Lower critical end point

Fig. 6. Qualitative piessuie—tempeiatuie diagiams depicting ctitical curves for the six types of phase behaviors for binary systems, where C or Cp corresponds to pure component critical point G, vapor 1, Hquid U, upper critical end point and U, lower critical end point. Dashed curves are critical lines or phase boundaries (5). (a) Class I, the Ar—Kr system (b) Class 11, the CO2—CgH g system (c) Class 111, where the dashed lines A, B, C, and D correspond to the H2—CO, CH —H2S, He—H2, and He—CH system, respectively (d) Class IV, the CH —C H system (e) Class V, the C2H -C2H OH...

Fig. 9. Sections at constant temperatures lying between the critical point of the first component M, and the lower critical end point, O.

Fig. 10. The mole fraction of carbon dioxide in saturated solutions in air at — 110°C (above the lower critical end point). The full line is the experimental curve of Webster and the dashed curves are 1, an ideal gas mixture 2, an ideal gas mixture with Poynting s correction and 3, the solubility calculated from Eq. 8 and the principle of corresponding states.

Ewald22 studied this system at 150° and 155°K. These temperatures are above the critical temperature of pure nitrogen, 126°K, but he found that they are below the lower critical end point of the mixture. The saturated vapor pressure of the system was 50 atm at 150°K and 57 atm at 155°K. The mole fraction of xenon in the saturated gas (X in Figs. 5 and 9) was 0.035 and 0.045 at these temperatures, respectively. 

Holder and Maass34 found that the lower critical end point was at 44.85°C, that is, 12.5°C above the critical temperature of pure ethane. They did not measure the pressure and their claim of having detected different solubilities in different parts of the fluid at temperatures above this point probably does not apply to a system at equilibrium in the absence of a gravitational field.66... 

So far, we have considered only one type of binary (liquid -I- liquid) equilibrium. Examples can be found in the literature where a lower critical end point (LCEP) is obtained instead of a UCEP, and where both a LCEP and a UCEP are obtained for the same system. Also, (liquid + liquid) equilibria can be combined with (vapor + liquid) equilibria to give interesting (fluid + fluid)... 

The S-L-V curve intersects the gas-liquid critical curve in two points the lower critical end point (LCEP) and the upper critical end point (UCEP). At these two points, the liquid and gas phases merge into a single fluid-phase in the presence of excess solid. At temperatures between Tlcep and Tucep a S-V equilibrium is observed. The solubility of the heavy component in the gas phase increases very rapidly with pressure near the LCEP and the UCEP. Near the LCEP the solubility of heavy component in the light one is limited by the low temperatures. In contrast, near the UCEP the solubility of heavy component in the light one is high, owing to the much higher temperatures [6],... 

We can use thermodynamics to predict the arithmetic sign of the excess molar properties above above the temperature (UCST) of the upper critical end point (UCEP), and below the temperature (LCST) of a lower critical end point (LCEP). At an (UCEP), the chemical potential goes through a point of inflection. The result is that... 

Equation (17.31) applies equally well at a lower critical end point (LCEP). Furthermore, the Gibbs-Duhem equation equation (11.22) requires that if these equations are valid for component 2, then the same must be so for component 1. That is... 

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. 

Dlepen and Scheffer ( 6) were the first to show that near either the lower or upper critical end point the solubility of a solid in a supercritical fluid is enhanced and also very sensitive to changes in temperature and pressure our solubility isotherms show this effect for both end points. First, the isotherms cross at about 140 bar so that the solubility at the lowest temperature (50.0°C) is largest at 120 bar. This is a result of approaching the lower critical end point region (which should be close to the critical point of pure C02 as previously mentioned). At temperatures and pressures near this LCEP the solubility enhancement results in lower temperature isotherms having the greater solubilities. The effect of the upper critical end point is also well shown by our data. The 58.5°C isotherm shows a large increase in solubility at about 235 bar the slope of the isotherm is near zero. As Van Welie and Diepen... 

The solubility of a solid in a supercritical fluid has been described by Gitterman and Procaccia.(lO) The region of interest chromatographically will be for infinitely dilute solutions whose concentration is far removed from the lower critical end point (LCEP) of the solution. Therefore the solubility of the solute in a supercritical fluid at infinite dilution far from criticality can be approximated as,... 

Type II (Solid-Fluid) System. In type II systems (when the solid and the SCF component are very dissimilar in molecular size, structure, and polarity), the S-L-V line is no longer continuous, and the critical (L = V) mixture curve also is not continuous. The branch of the three-phase S-L-V line starting with the triple point of the solid solute does not bend as much toward lower temperature with increasing pressure as it does in the case of type I system. This is because the SCF component is not very soluble in the heavy molten solute. The S-L-V line rises sharply with pressure and intersects the upper branch of the critical mixture (L = V) curve at the upper critical end point (LfCEP), and the lower temperature branch of the S-L-V line intersects the critical mixture curve at the lower critical end point (LCEP). Between the two branches of the S-L-V line there exists S-V equilibrium only (13). 

If the operating temperature is now increased to T, the phase behavior shown in figure 3.15d occurs. At Ty the mixture critical point pressure of the vapor-liquid envelope occurs precisely at the same pressure at which the three-phase SLV line is intersected. Hence, a vapor-liquid mixture critical point is observed in the presence of excess solid. This vapor-liquid mixture critical point in the presence of excess solid is the lower critical end point (LCEP) (Diepen and Scheffer, 1948a). If the temperature is increased slightly above the LCEP temperature, only solid-SCF phase behavior is observed at all pressures, since the three-j)hase (SLV) line ends at the LCEP. 

Category VI phase behavior, shown in Fig. 10.3-3/, occurs with components that are so dissimilar that component 2 has a melting or triple point (Mj) that is well above the critical temperature of component 1. In this case there are two regions of solid-liquid-vapor equilibrium (SLVE). One starts at the triple point of pure component 2 (M ) and intersects the liquid-vapor critical line at the upper critical end point U. The second solid-liquid-vapor critical line starts below the melting point Mt and intersects the vapor-liquid critical line starting at component 1 at the lower critical end point L. Between the lower and upper critical points only solid-vapor (or solid-fluid) equilibrium exists. 

A three-phase line will terminate when two of the three phases become identical such states mark the intersection of the three-phase line with a critical line. Consider the three-phase vapor-hquid-hquid situation. If the two liquid phases become identical, then the VLLE line has intersected a locus of liquid-liquid critical points. Similarly, if the vapor phase becomes identical to one of the liquid phases, then the VLLE line has intersected a gas-hquid critical line. These intersections are called upper critical end points (UCEP) if they occur at a maximum temperature on the VLLE locus they are called lower critical end points (LCEP) if they occur at a minimum temperature. The number and kinds of critical end points help distinguish the classes in the Scott-van Konynenburg scheme. 

LCEP LOWER CRITICAL END POINT UCEP UPPER CRITICAL END POINT... 

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