Model development, mixed micelle

The purpose of this paper is to develop realistic specific models of mixed micellization which (i) can describe properties of ionic/nonionic surfactant mixtures and effects of salt (ii) lead to tractable calculations and (iii) can be used for extracting information on micelle mixing and monomer concentrations from the limited experimental data which are usually... 

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... 

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. 

Many models have appeared in the literature describing interactions of surfactants in mixed micelles (1-14). For nonionic surfactants mixing nonideally, the key references up to 1984 have been recently summarized (15). Comparatively few models have been developed for ionic surfactants (5,6,10-12) and fewer models which acknowledge ionic/nonionic interactions are available (5-7). Since many practical surfactant mixtures involve ionic and nonionic surfactants which interact with each other and with added salts, it is important to develop explicit ionic/nonionic models. 

Most of the studies on thermodynamics of mixed micellar systems are based on the variation of the critical micellar concentration (CMC) with the relative concentration of both components of the mixed micelles (1-4). Through this approach It Is possible to obtain the free energies of formation of mixed micelles. However, at best, the sign and magnitude of the enthalpies and entropies can be obtained from the temperature dependences of the CMC. An Investigation of the thermodynamic properties of transfer of one surfactant from water to a solution of another surfactant offers a promising alternative approach ( ), and, recently, mathematical models have been developed to Interpret such properties (6-9). 

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... 

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. 

In. my opinion, the study o-f monolayer -formation has less practical importance than the study o-f micelles. Yet, the thermodynamics of monolayer formation has seen substantial study. I think that this is largely due to the fact that the monomer—monolayer equilibrium can be unambiguously and relatively easily measured using the Hutchinson method (25), as exploited by Rosen and Hua ( ), while this cannot be said for monomer—micelle equilibrium. Therefore, mixed monolayer formation will be a more fruitful field for model development in the near future than mixed micelles because of the availability of a method of obtaining experimental data for comparison. 

An amine oxide surfactant solution can be modeled as a binary mixture of cationic and nonionic surfactants, the composition of which is varied by adjusting the pH. The cationic and nonionic moieties form thermodynamically nonideal mixed micelles, and a model has been developed which quantitatively describes the variation of monomer and micelle compositions and concentrations with pH and... 

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 area, recent unrelated efforts of the groups of Bhattacharya and Fife toward the development of new aggregate and polymer-based DAAP catalysts deserve mention. Bhattacharya and Snehalatha [22] report the micellar catalysis in mixtures of cetyl trimethyl ammonium bromide (CTAB) with synthetic anionic, cationic, nonionic, and zwitterionic 4,4 -(dialkylamino)pyridine functional surfactant systems, lb-c and 2a-b. Mixed micelles of these functional surfactants in CTAB effectively catalyze cleavage of various alkanoate and phosphotriester substrates. Interestingly these catalysts also conform to the Michaelis-Menten model often used to characterize the efficiency of natural enzymes. These systems also demonstrate superior catalytic activity as compared to the ones previously developed by Katritzky and co-workers (3 and 4). 

Pseudophase models " were originally developed to treat mixed micellization of binary surfactants." The concept has been generahzed to mean that the totality of the surfactant aggregates present, for example, micelles, microemnlsions, vesicles, and so on, in homogeneous solutions are treated conceptually as a separate phase, or... 

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. 

Kamrath and Franses [85] developed a single-micelle-size mass action model for binary solutions of surfactants with the same hydrophilic group and counterion. The mass action model predicts micellar behavior more accurately than the pseudophase separation model [73] if the number of surfactant monomers in the mixed micelle is less than about 50. 

The adsorption of binary mixtures of anionic surfactants of a homologous series (sodium octyl sulfate and sodium dodecyl sulfate) on alpha aluminum oxide was measured. A thermodynamic model was developed to describe ideal mixed admicelle (adsorbed surfactant bilayer) formation, for concentrations between the critical admicelle concentration and the critical micelle concentration. Specific... 

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