A Self-Consistent Multicomponent Activity Coefficient Model for Ionic Micellar Surfactant Solutions

Abstract

The proposed model incorporates a distribution of micellar sizes self-consistently. The model is based on a mass-action equilibrium approach that includes micelle−micelle interactions as a function of size for a multicomponent surfactant solution consisting of micellar aggregates, monomer, counterions, and added electrolyte. The primary solution nonidealities are accounted for in the multicomponent model with excluded-volume and electrostatic interactions as a function of aggregate size. In addition, the model accounts for the Donnan equilibrium existing between an ionic surfactant solution and the electrolyte solution from which it is separated by a semipermeable membrane. Surfactant solutions of sodium dodecyl sulfate (SDS) and cetylpyridinium chloride (CPC) in 0.01 M NaCl are studied over the concentration range from the critical micelle concentration up to volume fractions of 0.19 (0.87 M) for SDS and 0.16 (0.56 M) for CPC. In comparison to the predictions of an ideal solution multiple-chemical equilibrium constant model, the activity-coefficient model predicts increased growth and polydispersity of the aggregates for both CPC and SDS at higher surfactant concentrations. Micellar interactions enhance the growth of the micelles due to excluded-volume effects that favor growth and electrostatic repulsions that oppose it. Micellar aggregates are found to be slightly globular for both SDS and CPC; however, a clear spherical to globular transition is predicted for the CPC micelles. The multicomponent model reflects experimental osmotic pressure data successfully.