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

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

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

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

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

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

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

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.