Modeling Micellar Growth and Branching in Mixtures of Zwitterionic with Ionic Surfactants

Zwitterionic surfactants are widely applied as dragreducing or thickening agents because their aggregation patterns may drastically change in response to variations of the system composition or external stimuli, which provides controllable viscoelasticity. For predicting aggregation behavior of surfactant mixtures, classical molecular thermodynamic models have been widely used. Particularly, the results of modeling have been reported for zwitterionic/ionic surfactant mixtures. However, for solutions containing a zwitterionic surfactant, no molecular thermodynamic model has been proposed for a micellar branch. In this work we extend the classical molecular thermodynamic aggregation model to describe aggregation in the aqueous mixtures that contain a zwitterionic and an ionic surfactant. We derive analytical expressions (1) for the contribution of dipoles to the electrostatic term of the standard free energy of aggregation into micellar branches and (2) for the dipolar contribution to the persistence length of wormlike micelles. The dependence of micellar branching on the surfactant concentration is taken into account by including the population of micellar branches in the material balance equations. This model is applied to predict aggregation equilibrium in aqueous salt solutions of betaine (oleoylamidopropylN,N-dimethylbetaine) mixed with sodium dodecyl sulfate (SDS) and the longer tail sodium n-alkyl sulfates. We discuss the predicted properties of the aggregates and micellar networks and compare our predictions with available experimental data.