Liquids critical behavior

As shown, CP varies in a continuous manner, but appears to diverge at Tx (= 2.17K at latm), resembling in this respect the behavior at the gas-liquid critical point (discussed... 

While the early work on molten NH4CI gave only some qualitative hints that the effective critical behavior of ionic fluids may be different from that of nonionic fluids, the possibility of apparent mean-field behavior has been substantiated in precise studies of two- and multicomponent ionic fluids. Crossover to mean-field criticality far away from Tc seems now well-established for several systems. Examples are liquid-liquid demixings in binary systems such as Bu4NPic + alcohols and Na + NH3, liquid-liquid demixings in ternary systems of the type salt + water + organic solvent, and liquid-vapor transitions in aqueous solutions of NaCl. On the other hand, Pitzer s conjecture that the asymptotic behavior itself might be mean-field-like has not been confirmed. 

Referring again to Figure 14.14, the isotherms at temperatures T3 and T4 are of the typical (gas + liquid) type, but at T2, a temperature below u, two critical points occur, one at f and the other at h. The one at f is a typical (liquid + liquid) critical point while the one at h is better characterized as a (gas + liquid) critical point. In most systems with type III behavior, the critical locus bh occurs over a narrow temperature range, and the double critical points occur only over this small range of temperature. 

Oag, R.M., PI. King, C.J. Mellor, M.W. George, J. Ke and M. Poliakoff, Probing the Vapor-Liquid Phase Behaviors of Near-Critical and Supercritical Fluids Using a Shear Mode Piezoelectric Sensor, Analytical Chemistry, 75, 479-485 (2003). 

In recent years, studies of the phase behavior of salt-water systems have primarily been carried out by Russian investigators (headed by Prof. Vladimir Valyashko) at the Kurnakov Institute in Moscow, particularly for fundamental understanding of the phase behavior of such systems. Valyashko [37,39,42,43], Ravich [38], Urosova and Valyashko [40], and Ravich et al. [41] have given a classification of the existence of two types of salts, depending on whether the critical behavior is observed in saturated solutions. Type 1 does not exhibit critical behavior in saturated solutions. The classic example of Type 1 is the NaCl-water system and has been studied by many authors [36,37,44-47]. The Type 2 systems exhibit critical behaviors in saturated solutions, and therefore have discontinuous solid-liquid-vapor equilibria. Table 1 shows the classification of binary mixtures of salt-water systems. 

It is worth remarking that the above phenomenology leads one to conclude that the marginal Fermi liquid behavior hypothesized for the optimally doped samples (x 0.16) does not reflect quantum critical behavior. 

What does your best value for the exponent j8 indicate about the nature of the critical behavior underlying the N-I transition (mean-field second-order or tricritical) Note that /3 and P describe the temperature variation of the nematic order parameter S, which is a basic characteristic of the liquid crystal smdied. Thus, the same j8 and P values could have been obtained from measurements of several other physical properties, such as those mentioned in the methods section. 

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... 

Liquid-Liquid Phase Separations and Critical Behavior of Electrolyte Solutions Driven by Long-Range and Short-Range Interactions... 

Electrolyte solutions are of long-standing interest, and in many respects our understanding of their thermodynamics is in a mature state. The discoveiy of liquid-liquid phase equilibria in such systems has, however, introduced new features. " Although already reported in 1903," and studied in more detail in 1963, such phenomena have remained almost unnoticed. New impetus in the this field has now come from interest in the critical properties of ionic fluids. Experiments at high temperatures have indicated that, at least on a first study, ionic fluids appear to exhibit classical critical behavior, as opposed to the /smg-like criticality of uncharged fluids. Recent experiments using liquid-liquid immiscibilities with critical points... 

Table 1 Liquid-liquid imtruniscibilities and critical behavior of electrolyte solutions...

The prime question is, how these various long-range Couiombic and short-range specific interactions affect the critical behavior. In general, liquid-gas and liquid-liquid coexistence curves in the asymptotic regime near the CP can be described by a power law of the form "... 

