The theory makes it possible to:
1- Interpret and predict different material’s behavior in a wide range of states and independent variables, viz. gases, low molecular weight organic liquids, metals, polymers in a glassy or molten state
2-Determine miscibility of gases or liquids in polymers
3- Compute the phase diagrams of polymer blends, etc.
1- Lattice, Cell, and Hole Theories
The statistical mechanics methods that use a pseudo-crystalline model of regularly placed elements on a “lattice” are known as lattice theories.
Many theories, known under the names of free volume, cell-hole, tunnel, Monte Carlo, or molecular dynamics belong here.
Of these, only two will be mentioned:
1- The first, and the best known, was originally developed by Huggins [1941] and by Flory [1941], then extended by many authors [e.g.
Utracki, 1962; Koningsveld, 1967].
2-The second, is the cell-hole Simha-Somcynsky [1969] theory that
has been incessantly evolving during the intervening years.
1.1 Huggins-Flory theory
For binary systems that contain an ingredient i = 1 or 2 (traditionally, for polymer solutions the subscript 1 indicates solvent, and 2 polymer) the Huggins-Flory, H-F, relation has been expressed in several equivalent forms
The drawback of the H-F theory was the initial assumption that all lattice cells are occupied by either solvent molecules or polymeric segments
that are of equal size. As a consequence the free volume contribution was neglected.
1.2 Equation of State Theories
Equation of State (EoS) or PVT Relationships .In his Ph.D. thesis of 1873, van der Waals proposed the first EoS. The relation is frequently
written in terms of reduced variables, indicating expected observance of the corresponding states principle:
Eq 2.16 also introduced the free volume concept — note that as T ?0, V ?b. Van der Waals considered that molecules move in “cells” made
by the surrounding molecules with a uniform potential. The volume within which the center of a molecule can freely move, is what defines the free volume. Thus, one may distinguish:
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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