Critical end-point

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

Fig. 2. The phase diagrams and terminology of a microemulsion system close to its two critical end points, where the middle phase and one of the binodals...

Fig. 3. Typical nonionic amphiphile—oil—water—temperature phase diagram, illustrating (a) the S-shaped curve of T, M, and B compositions, (b) the lines of plait points, (c) the lower and upper critical end points (at and respectively), and (d) the lower and upper critical tielines.

Fig. 5. Lower and upper critical tielines in a quaternary system at different temperatures and a plot of the critical end point salinities vs temperature, illustrating lower critical endline, upper critical endline, optimal line, and tricritical poiat for four-dimensional amphiphile—oil—water—electrolyte-temperature...

Changing the distance between the critical points requires a new variable (in addition to the three independent fractional concentrations of the four-component system). As illustrated by Figure 5, the addition of a fourth thermodynamic dimension makes it possible for the two critical end points to approach each other, until they occur at the same point. As the distance between the critical end points decreases and the height of the stack of tietriangles becomes smaller and smaller, the tietriangles also shrink. The distance between the critical end points (see Fig. 5) and the size of the tietriangles depend on the distance from the tricritical point. These dependencies also are described scaling theory equations, as are physical properties such as iuterfacial... 

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. 8. The (p, T) projection of a system in which the saturated vapor pressure curves cut the critical line at lower and upper critical end points,...

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. 

Dokoupil, van Soest, and Swenker18 have examined this system in detail from 25° to 70°K and at pressures up to 50 atm. The critical points of the pure substances are at 33° and 126°K and the lower and upper critical end points are at about 37° and 61°K. The majority of their measurements lie between the critical end points. 

Braune and Strassman8 measured the concentration of iodine in gaseous carbon dioxide at pressures up to 50 atm from 32° to 98°C. They passed the carbon dioxide over an excess of solid iodine and analyzed the effluent mixtures. Their pressures were too low to find the saturation vapor pressures or to show whether or not critical end points were formed. 

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... 

Detailed measurements of the solubility between the lower and upper critical end points have been made only for the solutions in ethylene of naphthalene,14 hexachlorethane,30 and />-iodochloro-benzene.21 Atack and Schneider2 have used dilute solutions of the last-named substance to study the formation of clusters near the gas-liquid critical point of ethane. 

Figure 8.17 Vapor fugacity for component 2 in a liquid mixture. At temperature T, large positive deviations from Raoult s law occur. At a lower temperature, the vapor fugacity curve goes through a point of inflection (point c), which becomes a critical point known as the upper critical end point (UCEP). The temperature Tc at which this happens is known as the upper critical solution temperature (UCST). At temperatures less than Tc, the mixture separates into two phases with compositions given by points a and b. Component 1 would show similar behavior, with a point of inflection in the f against X2 curve at Tc, and a discontinuity at 7V...

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

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)... 

Table 28 outlines the critical end-points for the organotin species and the estimated PNECs derived using appropriate uncertainty factors. For the purposes of comparability, all values have been converted to the chloride salt. 

NOAEL In this example, 18r NOAEL is the critical end point for which an intermediate inhalation exposure MRL is based. As you can see from the LSE figure key, the open-circle symbol indicates to a NOAEL for the test species-rat. The key number 18 corresponds to the entry in the LSE table. The dashed descending arrow indicates the extrapolation from the exposure level of 3 ppm (see entry 18 in the Table) to the MRL of 0.005 ppm (see footnote "b" in the LSE table). 

Sediment may be added by bulk mixing via imbricate thnisting (Bebout and Barton 2002), dehydration (Class et al. 2000), or melting (Johnson and Plank 1999). The latter two may differ in their P-T conditions and, therefore, residual mineralogy as well as relevant partition coefficients. In general, fluids are less effective transport agents than melts (i.e., trace elements are more soluble in melt than in pure water or even brine), but fluid/solid partitioning can fractionate some elements, notably Ba-Th and U-Th, more than melt/solid. However, as pressure increases, the distinction between fluid and melt decreases as their mutual solubility increases and they approach a critical end-point. 

Wilding, N. B., Critical end point behavior in a binary fluid mixture, Phys. Rev. E 1997,... 

NOAEL In this example, 18r NOAEL is the critical end point W which an intermediate... 

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