Pseudophase formation

Very extensive temperature-pressure-composition observations have been made on the rare earth higher oxides as is clear from the discussion of the previous sections. Certain observations should be made explicit. There are no instances of classical behavior, i.e., none of the single phases are line phases but have at least some range of composition and none of the two-phase isobaric transformations occur at a fixed temperature but rather over a range of temperatures. There is also clearly intrinsic hysteresis in all two-phase regions. Furthermore the hysteresis loops are not symmetric, but rather are skewed such as to give a retarded and almost linear approach when a phase of lower symmetry is being formed. This may occur either in oxidation or reduction is reproducible and intrinsic - it has been termed pseudophase formation (Hyde et al., 1966). 

Hysteresis and pseudophase formation are properly not displayed in equilibrium phase diagrams because they are metastable states but they are nevertheless features of real systems and anyone who wishes to describe real systems must take them into account. Earlier studies by Faeth and Clifford (1963) were... 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

The impact of salt concentration on the formation of micelles has been reported and is in apparent accord with the interfacial tension model discussed in Sect. 4.1, where the CMC is lowered by the addition of simple electrolytes [ 19,65, 280,282]. The existence of a micellar phase in solution is important not only insofar as it describes the behavior of amphipathic organic chemicals in solution, but the existence of a nonpolar pseudophase can enhance the solubility of other hydrophobic chemicals in solution as they partition into the hydrophobic interior of the micelle. A general expression for the solubility enhancement of a solute by surfactants has been given by Kile and Chiou [253] in terms of the concentrations of monomers and micelles and the corresponding solute partition coefficients, giving... 

Any surfactant adsorption will lower the oil-water interfacial tension, but these calculations show that effective oil recovery depends on virtually eliminating y. That microemulsion formulations are pertinent to this may be seen by reexamining Figure 8.11. Whether we look at microemulsions from the emulsion or the micellar perspective, we conclude that the oil-water interfacial free energy must be very low in these systems. From the emulsion perspective, we are led to this conclusion from the spontaneous formation and stability of microemulsions. From a micellar point of view, a pseudophase is close to an embryo phase and, as such, has no meaningful y value. 

The oxidation of D-fructose with cerium(IV) in sulfuric acid medium is inhibited by an increase in the acidity. A cationic surfactant, CTAB, catalyses the reaction, whereas SDS has no effect. The catalytic role of CTAB has been explained using the pseudophase model of Menger and Portnoy. A mechanism involving the formation of an intermediate complex between /3-D-fructopyranose and Ce(S04)32- has been proposed.61 The oxidation of cycloalkanones with cerium(IV) in sulfuric acid medium showed a negligible effect of acidity. Formation of an intermediate complex, which decomposes in the rate-determining step, has been suggested.62... 

The CMC has its most clear-cut interpretation within the (pseudo) phase separation model of micelle formation. Although the micelles and the surrounding solution form a single phase, the amphiphile association shows a cooperativity that makes an analogy with a phase transition useful. Within this model, the CMC is the concentration at which the system enters a two phase region the two pseudophases formed being the aqueous system and the micelles. 

Armstrong et al. developed a chromatographic technique which could be used to evaluate the stoichiometry and all relevant binding constants for most substrate-CD systems (8). This method was not dependent on a solute s spectroscopic properties, conductivity, electrochemical behavior, or solubility. This work presented theory and chromatographic evidence for multiple cyclodextrin complex formation. Previous theoretical work considered only 1 1 complex formation (9-12). A two to one complexation equation was derived by expanding on the equation first used in 1981 to describe the 1 1 complexation behavior of a solute in a pseudophase system (13.14). Using this method, it was demonstrated that closely related compounds such as structural isomers of nitroaniline could exhibit different binding behaviors (8). 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Various approaches have been employed to tackle the problem of micelle formation. The most simple approach treats micelles as a single phase, and this is referred to as the phase-separation model. In this model, micelle formation is considered as a phase-separation phenomenon, and the cmc is then taken as the saturation concentration of the amphiphile in the monomeric state, whereas the micelles constitute the separated pseudophase. Above the cmc, a phase equilibrium exists with a constant activity of the surfactant in the micellar phase. The Krafft point is viewed as the temperature at which a solid-hydrated surfactant, the micelles, and a solution saturated with undissociated surfactant molecules are in equiUbrium at a given pressure. 

The equilibrium and dynamics of adsorption processes from micellar surfactant solutions are considered in Chapter 5. Different approaches (quasichemical and pseudophase) used to describe the micelle formation in equilibrium conditions are analysed. From this analysis relations are derived for the description of the micelle characteristics and equilibrium surface and interfacial tension of micellar solutions. Large attention is paid to the complicated problem, the micellation in surfactant mixtures. It is shown that in the transcritical concentration region the behaviour of surface tension can be quite diverse. The adsorption process in micellar systems is accompanied by the dissolution or formation of micelles. Therefore the kinetics of micelle formation and dissociation is analysed in detail. The considered models assume a fast process of monomer exchange and a slow variation of the micelle size. Examples of experimental dynamic surface tension and interface elasticity studies of micellar solutions are presented. It is shown that from these results one can conclude about the kinetics of dissociation of micelles. The problems and goals of capillary wave spectroscopy of micellar solutions are extensively discussed. This method is very efficient in the analysis of micellar systems, because the characteristic micellisation frequency is quite close to the frequency of capillary waves. 

There are two basic approaches to modeling the thermodynamics of micelle formation. The mass action model views the micelles as reversible complexes of the monomer that are aggregating and predicts the sharp change in tendency of incremental surfactant to form micelles instead of monomer at the CMC this sharp transition is a consequence of the relatively large number of molecules forming the aggregate. The mass action model predicts that micelles are present below the CMC but at very low concentrations. The ocher major model used to describe micelle formation is the pseudophase separation model, which views micelles as a separate thermodynamic phase in equilibrium with monomer. Because micelle formation is a second-order phase transition, micelles are not a true thermodynamic phase, and this model is an approximation. However, the assumption that there are no mi-celies present below the CMC, and that the surfactant activity becomes constant above the CMC. is close to reality. and the mathematical simplicity of the pseudophase... 

This differential increase in partitioning into the continuous phase over the subthreshold value of x = 0.013 suggests the formation of a third pseudo-phase assigned to percolating clusters of droplets. In this three-pseudo-phase model, if was assumed [58] that the molar ratio of water to AOT in the clusters is the same as that of the isolated swollen micelles, and it may then be concluded that this excess mole fraction derived for water in the continuous pseudophase represents the volume fraction of the percolating pseudo-phase ((Pe ). An order parameter (S) for the disperse pseudo-phase (clusters and isolated swollen micelles) was defined as [58, 59]... 

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