Figure 6-5 shows the evolution of the dynamic moduli for a LM pectin/caldum system in the vicinity of the gel point as a function of the aging time. The evolution of the dynamic moduli was similar to that one observed as a function of the calcium concentration. In the initial period of aging the system showed the typical liquid-like behavior. Then both moduli increased with time, G increasing more rapidly than G" and with lower dependence on frequency. After 15 hr of aging, the system was just above the critical gel point, with a viscoelastic exponent A in the range of0.65-0.68. After the gel point, G passed beyond G", first in the lower frequency range where one can observe the initial formation of the elastic plateau. 

Thus close to the critical point of phase separation the behavior is first nonmonotonic and then the scaling behavior of Ig e) becomes a two-index and then a one-index. Similar expressions can be derived for gas-liquid critical point behavior. 

There has been criticism directed toward the oversimplicity of the cubic equation form, especially in the modeling of supercritical vapor-liquid equilibriiun. Nevertheless, this representation does describe at least qualitatively all the important characteristics of vapor-liquid equilibrium behavior. Alternative equations of state have been suggested, but none have been widely used and tested. Also, other EOS are significantly more complex and bring with them additional parameters which must be evaluated by regression from experimental data. 

Although the technical applications of low molar mass liquid crystals (LC) and liquid crystalline polymers (LCP) are relatively recent developments, liquid crystalline behavior has been known since 1888 when Reinitzer (1) observed that cholesteryl benzoate melted to form a turbid melt that eventually cleared at a higher temperature. The term liquid crystal was coined by Lehmann (2) to describe these materials. The first reference to a polymeric mesophase was in 1937 when Bawden and Pirie (2) observed that above a critical concentration, a solution of tobacco mosaic virus formed two phases, one of which was bireffingent. A liquid crystalline phase for a solution of a synthetic polymer, poly(7-benzyl-L-glutamate), was reported by Elliot and Ambrose (4) in 1950. 

Hensel, F. Critical behavior of metallic liquids. J. Phys. Condens. Matter, 1990,2 (Suppl. A), p. SA33-SA45. 

Schroer, W., Kleemeier, M., Plikat, M., Weiss, V., and Wiegand, S. Critical behavior of ionic solutions in non-polar solvents with a liquid liquid phase transition. J. Phys. Condensed Matter, 1996, 8, p. 9321-7. 

It should be observed that the temperature stability of this liquid crystalline phase with liquid oil layers of large dimensions does not show a "critical behavior. Increased temperature leads to a reduced thickness of the layers in an orderly fashion (8). 

We consider these two types simultaneously because they share their distinctive feature. That feature is an interruption in the critical locus where two liquid phases appear over a short range of compositions before the critical locus reappears as a liquid-liquid critical point. Unlike low-temperature LL behavior, varying the pressure has a strong impact on type IV or V liquid-liquid-equilibria, (LLE) making it appear or entirely disappear over a remarkably narrow range of pressures. Systems that exhibit type IV behavior include methane -I- 1-hexene and benzene -I- polyisobutylene, the only polymer solution mentioned by van Konynenburg and Scott. Peters has also speculated that methane and ethane mixed with alkylbenzenes will form type II-rV solutions, in contrast to the I, III, V solutions of the n-alkanes.f ... 

In the presence of polymorphs, developing a proper crystaUization process to control the desired crystal form is a real challenge. A good understanding of solid-liquid equilibrium behaviors under different conditions—for example, the temperature or solvent mixmre— is a must. Seeding and control of supersaUiration are two critical, if not indispensable, requirements. Example 7-5 shows an example of developing a crystallization process for a polymorphic compound. 

The earliest applications of the replica integral equation approach date back to the beginning of the 1990s. They focused on quite simple QA systems such as hard-sphere (HS) and LJ (12,6) fluids in HS matrices (see, for example. Refs. 4, 286, 290, 298, 303, 312, and 313 for reviews). Fiom a technical point of view, these studies have shown that the replica integral equations yield accurate correlation functions compared with parallel computer simulation results [292, 303, 314, 315]. Moreover, concerning phase behavior, it turned out that the simple LJ (12,6) fluid in HS matrices already displays features also observed in experiments of fluids confined to aerogels [131, 132]. These features concern shifts of the vapor liquid critical temperature toward values... 

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