Critical micellization concentration of surfactants in aqueous solution and free energy of micellization

The relationship between the critical micellization concentration (cmc) of a surfactant in solution and its free energy of micellization Delta G degrees(M) is probably the most widely used one in surfactant science. Until recently, most surfactants discussed in the literature were made up of one polar head group, nonionic or ionic, bonded to a single hydrophobic moiety. Recently, studies have been initiated on new types of ionic surfactants: bolaforms, surfactants with divalent counterions, gemini, or dimeric surfactants, etc. This paper first derives the relationship between the cmc and Delta G degrees(M) for a very general type of ionic surfactant, made up of a surfactant ion containing i polar groups of valency z(s) bonded to j alkyl chains, with counterions of valency z(c). The form of this relationship is examined for several types of ionic surfactants. It is shown that many reported studies did not use the correct relationship to evaluate the free energy of micellization from the value of the cmc. In particular, the counterion contribution was often neglected, which resulted in large errors. The use of the correct equations is shown to yield values for the free energy of transfer of a methylene group from water to the micellar pseudophase which are largely independent of the surfactant chemical structure, as it is to be expected.