Classic Thermodynamics of Micelle Formation

In the literature on micelle formation two primary models have gained general acceptance as useful (although not necessarily accurate) models for understanding the energetics of the process of self-association. The two approaches are the mass-action model, in which the micelles and monomeric species are considered to be in a kind of chemical equilibrium 

It is usually observed that the critical micelle concentration for a surfactant is relatively sharp and characteristic. Although the detailed theory of micelle formation can become quite complex, the sharpness of the cmc can be explained conceptually in terms of the law of mass action. If Q denotes the total concentration of surfactant in solution, Q the fraction of surfactant present as free molecules, and Cm that in the aggregated state. Equation (15.3) may be written 

In the process of micelle formation, there will be some concentration, Ceq, at which the number of surfactant molecules in the micellar form will be equal to that in the form of free surfactant molecules. At that concentration, Cm = Cs = zCeq. Using Equation (15.4), one can then write that 

TABLE 15.1. Percentage of Total Surfactant Molecules in MiceDar Form Near 

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. 

---