Refining of nonionic surfactant micellization theory based on the law of mass action

Two approaches to determining critical micelle concentration (CMC) are assessed, i.e., from the inflection point in the curve for the concentration dependence of the degree of micellization and as K1/(1–n), where K is the constant of the law of mass action and n is the aggregation number. The latter approach makes the theory simpler, while the former explicitly expresses the critical degree of micellization via the aggregation number. The concentrations of monomers and micelles are analyzed as functions of the overall concentration of a surfactant in a micellar solution. These functions look much simpler in the graphical form as compared with their complex exact analytical representation. This has resulted in derivation of simple analytical approximations for these functions, with these approximations being useful for calculations. The concentration dependence of the surfactant diffusion coefficient has been considered based on these approximations. It turned out that this dependence not only provides the known method for determining the diffusion coefficient of micelles, but also gives the possibility in principle to determine the aggregation number from the slope of the dependence of the diffusion coefficient on the inverse concentration (counted from the CMC in the CMC units). This new method for determining the aggregation number has been tested using the literature data on the diffusion coefficient of penta(ethylene glycol)-1-hexyl ether in an aqueous solution.