The concept of micelles was first proposed in 1913 by McBain and the packing parameter principle of micellar architecture and its thermodynamic theory have been used to successfully rationalize numerous experimental results in the last century. It is generally agreed that the aggregation number for spherical micelles gradually changes with changes in solvent conditions and that has no exact value but rather a distribution in the value. However, our studies of spherical micelles made from calix[4]arene-based lipids and other systems by use of scattering, fractionation, and ultracentrifugation techniques, showed that they were monodisperse with a defined aggregation number whose values are chosen from 4, 6, 8, 12, 20, and 32. Interestingly, some of these numbers coincide with the face number of Platonic solids (or regular polyhedra). Our results indicate that a suitable combination of tail length, head volume, and sufficiently small is required to achieve such monodispersity and discreteness of; we named these systems “Platonic micelles”. The preferred values were explained in relation to a mathematical quiz called the Tammes problem i.e. how to obtain the best coverage (D(<i>N</i>)) of a sphere surface with multiple identical circles. This is because better coverage results in lower interface free energy due to reduced interaction between water and hydrophobic tails. For the Tammes problem, the coverage ratio can be calculated and produces maxima at the certain circle numbers, coinciding with the  values observed in our systems. We presume that “the platonic nature” may hold for any spherical micelles when is sufficiently small.

Platonic micelles: Thermodynamic consideration of the micelles with the discrete aggregation numbers and mon-dispersity

253rd National Meeting (2017)

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