Micellization phase separation model

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

The phase separation model for nonionic micelle formation has been modified for ionic micelle formation to give an equation close to Equation 12 for Ai (26.). ... 

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 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. 

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 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 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. 

Various approaches have been employed to tackle the problem of micelle formation. The most simple approach treats micelles as a single phase, and this is referred to as the phase-separation model. In this model, micelle formation is considered as a phase-separation phenomenon, and the cmc is then taken as the saturation concentration of the amphiphile in the monomeric state, whereas the micelles constitute the separated pseudophase. Above the cmc, 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 a solid-hydrated surfactant, the micelles, and a solution saturated with undissociated surfactant molecules are in equiUbrium at a given pressure. 

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.. 

In conclusion, nanocasting gives detailed information about the formation and structure of molecules in lyotropic liquid crystals, without having investigated organic matter. Just the fine details of the pore structure reveal these secrets It seems that a classical two-phase separation model is not fully applieable to lyotropic liquid crystals (high-concentration situation), but it seems that a fraction of the hydrophilic block belongs to the micellar core. Furthermore, it was seen that the chain conformation is an intermediate between stretehed (micelles) and coiled (polymer melt). 

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... 

In this model, micelle formation is considered as being akin to a phase separation, with the micelles being the separated (pseudo-) phase, and the CMC the saturation concentration of surfactant in the unimeric state. Surfactant addition above the CMC consequently only affects the micelle concentration, but not the unimer concentration. In many physico-chemical investigations, we observe a number average over the different states that a surfactant molecule can occupy. The phase separation model is particularly simple for the interpretation of experimental observations. Below the CMC, we have only unimers and the average of a quantity Q is simply given as follows ... 

The phase separation model is simple to apply, illustrative and sufficient for many considerations. As we would expect, it becomes a better approximation the higher the aggregation number, i.e. the number of surfactant unimers in the micelle. 

The alternative approach to modeling micelle formation is to think in terms of a phase separation model in which, at the cmc, the concentration of the free surfactant molecules becomes constant (like a solubihty limit or Ksp), and all additional molecules go into the formation of micelles. Analysis of the two approaches produces the same general result in terms of the energetics of micelle formation (with some slight differences in detail), so that the choice of model is really a matter of preference and circumstances. There is evidence that the activity of free surfactant molecules does increase above the cmc, which tends to support the mass-action model however, for most purposes, that detail is of little consequence. 

The phase separation model is particularly useful in describing micelles formed in solutions of surfactant mixtures, as discussed below. 

Experimental data indicate that the changes in rates of variation of physical properties near the CMC actually occur over a narrow range of concentrations and not discontinuously at a single concentration. Hraice a chemical reaction or mass action model should be more realistic than the phase separation model for describing the thermodynamics of micellization. That is, we consider that micelle formation occurs as follows ... 

For binary surfactant mixtures, one might expect that micelles formed at the CMC of the mixture would be enriched in the less hydrophilic surfactant (i.e., the one with the lower CMC). Analysis based on the phase separation model confirms this expectation. The simplest approach is to assume an ideal mixture in the micellar phase (i.e., activity of each species equal to its mole fraction). With this assumption one obtains the following expression for the ratio x Jx2 of the two surfactants in the micellar phase at the CMC (see Problem 4.3) ... 

Since micelle aggregation numbers are large and initial micelle formation occurs over a narrow concentration range, micelle formation, including that with mixed surfactants, can be modeled with reasonable success by a phase separation model. Assume that the following expressions give the chemical potential of a surfactant species in the aqueous and micellar phases, respectively ... 

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