A patchy-particle three-dimensional octagonal quasicrystal

Abstract

We devise an ideal three-dimensional octagonal quasicrystal that is based upon the two-dimensional Ammann-Beenker tiling and that is potentially suitable for realization with patchy particles. Based on an analysis of its local environments, we design a binary system of five- and eight-patch particles that in simulations assembles into a three-dimensional octagonal quasicrystal. The local structure is subtly different from the original ideal quasicrystal possessing a narrower coordination-number distribution; in fact, the eight-patch particles are not needed and a one-component system of the five-patch particles assembles into an essentially identical octagonal quasicrystal. We also consider a one-component system of the eight-patch particles; this assembles into a cluster with a number of crystalline domains, which, because of the coherent boundaries between the crystallites, has approximate eightfold order. We envisage that these systems could be realized using DNA origami or protein design.