(301e) Why Ionic Surfactants Exhibit Linear Conductivity-Concentration Dependence in Non-Polar Liquids

It is known that addition of ionic surfactants to non-polar liquids enhances conductivity by orders of magnitude. Conductivity increases linearly with the concentration of the added surfactant. This fact was considered as contradicting to the classical dissociation theory and Bjerrum-Onsager-Fuoss theory of ion pairs in on-polar liquids. It serves as justification for introduction of alternative, so-called disproportionation theory.

We show that there is no contradiction between this fact and theory of ion-pairing. Mass action law of dissociation model predicts existence of a “critical ionic strength” below which ion-pairs do not form. Concentration of ions below this critical concentration is so low that rate of ions collisions cannot compensate for the rate of ion-pairs breakup. We have estimated this “critical ionic strength” using known size information of the inverse micelles ions formed by ionic surfactants. Indeed, it is orders of magnitude higher than ionic strength usually achieved with ionic surfactants.      

In contrary, non-ionic surfactants do exhibit non-linear conductivity-concentration dependence. At the same time, non-ionic surfactants generate conductivity by orders of magnitude higher than ionic ones. Therefore they produce higher ionic strength that exceeds “critical ionic strength” of ion-pairs formation. Observed non-linearity is associated with ion-pairs formation in agreement with the classical theory.