Theory of surfactant aggregation in water/ethylene glycol mixed solvents

The aggregation behavior of surfactants in mixed solvents composed of water and ethylene glycol is predicted using an extension to our theory of aqueous surfactant solutions. The extension accounts for the dependence of (i) the surfactant tail transfer free energy, (ii) the aggregate core-solvent interfacial free energy, and (iii) the headgroup interaction free energy on the composition of the mixed solvent. As the proportion of ethylene glycol in the mixed solvent increases, the model predicts an increase in the critical micelle concentration (cmc), a decrease in the average aggregate size, an increase in the aggregate polydispersity, and a stronger dependence of the average aggregation number on the total surfactant concentration. The model reveals that (a)large values for cmc originate primarily from the smaller magnitude of the surfactant tail transfer free energy in the mixed solvent, (b) the aggregation numbers are small mainly because of the smaller magnitude of the hydrocarbon-mixed solvent interfacial tension, and (c) neither the cmc nor the aggregate size are greatly affected by the lower dielectric constant of the mixed solvent. The predicted aggregation characteristics of cetyl pyridinium bromide, cetyl trimethylammonium bromide, and sodium dodecyl sulfate at various compositions of the mixed solvent are presented for illustrative purposes and are compared with available measurements.