Temperature—pressure critical locus

Upon lowering the temperature the critical locus, as already indicated, intersects the crystallizatimi surfiue in the ndghborhood of 1,900 atm and 110° C (9, 11) and at about 1.5 to 2 weight per cent polymer for a typical high pressure polyethylene (9). Diepen and coworkers refer to point of intersection as "second critical end point" (27). It is cmmected to the mdting point at normal temperature and... 

SFC (see Figure 7.6) occurs when both the critical temperature and critical pressure of the mobile phase are exceeded. (The locus of critical points is indicated in Figure 7.2 by the dashed line over the top of the two-phase region. It is also visible or partly visible in Figures 7.3-7.8). Compressibility, pressure tunability, and diffusion rates are higher in SFC than in SubFC and EFLC, and are much higher than in LC. 

Fig. 5.12 Two different 3-D representations of the phase diagram of 3-methylpyridine plus wa-ter(H/D). (a) T-P-x(3-MP) for three different H2O/D2O concentration ratios. The inner ellipse (light gray) and corresponding critical curves hold for (0 < W(D20)/wt% < 17). Intermediate ellipses stand for (17(D20)/wt% < 21), and the outer ellipses hold for (21(D20)/wt% < 100. There are four types of critical lines, and all extrema on these lines correspond to double critical points, (b) Phase diagram at approximately constant critical concentration 3-MP (x 0.08) showing the evolution of the diagram as the deuterium content of the solvent varies. The white line is the locus of temperature double critical points whose extrema (+) corresponds to the quadruple critical point. Note both diagrams include portions at negative pressure (Visak, Z. P., Rebelo, L. P. N. and Szydlowski, J. J. Phys. Chem. B. 107, 9837 (2003))...

We now extend the discussion of excess properties to examples that help us to better understand the nature of interactions in a variety of nonelectrolyte mixtures. We will give examples showing temperature and pressure effects, including an example of solutions near the critical locus of the mixture and into the supercritical fluid region. 

Two early studies of the phase equilibrium in the system hydrogen sulfide + carbon dioxide were Bierlein and Kay (1953) and Sobocinski and Kurata (1959). Bierlein and Kay (1953) measured vapor-liquid equilibrium (VLE) in the range of temperature from 0° to 100°C and pressures to 9 MPa, and they established the critical locus for the binary mixture. For this binary system, the critical locus is continuous between the two pure component critical points. Sobocinski and Kurata (1959) confirmed much of the work of Bierlein and Kay (1953) and extended it to temperatures as low as -95°C, the temperature at which solids are formed. Furthermore, liquid phase immiscibility was not observed in this system. Liquid H2S and C02 are completely miscible. 

For binary mixtures of hydrogen sulfide and carbon dioxide, the critical locus extends uninterrupted from the critical point of C02 to that of H2S. The critical point of a binary mixture can be estimated from the next two figures. Figure 3.4 shows the critical temperature as a function of the composition, and figure 3.5 gives the critical pressure. 

The critical point of a binary mixture occurs where the nose of a loop in Fig. 10.3 is tangent to the envelope curve. Put another way, the envelope curve is the critical locus. One can verify tliis by considering two closely adjacent loops and noting what happens to the point of intersection as their separation becomes infinitesimal. Figure 10.3 illustrates that the location of the critical point on the nose of the loop varies with composition. For a pure species the critical point is the highest temperature and highest pressure at which vapor and liquid phases can coexist, but for a mixture it is in general neither. Therefore under certain conditions a condensation process occurs as the result of a reduction in pressure. 

Figure 4. Temperature-pressure Figure 5. Critical temperature locus critical locus for CO2 - 1-hexene mixtures.

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 P-T projections, the composition axis is collapsed into the pressure-temperature plane. The vapor pressure curve for component A is labeled LV(A) and that for component B is labeled LV(B). These curves terminate at the component critical points (L = V) designated as hollow circles. In Fig. 2, dew pressure and bubble pressure curves for an intermediate composition x intersect at a point on the (L = V) critical locus where the liquid and vapor phases become critically identical. Normally, dew and bubble pressure curves are not shown in projections. They are shown here so that the construction of the related P-x at fixed T, and T-x at fixed P, phase diagrams is clearly illustrated. Each critical point on the critical locus corresponds to a fixed composition. Points close to the critical point of component A are critical points for mixtures with high concentrations of A, whereas points closer to the critical point of... 

In Fig. 3.2, we show the pressure-temperature view of the phase diagram for binary mixtures of methane and ethane. The point Ci represents the critical point of pure methane, and the point C2 represents the critical point of pure ethane. The curve connecting the points A and Ci is the vapor pressure curve for pure methane the curve connecting points B and C2 is the vapor pressure curve for pure ethane. The dotted curve connecting the points C and C2 is the critical locus. The critical points of the mixtures, where the coexisting liquid and vapor phases become identical, lie on this critical locus. 

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... 

Kikic et al. (41) employed only the values of P and T at the UCEP to evaluate these two constants ky and /y). The location of the UCEP was estimated from the experimental data by locating the intersection of the S-L-V line and (L = V) critical locus curve. For a type IP-Ttrace (with no temperature minimum with increasing pressure, e.g., a naphthalene-ethylene system), the solubility isotherm at Tucep provides an inflection point at P = PucEP (13). By setting the first and second derivatives to zero at this point, one can obtain the two equations needed for the two binary interaction parameters, kij and ly, respectively. When this approach was used for the inter-... 

Bubble points and dew points may be generated as described above for a given mixture over ranges of temperature and pressure. The locus of bubble points is the bubble point curve and the locus of dew points is the dew point curve. The two curves together define the phase envelope. In addition to the bubble point curve (total liquid saturated) and the dew point curve (total vapor saturated), other curves may be drawn representing constant vapor mole fraction. All these curves meet at one point, the critical point, where the vapor and liquid phases lose their distinctive characteristics and merge into a single, dense phase. 

In Fig. 10.3-2 we have plotted, for various fixed compositions, the bubble and dew point pressures of this mixture as a function of temperature. The leftmost curve in this figure is the vapor pressure of pure ethane as a function of temperature, terminating in the critical point of ethane (for a pure component, the coexisting vapor and liquid are necessarily of the same composition, so the bubble and dew pressures are identical and equal to the vapor pressure). Similarly, the rightmost curve is the vapor pressure of pure propylene, terminating at the propylene critical point. The intermediate curves (loops) are the bubble and dew point curves relating temperature and pressure for various fixed compositions. Finally, there is aline in Fig. 10.3-2 connecting the critical points of the mixtures of various compositions this line is the critical locus of ethane-propylene mixtures. 

One example will serve to underscore the reason for the advantage over Chao-Seader at high pressure. Figure 1 shows the convergence of RKJZ K-values to unity as the mixture critical pressure is approached, for a temperature and composition on the mixture critical locus for the methane-ethane-butane ternary (20). This mixture was chosen in order to check RKJZ apparent critical pressure vs. the 1972 corresponding-states correlation of Teja and Rowlinson (21), which presumably has a better theoretical basis than the RKJZ method. In these comparisons, the Teja and Rowlinson correlation uses two interaction parameters per binary pair, based primarily on fits to binary critical loci the RKJZ method uses Cij = 0 for all binaries, based on binary VLE data. 

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