Thermodynamics of Solubilization

Micelle formation is well expressed by the following association equilibrium between surfactant monomers S and micelles 

Monomer concentrations of surfactants, [S], and solubilizate, [R]. From monomer-micelle (9.1) and micelle-solubilizate (9.2) equilibria, the micelle concentrations without and with solubilizates are given respectively by the following equations  

Total equivalent concentrations of surfactant, [St], and solubilizate, [Rt]. This is the most commonly used set of variables. The total equivalent concentration of surfactant is 

the total equivalent concentration can also be expressed by the function of [S] and [R]. On the other hand, the total equivalent concentration of solubilizate is 

Total micelle concentration, [Mt], and average number of solubilizates per micelle, R. The total micelle concentration is given by 

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The approach to the thermodynamics of solubilization in micellar solutions is based on the determination of a given partial molar property of the solute (volume, enthalpy, heat capacity, compressibility) as a function of the surfactant content. The simplest approach is to use the pseudophase model. The partial molar quantity, L will thus be an average value of Y in the micellar and aqueous phases, as described by... 

TMS (Figure 19.12) is an example of a solubilized compound or a solubilizate , i.e. a compound which becomes soluble due to the presence of micelles. Typically, the solubility stays very low until the CMC is reached, while above the CMC it increases rapidly and almost linearly with the surfactant concentration (Figure 19.14). Solubilization is one of the most important phenomena for surfactant solutions, with a direct bearing on, inter alia, detergency and the formulation of pharmaceuticals. In order to study the solubilization equilibria, and thus obtain information on the thermodynamics of solubilization, the mentioned self-diffusion technique is the most general and useful approach. 

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