Dodecagonal Quasicrystals in Mesoporous Silica: A New Route from Hard- to Soft-Sphere Packings

Quasicrystals attract considerable attention due to their unique physical and structural properties. An increasing number of quasicrystals have been reported from self-assembly processes in soft matter systems; however, no generic synthesis conditions that yield mesoscopic quasicrystals have been fully clarified yet. This paper presents a new synthesis system for mesoporous silica crystals that yields dodecagonal quasicrystals, employing a gemini cationic surfactant as a template, carboxyethylsilanetriol sodium salt as a co-structure-directing agent, and tetraethyl orthosilicate as a silica source. We show structural changes from cubic close packing to a composite of cubic and hexagonal close packings, and further to tetrahedral close packings derived from dodecagonal tilings with squares and triangles as the concentration of the co-structure directing agent is gradually decreased. These structural changes are attributable to the softening of the spherical micelles, i.e., the building units of the structure while in solution, considering that area-minimizing duals are energetically favored by the packing of soft spheres. A possible relevance of the present findings to a recent prediction on the stability of dodecagonal quasicrystalline dry foams is pointed out.