Rod Formation of Ionic Surfactants: Electrostatic and Conformational Energies

We present a thermodynamic model that describes the formation of micelles from ionic surfactants in aqueous solution at varying counterion concentrations. The micellar aggregates may be spheres, dumbbells, and rods. A former theory [Heindl, A.; Kohler, H.-H. Langmuir 1996, 12, 2464] is refined by the introduction of detailed models for the conformational energy of the surfactant chains and the electrostatic interaction of the ionic headgroups. The standard Gibbs energy of a surfactant ion is minimized under constraints imposed by the micelle shape. The conformational energy is calculated from an appropriately modified single-chain mean-field model proposed in another work [Ben-Shaul, A.; Gelbart, W. M. In Membranes, Microemulsions and Monolayers; 1994]. For the electrostatic interactions, we use a previously developed local balance model for a charged interface [Woelki, S.; Kohler, H.-H. Chem. Phys. 2000, 267, 411-419; 421-438]. This leads to a marked counterion specificity of the standard Gibbs energies of the micelles. Interfacial tension, steric headgroup repulsion, and direct counterion adsorption are taken into consideration. From the standard Gibbs energies, the size distribution of the micelles can be obtained by application of the law of mass action. This distribution is used to calculate the viscosity of the micellar solution at a given concentration of surfactant and salt. A single fitting parameter - the counterion dissociation constant - is used to fit the model to experimental viscosity data for cetylpyridinium chloride, bromide, iodide, and nitrate. It is shown that two alternative models for the shape of the rods can be used to explain the observed counterion specificity.