Flory-Huggins model of polymer mixtures

The Flory-Huggins theory is a workhorse model of phase equilibria involving polymeric fluids. It gives the description 

In recent years, there have been substantial efforts to measure the composition dependence of the interaction parameter X12 (Bates et a/., 1988 Han et al, 1988) - see Fig. 4.4, p. 79 - and thus to refine our understanding of this theory. The original and customary derivations of the Flory-Huggins model introduced an interaction parameter that was considered to be independent oi 4 i but it has long been recognized that this is not the typical case (Flory, 1970). We depart here from the customary derivations to lay a groundwork for a basic reconsideration of that composition dependence. For example, we don t insist here that X12 is the traditional Rory-Huggins i2 parameter. 

As with the composition dependence, the pressure dependence of i2 has recently begun to receive more specific study (Beiner et al, 1998). With regard 

Here we develop a derivation of the Flory-Huggins model that is broader than the customary derivations. The derivation below doesn t, at an initial stage, express various quantities related to polymeric materials on a per monomer basis, as is customary. The chief reason for this is that such a definition at an initial stage is typically based upon lattice modeling of the problem, and we wish here to avoid premature idealizations. 

We consider the mixing of two liquids. We will assume, in the first place, that a satisfactory separation of attractive and repulsive intermolecular interactions 

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