Pseudo phase

Distribution of benzodiazepines in system micellar pseudophase - water was investigated in micellar solutions of sodium dodecylsulfate. The protonization constants of benzodiazepines were determined by the UV-spectophotometry. Values of protonization constants increase with increasing of sodium dodecylsulfate concentration. The binding constants of two protolytic forms of benzodiazepines with a micellar pseudo-phase and P, values were evaluated from obtained dependence. 

The novel element in these models is the introduction of a third phase in the Hashin-Rosen model, which lies between the two main phases (inclusions and matrix) and contributes to the progressive unfolding of the properties of the inclusions to those of the matrix, without discontinuities. Then, these models incoporate all transition properties of a thin boundary-layer of the matrix near the inclusions. Thus, this pseudo-phase characterizes the effectiveness of the bonding between phases and defines a adhesion factor of the composite. 

In order to alleviate this singular and unrealistic situation, a series of models was presented in this study, in which a third pseudo-phase was considered as developed along a thin boundary layer between phases, during the polymerization of the matrix, whose properties depend on the individual properties of the phases and the quality of adhesion between them. 

The models could readily be extended to three-phase impregnated composites, where the impregnation of the inclusions constitutes a third thin phase, and two further pseudo-phases may be assumed as developed between inclusions and impregnation, and impregnation and matrix. A consecutive application of the models may yield interesting results concerning the behavior of such impregnated composites. 

In Menger and Portnoy s model, the variation of the rate constant with surfactant concentration has been treated on the basis of assumption that substrate S is distributed between aqueous and micellar pseudo-phase given as follows ... 

Let us consider a fluorescent probe and a quencher that are soluble only in the micellar pseudo-phase. If the quenching is static, fluorescence is observed only from micelles devoid of quenchers. Assuming a Poissonian distribution of the quencher molecules, the probability that a micelle contains no quencher is given by Eq. (4.22), so that the relationship between the fluorescence intensity and the mean occupancy number < > is... 

Fluorescence quenching studies in micellar systems provide quantitative information not only on the aggregation number but also on counterion binding and on the effect of additives on the micellization process. The solubilizing process (partition coefficients between the aqueous phase and the micellar pseudo-phase, entry and exit rates of solutes) can also be characterized by fluorescence quenching. 

The derivation of a pseudo-phase separation model for treating nonideal mixed micellization is given in detail in reference 3. This leads to the generalized result... 

Ideal Mixed Micelles. The Critical Micelle Concentration (CMC) is the lowest surfactant concentration at which micelles form the lower the CMC, the greater the tendency of a system to form micelles. When the total surfactant concentration equals the CMC, an infintesimal fraction of surfactant is present as micelles therefore, the CMC is equal to the total monomer concentration in equilibrium with the micellar pseudo—phase. The CMC for monomer—micelle equilibrium is analogous to the dew point in vapor—liquid equilibrium. 

The mass action model (MAM) for binary ionic or nonionic surfactants and the pseudo-phase separation model (PSM) which were developed earlier (I EC Fundamentals 1983, 22, 230 J. Phys. Chem. 1984, 88, 1642) have been extended. The new models include a micelle aggregation number and counterion binding parameter which depend on the mixed micelle composition. Thus, the models can describe mixtures of ionic/nonionic surfactants more realistically. These models generally predict no azeotropic micellization. For the PSM, calculated mixed erne s and especially monomer concentrations can differ significantly from those of the previous models. The results are used to estimate the Redlich-Kister parameters of monomer mixing in the mixed micelles from data on mixed erne s of Lange and Beck (1973), Funasaki and Hada (1979), and others. 

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) ... 

A generalized nonideal mixed monolayer model based on the pseudo-phase separation approach is presented. This extends the model developed earlier for mixed micelles (J. Phys. Chem. 1983 87, 1984) to the treatment of nonideal surfactant mixtures at interfaces. The approach explicity takes surface pressures and molecular areas into account and results in a nonideal analog of Butler s equation applicable to micellar solutions. Measured values of the surface tension of nonideal mixed micellar solutions are also reported and compared with those predicted by the model. 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

The pseudo-phase separation approach has been successfully applied in developing a generalized nonideal multicomponent mixed micelle model (see I4) and it is Interesting to consider whether this same approach can be used to develop a generalized treatment for adsorbed nonideal mixed surfactant monolayers. The preferred form for suoh a model is that it be suitable (at least in principle) for treating multiple components and be extendable to other interfaoes and properties of interest suoh as oontaot angles. Earlier models (5, 18, 27) based on the pseudo-phase separation approach and... 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

Figure 1. Mixed cmc s and surface tensions at the cmc for mixtures of C qPO and SDS in 1 mM Na2C0T (at 24°C). The plotted points are experimental results, the solid lines the prediction of the nonideal model for 8 = -3 7 and 8 = -3.5 respectively, and the dashed lines the prediction for ideal mixing in the pseudo-phase.

For the ionic surfactants (1-1 type), we should take account of the electrically charged species and the possibility of doing electrical work. The micelle may be regarded as a charged pseudo-phase, and the chemical potential is replaced by the electrochemical potential (12). The effective electrical work in micelle formation is... 

To this point, only models based on the pseudo—phase separation model have been discussed. Mixed micelle models utilizing the mass action model may be necessary for micelles with small aggregation numbers, as demonstrated by Kamrath and Franses ( ). However, even for large micelles, the fundamental basis for the pseudophase separation model needs to be examined. In micelles, how much solvent or how many counterions (bound or in the electrical double layer) should be included in the micellar pseudo-phase is unclear. The difficulty is normally surmounted by assuming that the pseudo—phase consists of only the surfactant components i.e., solvent or counterions are ignored. The validity of treating the micelle on a surfactant—oniy basis has not been verified. Funasaki and Hada (22) have questioned the thermodynamic consistency of such an approach. 

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