Mixed micelles model

Titration results for the mixed erne s of the SDS/CgE4 and C12E2S/C8E4 systems as a function of their relative mole fraction in solution are shown in Figures 2 and 3, respectively. Here, the experimentally determined points are compared with calculated results from the nonideal mixed micelle model (solid line) and the ideal mixed micelle model (dashed line). Good agreement with the nonideal model is seen in each case. 

Figure 2. Cmc s of mixtures of SDS and CgE4 in distilled water (at 25°C). The plotted points are experimental data, the solid line is the result for the nonideal mixed micelle model with B = -3.3, and the dashed line is the result for ideal mixing.

The finding that the assumptions of the regular solution approximation do not hold for the mixed micellar systems investigated here suggests a re-examination of how the thermodynamics of mixing enter the nonideal mixed micelle model. 

The mixed cmc behavior of these (and many other) mixed surfactant systems can be adequately described by a nonideal mixed micelle model based on the psuedo-phase separation approach and a regular solution approximation with a single net interaction parameter B. However, the heats of micellar mixing measured by calorimetry show that the assumptions of the regular solution approximation do not hold for the systems investigated in this paper. This suggests that in these cases the net interaction parameter in the nonideal mixed micelle model should be interpreted as an excess free energy parameter. 

If the mixed micelle model already presented is used to predict the ionic surfactant monomer concentration, and a simple concentration—based solubility product is assumed to hold between the unbound counterion and monomer, the salinity tolerance of an anionic/nonionic surfactant mixture can be accurately predicted (91). supporting this view of the mechanism of tolerance enhancement by nonionic surfactant. 

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... 

Results for the various binary mixed surfactant systems are shown in figures 1-7. Here, experimental results for the surface tension at the cmc (points) for the mixtures are compared with calculated results from the nonideal mixed monolayer model (solid line) and results for the ideal model (dashed line). Calculations of the surface tension are based on equation 17 with unit activity coefficients for the ideal case and activity coefficients determined using the net interaction 3 (from the mixed micelle model) and (equations 12 and 13) in the nonideal case. In these calculations the area per mole at the surface for each pure component, tOj, is obtained directly from the slope of the linear region in experimental surface tension data below the cmc (via equation 5) and the maximum surface pressure, from the linear best fit of... 

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. 

The possibility for nucleaiion by mixed-micelle formation (process G) has also been proposed (van der Hoff. I960), and quite recently experimental work has investigated this mechanism (Munro et ol., 1979 Chen and Phrma, 1980). Evidence has been found indicating assodiation of the sur ce active oligomers in systems both with and without emulsifiers (below the CMC). No quantitative treatment was given by these authors. It may be questioned i ether there is any real difference between the self-nucleation and the mixed-micelle models. When emulsifier is absent, there is clearly a... 

Marrink SJ and Mark AE. Molecular Dynamics Simulations of Mixed Micelles Modeling Human Bile. Biochemistry 2002 41 5375-5382. 

Effluent profiles obtained from a core-flood performed with a mixture of two surface-active components (C12 and C18) separated from a commercially available sulfobetaine are shown in Figure 24 (115). The points represent experimental data, and the lines were obtained by simulating the core-flood with a convection—dispersion—adsorption model that is based on the surface excess concept and takes into account monomer—micelle equilibrium (115). Because the mixture contains different homologues of the same surfactant, the ideal mixed micelle model... 

Fig. 7.8 Schematic mixed-micelle model. Fluorocarbon chains (hatched) form intersecting bands which wind gradually through the structure. The more flexible hydrocarbon chains (open circles) fill the channels. (From Ref. 72. Reproduced by permission of Dr. Dietrich Steinkopf Verlag.)...

Burkitt et al [228,229] suggested that perfluorooctanoate and decanoate chains can mix and form mixed micelles. However, their mixed micelle model allows for segregation between hydrocarbon and fluorocarbon chains within the micelle. 

Holland, P.M., Ruhingh, D.N. Nonideal multicomponent mixed micelle model. J. Phys. Chem. 1983, S7(ll), 1984-1990. 

---