Predicting the critical micelle concentrations of aqueous solutions of ionic liquids and other ionic surfactants

Some ionic liquids (ILs) are structurally analogous to surfactants, especially those that consist of a combination of organic and inorganic ions. The critical micelle concentration (CMC) is a basic parameter of surface chemistry and colloid science. A significant amount of research has already been carried out to determine the CMCs of ILs. However, because of the many varied cation/anion combinations, it is a daunting task to measure the CMCs of all possible ILs. Herein we suggest a general rule for predicting the CMCs of ionic surfactants in water based on data from COSMO-RS calculations. In accordance with the Stauff-Klevens rule, the molecular volume (V(m)) is sufficient to describe similar homologous series of cationic surfactants such as imidazolium- and ammonium-based ionic liquids with varying side-chain lengths. However, to also include anionic surfactants like Na[C(n)SO(4)] in a more general correlation, V(m) has to be exchanged by the cubed molecular radius (r3(m)) and the molecular surface has to be used as an additional descriptor. Furthermore, to describe double amphiphilic compounds like [C(4)MIm][C(8)SO(4)], the enthalpies of mixtures calculated by COSMO-RS have to be taken into account. The resulting equation had allowed us to predict the CMCs of all of the 36 tested surfactants with an error similar to or smaller than the usual experimental errors (18 different cations, 10 different anions: root mean squared error (rmse)=0.191 logarithmic units; R(2)=0.994). We discuss the factors governing micelle formation on the basis of our calculations and show that the structure of our equation can be related to Gibbs' theory of crystallization.