Mixed micelles theory

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 ... 

Non-ideal solution theory is used to calculate the value of a parameter, S, that measures the interaction between two surfactants in mixed monolayer or mixed micelle formation. The value of this parameter, together with the values of relevant properties of the individual, pure surfactants, determines whether synergism will exist in a mixture of two surfactants in aqueous solution. 

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... 

The mixed admicelle is very analogous to mixed micelles, the thermodynamics of formation of which has been widely studied. If the surfactant mixing in the micelle can be described by ideal solution theory, the Critical Micelle Concentration (CMC) or minimum concentration at which micelles first form can be described by (21) ... 

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) ... 

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... 

Others have studied the volumetric changes occurring in mixed micelles of anionic-anionic and nonionic-nonionic surfactants as a determinant of intermolecular interactions and a measure of the thermodynamic ideality of mixing. In particular, Funasaki et al. (1986) have studied the volumetric behavior of mixed micelles of ionic and nonionic surfactants and analyzed their results in terms of regular solution theory. They found that in water, anionic surfactants such as SDS bind to PEG,... 

In the molecular-thermodynamic theory of mixed micellization, the size and shape of the mixed micelles can also be predicted by calculating the size and composition distribution. This distribution can be expressed as a function of two fundamental parameters that control the size of the mixed micelles. The Lrst parameter, is deLned as (Puwada and Blankschtein, 1992a,b) to be... 

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... 

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... 

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... 

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 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) ... 

Thus the theory of regular solutions turns out to be a useful tool to describe mixed micelle formation. However, some of the assumptions of this theory are inconsistent with a strict thermodynamic treatment. Scamehorn [43] and later Nishikido [34] presented experimental evidences of its inapplicability. Their arguments can be summarised as follows ... 

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

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