Upper critical solution temperature , for

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. 

Interactions between different distant parts of the molecule tend to expand it, so that in the absence of other effects a would be greater than unity, but in solution in poor solvents interactions with the solvent tend to contract it. According to Flory s theory (18) these two tendencies will just balance so that a — 1 at a particular temperature T—0 (the theta temperature ), and at this temperature A2 =0 and further this temperature is the limit as Mn- go of the upper critical solution temperature for the polymer-solvent system in question. Quantities relating to T=0 will be denoted by subscript 0. Flory s theory implies that ... 

All of the evidence presented above supports the conclusion that the diblock copolymers are essentially homogeneous. On the other hand, the corresponding homopolymers have been shown to be incompatible in essentially all proportions under similar conditions of sample preparation. Thus, if at room temperature the BR and IR can be made compatible by the addition of a single chemical bond, i.e., the one linking the two segments in the diblock copolymer, it is not unreasonable to expect that an upper critical-solution temperature for the homopolymers might exist not far above room temperature. The direct determination of this temperature by visual methods (27) was not feasible in the present case because of the nearly equal indices of refraction of BR and IR. As an alternative, the dynamic shear properties of a 50/50 blend of IR and BR were determined in the Mechanical Spectrometer from 30° to 200°C. 

Meier et al. [13] assumed that above 353 K the upper critical solution temperature for the a-tocopherol/carbon dioxide system could be reached, above which the liquid and supercritical gas phase are completely soluble in each other. Measurements of phase equilibria carried out by Hoffmann-La Roche AG and our investigations contradict the assumption mentioned. Two coexisting phases are still present at 423 K and 27.5 MPa (see Figure 4). 

Harismiadis, V.I. et al.. Application of the van der Waals equation of state to polymers. III. Correlation and prediction of upper critical solution temperatures for polymer solutions. Fluid Phase Equilibria, 100, 63-102, 1994. 

Di-(C7-Glu) also has a biphasic H/Li phase forming at 62 wt% surfactant existing to =60 °C. The H] phase melts over the range 62-80°C. Between the H and 1 phases is another biphasic region between 71 and 75 wt%. This, and the L( phase exist to >90 °C. A two phase loop occurs at low surfactant concentrations and temperatures (<8 wt% and <50 °C). The authors believe this to be the first observation of an upper critical solution temperature for a nonionic surfactant. The shape of the upper consolute loop is extremely unusual suggesting remarkable changes in micellar interactions. .. or the presence of impurities. One would be pleased to see these observations verified by other groups. Di-(Cg-Glu) shows only a L phase but with a wide miscibility gap to a dilute aqueous solution. This is not remarkable. 

It should be noted that the modern view is that all partially miscible liquids should have both a lower and upper critical solution temperature so that all such systems really belong to one class. A closed solubility curve is not obtain in all cases because the physical conditions under normal pressure prevent this. Thus with liquids possessing a lower C.S.T., the critical temperature (the critical point for the liquid vapour system for each component, the maximum temperature at which liquefaction is possible) may be reached before the consolute temperature. Similarly for liquids with an upper C.S.T., one or both of the liquids may freeze before the lower C.S.T. is attained. 

Influence of added substances upon the critical solution temperature. For a given pressure the C.S.T. is a perfectly defined point. It is, however, affected to a very marked extent by the addition of quite a small quantity of a foreign substance (impurity), which dissolves either in one or both of the partially miscible liquids. The determination of the consolute temperature may therefore be used for testing the purity of liquids. The upper consolute temperature is generally employed for this purpose. 

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

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... 

Figure 8.17 Vapor fugacity for component 2 in a liquid mixture. At temperature T, large positive deviations from Raoult s law occur. At a lower temperature, the vapor fugacity curve goes through a point of inflection (point c), which becomes a critical point known as the upper critical end point (UCEP). The temperature Tc at which this happens is known as the upper critical solution temperature (UCST). At temperatures less than Tc, the mixture separates into two phases with compositions given by points a and b. Component 1 would show similar behavior, with a point of inflection in the f against X2 curve at Tc, and a discontinuity at 7V...

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

For the two-component, two-phase liquid system, the question arises as to how much of each of the pure liquid components dissolves in the other at equilibrium. Indeed, some pairs of liquids are so soluble in each other that they become completely miscible with each other when mixed at any proportions. Such pairs, for example, are water and 1-propanol or benzene and carbon tetrachloride. Other pairs of liquids are practically insoluble in each other, as, for example, water and carbon tetrachloride. Finally, there are pairs of liquids that are completely miscible at certain temperatures, but not at others. For example, water and triethylamine are miscible below 18°C, but not above. Such pairs of liquids are said to have a critical solution temperature, For some pairs of liquids, there is a lower (LOST), as in the water-tiiethylamine pair, but the more common behavior is for pairs of liquids to have an upper (UCST), (Fig. 2.2) and some may even have a closed mutual solubility loop [3]. Such instances are rare in solvent extraction practice, but have been exploited in some systems, where separations have been affected by changes in the temperature. 

Note 1 Below the LCST and above the upper critical solution temperature (UCST), if it exists, a single phase exists for all compositions. 

The instance we have considered here, that of a polymer in a poor solvent, results in an upper critical solution temperature (UCST) as shown in Figure 2.33. This occurs due to (a) decreased attractive forces between like molecules at higher temperatures and (b) increased solubility. For some systems, however, a decrease in solubility can occur, and the corresponding critical temperature is located at the minimum of the miscibility curve, resulting in a lower critical solution temperature (LCST). This situation is illustrated in Figure 2.34. 

In type VI phase behaviour a three-phase curve l2hg is found with an LCEP and an UCEP. Both critical endpoints are of the type (l2=li)+g and are connected by a l2=h critical curve which shows a pressure maximum. For this type of phase behaviour at constant pressure closed loop isobaric regions of l2+li equilibria are found with a lower critical solution temperature and an upper critical solution temperature. 

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