Phase separation model

Quinn, P.J. (1985). A lipid-phase separation model of low temperature damage to biological membranes. Cryobiology, 22, 128-40. 

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 basis for the phase-separation model (Mukerjee, 1967) assumes that the occurrence of thf phase change happens at the CMC. This model uses the chemical potentials of the free surfactant ii the aqueous phaseassociated surfactant in the micellar pha 0,Gu,... 

The van der Waals scheme is the simplest scheme to describe the spinodal phase separation that has been used to describe the co-existence of a polaronic gas (low density insulating phase) and a polaronic liquid (high density metallic phase) by Emin [1], or for more complex phase separation models including magnetic interactions [2-3],... 

Determine an enthalpy of micellisation in accord with the phase separation model. 

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,... 

An alternative to the phase separation model which has nearly the same simplicity is the mass action law model. In this model it is assumed that a single micellar species, of aggregation number n, is in equilibrium with the monomers ... 

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)... 

---