Hass action model micellization

A mass action model (MAM) with monodisperse aggregation number N which depends on the micelle mole fraction x and the counterion binding parameter /3(x) has been developed for binary surfactants either ionic/ionic or nonionic/ionic. 

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 thermodynamics of micelle formation has been studied extensively. There is for example a mass action model (Wennestrdm and Lindman, 1979) that assumes that micelles can be described by an aggregate Mm with a single aggregation number m, so that the only descriptive equation is mMi Mm. A more complex form assumes the multiple equilibrium model, allowing aggregates of different sizes to be in equilibrium with each other (Tanford, 1978 Wennestrdm and Lindman, 1979 Israelachvili, 1992). 

Summarizing the statements of these three most commonly used models, it appears that the so-called mass action and phase-separation models simulate a third condition which must be fulfilled with respect to the formation of micelles a size limiting process. The latter is independent of the cooperativity and has to be interpreted by a molecular model. The limitation of the aggregate size in the mass action model is determined by the aggregation number. This is, essentially, the reason that this model has been preferred in the description of micelle forming systems. The multiple equilibrium model as comprised by the Eqs. (10—13) contains no such size limiting features. An improvement in this respect requires a functional relationship between the equilibrium constants and the association number n, i.e.,... 

Aggregation of surfactants in apolar solvents, e.g., aliphatic or aromatic hydrocarbons, occurs provided that small amounts of water are present [1,126,127], These aggregates are often called reverse micelles, although the solutions do not always appear to have a critical micelle concentration, and surfactant association is often governed by a multiple equilibrium, mass action, model vith a large spread of aggregate sizes [130,131], It has recently been suggested that the existence of a monomer f -mer equilibrium should be used as a criterion of micellization, and that this term should not be applied to self-associated systems which involve multiple equilibria [132],... 

The micelle has too small an aggregation number to be considered as a phase in the usual sense, and yet normally contains too many surfactant molecules to be considered as a chemical species. It is this dichotomy that makes an exact theory of solubilization by micelles difficult. The primary theoretical approaches to the problem are based on either a pseudophase model, mass action model, multiple equilibrium model, or the thermodynamics of small systems [191-196]. Technically, bulk thermodynamics should not apply to solute partitioning into small aggregates, since these solvents are interfacial phases with large surface-to-volume ratios. In contrast to a bulk phase, whose properties are invariant with position, the properties of small aggregates are expected to vary with distance from the interface [195]. The lattice model of solute partitioning concludes that virtually all types of solutes should favor the interface over the interior of a spherical micelle. While for cylindrical micelles, the internal distribution of solutes... 

Although the mass action approach could account for a number of experimental results, such as the small change in properties around the c.m.c., it has not escaped criticism. For example, the assumption that surfactants exist in solution in only two forms, namely single ions and micelles of uniform size, is debatable. Analysis of various experimental results has shown that micelles have a size distribution that is narrow and concentration dependent. Thus, the assumption of a single aggregation number is an oversimplification and, in reaUty, there is a micellar size distribution. This can be analyzed using the multiple equilibrium model, which can be best formulated as a stepwise aggregation [2],... 

Micellar colloids represent dynamic association-dissociation equilibria. However, the theoretical treatment of micelles depends on whether the micelle is regarded as a chemical species or as a separate phase. The mass action model which has been used ever since the discovery of micelles, takes the former point of view," " whereas the phase separation model regards micelles as a separate phase. To apply the mass action model strictly, one must know every association constant over the whole stepwise association from monomer to micelle, a requirement almost impossible to meet experimentally. Therefore, this model has the disadvantage that either monodispersity of the micelle aggregation number must be employed or numerical values of each association constant have to be assumed. " The phase separation model, on the other hand, is based on the assumption that the activity " of a surfactant molecule and/or the surface tension of a surfactant solution remain constant above the CMC. In... 

It is evident that a small temperature increase brings about a large increase in solubility, and that the micelle aggregation number n has a very strong influence (Fig. 4.2). As is clear from the above discussion, the abrupt increase in the total solubility above T is due not to an increase in the solubility of the monomeric surfactant but rather to an increasing number of micelles. In addition, the treatment of micelles as a separate phase has turned out to be incorrect, whereas the mass action model is consistent not only with the phase rule but also with the solubility increase. 

