ENGR-1100 Introduction to Engineering Analysis

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Lecture 22 Polymer Solutions

• The model
• Ideal polymer solution
• Bragg-Williams approximation

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Lattice model polymer solution
N1 solvent molecules and N2 polymer molecules
each consisting of n units (monomers) all
distributed on N sites N1 nN2 N
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Ideal solution
Only entropy matters. Where omega is number
of ways of placing N1 polymers on N sites.
Placing first segment of i1 th chain can be
done in ways. Placing the
second in ways. And placing next in ways
since one site is occupied by previous segment
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Ideal solution - entropy
Combining previous expressions placing i1
molecule Similarly placing i
molecule Placing all polymer molecules can
be done in ways
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Ideal solution - entropy II
After some algebra And using Stirlings
approximation
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Ideal solution - entropy of mixing
Entropy of pure solvent is zero (one way of
filling) and entropy of pure polymer is
Therefore the entropy of mixing Per mol of
molecules where
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Non-ideal solution
Using Bragg-Williams approximation And on
the molar bases
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Polymer blends
Mixture of two polymers with degree of
polymerization of n1 and n2. The molar entropy
of mixing is Take for example n1 n2 n
and X1 X2 0.5 Which differs from the
expression for small molecules by n factor in
energy, which implies that small energetic
differences for polymers will have large effects.