The Cahn--Hilliard--de Gennes and generalized Penrose--Fife models forpolymer phase separation

Irena PawŁow

doi:10.3934/dcds.2015.35.2711

Article Contents

2015, Volume 35, Issue 6: 2711-2739. Doi: 10.3934/dcds.2015.35.2711

This issue Previous Article Implicit functions and parametrizations in dimension three: Generalized solutions Next Article Uniform Poincaré-Sobolev and isoperimetric inequalities for classes of domains

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

Irena PawŁow^1,

1.
Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw

Received: December 2013

Revised: March 2014

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Isothermal and nonisothermal Cahn--Hilliard--de Gennes models,
generalized Penrose--Fife model,
polymer phase separation.

Mathematics Subject Classification: Primary: 35K35, 35K65, 35K67; Secondary: 82D60.

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