Phase Rule of Solubilization

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. 

If the micelles are regarded as a phase, then adding an excess solubilizate phase means there are three phases (the third is the intermicellar bulk phase). The total number of components is three (solvent, surfactant, and solubilizate), so the presence of three phases makes the system divariant. That would mean that surfactant concentration would be constant at constant temperature and pressure— but, in fact, the maximum additive concentration (MAC) changes with total surfactant concentration. Even if it were postulated that the increase in the MAC with surfactant concentration above the CMC is due to an increase in the total micellar phase, the concentration of solubilizate in the micellar phase should still remain constant, because the concentration is an intensive property of the system and is therefore homogeneous throughout the micellar phase. 

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. 

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