Statistical thermodynamics of blends: Equation of state and phase relations

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Abstract
We discuss the free‐energy expressions for homogeneous melts and their blends, based on our hole theory. Equation of state (PVT) and free energy of mixing (ΔGm) are considered from a common point of view without the introduction of additional parameters to pass from the first to the second set of properties. Practical problems arise from the fact that ΔGm represents a difference between large quantities. As illustrations we analyze two typical systems. One is the n − C6 + n − C16 pair where PVT and ΔGm, the latter at atmospheric pressure only, have been studied experimentally. The other is n ‐ C6 with a low and high molecular weight respectively of polyethylene as solute. Here the PVT relations of the components only are known. The effects of intercomponent attractions, temperature, pressure, and molecular weight on phase behavior are investigated. Critical coordinates, lower critical‐solution temperatures (LCST) and their pressure dependence are computed. An iso‐free volume condition obtains for this dependence where free volume is defined by the hole fraction inherent in the theory. Comparisons with experimental observations and other theoretical computations for different molecular weights are limited by the effect of polydispersity. Moreover, cloud point curves are shown. We finally compute the composition and pressure dependence of the χ‐parameter which is implicit in the theory. We conclude with some comments regarding polymer blends.

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