Upper critical endpoint

In Figure 2.2-3 the curves Ig are the vapour pressure curves of the pure components which end in a critical point l=g. The curves l=g, h=g and h=g are vapour-liquid critical curves and the curves h=h are curves on which two liquid phases become critical. The points of intersection of a critical curve with a three-phase curve hhg is a critical endpoint. Distinction can be made between upper critical endpoints (UCEP) and lower critical endpoints (LCEP). The UCEP is highest temperature of a three-phase curve, the LCEP is the lowest temperature of a three-phase curve. The point of intersection of the hhg curve with a l/=g curve is a critical endpoint in which the li liquid phase and the vapour phase are critical in the presence of a non-critical l2 phase (h+(h=g)) and the point of intersection of the hhg curve with a h=h curve is a critical endpoint in which the two liquid phases h and // are critical in the presence of a non-critical vapour phase (h=h)+g)-... 

The four-phase line shows an upper critical endpoint (UCEP) at 313.10 K and 8.232 MPa. At higher temperatures an interesting phenomenum can be oberseved. With increasing temperature the two critical lines (L2=L3)V and L2(L3=V), which bound the three-phase region L2L3V, appproach and finally meet at a common endpoint, a tricritical point where phases L2, L3, and V become critical simultaneously. The procedure to determine the tricritical point has been described previously [4], The tricritical point TCP was determined to 320.75 K and 9.26 MPa. 

Stacking the isothermal Gibbs triangles on top of each other results in a phase prism (see Fig. 1.3(a)), which represents the temperature-dependent phase behaviour of ternary water-oil-non-ionic surfactant systems. As discussed above, non-ionic surfactants mainly dissolve in the aqueous phase at low temperatures (2). Increasing the temperature one observes that this surfactant-rich water phase splits into two phases (a) and (c) at the temperature T of the lower critical endpoint cepp, i.e. the three-phase body appears. Subsequently, the lower water-rich phase (a) moves towards the water corner, while the surfactant-rich middle phase (c) moves towards the oil corner of the phase prism. At the temperature Tu of the upper critical endpoint cepa a surfactant-rich oil phase is formed by the combination of the two phases (c) and (b) and the three-phase body disappears. Each point in such a phase prism is unambiguously defined by the temperature T and two composition variables. It has proved useful [6] to choose the mass fraction of the oil in the... 

At the oil-rich side, the phase behaviour is inverted temperature-wise as can be seen in the T( wA)-section provided in Fig. 1.7(c). Thus, the near-critical phase boundary 2 —1 starts at low temperatures from the lower n-octane-QoEs miscibility gap (below <0°C) and ascends steeply upon the addition of water. With increasing wA, this boundary runs through a maximum and then decreases down to the upper critical endpoint temperature Tu. The emulsification failure boundary 1 —r 2 starts at high temperatures and low values of wA, which means that only small amounts of water can be solubilised in a water-in-oil (w/o) microemulsion at temperatures far above the phase inversion. Increasing amounts of water can be solubilised by decreasing the temperature, i.e. by approaching the phase inversion. At Tu the efb intersects the near-critical phase boundary and the funnel-shaped one-phase region closes. 

B. Structure and Topology off Microemulsions Between Lower and Upper Critical Endpoints... 

For systems containing oil, water, and a nonionic amphiphile, three-phase coexistence of the microemulsion with an oil-rich and a water-rich phase is possible only in a temperature interval Ti < T < T. At the lower critical endpoint T/, the microemulsion and the water-rich phase become identical, while at the upper critical endpoint the microemulsion merges with the oil-rich phase [83,84],... 

Figure la is a representation of type-III fluid phase behavior. Towards higher temperature and pressure, the three-phase line g is terminated by an upper critical endpoint of the nature =g " (UCEP which can be seen as the characteristic feature for this type of fluid phase behavior. A critical line connects this CEP with the critical point of pure component A. Another critical line emerges fi om the critical point of component B and tends towards higher pressures. Very often this critical line may show a minimum and a maximum in pressure and/or temperature (although temperature maxima are quite rare) and gradually chants nature into = ... 

McLure, I. A., Thermodynamics of linear dimethylsiloxane-perfluoroalkane mixtures Part 1.—Liquid-liquid coexistence curves for hexamethyldisiloxane-, octamethyltrisiloxane- or decamethyltetrasiloxane-tetradecafluorohexane near the upper critical endpoint and upper coexistence temperatures for 21 other dimethylsiloxane-perfluoroalkane mixtures. J. Chem. Soc., Faraday Trans., 1997, 93, 249-256. 

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. 

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... 

Let us consider first how the approach to the critical endpoint (CEP) is described in the mean-field approximation, where the phase behavior is obtained simply by considering the minima of the free energy density/(O). Since we want to describe a system at three-phase coexistence,/(O) has to have three minima of equal depth. As the upper CEP is approached, the two minima describing the microemulsion and the oil-rich phase approach each other and merge at the CEP temperature Tu. Similarly, the minima of the microemulsion and the water-rich phase merge at the lower CEP 7). Thus, in a series expansion in powers of O, the free energy density has to have the form... 

The question as to why the interfacial tensions are so low is an extremely interesting one, to which several answers have been given. It was once thought that the answer lay in the fact that the system is near a critical point [105]. That this is clearly not the case appears when one notes that the compositions of the oil-rich and water-rich phases that exhibit such low tensions are not at all similar in composition as they would be near a tricritical point. It has also been argued [84] that the interfacial tension is so low because the upper and lower critical endpoints are so close to one another in temperature. It is true that the tension of the oil/microemulsion interface, must vanish at one critical endpoint, and the tension of the water/microemulsion interface, cr, must vanish at the other. Furthermore, the oil/water interfacial tension, cto,, satisfies the inequality... 

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