Critical point consolute points

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. 

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. 

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. 

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. 

At the time of writing, the only evidence for critical fluctuations near the consolute point known to us comes from the work of Damay (1973). The thermopower of Na-NH3 plotted against T at the critical concentration is shown in Fig. 10.21. We conjecture that this behaviour is due to long-range fluctuations between two metallic concentrations, and that near the critical point, where the fluctuations are wide enough to allow the use of classical percolation theory, the... 

The Al-Zn system was the first studied extensively in an attempt to verify the theory for spinodal decomposition [24], The equilibrium diagram for this system, shown in Fig. 18.12, shows a monotectoid in the Al-rich portion of the diagram. The top of the miscibility gap at 40 at. % Zn is the critical consolute point of the incoherent phase diagram. 

Besides the l.c. phases, the phase diagram of the p-l.c./water is very similar to the diagram of the m-l.c./water. The broad miscibility gap of the polymer/water system shows a lower critical consolute point, which is shifted to lower concentrations (3.2% of polymer). This is consistent with experiments and theory on the position of miscibility gaps in polymer solutions112). 

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. 

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). 

The interesting feature of Eq. (26) is that it predicts the diffusion coefficient will go to zero at a critical point or a consolute point. This is verified experimentally the diffusion coefficient does drop from a perfectly normal value by more than a million times over perhaps just a few degrees centigrade (Kim et al., 1997). Curiously, the drop occurs more rapidly than predicted by Eq. (26). In many ways, this is a boon, because the diffusion coefficient is small only in a very small region of little practical significance. However, it is disquieting that we do not understand completely why the drop is faster than it should be. 

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. 

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... 

The effect of pressure on the consolute temperature is thus determined by the curvature of the mean molar volume v x. ) at the critical point. We may represent the two simple cases by the curves (1) and (2) in fig. 18.6, and ignore for the moment any more complicated behaviour. 

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. 

The hypothesis advanced here is that the observed enhancement is due to thermocapillarity arising from the temperature dependence of the interfacial tension. Although we know of no theory for such a Marangoni effect in binary condensation per se, theory does exist for both mass transfer (M. 11) and heat transfer (16, 12) aeross an interface in the absence of bulk flow. We note that the sign of the derivative of the interfacial tension with respect to temperature is positive near a lower consolute point and that this is in the correct direction to sustain disturbances in condensation rate. Thus, in retrograde condensation, provided a critical temperature gradient normal to the interface is exceeded, a local increase in condensation flux toward the vapor liquid interface will result in its cooling. 

Zhang, K.C., Briggs, M.E., Gammon, R.W., and Levelt Sengers, J.M.H. The susceptibility critical exponent for a nonaqueous ionic binary mixture near a consolute point. 

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. 

Light Scattering Data and Critical Consolute Point... 

The contact point = c is a critical consolute point. The calculated critical values of the virial coefficient and of the droplet volume fraction (B =-21 and <(ic JO. 13) for a hard-sphere model with an attractive potential are in qualitative agreement with the experimental observations (Figure 2). Around those critical values, a very large turbidity is observed. If the temperature is varied, the microemulsion separates into two turbid microemulsions. Angular variations of the scattered intensity and of the diffusion coefficient are observed (16) but the correlation function remains exponential. All these features are characteristic of the vicinity of a critical consolute point. The data can be fitted with theoretical predictions (17) ... 

Close to the boundaries Sj and S2 in the three phase domain, the interfacial tensions were found to be very low. In that case, the theoretical model presented above is no longer valid, first of all because the middle phase microemulsion structure is not simply a droplet dispersion. Furthermore the interaction term F becomes evidently dominant and is difficult to evaluate since the nature of the forces is not perfectly known. However, such low interfacial tensions are characteristic of critical consolute points. It was then tempting to check that the behavior of the interfacial tensions was compatible with the universal scaling laws obtained in the theory of critical phenomena. In these theories the relevant parameter is the distance e to the critical point defined by ... 

The interpretation of the bulk properties of the microemulsions phases, close to Sx, in terms of critical phenomena, is then less satisfying. Near this boundary, the samples are further from a critical consolute point than in the case of the boundary S2. As far as bulk properties are concerned, light scattering experiments are rather sensitive to droplets elongation as it will be observed in viscosity measurements. 

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