Critical consolution points solutions

An application has been found in which a system that exhibits an upper, or lower, critical consolute point, UCST or LCST, respectively, is utilized. At a temperature above or below this point, the system is one homogeneous liquid phase and below or above it, at suitable compositions, it splits into two immiscible liquids, between which a solute may distribute. Such a system is, for instance, the propylene carbonate - water one at 25°C the aqueous phase contains a mole fraction of 0.036 propylene carbonate and the organic phase a mole fraction of 0.34 of water. The UCST of the system is 73 °C (Murata, Yokoyama and Ikeda 1972), and above this temperature the system coalesces into a single liquid. Temperature cycling can be used in order to affect the distribution of the solutes e.g. alkaline earth metal salts or transition metal chelates with 2-thenoyl trifluoroacetone (Murata, Yokayama and Ikeda 1972). 

Future work in this area should focus on further development of novel extraction schemes that exploit one or more of the cited advantages of the nonionic cloud point method. It is worth noting that certain ionic, zwitterionic, microemulsion, and polymeric solutions also have critical consolution points (425,441). There appear to be no examples of the utilization of such media in extractions to date. Consequently, the use of some of these other systems could lead to additional useful concentration methods especially in view of the fact that electrostatic interactions with analyte molecules is possible in such media whereas they are not in the nonionic surfactant systems. The use of the cloud point event should also be useful in that it allows for enhanced thermal lensing methods of detection. 

The intensity of light scattered from a fluid system increases enormously, and the fluid takes on a cloudy or opalescent appearance as the gas-liquid critical point is approached. In binary solutions the same phenomenon is observed as the critical consolute point is approached. This phenomenon is called critical opalescence.31 It is due to the long-range spatial correlations that exist between molecules in the vicinity of critical points. In this section we explore the underlying physical mechanism for this phenomenon in one-component fluids. The extension to binary or ternary solutions is not presented but some references are given. 

The separation of polymer-solvent systems into two phases as the temperature increases is now recognized to be a characteristic feature of all polymer solutions. This presents a problem of interpretation within the framework of regular solution theory, as the accepted form of predicts a monotonic change with temperature and is incapable of dealing with two critical consolute points. 

Aqueous solutions of many nonionic amphiphiles at low concentration become cloudy (phase separation) upon heating at a well-defined temperature that depends on the surfactant concentration. In the temperature-concentration plane, the cloud point curve is a lower consolution curve above which the solution separates into two isotropic micellar solutions of different concentrations. The coexistence curve exhibits a minimum at a critical temperature T and a critical concentration C,. The value of Tc depends on the hydrophilic-lypophilic balance of the surfactant. A crucial point, however, is that near a cloud point transition, the properties of micellar solutions are similar to those of binary liquid mixtures in the vicinity of a critical consolution point, which are mainly governed by long-range concentration fluctuations [61]. 

Many modifications of the Flory-Stockmayer theory, e.g. the cascade formalism have been published. To some extent they allow for loops in the bond formation process. Refe. 1, 9, 11 give more references and details on theories which are based on an improved simple Flory-Stockmayer theory. The position of the gel point then shifts away frompc = l/(f - 1), i.e. the gel point is not universal. Ingeneral, however, theexponents remain the same. For exceptions see Refs. 42, 43 for example, in a solution at thermal equilibrium, when the critical consolute point is also a gel point the degree of polymerization DP may vary with (T - Tc) above is critical temperature but with (Tc - T)" ... 

M. L. Japas, J. M. H. Levelt Sengers. Critical behavior of a conducting ionic solution near its consolute point. J Chem Phys 94 5361-5368, 1994. 

From a global assessment of these results, it seems inescapable to conclude that mean-field behavior does not remain valid asymptotically close to the critical point. Rather, ionic systems seem to show Ising-to-mean-field crossover. Such a crossover has been a recurring result observed near liquid-liquid consolute points in Coulombic electrolyte solutions, in ternary aqueous electrolyte solutions containing an organic cosolvent, and in binary aqueous solutions of NaCl near the liquid-vapor critical line. 

Binary-Liquid Option. As an alternative to this study of critical behavior in a pure fluid, one can use quite a similar technique to investigate the coexistence curve and critical point in a binary-liquid mixture. Many mixtures of organic liquids (call them A and B) exhibit an upper critical point, which is also called a consolute point. In this case, the system exists as a homogeneous one-phase solution for all compositions if Tis greater than... 

For the hydrocarbon--CO2 systems studied here, at pressures above the critical pressure (7.383 MPa) and above the critical temperature (304.21 K) of C02 the isobaric x,T coexistence plots of liquid and vapor phases form simple closed loops. The minimum occurs at the lower consolute point or the Lower Critical Solution Temperature (LCST). Since pressure is usually uniform in the vicinity of a heat transfer surface, such diagrams serve to display the equilibrium states possible in a heat transfer experiment. 

Kleemeier, M., Wiegand, S., Derr, T., Weiss, V., Schroer, W., and Weingartner, H. Critical viscosity and Ising-to-mean-field crossover near the upper consolute point of an ionic solution. Ber. Bunsenges. Phys. Chem., 1996, 100, p. 27-32. 

Describe the similarities of the solution upper consolute point and the liquid-gas critical point. 

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. 

