Rediscovering the Monodispersity of Sulfonatocalix[4]arene-Based Micelles

When the micellar aggregation number ( N_agg) is small enough (<30), the N_agg matches the value of vertexes of a regular polyhedron: Platonic solids, and demonstrates perfect monodispersity. These micelles are named Platonic micelles and are particularly found in the system of calix[4]arene-based micelles due to the rigid structure of the backbone molecule. Although sulfonatocalix[4]arene-based micelles are among the most studied host molecules in supramolecular chemistry, their micellar properties as Platonic micelles have thus far been overlooked. In this study, we prepared various sulfonatocalix[4]arene-based amphiphiles bearing alkyl chains with different lengths and investigated their aggregation behavior. When the amphiphiles formed spherical micelles, they demonstrated monodispersity in terms of N_agg, whose value changed from 4 to 17, and then to 24, upon increasing the carbon number in each alkyl chain from C5 to C6, and then to C7, respectively. Although the numbers 17 and 24 do not match the vertices of regular polyhedra, these values can be reasonably explained by the Thomson problem, which considers the Coulomb potential for calculating the best packing on a sphere with multiple identical spherical caps. This study describes rediscovery of the monodispersity of sulfonatocalix[4]arene-based micelles, which is consistent with the idea of Platonic micelles.