Experimental Results on Binary Systems

Reciprocals of the critical temperatures, i.e., the maxima in curves such as those in Fig. 121, are plotted in Fig. 122 against the function l/x +l/2x, which is very nearly 1/x when x is large. The upper line represents polystyrene in cyclohexane and the lower one polyisobutylene in diisobutyl ketone. Both are accurately linear within experimental error. This is typical of polymer-solvent systems exhibiting limited miscibility. The intercepts represent 0. Values obtained in this manner agree within experimental error ( 1°) with those derived from osmotic measurements, taking 0 to be the temperature at which A2 is zero (see Chap. XII). Precipitation measurements carried out on a series of fractions offer a relatively simple method for accurate determination of this critical temperature, which occupies an important role in the treatment of various polymer solution properties. 

Entropy of dilution parameters xj/i are calculable, according to Eq. (7), from the slopes of the lines in Fig. 122. Values obtained in this manner are 0.65 and 1.055 for the polyisobutylene and the polystyrene systems, respectively. These are considerably higher than the values 

Ternary Systems Consisting of a Single Polymer Component in a Binary SolventMixture.—Three conditions must be satisfied for equilibrium between two liquid phases in a system of three components. In place of the conditions (1) we have 

The chemical potentials derived by an extension of the procedure used to obtain Eqs. (XII-26) and (XII-32) may be put in the forms  

Binodials calculated by Tompa are shown in Fig. 123,a for the special case of a nonsolvent [l], a solvent [2], and a polymer [3] with Vi = V2, X23 = 0, and xi2 = Xi3 = 1.5. Otherwise stated, the nonsolvent-solvent and the nonsolvent-polymer segment free energies of interaction are taken to be equal, while that for the solvent and polymer is assumed to be zero. It is permissible, then, to take Xi = X2 = l and o 3 = V3/vi. The number of parameters is thus reduced for this special case from five to two. Binodial curves are shown in Fig. 123,a for 0 3 = 10, 100, and 00 tie lines are shown for the intermediate curve only. The critical points for each curve, shown by circles, represent the points at which the tie lines vanish, i.e., where the compositions of the two phases in equilibrium become identical. 

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