Theory for Mixed Micelles

The interest in mixed surfactant systems has theoretical as well as practical reasons. The realization that surfactants are used most often as mixtures has shifted research from pure surfactants to mixed systems. Industrial fluorinated surfactants are usually mixtures [62,63] because (1) they are synthesized as a mixture of isomers or telomers which are difficult to separate or (2) different surfactants are mixed to enhance the performance of the individual components by synergistic interactions. Some commercial fluorinated surfactants contain hydrocarbon-type surfactants which have been blended with the fluorinated surfactant to improve its performance. 

Mixed systems containing fluorinated surfactants and hydrocarbon surfactants are currently investigated for several theoretical and practical reasons  

The increased efficiency of surfactant mixtures allows one to reduce the amount of a fluorinated surfactant needed. 

The fluorinated surfactant-hydrocarbon surfactant mixtures have unique properties. In two-phase systems of water and a hydrocarbon solvent, the fluorinated surfactant reduces surface tension and the hydrocarbon surfactant decreases the interfacial tension. For example, an aqueous foam of mixed surfactants spreads on a hydrocarbon solvent because the fluorinated surfactant adsorbs preferentially at the air-water interface, whereas the hydrocarbon surfactant adsorbs at the water-oil interface (see Chapter 8, Fire-fighting Foams). 

Because of the extensive practical and theoretical interest in mixed fluorocarbon-hydrocarbon surfactants, it is not surprising that the mixed-surfactant systems have been reviewed in two monographs [64,65], and numerous articles on fluorocarbon-hydrocarbon surfactant mixtures have appeared in print. 

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It should be noted that the exchange of alcohol between the mixed micelles and the surrounding solution also gives rise to a very fast relaxation process (in the 10-100 ns range) which has been investigated separately (32). Aniansson s theory for mixed micelles predicts this very fast process and gives the expression of the corresponding relaxation time. 

Interpretation of the kinetic data according to Aniansson theory for mixed micellization ... 

Nagarajan, R. Molecnlar theory for mixed micelles. Langmuir 1985, 7(3),... 

Mixed Micelles. The CMC values -for the two pure sur-factants and well de-fined mixtures thereo-f are shown in Figure 2. The experiments were run at a high added salt level (swamping electrolyte) so the counterion contributed by the dissolved sur-factant is negligible. Predicted mixture CMC values -for ideal mixing -from Equation 1 are also shown. Ideal solution theory describes mixed micelle -formation very well, as is usually the case -for similarly structured sur-factant mixtures (12.19.21—2A) ... 

Effects of addition of n-tetradecyltrimethylammonium bromide (C14TAB) on the micelle-monomer exchange processes of /f-decyltrimethylammonium bromide (CioTAB) were investigated by the ultrasonic relaxation method. The relaxation frequency increased and the relaxation strength decreased with increasing amount of CuTAB added. The dependence of the relaxation frequency on the amount of CuTAB added was in fair agreement with the relaxation theory of Annianson for mixed micelle... 

Another possible extension is to consider an excess oil phase which is a mixtnre of two or more species. Provided that mixing within the micelle can still be considered ideal and that activity coefficients for all species in the bulk oil mixture are known, an expression for for each solnte is readily obtained. Micelles formed from surfactant mixtures can be treated provided that micelle composition is known or can be calculated from theories of mixed micelles such as regular solution theory and that solubilization is low enough not to affect micelle shape or composition. Finally, nonideal mixing in the micelles can be included if some model for the nonideality is available as well as data for evaluating the relevant parameters. Perhaps the simplest scheme for incorporating nonideality with nonpolar solutes is to use volume fractions instead of mole fractions in the spirit of Flory-Huggins theory. 

The experimental findings for the heat of mixing for mixed micelles deviate from data obtained from the regular solution theory. 

Advances in the theory of mixed-micelle formation have made it possible to calculate the composition of mixed micelles formed by two or more surfactants. A thermodynamic treatment of micellar solutions of mixed surfactants is usually based on the pseudophase separation theory [61,71-74]. The pseudophase models developed for binary surfactant solutions assume ideal mixing of the surfactants in the micelle. 

