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 Nagg 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 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. The coverage ratio D(N) can be calculated and produces maxima at N = 6, 12, 20, and 32, coinciding with the observed Nagg values. We presume that this “Platonic nature” may hold for any spherical micelles when Nagg is sufficiently small.

A heterometallic and paramagnetic one-dimensional (1-D) chain (3) aligned as −Rh(+2)−Rh(+2)− Pt(+2)−Co(+2)−Pt(+2)− with direct metal−metal bonds was obtained by HOMO−LUMO interactions at the σ* (d z 2 ) orbital between two kinds of complexes. The 1-D chains in 3 have relatively straight backbones because the raw material complexes, [Rh 2 (O 2 CCH 3 ) 4 ] and [Pt 2 Co(piam) 4 (NH 3 ) 4 ], are connected and stacked in a face-to-face fashion, where Co---Co are separated by about 13.3 Å with four different metals.Physical measurements revealed that 3 has a band gap between the σ-type conduction and valence bands, where dorbitals of the Co ion with three unpaired electrons are laid among them. The magnetic behavior of 3 was investigated and found to be consistent with a complex interaction involving both zero-field splitting and Pauli paramagnetism attributed to band formation superimposed on relatively strong exchange coupling (zJ = −22.2 cm −1 ) between two high-spin Co(+2) ions separated by the diamagnetic Pt−Rh−Rh−Pt.

In 1997, a study based on X-ray crystallography revealed that resorcinarenes adopt a hexameric capsule-like structure. The function of resorcinarenes has been discussed on the basis of this structure; however, our recent study showed that the hexamer may be only one of resorcinarenes' polymorphic members. Here, we present the solvent dependence of the aggregation number of C-undecylresorcinarene in watersaturated toluene and chloroform using small-angle neutron and X-ray scattering and analytical ultracentrifugation measurements. We found that a new octamer was formed in toluene where the eight resorcinarene units were placed at the vertices of a regular cube; this contrasts to the previous structure in chloroform, namely, a hexamer with the six resorcinarenes located at the vertices of a regular octahedron that has a cavity inside where chloroform molecules are pooled.

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