Binary systems critical solution point

In the next chapter we shall show that at the critical solution point of a binary system... 

LIQUID-LIQUID CURVE AND CRITICAL SOLUTION POINT. In the now classical theory of regular solutions developed by Scatchard (10) and Hildebrand (5) with the nonideal entropy correction given by Flory and Huggins (5), the activities of the components of a binary system are given by... 

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. 

Gravitational Effects.—In one-component fluids, the existence of sizeable density gradients in equilibrium systems near the critical point are well known and their eflFect on the determination of critical exponents is recognized. " An analogous situation involves composition gradients near the critical solution point in binary mixtures whenever the densities of the two pure liquids are appreciably different. 

Fora quasi-binary system, the critical solution point is located in the extremum of the spinodal and hence the necessary condition is... 

For monodisperse primary chains, we have a strictly two-component system, and the thermodynamic stability limit (spinodal) is given by a cj), T) = 0, where cr is the factor (7.123). Further, for such strictly binary systems, the critical solution point, if it exists in the pregel regime, can be found by the additional condition d A o/dcp = 0. The condition is given explicitly by... 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

In most cases the critical temperature of the solute is above room temperature. As can be seen in the binary system H2S-H20 drawn in Fig. 6, the three-phase line HL2G is then intersected by the three-phase line HL G. The point of intersection represents the four-phase equilibrium HLXL2G and indicates the temperature... 

Ternary equilibrium curves calculated by Scott,who developed the theory given here, are shown in Fig. 124 for x = 1000 and several values of X23. Tie lines are parallel to the 2,3-axis. The solute in each phase consists of a preponderance of one polymer component and a small proportion of the other. Critical points, which are easily derived from the analogy to a binary system, occur at... 

Figu re I. I. The pressure-temperature projection of a typical binary solvent-solute system. See text for discussion. SLV, solid/liquid/vapor LCEP, lower critical end point UCEP, upper critical end point. 

As binary PPE/SAN blends form the reference systems and the starting point for the foaming analysis, their miscibility will be considered first. As demonstrated in the literature [41, 42], both miscibility and phase adhesion of PPE/SAN blends are critically dependent on the composition of SAN, more precisely on the ratio between styrene and acrylonitrile (AN). Miscibility at all temperatures occurs up to 9.8 wt% of AN in SAN, whereas higher contents above 12.4 wt% lead to phase separation, independent of the temperature. Intermediate compositions exhibit a lower critical solution temperature behavior (LCST). Taking into account the technically relevant AN content SAN copolymers between 19 and 35 wt%, blends of SAN and PPE are not miscible. As the AN content of the SAN copolymer, selected in this work, is 19 wt%, the observed PPE/SAN blends show a distinct two-phase structure and an interfacial width of only 5 nm [42],... 

The dec8y rate of the order-parameter fluctuations is proportional to the thermal diffusivity in case of pure gases near the vapor-liquid critical point and is proportional to the binary diffusion coefficient in case of liquid mixtures near the critical mixing point (6). Recently, we reported (7) single-exponential decay rate of the order-parameter fluctuations in dilute sugercritical solutions of liquid hydrocarbons in CO for T - T 10 C. This implied that the time scales associated with thermal diffusion and mass diffusion are similar in these systems. 

Besides these thermodynamic criteria, the most common approach used in the literature is based on the operation at pressures above the binary (liquid - SC-CO2) mixture critical point, completely neglecting the influence of solute on VLEs of the system. But, the solubility behavior of a binary supercritical COj-containing system is frequently changed by the addition of a low volatile third component as the solute to be precipitated. In particular, the so-called cosolvency effect can occur when a mixture of two components solvent+solute is better soluble in a supercritical solvent than each of the pure components alone. In contrast to this behavior, a ternary system can show poorer solubility compared with the binary systems antisolvent+solvent and antisol-vent+solute a system with these characteristics is called a non-cosolvency (antisolvent) system. hi particular, in the case of the SAS process, they hypothesize that the solute does not induce cosolvency effects, because the scope of this process lies in the use of COj as an antisolvent for the solute, inducing its precipitation. 

In the light of these considerations, a different approach based on ternary system thermodynamics could be considered. However, the phase behavior of temaiy systems could be very complex and there is a considerable lack of data on ternary systems containing a component of low volatility therefore, a possible compromise could be to consider that the solute addition can produce the shift of the mixture critical point (MCP) (i.e., the pressure at which the ternary mixture is supercritical) with respect to binary system VLEs and the modification of this kind of system that is formed according to the van-Konynenburg and Scott classification. ... 

Consider diffusion in a binary liquid mixture exhibiting an upper critical solution temperature (UCST) or lower critical solution temperature (LCST) (see Fig. 3.1). Let us take a mixture at the critical composition x at point A just above the UCST. Any concentration fluctuation at A will tend to be smeared out due to the effects of diffusion in this homogeneous mixture. On the other hand, any fluctuation of a system at point B, infinitesimally below the UCST, will lead to separation in two phases. Similarly, the mixture at point D, just below the LCST is stable whereas the mixture at point C, just above the LCST is unstable and will separate into two phases. 

As described in Figure 4b the phase behavior of a type II binary system is depicted by the vapor pressure (L-V boundary) curves for the pure components, sublimation (S-V boundary) and melting (S-L boundary) curves for the solid component, and especially the S-L-V line on the P-T space. For an organic solid drug solute, the triple-point temperature is sufficiently higher than the critical temperature of the SCF solvent. The (L = V) critical locus has two branches and is intersected by two S-L-V lines at LfCEP and LCEP, respectively, in the presence of the solid phase. The S-L-V line indicates that the melting of the solid is lowered in the presence of the SCF solvent component as it is dissolved in the molten (liquid) phase. The S-L-V line... 

The fit of the last binary pair, the methane-octane system, is shown in figure 5.3. This fit was obtained with a value of kij equal to 0.01. A few words of caution are warranted in this case. As noted in chapter 3, methane-hydrocarbon mixtures are expected to deviate from type-I behavior if the methane-solute carbon ratio is greater than 5. The P-x data shown in figure 5.3 are far above the temperatures where a three-phase LLV line is expected for this binary system. However, a three-phase LLV line is predicted near the critical point of methane using A ,y equal to 0.01. 

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 sodium-lithium phase system has been studied by thermal analysis in the liquid and solid regions to temperatures in excess of 400°C. Two liquid phases separate at 170.6°C. with compositions of 3.4 and 91.6 atom % sodium. The critical solution temperature is 442° zt 10°C. at a composition of 40.3 atom % sodium. The freezing point of pure lithium is depressed from 180.5°C. to 170.6°C. by the addition of 3.4 atom % sodium, and the freezing point of pure sodium is depressed from 97.8° to 92.2°C. by the addition of 3.8 atom % lithium. From 170.6° to 92.2°C. one liquid phase exists in equilibrium with pure lithium. Regardless of the similarity in the properties of the pure liquid metals, the binary system deviates markedly from simple nonideal behavior even in the very dilute solutions. Correlation of the experimentally observed data with the Scatchard-Hildebrand regular solution model using the Flory-Huggins entropy correction is discussed. 

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