Quantitative Phase Behavior

Analysis of the kinetics of the recovery process in terms of Tmax. Ton (Figure 6.2) provides a further means to assess quantitatively phase behavior. The structural dependence of these parameters has made it possible to investigate the phase... 

A third motivation for studying gas solubilities in ILs is the potential to use compressed gases or supercritical fluids to separate species from an IL mixture. As an example, we have shown that it is possible to recover a wide variety of solutes from ILs by supercritical CO2 extraction [9]. An advantage of this technology is that the solutes can be removed quantitatively without any cross-contamination of the CO2 with the IL. Such separations should be possible with a wide variety of other compressed gases, such as C2LL6, C2LL4, and SF. Clearly, the phase behavior of the gas in question with the IL is important for this application. 

In their test system, the researchers used the ionic liquid l-butyl-3-methylimidazol-ium hexafluorophosphate (bmim)(PF6), which is stable in the presence of oxygen and water, with naphthalene as a low-volatility model solute. Spectroscopic analysis revealed quantitative recovery of the solute in the supercritical CO2 extract with no contamination from the ionic liquid. They found that CO2 is highly soluble in (bmim)(PF6) reaching a mole fraction of 0.6 at 8 MPa, yet the two phases are not completely miscible. The phase behavior of the ionic liquid-C02 system resembles that of a cross-linked polymer-solvent system (Moerkerke et al., 1998), even though... 

More than half a century ago, Bawden and Pirie [77] found that aqueous solutions of tobacco mosaic virus (TMV), a charged rodlike virus, formed a liquid crystal phase at as very low a concentration as 2%. To explain such remarkable liquid crystallinity was one of the central themes in the famous 1949 paper of Onsager [2], However, systematic experimental studies on the phase behavior in stiff polyelectrolyte solutions have begun only recently. At present, phase equilibrium data on aqueous solutions qualified for quantitative discussion are available for four stiff polyelectrolytes, TMV, DNA, xanthan (a double helical polysaccharide), and fd-virus. 

Real substances often deviate from the idealized models employed in simulation studies. For instance, many complex fluids, whether natural or synthetic in origin, comprise mixtures of similar rather than identical constituents. Similarly, crystalline phases usually exhibit a finite concentration of defects that disturb the otherwise perfect crystalline order. The presence of imperfections can significantly alter phase behavior with respect to the idealized case. If one is to realize the goal of obtaining quantitatively accurate simulation data for real substances, the effects of imperfections must be incorporated. In this section we consider the state-of-the-art in dealing with two kinds of imperfection, poly-dispersity and point defects in crystals. 

Of course, nanocomposites are not the only area where mesoscale theories are being used to predict nanostructure and morphology. Other applications include—but are not limited to—block copolymer-based materials, surfactant and lipid liquid crystalline phases, micro-encapsulation of drugs and other actives, and phase behavior of polymer blends and solutions. In all these areas, mesoscale models are utilized to describe—qualitatively and often semi-quantitatively—how the structure of each component and the overall formulation influence the formation of the nanoscale morphology. 

The quantitative data associated with these samples have been reported earlier (18), and for comparison with Figure 14 the dependence of the various regions of phase behavior on Mn and W of the initial PS is summarized in Figure 18. 

In the previous section we have described the three types of phase behavior observed in the low-molecular-weight PMMA/PS system and reviewed the four types observed in the low-molecular-weight PS/PMMA system. These various phase relationships have been studied in terms of their dependence on the molecular weight (Mn) and weight percent (W) of the initial polymer present. Further, we have presented quantitative data concerning the sizes of the dispersed particles, again correlated to variations in Mn and W. In this section we will discuss the results in terms of the poly (methyl methacrylate )/polystyrene/styrene and poly-styrene/poly( methyl methacrylate)/methyl methacrylate ternary phase diagrams, whichever is appropriate. 

In a previous paper (6), we have reported (quantitative measurements of phase compositions and molar volumes for licquid-licquid-gas, licquid-licquid-licquid, and licquid-licquid-licquid-gas ecquilibria for ternary mixtures of water, carbon dioxide, and isopropanol at 40 , 50 , and 60 C and elevated pressures. The phase behavior observed at these conditions was found to be (quite complex. 

Although (quantitative phase compositions, temperatures, and pressures for such a highly non-ideal mixture cannot be expected from this e(quation of state, a reasonably accurate description of global phase behavior can be obtained. 

The experimental results in Figure 2 and Table II clearly show three qualitatively different behaviors an abrupt order-disorder transition a relatively rapid continuous transition and a gradual, smooth ordering of the polymer backbone. These observations are qualitatively identical to the three possible phase behaviors predicted by the theory. Moreover, a degree of quantitative understanding can be obtained. 

The qualitative phase behavior of hydrocarbon systems was described in the previous chapter. The quantitative treatment of these systems mil now be discussed and tire methods for calculating their phase behavior presented. It will became apparent that the liquid and vapor phases of mixtures of two or more hydrocarbons are in reality solutions (see below), so that it will be necessary to discuss the laws of solution behavior. Analogous to the treatment of gases, the behavior of a hypothetical fluid known as a perfect, or ideal, solution will be described. This will be followed by a description of actual solutions and tlie deviations from ideal solution behavior that occur. 

A, B, C, and D have been calculated in the preceding example. The point A at 22.75 psia represents the computed bubble-point pressure for a solution whose mole fraction of C4H10 is 0.50. Point B represents the composition of the vapor at the bubble point. Similarly, the points C and D represent the bubble point and composition of the vapor at the bubble point for a solution whose mole fraction of C4Hio>is 0.75. The points E and jP. represent the vapor pressure of pure butane and pure propane, respectively, at 0° F. The line FACE is tile bubble-point line and the line FBDE is the dew-point line. It is obvious that a pressure-composition diagram for any ideal binary system could be calculated in this manner and would serve to describe the phase behavior quantitatively. 

Our quantitative findings concern the phase behavior of the L and microemulsion systems are summarized in Figure 3. In the absence of alcohol, the maximum MMA content of the Lj phase is fixed by a limiting MMA/SLS mole ratio of approximately three. Higher mole ratios will invariably lead to a two-phase system. With alcohol... 

In regards to the intermolecular self-organization much can be learned from the physics of hairy-rod polymers [60] and PFs, especially PF2/6, are excellent model systems. As is the case in diblock polymers, a deceptively simple model parameterization of the key underlying interactions yields semi-quantitative predictions of the structural phase behavior. These model calculations can be directly compared to the experimental phenomena. The... 

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