Critical temperature locus

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

Figure 3 was constructed as mentioned previously from Fig. 2 by cross-plotting isotherms of reduced conductivity vs. A. The thermal conductivity data for carbon monoxide were not used. Then from Fig. 3 the values of k for tritium (A = 1.00) were obtained to predict the temperature dependence of the thermal conductivity of tritium along the vapor pressure curve as shown in Fig, 2. Lastly, it may be pointed out that an extension of the Ne data of Ldchtermann P ] to the critical-temperature locus would appear to give some values of the thermal conductivity which would be very near to those predicted for tritium, and would also require an S-shaped curve, which seems improbable in view of the value of T for neon, i.e, 1.247. A curve for the thermal conductivity of Ne predicated upon behavior similar to argon and tritium is also shown. Derivation of the thermal conductivities of the unsymmetrical isotopic species of hydrogen—HT, HD, and DT— is a triviality and can easily be obtained from Fig. 3. Note that de Boer s theory does not distinguish between the behavior of HT and D2 P ]. For the unsymmetric isotope HT the value of A should be computed after Friedmann [ ] as...

Figure 7.4 The Subcritical Fluid Cliromatography range. This occupies the volume in the phase diagram below the locus of critical temperatures, above and below the locus of critical pressures, and is composed mostly of the more volatile mobile-phase component. Reproduced by peimission of the American Chemical Society.

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. 

Figure 2-10 shows a more nearly complete pressure-volume diagram.2 The dashed line shows the locus of all bubble points and dew points. The area within the dashed line indicates conditions for which liquid and gas coexist. Often this area is called the saturation envelope. The bubble-point line and dew-point line coincide at the critical point. Notice that the isotherm at the critical temperature shows a point of horizontal inflection as it passes through the critical pressure. 

Notice that the locus of the critical points connects the critical pressure of ethane, 708 psia, to the critical pressure of methane, 668 psia. When the temperature exceeds the critical temperature of both components, it is not possible for any mixture of the two components to have two phases. 

From Figure 14.10, we see that the system represented by Figure 14.9 is of type I. Shown for this type of system are several possible projections of the critical locus that can occur. Mixtures represented by (1), in which the critical locus is convex upwards, are the most common, and occur when there are not large polarity differences between the molecules of the components, but moderately large differences between the critical temperatures. 

Mixtures whose critical locus is represented by (4) are extremely rare. For these mixtures the critical locus extends to temperatures above the critical temperatures of both components. The phase separation that occurs along this critical locus is sometimes referred to as (gas + gas) immiscibility, since two phases are present at a temperature above the critical temperatures of both components. 

Providing a satisfying interpolation of the susceptibility minimum, the temperature-dependence of the parameters %[ nm(T) and vmln(Tj (i.e., the locus of the minimum), as well as that of xa(T), is expected to yield the critical temperature Tc [cf. Eq. (27)]. Again, all the exponents determining the... 

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 essence of the above model is the assumption that pore segments of radius r in which the liquid is above the hysteresis temperature rH(/ i) cannot cause delayed desorption. This assumption is immediately plausible if 7h were to coincide with the pore critical temperature, as in this case the pore fluid is in a supercritical state above Tn, and thus the mass transport is not retarded by a gas/liquid meniscus. Some aspects of our model are remeniscent of the tensile strength hypothesis, although the concept of a pore critical temperature was not discussed at the time when that hypothesis was proposed. On the other hand, the present picture does not imply that the locus of lower closure points (p// o)L should be independent of the nature of the porous matrix. We conjecture that (/>/ o)l is given by the locus of pore hysteresis points of the fluid in open-pore systems of uniform pore size. A more comprehensive discussion of this model will be presented elsewhere."... 

As indicated before the locus of the phase diagram of a confined fluid compared to the coexistence curve of the bulk fluid is of importance for the occurence of pore condensation and hysteresis, i.e. for the shape of the sorption isotherm. It is expected that the critical temperature and the triple point temperature will be shifted to lower values for a confined fluid compared to a bulk fluid, i.e. the smaller the pore width the lower the critical temperature and triple point temperature of the pore fluid [8,9,20]. Pore condensation occurs whenever the pore... 

It would be convenient if the critical temperature of a mixture were the mole weighted average of the critical temperatures of its pure components, and the critical pressure of a mixture were simply a mole weighted average of the critical pressures of the pure components (the concept used in Kay s rule), but these maxims simply are not true, as shown in Fig. 3.22. The pseudocritical temperature falls on the dashed line between the critical temperatures of CO2 and SO2, whereas the actual critical point for the mixture lies somewhere else. The solid line in Fig. 3.22 illustrates how the locus of the actual critical points diverges from the locus of the pseudo critical points. 

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... 

Figure 14-6 Phase behavior and locus of critical temperatures and pressures for binary mixtures of components A and B.

At the critical temperature and pressure the liquid and vapor phases are indistinguishable. One such point exists for each envelope. The curve connecting the points for all envelopes is called the locus of criticals. ... 

The simplest class of binary phase diagram is class I as shown in Figure 1.2-3. The component with the lower critical temperature is designated as component 1. The solid lines in Figure 1.2-3(b) represent the pure component liquid-vapor coexistence curves which terminate at the pure component critical points (Cj and C2). The feature of importance in this phase diagram is that the mixture critical line (dashed line in Figure 1.2-3(b)) is continuous between the two critical points. The mixture critical line represents the locus of critical points for all mixtures of the two components. The area bounded by the solid and dashed lines represents the two-phase, liquid-vapor (LV) region. The mixture-critical... 

Success in correlating both thermal conductivity and viscosity by Thodos et al. pi.32] for the heavier diatomic molecules provides a basis for establishing the heavy-molecule end of the critical-point loci as nearly horizontal asymptotic lines. For the thermal conductivity no other good tie points exist, and the critical-point locus is therefore more conjectural. It is believed that a single critical point locus will adequately include all types of molecules. At the critical point the density is lower and hence the influence of orientational effects in two-body interactions will be smaller than at the triple point. Fortunately the effect of errors in locating the helium end of this locus is minimized with respect to predicting the behavior of the thermal conductivity for H2, D2, etc. The high-temperature ends of the He, He H2, D2, A, and N2 thermal conductivity curves were, in each case, extrapolated (broken lines) to their respective reduced critical temperatures. 

To obtain a value for the viscosity of He" at the critical temperature for this analysis, the following procedure was followed. The constant-density viscosity measurements of Tjerkstra were extrapolated linearly to Tc as shown in Fig. 5. The 17 values at Tc, so obtained, w ere then plotted vs. density on semilog paper and extrapolated (shown in Fig. 6) to the critical density as reported by Edwards and Woodbury [ ] to determine rjc. The critical-point locus of Fig. 4 was constructed through the He and He critical-point viscosity values and those for the N2 and CO limits obtained by Thodos. The H2, N2, and He viscosity curves of Fig. 4 were then extrapolated by smoothed curves (broken lines) to their respective critical temperatures. Figure 7 was constructed in much the same fashion as already described for Fig. 3. Values of reduced viscosity at A = 1.00 and 1.22 were then taken from Fig. 7 to predict the respective viscosities of tritium and deuterium (broken lines of Fig, 4). The viscosity curves of Ne and CO closely parallel those of A and N2, respectively. 

The prediction of liquid viscosities was greatly facilitated by extrapolation of the data of Tjerkstra for He to give the critical-point viscosity for He, as 31.2 x 10 g/cm-sec. This value was particularly useful in the construction of the viscosity critical-point locus. Values for those transport properties at the critical temperatures believed to be reliably predicted are given in Table IV. 

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