Application to a Polymer-Solvent System

In this section we will explore the ability of TPTl to describe the thermodynamic properties of polymer solutions. In what follows, we will restrict our attention to 

Before considering the description of the mixture, let us first address the critical behavior of the pure components alone. Table 3 (see above) summarizes the critical properties for both the monomer and the pentamer as obtained from simulation and theory. The agreement for the monomer is fairly good, as already noted previously [238]. For the pentamer the critical density and temperature are also in fair agreement, but the critical pressure is twice as large as the one obtained in simulations. This failure to predict the critical pressure of the pure pentamer will affect the predictions for the mixtures. 

we consider a mixture obeying the Lorenz-Berthelot rules, such that f = 1 (cf. Eq. (49)). In Fig. 27 we show a p-T projection of the phase diagram as obtained from simulation and theory. The theory correctly predicts the vapor pressure of the pure components. However, the predicted critical temperatures are higher, as expected from a mean field theory. For this reason, the critical line of the mixture is described only in a qualitative manner. Particularly, the predicted critical pressures 

On the contrary, the predictions for the composition of the vapor phase are far less satisfactory. The failure of the theory to properly describe the macroscopic fluctuations that occur in the neighborhood of the critical point has a large effect. Particularly, the critical pressure predicted by the theory is more than twice as large 

This example illustrates the similarity and difference of using an accurate equation of state instead of the simpler Flory— Huggins theory. The latter almost completely ignores the solvent, apart from its effect on the solute. Therefore, one does not know what the pressure of the system is, and there is no distinction between sub-or super-critical solvents. Only the requirement that it should behave as an incompressible fluid is built in. By using an equation of state of the kind that allows to include the solvent explicitely, one is able to accurately locate the behavior observed in the context of the phase diagram of the solvent. This has allowed us to suggest the existence of a 0 point at unexpected conditions. 

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