The mass-action model should be verified before we discuss micelle thermodynamics. Recent progress in electrochemical techniques makes it possible to measure monomeric concentrations of surfactant ions and counterions, and determination of the micellization constant has become possible. The first equality of (4.24) has three parameters to be determined— K , n, and m, which are the most important factors for the mass-action model of micelle formation. For monodisperse micelles, the following equations result from (4.13) and (4.14), respectively ... 

Now that the mass-action model has been supported by a number of observations, we move to the thermodynamics of micelle formation based on this model. As would be predicted from the above discussion, micelle formation can be well expressed by a single association constant, even though the process strictly involves multiple association equilibria. The error is less than 5%, for example, for micelles having an aggregation number more than 50. For nonionic surfactants, the standard free energy change AG° per mole of surfactant molecules follows directly from the equilibrium constant and is given from (4.21) and [S] = Q by... 

Almost thirty years ago the author began his studies in colloid chemistry at the laboratory of Professor Ryohei Matuura of Kyushu University. His graduate thesis was on the elimination of radioactive species from aqueous solution by foam fractionation. He has, except for a few years of absence, been at the university ever since, and many students have contributed to his subsequent work on micelle formation and related phenomena. Nearly sixty papers have been published thus far. Recently, in search of a new orientation, he decided to assemble his findings and publish them in book form for review and critique. In addition, his use of the mass action model of micelle has received much criticism, especially since the introduction of the phase separation model. Many recent reports have postulated a role for Laplace pressure in micellization. Although such a hypothesis would provide an easy explanation for micelle formation, it neglects the fact that an interfacial tension exists between two macroscopic phases. The present book cautions against too ready an acceptance of the phase separation model of micelle formation. 

Micelle formation has been explained by several theories which regard the micelle as either a chemical species or a separate phase. The simplest to understand and probably the most adequate is the mass action model [17-29], which regards the micelle as a chemical species. The mass action model is based on association of monomeric surfactant molecules in dynamic equilibrium with the micelle ... 

The combination of the pseudophase assumption with mass action binding constants of substrates and ion exchange of reactive and nonreactive counterions is called the pseudophase ion-exchange (PIE) model [10,48,66]. It successfully fits the kinetics of many bimolecular reactions and also shifts in apparent indicator equilibria in a variety of association colloids, especially reactions between organic substrates and inorganic ions in normal micelles over a range of surfactant and salt concentrations and types (up to about 0.2 M). It has also been successfully applied to cosurfactant-modified micelles [77,78], O/W microemulsions [79-81], and vesicles [82]. 

Plots of the dependence of the twist on the inverse temperature would reveal the entropic contribution to the chiral interaction which has also been considered by Osipov [13]. In order to describe chiral dispersion forces, macromolecules as well as micelles were modeled as anisometric bodies filled with a dielectric medium. The interaction of such particles is then determined through fluctuations of the electromagnetic field which can be influenced by molecular chirality. Within this frame the action of a chiral solvent can be imderstood, too. 

The authors concluded that for systems where n is large and changes little with temperature, Equations 3.44 to 3.46 may be approximated to the corresponding equations from the mass-action or phase-separation models. A more detailed treatment of multicomponent micelles has been developed by Hall [185]. 

An essentially equivalent approach to that of small-systems thermodynamics has been formulated by Corkill and co-workers and applied to systems of nonionic surfactants [94,176]. As with the small-systems approach, this multiple-equilibrium model considers equilibria between all micellar species present in solution rather than a single micellar species, as was considered by the mass-action theory. The intrinsic properties of the individual micellar species are then removed from the relationships by a suitable averaging procedure. The standard free energy and enthalpy of micellization are given by equations of similar form to Equations 3.44 and 3.45 and are shown to approximate satisfactorily to the appropriate mass-action equations for systems in which the mean aggregation number exceeds 20. 

Much of the published work on solubilization is on the phase-separation model of the micelle. Accordingly, solubilization has been treated as a partitioning of solubilizate molecules between a micellar phase and the intermicellar bulk phase." " A few papers are based on the mass-action approach, and theoretical discussions from this position have also appeared. Unfortunately, papers discussing solubilization from the standpoint of the Gibbs phase rule are very few. " This section examine solubilization in terms of the phase rule. 

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