Phase Diagram and Theta Solutions

The phase diagrams of polymer solutions reveal asymmetric characteristics due to the volume difference between solute and solvent molecules. The critical concentration is very low, and shifts toward a lower concentration with the molecular weight (Figure 2.17(a)). The critical point approaches the theta point in the limit of high molecular weight. 

Figure 5.13 Predicted phase diagrams for physical gels made from low-molecular-weight molecules with junctions of unrestricted functionality 4> is the total volume fraction of polymer, and Tr is here the reduced distance from the theta temperature, Tr = — Q/T. The parameter Aq controls the equilibrium constant among aggregates of various sizes. The outer solid lines are binodals, the inner solid lines are spinodals, and the dashed lines are gelation transitions. CP is a critical solution point, CEP is a critical end point, and TCP is a tricriti-cal point. (Reprinted with permission from Tanaka and Stockmayer, Macromolecules 27 3943. Copyright 1994 American Chemical Society.)...

Cloud-point curves or precipitation curves for different polymer-solvent systems have different shapes (Figs. 3.12 and 3.13). The maxima and minima on these curves indicate the upper critical solution temperature (UCST) and the lower critical solution temperature (LCST), respectively. As indicated in Figs. 3.12 and 3.13, the phase diagram of a polymer solution has two regions of limited miscibility (i) below UCST associated with the theta temperature (see Problem 3.16) and (ii) above LCST. 

The binary phase diagram for typical polymer-solvent systems is shown schematically in Fig. 3.8. Nonpolar polymer solutions usually display an upper and a lower critical solution temperature. In the limit of infinite polymer molecular weight, these would correspond to an upper (6,) and lower (dj) theta-temperature. This can be readily seen as follows. 

Fig. 4.4 Illustration of the phase diagrams for phase separation in polymer solutions. The upside is poor solvent, and the downside is good solvent. There are two kinds of demarcations one is athermal solvent with 6 = 0, and the other is theta solvent...

Fig. 2. (a) Schematic phase diagram of a polymer solution, at constant pressure, using temperature T and volume fraction 0 of the polymer as variables. Phase separation into a dilute or semidilute solution (with volume fraction 0e ex) a more concentrated solution (with volume fraction 0 x)occurs for states (T, 0) that fall in the two-phase region underneath the coexistence curve (binodal). The binodal ends in the critical point 0c(AO, TdN), where N is the degree of polymerization of the polymer. For iV - oo the critical point merges with the theta point of the dilute solution, ie, T = 0,0c(iV oo) = 0. For further explanations cf text,... 

A distinct mechanism, which also leads to attractive forces between adsorption layers, was investigated in experiments with dilute polymer solutions in bad solvents. An example is given by PS in cyclohexane below the theta temperature [51]. The subsequently developed theory [52] showed that the adsorption layers attract each other since the local concentration in the outer part of the adsorption layers is enhanced over the dilute solution and lies in the unstable two-phase region of the bulk phase diagram. Similar experiments were repeated at the theta temperature [53]. 

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