Controlled Self-Assembly of Soft-Matter Quasicrystals

A large number of soft-matter systems, whose building blocks range in size from several nanometers to almost a micron, have been shown in recent years to form ordered phases with dodecagonal (12-fold) symmetry (for recent reviews see [1]). Contrary to metallurgic quasicrystals, whose source of stability remains a question of great debate to this day, we show that the stability of certain soft-matter quasicrystals-interacting via pair potentials with repulsive cores, which are either bounded or only slowly diverging-can directly be explained. Their stability is attributed to the existence of two natural length scales in their isotropic pair potentials, along with an effective three-body interaction arising from entropy. We establish the validity of this mechanism at the level of a mean-field theory [2], and then use molecular dynamics simulations in two dimensions to confirm it beyond mean field, and to show that it leads to the formation of cluster crystals [3]. We demonstrate that our understanding of the stability mechanism allows us to generate a variety of desired structures, including decagonal and dodecagonal quasicrystals [3], suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles.