Critical consolution 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). 

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. 

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. 

This short analysis shows that in one component fluids only a single, isolated liquid - gas critical point should exist. This is associated with the selected values of temperatures and pressures Tq, ). For binary mixtures of limited miscibility with a critical consolute point (CP) a continuous line of critical points, in addition to the gas-liquid critical point, should appear, namely for... 

Consequently, one may consider the application of binary mixtures near the critical consolute point for SCF technologies instead of one component fluids near the gas - liquid critical point. It is also noteworthy that for one component fluids the presence of the second liquid - liquid (L-L) near-critical... 

Figure 4 indicates that this behavior can be associated with the evolution of the excess volume (V% since the excess enthalpy (ff J is always positive for mixtures with an upper critical consolute point. 

Rzoska, S. J., Urbanowicz, P., Drozd-Rzoska, A., Paluch, M., and Habdas, P. (1999) Pressure behaviour of dielectric permittivity on approaching the critical consolute point, Europhys. Lett. 45, 334-340... 

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. 

There are several circumstances in which the quadratic fluctuation theory presented here breaks down. When derivatives of any of the intensive parameters with respect to the extensive parameters are very small, the corresponding fluctuations are very large. The Taylor expansion of SE in the fluctuations are then very large and the Taylor expansion of SE in the fluctuations cannot be truncated at the second-order term. For example, the mean-square density fluctuation is given by Eq. (10.C.28), where the isothermal compressibility and correspondingly (Sp2y diverges when (dP/d V)t - 0. This happens at the gas liquid critical point. Likewise at the critical consolute point... 

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. 

Dioxane is a cyclic diether forming a six-membered ring [20]. Thus it is a nearly nonpolar symmetric molecule. 1,4-Dioxane is an extraordinary solvent, capable of solubilizing most organic compounds, and water in all proportions, and many inorganic compounds. The self-diffusion coefficient of dioxane is 1.1 x 10 cm /s, about half that of a water molecule. The effective diameter of dioxane is 5.5 A - about twice that of a water molecule. One should not forget that a water-dioxane mixture narrowly avoids a lower critical consolute point. However, the effects of criticality are reflected in the values of ffie mutual diffusion coefficient and viscosity. Note that binary mixtures are often chosen so that they are mixable (do not phase separate). Thus, the two components interact attractively and strongly. 

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)" ... 

A summary of these ten examples shows how the random percolation problem can be modified The critical exponents change only if the modification introduced can be seen on a scale which may become infinitely large, as in particular at the critical consolute point of phase separation. Otherwise, the modification concerns only inessential details and does not change the critical exponents. In some sense, the correlated site-bond percolation model described in Chapter D is only a further generalization of modifications 1 and 2 above providing similar results for the critical exponents. 

By adjusting the parametm-s of the function p = p(T) or p = p(T, 0), which corresponds experimentally to a change in the solvent, an interesting situation described by the central part of Fig. 7 results, where the sol-gel boundary meets the phase separation curve exactly at the critical consolute point. In this case, the Bethe lattice theory which corresponds to the Flory-Stockmayer model, gives classical exponents for random-bond percolation along the whole sol-gel boundary. This is true even for the special case where the critical consolute point and the end point of the gelation line coincide then, one has to use the concentration 0 and not the temperature T as a variable to define critical exponents. 

In contrast, different forms of the renormalization group theory show that random-percolation exponents are obtained along the entire gelation line except at the critical consolute point, if the latter is also the end point of the gelation line. In the latter case, the critical exponents are given by the lattice-gas exponents, i.e. the weight average... 

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