Non-dependence of dodecamer structures on alkyl chain length in Platonic micelles

When the micellar aggregation number (Nagg) is sufficiently small (Nagg < 30), the micelle shows an abnormal aggregation behavior: monodispersity without any distribution in Nagg, whose values coincide with the vertex number of a regular polyhedral structure, i.e., they are termed Platonic solids. Micelles with these characteristics are named "Platonic micelles". In this study, we investigated the aggregation behavior of calixarene-based micelles bearing primary amines-the first example of Platonic micelles-with increasing alkyl chain length by small-angle X-ray scattering, asymmetrical flow field flow fractionation coupled with multiangle light scattering, and analytical ultracentrifugation measurements. Morphological transition of the micelles from spherical to cylindrical was observed when the alkyl chain length was increased in this calixarene-based micellar system, which is similar to the case of conventional systems and is acceptable in terms of the packing parameter principle. However, although the micellar Nagg normally increases with an increase in the alkyl chain length, the structure of calixarene-based Platonic micelles bearing butyl (C4), heptyl (C5), and hexyl (C6) chains remains at 12-mer. This is presumably due to the relationship between the thermodynamic stability of the Platonic micelles and the coverage ratio defined by the Tammes problem.