ECCOMAS 2024

Consistent Lagrangean Formulation of Phase Separation in Chemoelastic Polymer Solutions at Large Strains

  • Gomero Soria, Andrea (Empa, ETH Zurich)
  • Stracuzzi, Alberto (Empa, ETH Zurich)
  • Ehret, Alexander (Empa, ETH Zurich)

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Large volume and shape changes may occur in polymer solutions subject to mechanical loads or undergoing solvent evaporation. These deformations can lead to local alterations in composition, triggering the separa-tion of the mixture into polymer-rich and solvent-rich phases. The study of microstructure evolution arising under such conditions thus necessitates a large strain formulation of the classical phase-field model for phase separation. To this end, a recent chemomechanical theory for biphasic media at large strains is amended to account for the energetic contribution of interfaces between phase domains. The model employs the well-established Cahn-Hilliard (CH) equation for diffusion, and the Flory-Huggins (FH) mixing energy for polymer-solvent sys-tems. All model contributions are formulated in a Lagrangean representation. The analysis of previous work revealed different treatments of this problem particularly in relation to the de-formation-dependence of the interfacial energy. In the present contribution, these approaches are compared to a model derived when the solvent volume fraction c of the classical CH and FH equations is interpreted as the current volume fraction and consistently expressed in the reference configuration. This introduces an addi-tional dependence of the interfacial energy on deformation, distinct from those found in existing literature. These models were implemented in FEniCS, enabling the numerical investigation of the effect of the choice of interfacial energy on the phase separation process and, consequently, on microstructure formation. This is ex-emplified through scenarios involving drying and/or deforming polymer solutions.