Ternary Systems Consisting of Two Polymeric Components in a Single Solvent

These simple expressions may also be obtained from the chemical potentials according to Eqs. (XII-26) and (XII-32) by appropriately changing subscripts and recalling that x in these equations represents the ratio of the molar volumes, which in the present case is unity. Owing to the identity of volume fractions with mole fractions in this case, Eqs. (18) and (19) are none other than the chemical potentials for a regular binary solution in which the heat of dilution can be expressed in the van Laar form. The critical conditions (see Eqs. 2) 

The physical reason for the inherent lack of incentive for mixing in a polymer-polymer system is related to that already cited in explanation of the dissymmetry of the phase diagram for a polymer-solvent binary system. The entropy to be gained by intermixing of the polymer molecules is very small owing to the small numbers of molecules involved. Hence an almost trivial positive free energy of interaction suffices to counteract this small entropy of mixing. 

Suppose now that there is chosen as the third component (component 1) a monomeric substance in which each of the polymer components (2 and 3) is separately miscible in all proportions in the absence of the other. In order that this condition may be fulfilled, both X12 and xi3 are required to be less than one-half. Aside from this stipulation the actual values of these parameters are of minor importance only hence we may let Xi2 = xi3- As before we take X2 = Xz = x, 

If the chemical potentials )U2 and in the two phases are expressed by Eq. (13) with parameters as specified above, then the result obtained on equating 1x2 to 1x2 according to the equilibrium conditions (11) may be rearranged to the following form, after taking advantage of the relations (20) applicable to this case  

Ternary equilibrium curves calculated by Scott,who developed the theory given here, are shown in Fig. 124 for x = 1000 and several values of X23. Tie lines are parallel to the 2,3-axis. The solute in each phase consists of a preponderance of one polymer component and a small proportion of the other. Critical points, which are easily derived from the analogy to a binary system, occur at 

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