Without going into this theory in detail, let us reproduce here the equation proposed by Rubingh for the activity factor of surfactant species making up mixed micelles in a binary system ... 

Among the purposes of this paper is to report the results of calorimetric measurements of the heats of micellar mixing in some nonideal surfactant systems. Here, attention is focused on interactions of alkyl ethoxylate nonionics with alkyl sulfate and alkyl ethoxylate sulfate surfactants. The use of calorimetry as an alternative technique for the determination of the cmc s of mixed surfactant systems is also demonstrated. Besides providing a direct measurement of the effect of the surfactant structure on the heats of micellar mixing, calorimetric results can also be compared with nonideal mixing theory. This allows the appropriateness of the regular solution approximation used in models of mixed micellization to be assessed. 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

I-f the interactions between sur-factants in the mixed micelle can be described by regular solution theory, the -following equations apply -for a binary system ... 

Equation 1 has proved to be a better predictor of the equilibrium which exists between monomer and micelles for mixed surfactant systems than is the regular solution theory model. It also predicts well the mixture CMC and shows the heat of mixing to be smaller than that predicted by the regular solution theory in agreement with the experiment (13). The purpose of this paper is to further explore... 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

This effect does not occur with the mixed micelles, where the spherical geometry of the hydrophobic core permits intimate contact between hydrocarbon chains of different lengths, so that the environment for hydrophobic groups is similar in the pure micelles as in the mixed micelles. As a result, ideal solution theory is obeyed. 

Model Development. There is vast opportunity for development of fundamentally based models to describe the thermodynamics of mixed micelle formation. As discussed in Chapter 1, regular solution theory has yielded useful relations to describe monomer—mi cel 1e equilibrium. 

The lack of certain critical data for these systems, as already discussed, has hampered development of improved theories. Models of mixed micelle formation need to be based on the fundamental forces causing nonidealities of mixing. Some of these have been discussed in Chapter 1. Chapter 2 Schechter is an example of the... 

In this paper, a molecular thermodynamic approach is developed to predict the structural and compositional characteristics of microemulsions. The theory can be applied not only to oil-in-water and water-in-cil droplet-type microemulsions but also to bicontinuous microemulsions. This treatment constitutes an extension of our earlier approaches to micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in the oil phase and the excluded-volume interactions among the droplets. Illustrative results are presented for an anionic surfactant (SDS) pentanol cyclohexane water NaCl system. Microstructur al features including the droplet radius, the thickness of the surfactant layer at the interface, the number of molecules of various species in a droplet, the size and composition dispersions of the droplets, and the distribution of the surfactant, oil, alcohol, and water molecules in the various microdomains are calculated. Further, the model allows the identification of the transition from a two-phase droplet-type microemulsion system to a three-phase microemulsion system involving a bicontinuous microemulsion. The persistence length of the bicontinuous microemulsion is also predicted by the model. Finally, the model permits the calculation of the interfacial tension between a microemulsion and the coexisting phase. 

In this paper, a predictive molecular thermodynamic approach is developed to calculate the structural and compositional characteristics of microemulsions. The theory applies not only to oil-in-water and water-in-oil droplet-type microemulsions but also to bicontinuous microemulsions. The treatment is an extension of our earlier theories for micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in oil and the volume-excluded interactions among... 

We now discuss the dependence of the relaxation frequency on the concentration of CuTAB along the line of the theory of Annianson for the relaxation process of mixed micelle. In this argument, the micellar solution consists of two kinds of surfactants. Under the condition that the dissociation rate constant of surfactant I is much larger than that of surfactant 2, the reciprocal of the relaxation time of the fast process is written in the following way... 

The two fundamental properties of surfactants are monolayer formation at interfaces and micelle formation in solution for surfactant mixtures, the characteristic phenomena are mixed monolayer formation at interfaces (Chapter 2, Section RIG) and mixed micelle formation in solution (Chapter 3, Section VIII). The molecular interaction parameters for mixed monolayer formation by two different surfactants at an interface can be evaluated using equations 11.1 and 11.2 which are based upon the application of nonideal solution theory to the thermodynamics of the system (Rosen, 1982) ... 

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