Consolute points

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 specific rates of hydrolysis of five organic halides in three water-based liquid mixtures near their respective equilibrium consolute points have been observed to be suppressed. The systems studied included t-amyl chloride in isobutyric acid water (upper consolute temperature), and 3-chloro-3-methylpentane in 2-butoxyethanol water (lower consolute temperature). The slowing effect occurred within a few tenths of a degree on either side of the consolute temperature. 

In metal-ammonia solutions most experimental work has been carried out at temperatures above the consolute point and here we believe that the system can be treated similarly to a Mott transition in a solid. However, there are differences. 

We note that at the consolute point the conductivity is still metallic, the appearance of an activation energy e2 occurring for somewhat lower concentrations. The reason for this, in our view, is as follows. The consolute point should occur approximately at the same concentration as the kink in the free-energy curve of Fig. 4.2, namely that at which the concentration n of carriers is of order given by n1/3aH 0.2. Above the consolute point there is no sudden disappearance of the electron gas as the concentration decreases its entropy stabilizes it, so metallic behaviour extends to lower concentrations, until Anderson localization sets in. Conduction, then, is due to excited electrons at the mobility edge, as discussed above. 

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... 

As pointed out by Thompson (1985), the calculated value of observed value of the conductivity at this point, which is changing rapidly with concentration. 

We have to ask whether there is any reason why the metal-insulator transition should take place at the consolute point. This should be so only if the curve of Fig. 10.12 is symmetrical about this point. This is unlikely to be the case, and in fact the concentration at which a = amin does decrease with increasing temperature (Thompson 1985, p. 125). 

Lower temperature tends to reduce miscibility, so the liquid-liquid coexistence region tends to spread to a wider composition range at lower T, as shown in Fig. 7.11 or (7.63). However, exceptional cases are known in which the liquid-liquid coexistence region terminates in a lower consolute point, so that complete miscibility can be achieved by cooling below this point. Perhaps most remarkable in this respect is the famous nicotine/water... 

In the hatched two-phase region of limited miscibility, the system separates heterogeneously into water-rich and nicotine-rich layers. However, at temperatures below the lower consolute point (about 61°C) or above the upper consolute point (about 210°C), the components become miscible in all proportions, resulting in a uniform homogeneous phase. The molecular-level origins of this extraordinary behavior, as well as more general aspects of consolute behavior in other (typically, hydrogen-bonded) systems, remain deeply obscure. 

We shall first describe representative behavior for each type (Sections 7.4.1-7.4.4), then sketch how continuous changes in intermolecular interactions are expected to lead continuously from one type of T-x behavior to another (Section 7.4.5), including rather uncommon features such as solid-solid consolute points. 

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. 

It is shown in Example 14.5 that phase splitting occurs for such a mixture if A > 2 the value of A = 2 corresponds to a consolute point, at x = X2 = 0.5. Thus, for a quadratic mixture, phase-splitting obtains if ... 

With respect to Eq. (A), increasing T makes GE/RT smaller, thus, the consolute point is an upper consolute point. Its value follows from ... 

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. 

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