals equilibrium morphologies across various parameters.
- Dynamical simulations confirm the emergence of multi-domain structures.
Conclusions:
- The geometric constraint of a closed, deformable filament significantly impacts its phase behavior and morphology.
- The model provides a more comprehensive understanding of elastic filament behavior in phase-separating systems.
- This work offers insights into the formation of complex multi-domain structures in confined elastic systems.
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