Aperiodic tilings in self-assembled soft matter quasicrystals
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Abstract
Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from (for example) kites and darts, squares and triangles, rhombi or shield-shaped tiles and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal (12-fold rotation symmetry) type, and many can be described in terms of square and equilateral triangular tiles. Here, we explore what contributes to the thermodynamic stability of soft-matter quasicrystals, both in two dimensions and in three, and how the details of how soft-matter particles interact leads to different kinds of aperiodic tilings. Although dodecagonal quasicrystals are the most common, this work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.
