Size distribution of mixed micelles: Rodlike surfactant-alcohol aggregates

The size and composition distributions of mixed surfactant-alcohol micellar aggregates are derived by minimizing the free energy of the system subject to mass conservation constraints. When regions of different geometry within the aggregate (e.g. the hemispherical "caps" and the cylindrical "body" of spherocylindrical (rodlike) micelles) are treated as different microphases, the minimization of the free energy leads to explicit expressions that relate uniquely the compositions of these microenvironments to each other and to the overall composition of the solution. It is shown that at high amphiphile concentrations (but still in the dilute solution regime) the average aggregation number of binary rodlike aggregates varies with the total amphiphile concentration, S, according to S^2/5, compared to the S^1/2 dependence for pure aggregates. The theory is applied to rodlike micelles comprising ionic surfactants and nonionic (long-chain alcohol) cosurfactants. The alcohol is modeled as a "spacer" that dilutes the charge density at the micelle-water interface, thereby reducing the electrostatic repulsion between the ionic head groups. It is shown that the alcohol is preferentially partitioned into the regions of lower curvature, where it is more efficient in relieving the electrostatic strain. It is found that the addition of very small amounts of cosurfactant first leads to a decrease in the average micellar size. After reaching a (typically shallow) minimum (at ∼1% cosurfactant concentration), further addition of alcohol leads to a monotonic increase in the average micelle size.