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Thermodynamics of polymer solutions and blends
Author(s) -
Hoch Michael
Publication year - 1996
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.10646
Subject(s) - thermodynamics , miscibility , gibbs free energy , phase diagram , mixing (physics) , entropy of mixing , materials science , enthalpy , spinodal decomposition , flory–huggins solution theory , polymer blend , mole fraction , binary number , polymer , enthalpy of mixing , binary system , phase (matter) , chemistry , physics , organic chemistry , mathematics , arithmetic , quantum mechanics , copolymer , composite material
To describe the thermodynamic behavior of binary and larger polymer blends, the Hoch‐Arpshofen model is used to describe highly asymmetric phase diagrams, and asymmetric enthalpies of mixing, where the miscibility gap and the extremum of the enthalpy of mixing leans toward one of the components. The Gibbs energy of mixing of polymer blends is described as\documentclass{article}\pagestyle{empty}\begin{document}$$ Gm/R = T\ast (z_1 {\rm In}\,z_{\rm 1} + z_2 {\rm In}\,z_2) + Wnz_1 [1-(1 - z_2)^{(n - 1)}] $$\end{document} where z can be mole fraction, volume fraction, or weight fraction. The Hoch‐Arpshofen model contains an interaction parameter W = A + B * T independent of composition and an integer number n (2, 3, 4, …), which defines the asymmetricity of the binary phase diagram and of the Gibbs energy of mixing curve. In a binary system n defines the composition where the Gibbs energy of mixing is maximum or minimum or the composition is where the temperature of a miscibility gap is maximum or minimum. In a binary system A‐B the maximum effect occurs at A n –1 B . The disorder reaction in polymers is treated as a transformation temperature, and defines T 0 , the temperature where the ordered and disordered material is equal.