A unified theory of free energy functionals and applications to diffusion

SignificanceThe free energy functional is a central component of continuum dynamical models used to describe phase transitions, microstructural evolution, and pattern formation. However, despite the success of these models in many areas of physics, chemistry, and biology, the standard free energy fr...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2022-06, Vol.119 (23), p.e2203399119
Main Authors: Li, Andrew B, Miroshnik, Leonid, Rummel, Brian D, Balakrishnan, Ganesh, Han, Sang M, Sinno, Talid
Format: Article
Language:English
Subjects:
Alloy systems
Dynamic models
Free energy
Germanium
Germanium base alloys
Mathematical models
Parameters
Physical Sciences
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Summary:SignificanceThe free energy functional is a central component of continuum dynamical models used to describe phase transitions, microstructural evolution, and pattern formation. However, despite the success of these models in many areas of physics, chemistry, and biology, the standard free energy frameworks are frequently characterized by physically opaque parameters and incorporate assumptions that are difficult to assess. Here, we introduce a mathematical formalism that provides a unifying umbrella for constructing free energy functionals. We show that Ginzburg-Landau framework is a special case of this umbrella and derive a generalization of the widely employed Cahn-Hilliard equation. More broadly, we expect the framework will also be useful for generalizing higher-order theories, establishing formal connections to microscopic physics, and coarse graining.
ISSN:0027-8424
1091-6490
1091-6490
DOI:10.1073/pnas.2203399119