Thermodynamic modeling of CTAB aggregation in water-ethanol mixed solvents

Accurate estimation of the CMC and aggregation numbers of individual surfactants is necessary to predict aggregation properties of surfactant mixtures, as well as to produce materials with controlled structures in the template synthesis. Thermodynamic equations are established to predict the aggregation behavior of cetyltrimethylammonium bromide (CTAB) in water-ethanol mixed solvent based on Nagarajan's thermodynamic models. The calculated CMC and the aggregate size distribution are consistent with the experimental data and indicate that ethanol increases the CMC value and broadens the aggregate size distribution of CTAB. The calculated free energy reveals that ethanol greatly affects the transfer free energy of surfactant tails, the aggregate core-solvent interface free energy, and the ionic component of the free energy of head group interaction. The small angle XRD analysis of the pore structure of template-synthesized silica demonstrates that the suggested model can provide reasonable estimation of the CMC and the aggregation number of CTAB in water-ethanol mixed solvent, as well as indicates that the ethanol content in a solvent is one of the important factors affecting the periodic mesostructure of silica.