Equilibrium-phase behavior

Basic Thermodynamics. Equilibrium-phase behavior of mixtures is governed by the free energy of mixing and how this quantity, consisting of enthalpic... 

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

The literature contains extensive reports on investigations of the equilibrium-phase behavior for an enormous number of polymer—polymer pairs (1,97). The number of blends known to be miscible has grown so rapidly since the mid-1980s that it is more instructive to attempt to understand these observations in terms of the molecular structures of the components rather than to catalog them. 

A correlation of the detergency performance and the equilibrium phase behavior of such ternary systems is expected, based on the results presented by Miller et al. (3,6). The phase behavior of surfactant - oil - water (brine) systems, particularly with regard to the formation of so-called "middle" or "microemulsion" phases, has been shown by Kahlweit et al. (7,8) to be understandable in teims of the... 

Fig. 33. Equilibrium phase behavior of polystyrene latices of radius a at volume fraction containing soluble dextran of radius of gyration R, at fluid concentration pb (Patel and Russel, 1989a). (a) a/Rt = 6.9 5, measured compositions l—I, bounds on transition —, predicted phase...

To truly control crystallization to give the desired crystalline microstructure requires an advanced knowledge of both the equilibrium phase behavior and the kinetics of nucleation and growth. The phase behavior of the particular mixture of TAG in a lipid system controls both the driving force for crystallization and the ultimate phase volume (solid fat content) of the solidified fat. The crystallization kinetics determines the number, size, polymorph, and shape of crystals that are formed as well as the network interactions among the various crystalline elements. There are numerous factors that influence both the phase behavior and the crystallization kinetics, and the effects of these parameters must be understood to control lipid crystallization. 

Nelson Type Emulsions The different types of phase behavior in microemulsions are denoted as Nelson type II(-), II(+), and III. These refer to equilibrium phase behaviors and distinguish, for example, the number of phases that may be in equilibrium and the nature of the continuous phase. See also reference 10. Winsor type emulsions are similarly identified, but with different type numbers. 

We thus see a pre-synthesis analysis that characterizes the behavior of the species and a post-synthesis analysis that requires us to design equipment. Both require that we compute equilibrium phase behavior (vapor/liquid, liquid/liquid, vapor/liquid/liquid, etc.)... 

After describing the experimental technique in the next section, we report our observations of intermediate phase formation and spontaneous emulsification in three parts corresponding to three types of equilibrium phase behavior found when equal volumes of oil and the surfactant-alcohol-brine mixtures are equilibrated. The three types are well known (8-9) and, in order of increasing salinity, are a "lower" phase, oil-in-water microemulsion in equilibrium with excess oil, a "surfactant" or "middle" phase, probably of varying structure, in equilibrium with both excess oil and excess brine, and an "upper" phase, water-inoil microemulsion in equilibrium with excess brine. 

As indicated by Figure 16, which shows the positions of the brine-oil interface for two PDM experiments as functions of t1, the oil phase grew in volume with time. This solubilization of brine into the oil contrasts with the behavior at lower salinities where the oil phase was consumed by the microemulsion. Based on equilibrium phase behavior, one can conclude that conversion of oil to a water-in-oil microemulsion was occurring above the brine interface. Also, as shown in Table IV, the position of the interface between brine and this oil-continuous phase varied as the square root of time, indicating no extensive convection in these samples. 

In the three-phase regime of equilibrium phase behavior, the diffusion path studies were based on a dimensionless parameter S which indicates the position of the system within the regime. Thus, S = 0 corresponds to the salinity where the three-phase region first appears via a critical tie line (14), and S = 1 corresponds to the salinity where it disappears into another critical tie line. The optimum salinity occurs at S 0.5. 

The argument to use a two-phase model to represent surfactant phase behavior without type III microemulsion is that experiments (Seethepalli et al., 2004 Zhang et al., 2006 Liu et al., 2008) indicate that the volume of type III microemulsion phase is small if the overall surfactant concentration is low (<0.1 wt.%). In the cases of low surfactant concentration, a type III microemulsion system was not observed by Salager et al. (1979b). The reason is that if we cannot make a sufficient number of salinity scans, and the volume of the type III microemulsion phase is small, the equilibrium phase behavior... 

Salager JL, Loaiza-Maldonado I, Minana-Perez M, Silva F. Surfactant—oil-water systems near the affinity inversion. Part I Relationship between equilibrium phase behavior and emulsion type and stability. J Dispersion Sci and Technol 1982 3 279-292. 

The equilibrium phase behavior of systems of oil and water containing appreciable amounts of surfactant is characterized by the presence of microemulsions. The microemulsions are stable oil-water dispersions caused by the incorporation of amphipathic molecules (surfactants and co-surfactants) in the oil and water phases. 

Figure 4 shows a comparison of the experimental and predicted liquid phase compositions for the p-diketone/C02 systems studied at 35.0 C. This plot reveals all the salient features of the equilibrium phase behavior of these alkylated and/or fluorinated ligand/COa systems. Namely, the bubble point compositions of the TFA and FOD/CO2 systems are higher at lower pressures i.e., at a given pressure more CO2 dissolves in the two fluorinated ligands, TFA and FOD, than in the other p-diketones. However, at higher pressures the TFA and FOD equilibrium compositions are very similar to those of the ACAC, THD, and TOD/CO2 systems. 

MAD Madbouly, S.A. and Wolf, B.A., Equilibrium phase behavior of poly(ethylene oxide) and of its mixtures with tetrahydronaphthalene or/and poly(ethylene oxidc-block-dimethylsiloxane) (experimental data by S.A. Madbouly), J. Chem. Phys., 117, 7357, 2002. 

Two issues of great importance for the study of microemulsions are their equilibrium phase behavior and microstructure characterization. It should be noted that the pioneers in... 

This chapter focuses mainly on the microstructures encountered in mixtures of oil and water with surfactants (mostly nonionic from the family of ethoxylated alcohols, designated as CjEj or Q(EO) , where i and j are the number of carbon atoms in the alkyl chain and the number of ethylene oxide (EO) groups of the polar head, respectively, of the surfactant molecule) and sometimes in the presence of alcohols. However, a short survey concerning the investigation of the equilibrium phase behavior of these systems seems to be in order. 

Interface instabilities, known as myelins, are an example of exotic nonequilibrium behavior present during dissolution in a number of surfactant systems. Although much is known about equilibrium phase behavior much still remains to be understood about nonequilibrium processes present in surfactant dissolution. In this chapter nucleation and growth, self and collective diffusion processes and nonlinear dynamics and instabilities observed in various polymeric systems are reviewed. These processes play an important role in our understanding of myelin instabilities. Kinetic maps and the concept of the free energy landscape provide a useful approach to rationalize some of the more complex behavior sometimes observed. 

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