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Predicting elastic moduli of heterogeneous polymer compositions
Author(s) -
Coran A. Y.,
Patel R.
Publication year - 1976
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1976.070201108
Subject(s) - moduli , materials science , volume fraction , phase (matter) , upper and lower bounds , polymer , morphology (biology) , thermodynamics , elastic modulus , series (stratigraphy) , composite material , mathematics , physics , mathematical analysis , chemistry , organic chemistry , paleontology , biology , genetics , quantum mechanics
A new method for predicting elastic moduli M of heterogeneous polymer compositions is proposed. It is based on a phenomenological adjustment between parallel and series models for upper and lower bound moduli M U and M L . Thus,\documentclass{article}\pagestyle{empty}\begin{document}$$ M = \phi _H ^n (n\phi _S + 1)(M_U ‐ M_L ) + M_L $$\end{document} where ϕ H is the volume fraction of hard phase, ϕ S is the volume fraction of soft phase, and n is the only adjustable parameter since the upper and lower bound moduli are given by\documentclass{article}\pagestyle{empty}\begin{document}$$ M_U = \phi _H M_H + \phi _S M_S $$\end{document} and\documentclass{article}\pagestyle{empty}\begin{document}$$ M_L = (\phi _H /M_H + \phi _S /M_S )^{ ‐ 1} $$\end{document} where M H and M S are the moduli of the pure hard and soft phases, respectively. Predicted values of M are in agreement with measured values in a number of systems which include polyblends and composite materials of fixed morphology. The significance of n is discussed relative to concentrations in the area of a phase transition for the polyblends or relative to phase morphology in the case of fixed morphology compositions. Interestingly, the relationship, by analogy, is in agreement with measured values of polyblend melt viscosities.