Pseudophase behavior

Earlier isobaric studies confirmed that at lower pressures the lower composition limit of the iota phase is near Pr Oia and that the phase does have a small but easily demonstrated range of composition on the oxygen-rich side, PrjOia+a. At higher pressures complications arise and prominent pseudophase behavior is observed. 

Pseudophase Behavior in the Epsilon and Iota Regions of the Praseodymium Oxide-Oxygen System, R.P. Turcotte, M.S. Jenkins and L. Eyring, J. Solid State Chem., 7, 454-460 (1973). 

Surfactants have also been of interest for their ability to support reactions in normally inhospitable environments. Reactions such as hydrolysis, aminolysis, solvolysis, and, in inorganic chemistry, of aquation of complex ions, may be retarded, accelerated, or differently sensitive to catalysts relative to the behavior in ordinary solutions (see Refs. 205 and 206 for reviews). The acid-base chemistry in micellar solutions has been investigated by Drummond and co-workers [207]. A useful model has been the pseudophase model [206-209] in which reactants are either in solution or solubilized in micelles and partition between the two as though two distinct phases were involved. In inverse micelles in nonpolar media, water is concentrated in the micellar core and reactions in the micelle may be greatly accelerated [206, 210]. The confining environment of a solubilized reactant may lead to stereochemical consequences as in photodimerization reactions in micelles [211] or vesicles [212] or in the generation of radical pairs [213]. 

By combining (1), (3) and (4), expressions (5) and (6) are obtained. These, or similar, equations readily explain why first-order rate constants of micelle-assisted bimolecular reactions typically go through maxima with increasing surfactant concentration if the overall reactant concentration is kept constant. Addition of surfactant leads to binding of both reactants to micelles, and this increased concentration increases the reaction rate. Eventually, however, increase in surfactant concentration dilutes the reactants in the micellar pseudophase and the rate falls. This behavior supports the original assumption that substrate in one micelle does not react with reactant in another, and that equilibrium is maintained between aqueous and micellar pseudophases. 

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... 

For a surface active betaine ester the rate of alkaline hydrolysis shows significant concentration dependence. Due to a locally elevated concentration of hydroxyl ions at the cationic micellar surface, i.e., a locally increased pH in the micellar pseudophase, the reaction rate can be substantially higher when the substance is present at a concentration above the critical micelle concentration compared to the rate observed for a unimeric surfactant or a non-surface active betaine ester under the same conditions. This behavior, which is illustrated in Fig. 10, is an example of micellar catalysis. The decrease in reaction rate observed at higher concentrations for the C12-C18 1 compounds is a consequence of competition between the reactive hydroxyl ions and the inert surfactant counterions at the micellar surface. This effect is in line with the essential features of the pseudophase ion-exchange model of micellar catalysis [29,31]. 

To this point we have used no specific mixing rule to describe the interactions of monomers of surfactants 1 and 2 in the micellar pseudophase. We have assumed, however, that only one micellar pseudo-phase exists. For our calculations we have used the Redlich-Kister expansion for w(x) with up to two parameters (10,12). Moreover, we have not yet specified the form of the function y9(x), which can be varied for modeling specific counterion association behavior. For our calculations we have used the following linear function for /3(x) ... 

Lantz, A.W., Pino, V., Anderson, J.L., and Armstrong, D.W., Determination of solute partition behavior with room-temperature ionic liquid based micellar gas-liquid chromatography stationary phases using the pseudophase model, /. Chromatogr. A, 1115, 217-224, 2006. 

Equations (26)-(28) can then be numerically solved, allowing a detailed description of the singlet-oxygen behavior in this three-pseudophase system. Fitting of the data obtained between 30 and 100 psec after excitation required apparent... 

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. 

The quantitative treatment of kinetic data is based on the pseudophase separation approach, i.e. the assumption that the aggregate constitutes a (pseudo)phase separated from the bulk solution where it is dispersed. Some of the equations below are reminiscent of the well-known Michaelis- Menten equation of enzyme kinetics [101]. This formal similarity has led many authors to draw a parallel between micelle and enzyme catalysis. However, the analogy is limited because most enzymatic reactions are studied with the substrate in a large excess over the enzyme. Even for systems showing a real catalytic behavior of micelles and/or vesicles, the above assumption of the aggregate as a pseudophase does not allow operation with excess substrate. The condition... 

Aqueous cationic micelles speed and anionic micelles inhibit bi-molecular reactions of anionic nucleophiles. Both cationic and anionic micelles speed reactions of nonionic nucleophiles. Second-order rate constants in the micelles can be calculated by estimating the concentration of each reactant in the micelles, which are treated as a distinct reaction medium, that is, as a pseudophase. These second-order rate constants are similar to those in water except for aromatic nucleophilic substitution by azide ion, which is much faster than predicted. Ionic micelles generally inhibit spontaneous hydrolyses. But a charge effect also occurs, and for hydrolyses of anhydrides, diaryl carbonates, chloroformates, and acyl and sulfonyl chlorides and SN hydrolyses, reactions are faster in cationic than in anionic micelles if bond making is dominant. This behavior is also observed in water addition to carbocations. If bond breaking is dominant, the reaction is faster in anionic micelles. Zwitterionic sulfobetaine and cationic micelles behave similarly. 

