Critical concentration of ion-pairs formation in nonpolar media

It is known that nonpolar liquids can be ionized by adding surfactants, either ionic or nonionic. Surfactant molecules serve as solvating agents, building inverse micelles around ions, and preventing their association back into neutral molecules. According to the Bjerrum-Onsager-Fuoss theory, these inverse micelle ions should form "ion pairs." This, in turn, leads to nonlinear dependence of the conductivity on the concentration. Surprisingly, ionic surfactants exhibit linear conductivity dependence, which implies that these inverse micelle ions do not form ion pairs. Theory predicts the existence of two ionic strength ranges, which are separated by a certain critical ion concentration. Ionic strength above the critical one is proportional to the square root of the ion concentration, whereas it becomes linear below the critical concentration. Critical ion concentration lies within the range of 10(-11) -10(-7) mol/L when ion size ranges from 1 to 3 nm. Critical ion concentration is related, but not equal, to a certain surfactant concentration (critical concentration of ion-pairs formation (CIPC)) because only a fraction of the surfactant molecules is incorporated into the micelles ions. The linear conductivity dependence for ionic surfactants indicates that the corresponding CIPC is above the range of studied concentrations, perhaps, due to rather large ion size. The same linearity is a sign that charged inverse micelles structure and fraction are concentration independent due to strong charge-dipole interaction in the charge micelle core. This also proves that CIPC is independent of critical concentration of micelle formation. Nonionic surfactants, on the other hand, exhibit nonlinear conductivity dependence apparently due to smaller ion sizes.