Phase boundary curve

The normal melting, boiling, and triple points give three points on the phase boundary curves. To construct the curves from knowledge of these three points, use the common features of phase diagrams the vapor-liquid and vapor-solid boundaries of phase diagrams slope upward, the liquid-solid line is nearly vertical, and the vapor-solid line begins at P = 0 and P = 0 atm. 

Binary liquid-liquid equilibria are usually represented as temperature-vol-ume fraction diagrams. These diagrams give the mutual solubilities in the two coexisting liquid phases, as functions of temperature. Figure 2F-3 illustrates six types of phase behavior that have been observed in binary LLE. A horizontal line intersects the phase boundary curve at two points which give the compositions of the two phases in equilibrium at the corresponding temperature. 

The slope of the phase boundary curve dpidt can be estimated from the Ttr - Pit plot obtained by using a PVT or high-pressure differential thermal analysis (DTA) method [118,119]. The volume-dependent entropy (correction for the volume change) ASy, the transition entropy (AStr)p under ordinary pressure, and the constant-volume entropy (AStr)v obtained therefrom are arranged in this order in Tables 2,3, and 4. 

The relation between the slope of the phase boundary curve and properties of the substance is discussed in Section 9.2... 

Figure 6. Domains of miscibility (shaded areas) at 290°C compared with calculated phase boundaries (curves) = - 0.043, = 0.200, g = 0.150.

In an amorphous polymer blend system, we can determine the phase boundary curve, i.e. a temperature versus composition phase diagram, by using DSC to follow the appearance of two separate T s at a certain annealing temperature. The phase diagram can also be obtained simply by optical observation. The temperature at which the first faint opalescence appears on heating is designated the cloud point. 

Figure 3.6 Compatibility triangles (dashed lines) superimposed on the stability fields 1 to 10, and directions of falling temperatures on the phase boundary curves (arrowheads), determined according to the Alkemade theorem.

A repositioning of the phase boundary curves in high-temperature direction indicates that two-phase heterogeneous region, terminated by critical curve CH4 - H2O in the binary system, is spreading into higher temperature region with the addition of NaCl. 

The behavior changes as /Ac decreases. At xAc — 60, the G appears between the L and C phases, extending over a composition range of a few percent on each side of the diagram, but no other ordered phase becomes stable. As xAc decreases further, all phase boundaries curve toward /a = 0.5. The G phase terminates at triple points at xAc = 11.14 and /a = 0.452 and 0.548, where it coexists with the L and C phases. Similarly, the cp-S phase terminates at triple points at xAc = 17.67 and/a = 0.235 and 0.765 where it coexists with the D and bcc-S phases. However,... 

Figure 5. Phase boundary curves for constant concentrations (isopleths) for the ternary system H O-COt-NaCl...

On further investigation, Shashidar [20] explains, a remarkable situation was found. In every case, one of the materials had an inherent SmC phase, while the other did not. As there was no observed miscibility gap, in every case there had to be a N-SmA-SMC point at very low temperatures. They also knew from their studies at high pressure [54] as well as their detailed studies on mixtures exhibiting the N-SmA-SmC and the Nre-SmC-SmA point (see Figs. 4 and 12) [16], that the phase diagram has the universal spiral topology where phase boundaries curve as the N-SmA-SmC point is approached. Shashidhar [20] concludes that, as re-entrance in nonpolar compounds results from the universal curvature of the phase boundaries as the N-SmA-SMC point is approached, its origin is the fluctuations associated with the N-SmA-SmC multicritical point. 

Following Example 4.1, approximate ln(T2/Ti) by rewriting it as ln(l + x) with X = (T2- Ti)/Ti and truncating the power series expansion (see Appendix A) to the first term in x. Does this indicate that the phase boundary curves between liquids and solids can be approximated as straight lines If so, for what conditions does this hold ... 

It is expected [16-18] that thermally induced phase separation can be reversed when polymer blends are annealed below their respective LCST s if the system is in equilibrium. However, in the present PES/PI systems, as in the PBI/PI systems [19], reversibility is not observed. It is obvious that the data presented above represent only apparent phase boundary curves. Because of the ridigity of the PES and PI chains, the mobility of the segments is limited and the system is highly viscous. The observed one-phase system corresponds to a homogeneous "frozen" structure fomied from a solution of the constituents as the solvent evaporates. When relaxation times are sufficiently reduced, the chains have sufficient mobility to fomi a stable two-phase state. The location of the true phase boundary curve in the present case for PES/PI blends may lie below the Tg-composition line. 

As discussed above it is clear that the phase boundary curves obtained under these conditions are true equilibrium curves. Reversible phase separation was observed for PES/PI XU 218 blends at a TMS content of 25 wt% or greater and for PES/PI 2080 blends at a TMS content of 30 wt% or greater. 

Figure 7. Tg-composition line and phase boundary curve for PES/PI XU 218 blends containing 15 wt%...

To obtain a true equilibrium phase boundary curve for solvent-free PES/PI blends, the data collected for samples containing different amounts of TMS were extrapolated to zero solvent content. For a 50/50 wt% PES/PI XU 218 blend a phase separation temperature of 140 C is obtained, a temperature lower than the blend Tg (267°C). Similar results are observed for PES/PI 2080 blends. Figure 9. 

We note some similarities between the present PES/PI/TMS blends and the PMMA/SAN/DMP system reported by Bernstein et al. [20], These authors found that phase separation in the PMMA/SAN system is not reversible but addition of 15 wt% or more of DMP induced reversibility. These effects were explained by the proposal that "equation of state" and "entropy of mixing" factors are working in opposition. In this system it is our belief that the reversible and irreversible processes merely reflect thermodynamic and kinetic considerations. The displacement of the phase boundary curve for the PES/PI/TMS system to higher temperatures is due to contributions to the free volume from TMS [21-23]. 

When tetramethylene sulfone was added to PES/PI blends the blend Tg s were sufficiently depressed and the window between the phase boundary curve and the Tg-composition line was expanded so that equilibrium data could be obtained. At TMS contents greater than 25 or 30 wt% an equilibrium LCST could be detected which occurred at higher temperatures as the TMS content increased. Concurrently, the phase separation process became experimentally reversible. 

As may also be noted from Figure 9.2, all three of the phase boundary curves intersect at a common point, which is labeled O (for this H2O system, at a temperature of 273.16 K and a pressure of 6.04 X 10 atm). This means that at this point only, all of the sohd, hquid, and vapor phases are simultaneously in equilibrium with one another. Appropriately, this, and any other point on a P-T phase diagram where three phases are in equilibrium, is called a triple point sometimes it is also termed an invariant point inasmuch as its position is distinct, or fixed by definite values of pressure and temperature. Any deviation from this point by a change of temperature and/or pressure will cause at least one of the phases to disappear. 

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