The thermodynamic behavior of fluids near critical points is drastically different from the critical behavior implied by classical equations of state. This difference is caused by long-range fluctuations of the order parameter associated with the critical phase transition. In one-component fluids near the vapor-liquid critical point the order parameter may be identified with the density or in incompressible liquid mixtures near the consolute point with the concentration. To account for the effects of the critical fluctuations in practice, a crossover theory has been developed to bridge the gap between nonclassical critical behavior asymptotically close to the critical point and classical behavior further away from the critical point. We shall demonstrate how this theory can be used to incorporate the effects of critical fluctuations into classical cubic equations of state like the van der Waals equation. Furthermore, we shall show how the crossover theory can be applied to represent the thermodynamic properties of one-component fluids as well as phase-equilibria properties of liquid mixtures including closed solubility loops. We shall also consider crossover critical phenomena in complex fluids, such as solutions of electrolytes and polymer solutions. When the structure of a complex fluid is characterized by a nanoscopic or mesoscopic length scale which is comparable to the size of the critical fluctuations, a specific sharp and even nonmonotonic crossover from classical behavior to asymptotic critical behavior is observed. In polymer solutions the crossover temperature corresponds to a state where the correlation length is equal to the radius of gyration of the polymer molecules. A... 

The two-term crossover Landau model has been successfully applied to the description of the near-critical thermodynamic properties of various systems, that are physically very different the 3-dimensional lattice gas (Ising model) [25], one-component fluids near the vapor-liquid critical point [3, 20], binary liquid mixtures near the consolute point [20, 26], aqueous and nonaqueous ionic solutions [20, 27, 28], and polymer solutions [24]. 

The typical dependence of a miscibility gap on temperature is shown in Fig. 13.5 on the next page. The miscibility gap (the difference in compositions at the left and right boundaries of the two-phase area) decreases as the temperature increases until at the upper consolute temperature, also called the upper critical solution temperature, the gap vanishes. The point at the maximum of the boundary curve of the two-phase area, where the temperature is the upper consolute temperature, is the consolute point or critical point. At this point, the two liquid phases become identical, just as the liquid and gas phases become identical at the critical point of a pure substance. Critical opalescence (page 205) is observed in the vicinity of this point, caused by large local composition fluctuations. At temperatures at and above the critical point, the system is a single binary liquid mixture. 

In the cases first studied by Antonow, the two liquids p and y were formed from two incompletdy miscible, pure components not far from their consolute point (critical solution point). From our present knowledge we ate able to say that in just those drcumstances we would expect one of the liquid phases to wet completely the interface between the other liquid phase and the vapour. (We shall see why, in 8.5.) The picture in those cases would then be that of Rg. 8.3, so (8.8) would hold Antonow was right. But we can imagine a hypoflietical case, even of such a two-component liquid-liquid- apour system near the consolute point of the liquids, in which Antonow s rule must fail. Suppose the two components are an incompletely miscible enantiomeric pair, so that the two liquid phases p and y, ea slightly richer in one of the two components, are mirror images and suppose a is their common vapour. Then a =... 

Figure 5.9 General phase diagram of a surfactant solution, showing the CMC line, the Krafft point (temperature) and the lower consolute point (or lower critical temperature). As can be seen, the phase behaviour of aqueous surfactant solutions is rather complex and various phases are distinguished. At high concentrations, we can see various special surfactant phases (hexagonal, lamellar, cubic). These are called liquid crystalline phases and although there are 18 different types, the three mentioned are the most important. Many of these complex structures have found exciting applications (e.g. liquid crystal displays and study of biological membranes)...

The highest point in the tie-line region at temperature Tc is called an upper critical solution point or an upper consolute point. It has a number of properties similar to those of the gas-liquid critical point in Figure 1.5. If a mixture has the same overall composition as that of the consolute point, it will be a two-phase system at a temperature below the consolute temperature. If its temperature is gradually raised, the meniscus between the phases becomes diffuse and disappears, in the same way that the meniscus... 

The point C (cf. Fig. 1.8.2) where the two liquid layers become identical is called the critical solution point or consolute point. 

We begin our discussions by considering spinodal limits, including consolute points. To focus the discussion, imagine we have two partially miscible liquids. When we dissolve a trace of one solute liquid in the other solvent liquid, we get a true solution. As we increase the amount of solute, we will saturate the solution. This saturation limit is called the binodal. If we are careful, the solution will remain one supersaturated phase. If we continue to increase the solute concentration, we will reach a new limit of thermodynamic stability called the spinodal. At a specific temperature, the spinodal will equal the binodal at a concentration called the consolute point. This point is for liquid-liquid mixtures what the critical point is for gas-liquid phase behavior. 

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. 

The cloud point is close to, but not necessarily equal to the lower consolute solution temperature for polydisperse nonionic surfactants (97). These are equal if the surfactant is monodisperse. Since the lower consolute solution temperature is like a critical point for liquid—liquid mixtures, the dilute and coacervate phases have the same composition, and the volume fraction of solution which the coacervate comprises is a maximum at this temperature (98). If a coacervate phase containing a high concentration of surfactant is desired, the solution should be at a temperature well above the cloud point. 

The cloud point phenomena as a lower consolute solution temperature is becoming better understood in terms of critical solution theory and the fundamental forces involved for pure nonionic surfactant systems. However, the phenomena may still occur if some ionic surfactant is added to the nonionic surfactant system. A challenge to theoreticians will be to model these mixed ionic/nonionic systems. This will require inclusion of electrostatic considerations in the modeling. 

Ternary Critical Point. The point where, upon adding a mutual solvent to two partially miscible liquids (as adding alcohol to ether and water), the two solutions become consolute and one phase results. 

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