title: Platonic Micelles: Monodisperse Micelles with Discrete Aggregation Numbers Corresponding to Regular Polyhedra.
abstract: The concept of micelles was first proposed in 1913 by McBain and has rationalized numerous experimental results of the self-aggregation of surfactants. It is generally agreed that the aggregation number (Nagg) for spherical micelles has no exact value and a certain distribution. However, our studies of calix[4]arene surfactants showed that they were monodisperse with a defined Naggwhose values are chosen from 6, 8, 12, 20, and 32. Interestingly, some of these numbers coincide with the face numbers of Platonic solids, thus we named them "Platonic micelles". The preferred Naggvalues were explained in relation to the mathematical Tammes problem: how to obtain the best coverage of a sphere surface with multiple identical circles. The coverage ratio D(N) can be calculated and produces maxima at N = 6, 12, 20, and 32, coinciding with the observed Naggvalues. We presume that this "Platonic nature" may hold for any spherical micelles when Naggis sufficiently small.
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Shota
authors.initials: S
authors.lastname: Fujii
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Shimpei
authors.initials: S
authors.lastname: Yamada
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Sakiko
authors.initials: S
authors.lastname: Matsumoto
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Genki
authors.initials: G
authors.lastname: Kubo
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Kenta
authors.initials: K
authors.lastname: Yoshida
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Eri
authors.initials: E
authors.lastname: Tabata
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Rika
authors.initials: R
authors.lastname: Miyake
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Yusuke
authors.initials: Y
authors.lastname: Sanada
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Isamu
authors.initials: I
authors.lastname: Akiba
authors.affiliation: Department of Chemical Science and Engineering, Ariake National College of Technology, 150 Higashihagio-Machi, Omuta, Fukuoka 836-8585, Japan.
authors.forename: Tadashi
authors.initials: T
authors.lastname: Okobira
authors.affiliation: Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), 1-1-1 Kouto, Sayo, Sayo, Hyogo 679-5198, Japan.
authors.forename: Naoto
authors.initials: N
authors.lastname: Yagi
authors.affiliation: Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), 1-1-1 Kouto, Sayo, Sayo, Hyogo 679-5198, Japan.
authors.forename: Efstratios
authors.initials: E
authors.lastname: Mylonas
authors.affiliation: Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), 1-1-1 Kouto, Sayo, Sayo, Hyogo 679-5198, Japan.
authors.forename: Noboru
authors.initials: N
authors.lastname: Ohta
authors.affiliation: Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), 1-1-1 Kouto, Sayo, Sayo, Hyogo 679-5198, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Sekiguchi
authors.affiliation: Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
authors.forename: Kazuo
authors.initials: K
authors.lastname: Sakurai