We review briefly the general assumptions underlying hole theories of the configurational thermodynamic functions for single and multiconstituent systems. From the original Simha-Somcynsky theory several important modifications have recently evolved. First, there is a revision of the combinatorial entropy originating from the mixing of segments and holes in the spirit of Huggins's theory. With consistent additional modifications of the configurational free energy, quantitatively significant consequences for certain aspects of phase equilibria can arise. Finally, allowance for nonrandom mixing of constituents species and holes has been made. We illustrate the theory's potentials first in terms of pressurevolume-temperature (PVT) data for high and low molar mass species and their miscible mixtures. The influence of PVT properties on the miscibility behavior of solutions and blends is examined next. Of particular concern are the connections between predictability of lower from upper mixing spinodals, pressure effects, and the binary interaction ,y-function.
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The Simha-Somcynsky hole theory of polymeric fluids is here modified in several ways: (1) the Huggins expression replaces that of Flory for the conformational entropy; (2) contact fractions replace site fractions in expressions for the internal energy and for the segmental free length. These modifications produce relatively minor effects on the equation of state of a pure polymer but (as described in the following paper) lead to improved correlations of miscibility behavior.
It is well known that equilibrium thermodynamic properties are governed by different functional derivatives of the thermodynamic functions of state. For example, the phase behavior of mixtures of low and/or high molar mass components is determined by the compositional derivatives of the free energy. In this contribution, the merits of the Simha-Somcynsky theory in describing and predicting the phase behavior of mixtures are considered. The influence of temperature and composition on the miscibility behavior for practically binary polymer solutions are studied. Furthermore, the important aspect of polydispersity, inherent to synthetic polymer systems will be addressed.
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