Gels: Energetics, Singularities, and Cavitation

Autor: Maria-Carme Calderer, Duvan Henao, Manuel Sanchez, Ronald A. Siegel, Sichen Song
Rok vydání: 2023
Předmět:
Zdroj: Journal of Elasticity.
ISSN: 1573-2681
0374-3535
Popis: This article studies equilibrium singular configurations of gels and addresses open questions concerning gel energetics. We model a gel as an incompressible, immiscible and saturated mixture of a solid polymer and a solvent that sustain chemical interactions at the molecular level. We assume that the energy of the gel consists of the elastic energy of its polymer network plus the Flory-Huggins energy of mixing. The latter involves the entropic energies of the individual components plus that of interaction between polymer and solvent, with the temperature dependent Flory parameter, chi, encoding properties of the solvent. In particular, a good solvent promoting the mixing regime, is found below the threshold value chi=0.5, whereas the phase separating regime develops above that critical value. We show that cavities and singularities develop in the latter regime. We find two main classes of singularities: (i) drying out of the solvent, with water possibly exiting the gel domain through the boundary, leaving behind a core of exposed polymer at the centre of the gel; (ii) cavitation, in response to traction on the boundary or some form of negative pressure, with a cavity that can be either void or flooded by the solvent. The straightforward and unified mathematical approach to threat all such singularities is based on the construction of appropriate test functions, inspired by the particular states of uniform swelling or compression. The last topic of the article addresses a statistical mechanics rooted controversy in the research community, providing an experimental and analytic study in support of the phantom elastic energy versus the affine one. Mathematics Subject Classification (2020) 35B40 · MSC 35J57 · 74B20 · 74G65 · 74R99
Databáze: OpenAIRE
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