1. Lecture 22 Polymer Solutions The model Ideal polymer solution
Bragg-Williams approximation

2. 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

3. Ideal solution Only entropy matters.
Where omega is number of ways of placing N1 polymers on N sites.
Placing first segment of i+1 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

4. Ideal solution - entropy
Combining previous expressions placing i+1 molecule
Similarly placing i molecule
Placing all polymer molecules can be done in
ways

5. Ideal solution - entropy II
After some algebra
And using Stirling’s approximation

6. 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

7. Non-ideal solution Using Bragg-Williams approximation
And on the molar bases

8. 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.