Critical solution line

At the point C the two liquid layers become identical, and this is called the critical solution point or con-solute point. If the total applied pressure is varied, both the critical temperature and composition of the critical mixture alter and we obtain a critical solution line. As an example of this we give in table 16. If the dependence of the critical solution temperature on pressure for the system cyclohexane -f aniline. An increase of pressure raises the critical solution temperature, and the mutual solubility of the two substances is decreased. We saw earlier that the applied pressure had only a small effect on the thermodynamic properties of condensed phases, and we notice in this case that an increase of pressure of 250 atm. alters the critical temperature by only 1.6 °C. 

Fig. 16.21. Critical solution line in a ternary system at constant pressure. ...

Figure A2.5.17. The coefficient Aias a fimction of temperature T. The line IRT (shown as dashed line) defines the critical point and separates the two-phase region from the one-phase region, (a) A constant K as assumed in the simplest example (b) a slowly decreasing K, found frequently in experimental systems, and (c) a sharply curved K T) that produces two critical-solution temperatures with a two-phase region in between.

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

The phase behaviour of many polymer-solvent systems is similar to type IV and type HI phase behaviour in the classification of van Konynenburg and Scott [5]. In the first case, the most important feature is the presence of an Upper Critical Solution Temperature (UCST) and a Lower Critical Solution Temperature (LCST). The UCST is the temperature at which two liquid phases become identical (critical) if the temperature is isobarically increased. The LCST is the temperature at which two liquid phases critically merge if the system temperature is isobarically reduced. At temperatures between the UCST and the LCST a single-phase region is found, while at temperatures lower than the UCST and higher than the LCST a liquid-liquid equilibrium occurs. Both the UCST and the LCST loci end in a critical endpoint, the point of intersection of the critical curve and the liquid liquid vapour (hhg) equilibrium line. In the two intersection points the two liquid phases become critical in the presence of a... 

In a blend of immiscible homopolymers, macrophase separation is favoured on decreasing the temperature in a blend with an upper critical solution temperature (UCST) or on increasing the temperature in a blend with a lower critical solution temperature (LCST). Addition of a block copolymer leads to competition between this macrophase separation and microphase separation of the copolymer. From a practical viewpoint, addition of a block copolymer can be used to suppress phase separation or to compatibilize the homopolymers. Indeed, this is one of the main applications of block copolymers. The compatibilization results from the reduction of interfacial tension that accompanies the segregation of block copolymers to the interface. From a more fundamental viewpoint, the competing effects of macrophase and microphase separation lead to a rich critical phenomenology. In addition to the ordinary critical points of macrophase separation, tricritical points exist where critical lines for the ternary system meet. A Lifshitz point is defined along the line of critical transitions, at the crossover between regimes of macrophase separation and microphase separation. This critical behaviour is discussed in more depth in Chapter 6. 

Figure 14.10 The five types of (fluid + fluid) phase diagrams according to the Scott and van Konynenburg classification. The circles represent the critical points of pure components, while the triangles represent an upper critical solution temperature (u) or a lower critical solution temperature (1). The solid lines represent the (vapor + liquid) equilibrium lines for the pure substances. The dashed lines represent different types of critical loci. (l) [Ar + CH4], (2) [C02 + N20], (3) [C3H8 + H2S],...

Figure 13.15 is drawn for a single constant pressure equilibrium phase compositions, and hence the locations of the lines, change with pressure, but the general nature of the diagram is the same over a range of pressures. For the majority of systems the species become more soluble in one another as the temperature increases, as indicated by lines CG and DH of Fig. 13.15. If this diagram is drawn for successively higher pressures, the corresponding three-phase equilibrium temperatures increase, and lines CG and DH extend further and further until they meet at the liquid/liquid critical point Af, as shown by Fig. 13.16. The temperature at which this occurs is known as the upper critical solution temperature, and at this temperature the two liquid phases become identical and merge into a single phase.

Finally, it has been shown that in some cases, the use of a lower critical solution temperature colloidal stabiliser can control ink behaviour on the substrate. Above 37°C, the solubility of the stabiliser decreases causing a dramatic increase in viscosity. Lines printed using this approach did not display deviations at their starts and ends, and bulges in the line were prevented. 

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.)...

As tire pressure increases, line C D becomes shorter and shorter (indicated in Fig. 14.17 by lines CD and C"D"), until at point M it dimiirishes to a differential length. For still Irigher pressures (P4) the temperature is above tire critical-solution temperature, and there is but a single hquid phase. The diagram then represents two-phase VLE, and it has the form of Fig. 10.9(d), exhibiting a minimum-boiling azeotrope. 

The two branches of the coexistence curve meet in the point K, and the tangent at this point is the limit to which the tie lines tend as K is approached. Beyond K there are no tie lines and the system exists as a single stable phase. K is the critical solution point at the temperature and pressure under consideration. It also lies on the spinodal curve since it must of necessity lie on the boundary between stable and unstable states. 

In general, the miscibility of a pair of polymers depends on temperature and composition. Figure 10.1 schematically shows three typical phase diagrams. The ordinate and the abscissa axes represent temperature and composition, respectively. The solid line in Fig. 10.1(a), below which the blend becomes immiscible (two-phase), is referred to as an upper critical solution temperature (UCST). However, Fig. 10.1(b) shows a lower critical solution temperature (LCST) behavior. Some polymer pairs display both UCST and LCST as shown in Fig. 10.1(c). As will be shown in the following, UCST is rarely observed for a polymer blend. 

It should, perhaps, be pointed out that the two branches of the dotted curve below the temperature of the line DE represent stable systems. The rounded curve lying above DE represents no realisable system, since it lies above the melting-point of the solid solution. It has been put in merely to indicate more clearly the analogy between the mutual solubility curve for two liquids and that for two solids. A lower critical solution temperature, it may be added, has been realised in the case of solid solutions of ammonium chloride and manganous chloride dihydrate (Clen-dinnen and Rivett,y. Chem, Soc, 1923, X23, 1344). 

If a solution represented by any point in the field lying below the curve bed is heated to a temperature above d the critical solution temperature, then the concentration of the nitrile can be increased to any desired amount without at any time two liquid phases making their appearance the system can then be cooled down to a temperature represented by any point between the curves dPe, In this way it is possible to pass continuously from a solution containing excess of one component to solutions containing excess of the other, as represented by the dotted line %%%%. At no point is there formation of two liquid phases. 

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