Flory-Huggins Treatment of Compatibility

Flory and Huggins devised a general scheme which enables one to deal with the mixing properties of a pair of polymers. It provides a basic understanding of the occurrence of different types of phase diagrams, in dependence on temperature and the molecular weights. 

The decomposition of A mix in these two contributions points to the two main aspects of the mixing process but this alone would not be of much value. What is needed, for practical uses, are explicit expressions for ASt and A ioc, so that the sum of the two contributions can be calculated. The Flory-Huggins treatment is based on approximate equations for both parts. We formulate them first and then discuss their origins and the implications. The equations have the following forms  

Introducing the volume fractions 0a and 0b of the two components in the mixture, given by 

It includes two parameters. The less important one is Uc, denoting the (molar) volume of a reference unit common to both polymers. Principally it can be chosen arbitrarily, but usually it is identified with the volume occupied by one of the monomeric units. The decisive factor is the Flory-Huggins parameter x- It is dimensionless and determines in an empirical manner the change in the local free energy per reference unit. 

Regarding the expression for A ioc we may first note that Eq. (3.81) represents the simplest formula which fulfills the requirement, that A ioc must vanish for (/ a 0 and (/ b — 0. More about the background may be learned 

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