Mass Action Model for Micellization

Consider a solution of the amphiphilic substance A in which the molecules of A are present as monomers, dimers, trimers, tetramers, and so on. The mole fractions of the amphiphile in the monomeric state and the respective associated states are denoted as = X /i). 

Micelles are formed if Aaj cmc (where the cmc is expressed in mole fraction of Aj, which, for dilute systems, is proportional to the concentration of Aj). Then, 

The standard Gibbs energy for the transfer of a monomer from solution into an f-mer is 

In micelles, i is on the order of tens to hundreds. That is the reason why the transition between the monomeric and the micellar solution is so sharp. Upon adding A to the system Aaj varies proportionally with (Xai )( For instance, an increase of Xf. by a 

FIGURE 11.10 Micellization. (a) Mole fraction of micelles, Xa, as a function of the mole fraction of monomers in solution, for different values, i, of monomers in the micelles. For 

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We see in Section 8.8 that surfactants undergo aggregation in nonaqueous solvents also, but the degree of aggregation is very much less (n < 10), and the threshold for aggregation is far less sharp than in water. The mass action model for micellization seems preferable for nonaqueous systems. 

The light scattering results could be fitted by Attwood and Udeala [14] using the mass action model for micellization. 

In the previous chapters, the dissolution and micellization of surfactants in aqueous solutions were discussed from the standpoint of the degrees of freedom as given by the phase rule. The mass-action model for micelle formation was found to be better for explaining the phenomena of surfactant solutions than the phase-separation model. Two models have similarly been used to explain the Krafft point, one postulating a phase transition at the Krafft point and the other a solubility increase up to the CMC at the Krafft point. The most recent version of the first approach is a melting-point model for a hydrated surfactant solid. The most direct approach to the second model of the Krafft point rests entirely on measurements of the solubility and CMC of surfactants with temperature. From these mesurements the concept of the Krafft point can be made clear. This chapter first reviews the concepts used to relate the dissolution of surfactants to their micellization, and then shows that the concept of a micelle temperature range (MTR) can be used to elucidate various phenomena concerning dissolution... 

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