Department of Chemistry and Biochemistry, University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan.
Department of Chemical Science and Engineering, Ariake National College of Technology, 150 Higashihagio-Machi, Omuta, Fukuoka 836-8585, Japan.
Sci Rep. 2017 Mar 14;7:44494. doi: 10.1038/srep44494.
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 (N) 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 N whose 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 N values 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 N values. We presume that this "Platonic nature" may hold for any spherical micelles when N is sufficiently small.
胶束的概念最早是在 1913 年由 McBain 提出的，它使许多表面活性剂自聚集的实验结果得到了合理化。人们普遍认为，球形胶束的聚集数（N）没有确切的值，而是具有一定的分布。然而，我们对杯[4]芳烃表面活性剂的研究表明，它们是单分散的，具有确定的 N 值，这些值选自 6、8、12、20 和 32。有趣的是，其中一些数字与柏拉图立体的面数重合，因此我们将它们命名为“柏拉图胶束”。首选的 N 值与数学 Tammes 问题有关：如何用多个相同的圆获得最佳的球体表面覆盖。覆盖比 D（N）可以计算出来，并在 N=6、12、20 和 32 处产生最大值，与观察到的 N 值一致。我们假设，当 N 足够小时，这种“柏拉图性质”可能适用于任何球形胶束。
