Weight ternary systems

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

The composition of the nonsolvent-solvent mixture representing the critical composition of the ternary system with polymer of infinite molecular weight (see Fig. 123,a) possesses unique significance. Scott and Tompa have shown that the composition at the critical point in the limit of infinite molecular weight is specified by... 

A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

Fig. 9. Phase diagrams of quasi-ternary systems containing two different molecular weight samples a PHIC-toluene with (Ni, N2) = (4.46,0.38) [73] b schizophyllan-water system with (Nt, N2) = (0.930, 0.0765) [75,76]. (O, A) experimental coexisting isotropic phase ( , , ) experimental coexisting anisotropic phase dashed segments, experimental tie lines the shadowed triangular region, the IAA triphasic region thick full curves, theoretical binodals thin full segments, theoretical tie lines...

Fig. 21. Average molecular weight MJ, dependence of T 0 for the quasi-ternary system containing two xan-than samples with (N, Nj) = (0.54,4.5) in 0.1mol/l NaCl [144], Solid curves represent the Mv dependence of T 0 for quasi-binary solutions of xanthan at 0.1 mol/1 NaCl...

Figure 8. Crossover temperature Tx in the ternary system 3-methylyridine + water + sodium bromide as a function of the salt concentration given in weight-percent. For details see text. Redrawn from Ref. 165 with permission.

Systems containing monomer and DMF but no other diluent were discussed in the previous section, and it was noted that a maximum rate is associated with intermediate monomer-DMF compositions. Imoto (79) observed a similar effect with monomer-benzene-DMF mixtures. A shallow minimum in polymerization rate was found at a low benzene level and then a very pronounced maximum at a higher benzene content. Molecular weight increased monotonically, however, with the benzene/ DMF ratio. In these ternary systems the amount of DMF was not enough to keep the polymer in solution but considerable swelling must have occurred. Thomas, Thomas and Deichert (130) show electron photomicrographs of polymer made under these conditions. 

In those cases in which V2/Vi is known, both gv° and g ° are given. For the rest of the systems, only gv° is given. Prediction of thermodynamic properties on ternary systems formed by a polymer and two solvents or two polymers and a solvent requires the knowledge of the parameter g°, characteristic of the interaction of the corresponding binary pairs [9], However, due to the variety of sources for the several systems studied, the data correspond to different polymer molecular weights, m, and to different temperatures. Since the variation of x with concentration may depend on M for low M s, it has selected data only for M > 2 x 109, where no M dependence is detected. 

Figure 13 shows a similar pair of chromatograms of a binary sample of a hard coal tar pitch with many high moleular weight PAH s present. In the upper chromatogram, the pyrene peak has a shoulder, which is nearly completely resolved in the ternary system chromatogram. The two peaks between Pyrene and Benz(a)anthracene above are seen as four peaks in the lower chromatogram,... 

The earliest study of the ternary system was by Gulbransen and his associates (6, 17), who obtained data on the 50 weight % uranium alloy. Their chief concern was the possible weakening effects of hydrogen absorption by such alloys in a pressurized-water reactor. More recently, La Grange et al. (9) examined... 

Phase separation in ternary systems may be studied using the cloud point isotherm method. Solvent, here defined as component 1, is added to a turbid mixture containing a mixture of components 2 and 3 until the agitated mixture becomes clear. A series of such experiments at various component 2-component 3 weight ratios establishes the cloud point... 

N,N-Dimethylacetamide (DMAC). The two polymers exhibit similar conformations and both exist in anisotropic phases above a certain critical concentration. It was found that when the ternary systems were examined, two anisotropic phases exist above the critical volume fraction. Further, each of the stable anisotropic phases contain pure polymer. The authors conclude that miscibility between polymers forming the same type of mesophase isn t necessarily observed, in contrast to low molecular weight liquid crystals. 

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