Critical solution temperature, binary upper

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. 

We consider a binary liquid mixture of components 1 and 3 to be consistent with our previous notation, we reserve the subscript 2 for the gaseous component. Components 1 and 3 are completely miscible at room temperature the (upper) critical solution temperature Tc is far below room temperature, as indicated by the lower curve in Fig. 27. Suppose now that we dissolve a small amount of component 2 in the binary mixture what happens to the critical solution temperature This question was considered by Prigogine (P14), who assumed that for any binary pair which can be formed from the three components 1, 2 and 3, the excess Gibbs energy (symmetric convention) is given by... 

Equations (115)—(117), indicate that under the conditions just described, 8Tc/8x2 is both large and positive, as desired i.e., dissolution of a small amount of component 2 in the 1-3 mixture raises the critical solution temperature, as shown in the upper curve of Fig. 27. From Prigogine s analysis, we conclude that if component 2 is properly chosen, it can induce binary miscible mixtures of components 1 and 3 to split at room temperature into two liquid phases having different compositions. 

For example, 0 describes the temperature dependence of composition near the upper critical solution temperature for binary (liquid + liquid) equilibrium, of the susceptibility in some magnetic phase transitions, and of the order parameter in (order + disorder) phase transitions. 

Draw the liquid portion of a phase diagram for a binary system that shows hoth an upper and a lower critical solution temperature. 

Chen et al. [67,68] further extended the study of binary blends of ESI over the full range of copolymer styrene contents for both amorphous and semicrystalline blend components. The transition from miscible to immiscible blend behavior and the determination of upper critical solution temperature (UCST) for blends could be uniquely evaluated by atomic force microscopy (AFM) techniques via the small but significant modulus differences between the respective ESI used as blend components. The effects of molecular weight and molecular weight distribution on blend miscibility were also described. 

If 13 < A < 15, the solvents may be only partially miscible with an upper critical solution temperature (UCST) between 25 and 50°C. This is a borderline case. If the binary mixture is miscible, then adding a relatively small amount of water likely will induce phase splitting. 

Consider diffusion in a binary liquid mixture exhibiting an upper critical solution temperature (UCST) or lower critical solution temperature (LCST) (see Fig. 3.1). Let us take a mixture at the critical composition x at point A just above the UCST. Any concentration fluctuation at A will tend to be smeared out due to the effects of diffusion in this homogeneous mixture. On the other hand, any fluctuation of a system at point B, infinitesimally below the UCST, will lead to separation in two phases. Similarly, the mixture at point D, just below the LCST is stable whereas the mixture at point C, just above the LCST is unstable and will separate into two phases. 

The phase diagrams of polymer blends, the pseudo-binary polymer/polymer systems, are much scarcer. Furthermore, owing to the recognized difficulties in determination of the equilibrium properties, the diagrams are either partial, approximate, or built using low molecular weight polymers. Examples are fisted in Table 2.19. In the Table, CST stands for critical solution temperature — L indicates lower CST, U indicates upper CST (see Figure 2.15). 

The formulation of Scott (44) does not present the range of phenomena occurring in polymer blends. Various binary blends exhibit lower critical solution temperatures (LCST) where phase separations occur at lower temperature. Other blends exhibit upper critical solution temperatures (UCST) where miscible blends exhibit phase separations at higher temperatures (45). It was shown by McMaster (46) that volume changes occurred in mixing. 

According to the type of T versus q> diagram (Fig. 25.4), the binary solution can exhibit an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), or both (close-loop phase behavior). Above the UCST or below the LCST the system is completely miscible in all proportions [82], Below the UCST and above LCST a two-phase liquid can be observed between cp and cp". The two-phase liquid can be subdivided into unstable (spontaneous phase separation) and metastable (phase separation takes some time). These two kinds of mixtures are separated by a spinodal, which is outlined by joining the inflexion points (d AGIdcp ) of successive AG versus cp phase diagrams, obtained at different temperatures (Fig. 25.3b). Thus, the binodal and spinodal touch each other at the critical points cp and T. ... 

Figure 27.2 Phase diagram for binary blends showing the different phase regions and the upper and lower critical solution temperatures (UCST and 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. 

With binary solvent systems, it is common to determine a consolute or upper critical solution temperature above which phase separation cannot occur, whatever the composition. Consolute temperatures are usually found for 50 50 mixtures however, the fiill phase diagrams show that solvents can become miscible in other... 

The Txx diagram shown in Figure 8.20 is typical of most binary liquid-liquid systems the two-phase curve passes through a maximum in temperature. The maximum is called a consolute point (also known as a critical mixing point or a critical solution point), and since T is a maximum, the mixture is said to have an upper critical solution temperature (UCST). A particular example is phenol and water, shown in Figure 9.13. At T > T, molecular motions are sufficient to counteract the intermolecular forces that cause separation. 

In the phenomenological model of Kahlweit et al. [46], the behavior of a ternary oil-water-surfactant system can be described in terms of the miscibility gaps of the oil-surfactant and water-surfactant binary subsystems. Their locations are indicated by the upper critical solution temperature (UCST), of the oil-surfactant binary systems and the critical solution temperature of the water-surfactant binary systems. Nonionic surfactants in water normally have a lower critical solution temperature (LCST), Tp, for the temperature ranges encountered in surfactant phase studies. Ionic surfactants, on the other hand, have a UCST, T. Kahlweit and coworkers have shown that techniques for altering surfactant phase behavior can be described in terms of their ability to change the miscibility gaps. One may note an analogy between this analysis and the Winsor analysis in that both involve a comparison of oil - surfactant and water-surfactant interactions. 

Certain principles mnst be obeyed for experiments where liquid-liquid equilibrium is observed in polymer-solvent (or snpercritical flnid) systems. To understand the results of LLE experiments in polymer solutions, one has to take into acconnt the strong influence of polymer distribution functions on LLE, because fractionation occnrs dnring demixing. Fractionation takes place with respect to molar mass distribution as well as to chemical distribution if copolymers are involved. Fractionation during dentixing leads to some effects by which the LLE phase behavior differs from that of an ordinary, strictly binary mixture, because a common polymer solution is a mnlticomponent system. Clond-point cnrves are measnred instead of binodals and per each individnal feed concentration of the mixtnre, two parts of a coexistence cnrve occnr below (for upper critical solution temperatnre, UCST, behavior) or above the clond-point cnrve (for lower critical solution temperature, LCST, behavior), i.e., produce an infinite nnmber of coexistence data. 

Binary mixtures of non-aromatic fluorocarbons with hydrocarbons are characterized by large positive values of the major thermodynamic excess functions G , the excess Gibbs function, JT , the excess enthalpy, 5 , the excess entropy, and F , the excess volume. In many cases these large positive deviations from ideality result in the mixture forming two liquid phases at temperatures below rSpper. an upper critical solution temperature. Experimental values of the excess functions and of Tapper for a representative sample of such binary mixtures are given in Table 1. 

It is now established both theoretically and experimentally that many thermodynamic variables assume a simple power-law behaviour at or near critical points in both pure and mixed fluids. The actual functional dependence of one variable on another can be characterized by the so-called critical indices a, 5, etc. The critical index j8, for example, defines both the shape of the gas-liquid coexistence curve for a pure fluid and the liquid-liquid coexistence curve of a binary mixture in the vicinity of either an upper or a lower critical solution temperature. The correspondence between critical phenomena in one-, two-,... 

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