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# The Cahn--Hilliard--de Gennes and generalized Penrose--Fife models for polymer phase separation

• The goal of this paper is twofold. Firstly, we overview the known Flory--Huggins--de Gennes (FHdG) free energy and the associated degenerate singular Cahn--Hilliard--de Gennes (CHdG) model for isothermal phase separation in a binary polymer mixture. Secondly, motivated by the structure of the FHdG free energy, in which the gradient term is made up of energetic and entropic contributions, we set up a corresponding thermodynamically consistent model for nonisothermal phase separation in such mixture. The model is characterized by the modified both energy and entropy fluxes by suitable extra" terms. In this sense it generalizes the well-known Penrose--Fife model in which only entropy flux is modified by an extra" term.
Mathematics Subject Classification: Primary: 35K35, 35K65, 35K67; Secondary: 82D60.

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