Related Experiment Video
Updated: Jan 24, 2026

Microwave-assisted Functionalization of Polyethylene glycol and On-resin Peptides for Use in Chain Polymerizations and Hydrogel Formation
Published on: October 29, 2013
Monodisperse micelles composed of poly(ethylene glycol) attached surfactants: platonic nature in a macromolecular
Ji Ha Lee1, Hayata Matsumoto1, Shota Fujii1
1Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan. sakurai@kitakyu-u.ac.jp.
Abstract:
Among the many studies on micelles, dating back more than 100 years, we first found a series of monodisperse micelles: spherical micelles made from calix[4]arene surfactants exhibited monodispersity in aggregation number (Nagg) with values of 4, 6, 8, 12, and 20. We named these Platonic micelles because these values coincided with the face numbers of the Platonic solids. The preferred Nagg values were explained in relation to the mathematical Tammes problem: how to obtain the best coverage of a sphere surface with multiple identical circles. In this paper, we synthesized poly(ethylene glycol)-attached surfactants and carried out small-angle X-ray scattering (SAXS) and analytical ultracentrifugation (AUC) to determine the Nagg. We found that these polymeric surfactants also formed monodispersed micelles and Nagg discontinuously increased from 20 to 24, and then 32 with increasing the alkyl carbon numbers from 9 to 11 continuously. The determined Nagg was greater than 20 and the Platonic solid numbers. We assumed that the preferred Nagg values could be explained in relation to the Tammes problem as well.
Related Concept Videos
Attachment
Attachment Styles
What is Natural Selection?
Nature and Nurture
Attachment of Sister Chromatids
Theory of Romantic Attachment in Adulthood

