PMID- 31157356 OWN - NLM STAT- PubMed-not-MEDLINE LR - 20190725 IS - 1744-6848 (Electronic) IS - 1744-683X (Linking) VI - 15 IP - 27 DP - 2019 Jul 10 TI - Monodisperse micelles composed of poly(ethylene glycol) attached surfactants: platonic nature in a macromolecular aggregate. PG - 5371-5374 LID - 10.1039/c9sm00943d [doi] AB - 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. FAU - Lee, Ji Ha AU - Lee JH AUID- ORCID: 0000-0002-4456-0128 AD - Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan. sakurai@kitakyu-u.ac.jp. FAU - Matsumoto, Hayata AU - Matsumoto H AD - Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan. sakurai@kitakyu-u.ac.jp. FAU - Fujii, Shota AU - Fujii S AUID- ORCID: 0000-0002-6594-5211 AD - Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan. sakurai@kitakyu-u.ac.jp. FAU - Takahashi, Rintaro AU - Takahashi R AUID- ORCID: 0000-0003-2168-9436 AD - Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan. sakurai@kitakyu-u.ac.jp. FAU - Sakurai, Kazuo AU - Sakurai K AUID- ORCID: 0000-0002-9737-0061 AD - Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan. sakurai@kitakyu-u.ac.jp. LA - eng PT - Journal Article PL - England TA - Soft Matter JT - Soft matter JID - 101295070 EDAT- 2019/06/04 06:00 MHDA- 2019/06/04 06:01 CRDT- 2019/06/04 06:00 PHST- 2019/06/04 06:00 [pubmed] PHST- 2019/06/04 06:01 [medline] PHST- 2019/06/04 06:00 [entrez] AID - 10.1039/c9sm00943d [doi] PST - ppublish SO - Soft Matter. 2019 Jul 10;15(27):5371-5374. doi: 10.1039/c9sm00943d.