The pseudophase-separation model for surfactant solutions (84, 132, 135) states that a surfactant solution above its critical micelle concentration (CMC) consists of two pseudophases in equilibrium with each other singly dispersed surfactant monomer molecules and micelles. When the surfactant solution is in contact with a solid, the adsorbed phase constitutes a third pseudophase (40). Strong experimental evidence suggests that surfactant adsorption takes place from the surfactant monomer phase but not from the micelles (84), behavior that leads to competition of both the micelles and the adsorbed phase for surfactant molecules from the monomer phase. Adsorption from a surfactant solution above the CMC then depends not only on the affinity of the surfactant for the solid surface but also on its tendency to form micelles. If a mixture can be formulated such that at least one of the surfactants is incorporated into micelles preferentially over the adsorbed phase, then the micelles act as a sink for the surfactant and thus prevent it from being adsorbed. 

Complex fluids composed of several pseudophases with a liquid-liquid interface (emulsions, macroemul-sions, cells, liposomes) or liquid-solid interface (suspensions of silica, carbon black, latex, etc.) can, from a dielectric point of view, be considered as classical heterogeneous systems. Several basic theoretical approaches have been developed in order to describe the dielectric behavior of such systems. Depending on the concentration, the shape of the dispersed phase, and the conductivity of both the media and disperse phase, different mixture formulas can be applied to describe the electric property of the complex liquids (11-15). 

Although two variables usually suffice for samples of moderate complexity to obtain a satisfactory separation, inclusion of a third variable will often further improve the quality of the separation, with respect to both resolution and analysis time. In the first methods developed in MLC for the analysis of compounds showing an acid-base behavior, the pH was usually previously chosen and only the concentrations of surfactant and modifier were optimized. The best pH for the separation was selected after examining the retention in a reduced number of mobile phases, at two or three pH values. However, for an adequate method development, this variable should be simultaneously optimized with the concentrations of surfactant and modifier, especially because the protonation constants of solutes suffer shifts, depending on the composition of the mobile phase. This is caused by the different partitioning of the acidic and basic species of solutes in the micellar pseudophase, due to electrostatic interactions. 

First application of IL-based surfactants as pseudophases in MLC was reported in 2009 [42], It was a preliminary study regarding the retention behavior of benzene using three different LC stationary phases (Eehpse XDB C8,Zorbax C8,and Gemini C18) and Cj C Im-Br. A comparison was also made with the conventional cationie surfactant cetyltrimethylammonium bromide (CTAB) showing similar performanee. 

More recently, Flieger et al. [43] used Cj MIm-Cl as a pseudophase in MLC for the separation of eight derivatives of 1,4-thiosemicarbazides, employing two different LC stationary phases (Kromasil C18 and Zorbax SB-CN). In this case, the comparison was established with the most common surfactant in MLC, the anionic surfactant sodium dodecyl sulfate (SDS). SDS also showed adequate behavior. 

At very low temperatures, i.e., in pseudophase ACl, we have argued in the previous section that the dominant polymer conformation is the most compact single-layer film. This is confirmed by the behavior of R and Rj ), the latter being zero in this phase. A simple argument that the structure is indeed maximally compact is as follows. It is well known that the most compact shape in the two-dimensional continuous space is the circle. For n monomers residing in it, n nr, where r is the (dimensionless) radius of this circle. The usual squared gyration radius is... 

The second remarkable result is that the pseudophases DC, DE, AE, and AG are bulky, while all AC subphases are highly localized in the plot of the free-energy minima, Comparing with Fig. 13.2, the conclusion is that conformations in the AC phases are energetically favored (more explicitly, for s/T>Q.% in ACl and s/T> 2.2 in the AC2 subphases), while the behavior in the other pseudophases is entropy-dominated The number of conformations with similar contact munbers in the globular or expanded regime is... 

We may conclude that, in particular, the high-temperature pseudophases DE, DC/DG, AG, AE, nicely correspond to each other in both models. Noticeable qualitative deviations occur, as expected, in those regions of the pseudophase diagram where compact conformations are dominant and (unphysical) lattice effects are influential. Thus, the choice of the appropriate model depends on the question one wants to answer. Unlike temperatures are not too small and the polymer chain not too short, lattice models are perfectly suitable for the investigation of structural phases. This is particularly true for scaling analyses toward the thermodynamic limit. However, if the focus is more on finite-size effects and the behavior at low temperatures, off-lattice models should generally be preferred. 

Eventually, let us compare the adsorption behavior with what we had found in Chapter 13 for simplified hybrid lattice models of polymers and peptides near attractive substrates. The adhesion of the jjeptides at the Si(lOO) substrate exhibits very similar features. Exemplified for peptide S3, Fig. 14.13 shows the plot of the canonical probability distributionpcan E, q) 8 E — E(X))S(q — q(X))) at room temperature (T = 300 K). The peak at E, q) (80.5 kcal/mole, 0.0) corresponds to conformations that are not in contact with the substrate. It is separated from another peak near (E, q) (74.5 kcal/mole, 0.2) and belongs to conformations with about 17% of the heavy atoms with distances < 5 A from the substrate surface (compare with Fig. 14.12). That means adsorbed and desorbed conformations coexist and the gap in between the peaks separates the two pseudophases in g -space, which causes a kinetic free-energy barrier. Thus, the adsorption transition is a first-order-like pseudophase transition in q, but since both structural phases (adsorbed and desorbed) coexist almost at the same energy, the transition in E space is weakly of first order. ... 

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). 

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