Phase separation model of micellization

Phase separation model, of micellization, 24 128-129 Phase structure(s)... 

The CMC has its most clear-cut interpretation within the (pseudo) phase separation model of micelle formation. Although the micelles and the surrounding solution form a single phase, the amphiphile association shows a cooperativity that makes an analogy with a phase transition useful. Within this model, the CMC is the concentration at which the system enters a two phase region the two pseudophases formed being the aqueous system and the micelles. 

In the phase separation model of micelle formation (cf. Sect. 3.1) it is also possible to include the counterions specifically. One has made the distinction between the uncharged phase and the charged micellar pseudophase295). These models can, for example, be used to predict how the CMC varies with salt concentration46, but as used they are open to the same kind of criticism as is the equilibrium model. 

In the case of low concentrations of the oil molecules, it is also useful to determine the extent of solubilization in the simulations, which can be represented in terms of the partition coefficient, K. If the micelles are considered to be a separate phase (as in the phase separation model of micellization [20,21]), then the concentrations of the solute in the aqueous and micellar phases can be related as... 

The data presented in Fig. 5.7 demonstrate the enormous increase in counterion quadrupole relaxation rate which accompanies micelle formation. Temperature dependence studies [319-321 324 326], as well as studies of the bromine isotope effect [303 319-321 324 326], show that the counterions exchange between different binding environments at a rapid rate compared to that of relaxation. To rationalize the concentration dependence of counterion quadrupole relaxation in micellar solutions it has been assumed that only two binding sites for the counterions have to be considered, i,e, the counterions are either free or attached to the micelles. It is further assumed that the ratio of counterions to surfactant ions in the micelles is independent of concentration and that the pseudo-phase separation model of micelle formation applies. This model [313] treats micelle formation analogously to a phase separation, with the c.m.c. corresponding to the saturation concentration of the molecule-disperse amphiphile. With these assumptions it may be shown [322] that for concentrations below the... 

For solubilizates with significant water solubility, it is of interest to know both the distribution ratio of solubilizate between micelles and water under saturation and unsaturation conditions. For measuring the distribution ratio under unsaturation conditions, a dialysis technique can be employed using membranes that are permeable to solubilizate but not to micelles. Ultrafiltration and gel filtration techniques can be applied to obtain the above information. The data are treated using the phase separation model of micellization (micelles are considered to be a separate phase in equilibrium with monomers). 

In treating data from partition experiments, most workers have utilized the phase separation model of micellization, i.e. they have treated the micelles as a separate... 

These equations are equivalent to those for the phase-separation model of micelle formation. 

If, on the other hand, the micelles are regarded as a phase and the system does not contain an excess solubilizate phase, there are three degrees of freedom. The surfactant concentration is then a unique variable that determines every intensive property of the system at constant temperature and pressure. In other words, the solubilizate monomer concentration in the intermicellar bulk phase (and therefore also in the micellar phase) is set automatically by the surfactant concentration, irrespective of the total solubilizate concentration in the system. This is not only totally incorrect as theory but is contrary to the experimental evidence that the concentration of solubilizates is determined only by the amount added to the system. Clearly, the phase-separation model of micelles and the partition model of solubilization disagree with reality. This contradiction is easily solved by treating the micelles as a chemical species, as shown in the following section. 

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. 

The simplest thermodynamic model for solubilization is the pseudophase or phase separation model. The micelles are treated as a separate phase consisting of surfactant and the solubilized molecules. Solubilization is regarded as a simple distribution or equilibrium of the solute between the aqueous and the miceUar phases, i.e.. 

Two general approaches have been employed to tackle micelle formation. The first and simplest approach treats micelles as a single phase, and is referred to as the phase separation model. Here, micelle formation is considered as a phase separation phenomenon and the c.m.c. is then the saturation concentration of the amphi-phile in the monomeric state whereas the micelles constitute the separated pseudophase. Above the c.m.c., a phase equilibrium exists with a constant activity of the surfactant in the micellar phase. The KrafFt point is viewed as the temperature at which solid hydrated surfactant, micelles and a solution saturated with undissociated surfactant molecules are in equilibrium at a given pressure. 

The transition between molecules and micelles upon increasing am-phiphile concentration becomes sharper for larger association numbers. In the limit of very large association numbers, the amphiphile solution above the CMC can be modelled as a pseudo-phase-separated system of micelles and unimers. The CMC then corresponds to the saturation concentration of surfactant in the unimer state. In equilibrium, the molar chemical potentials of unimer in the aqueous phase and of associated amphiphile in the micellar phase are equal. Erom this, it can be shown that (Q. 4.10) the molar Gibbs energy of micellization is given by Eq. (4.40). 

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... 

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. 

In this modification, the ionic micelle has been considered as the charged phase, which has difficulties from the thermodynamic viewpoint. The precise measurement of the surface tension of aqueous sodium dodecyl sulfate solutions revealed the cotlnuous decrease of surface tension above the cmc and indicated that the charged phase separation model is not correct (27). ... 

The derivation of a pseudo-phase separation model for treating nonideal mixed micellization is given in detail in reference 3. This leads to the generalized result... 

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. 

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. 

There are several approaches to derive the Gibbs free energy of micellization. We only discuss one of them which is called the phase separation model. Even this approach only leads to approximate expressions for nonionic surfactants. More detailed discussions of the thermodynamics of micellization can be found in Refs. [3,528,529],... 

In the phase separation model we take advantage of the fact that micellization has much in common with the formation of a separate liquid phase. At low concentration the chemical potential of the dissolved surfactants can be described by... 

Several models have been developed to interpret micellar behavior (Mukerjee, 1967 Lieberman et al., 1996). Two models, the mass-action and phase-separation models are described here in mor detail. In the mass-action model, micelles are in equilibrium with the unassociated surfactant or monomer. For nonionic surfactants with an aggregation numb itbfe mass-action model predicts thatn molecules of monomeric nonionized surfactaStajeact to form a micelleM ... 

The phase separation model is particularly useful for describing the amount of micellized amphiphile and how molecular properties vary with amphiphile concentration. The average of a quantity Q (which can be a diffusion coefficient, a NMR chemical shift, a NMR relaxation time etc.) is determined by the fractions micellized,... 

In calorimetric studies of micelle formation it is often difficult to relate the measured enthalpy changes to specified steps in the aggregation process. Instead one perferably determines the partial molar enthalpy hA of the amphiphile as a function of concentration12). The ideal case of the phase separation model predicts that hA is constant up to the CMC where it discontinuously jumps to another constant value. 

In view of this phase concept which is confirmed by the micellization phenomena in many nonpolar detergent solutions, it has been suggested by Eicke and Christen40 that in line with this reasoning a nucleation step is to be expected (in the approximation of the phase separation model). In order to explain the origin of the energy necessary to overcome the potential barrier associated with the postulated... 

The phase separation model follows exactly the description of a two-phase equilibrium, i.e., equating the respective chemical potentials of the particular surfactant in both phases (i.e., monomers in the nonpolar solvent and the micelles) at the critical concentration (CMC). Thus, (assuming ideal condition)... 

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.,... 

We found the 31p-NMR chemical shift of monomeric dihexanoyl PC increases upon the addition of the nonionic detergent Triton X-100. This phenomenon was used to quantitate the solubilization of this phospholipid by the detergent micelles as a function of detergent concentration using a simple phase separation model ( 5). Similar studies were carried out on dibutyryl PC. At a phospholipid concentration of 7 mM and 56 mM detergent, 85% of the dihexanoyl PC, but only 3% of the dibutyryl PC was incorporated into the micelles. 

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