How to design an icosahedral quasicrystal through directional bonding

Colloidal cubic diamond photonic crystals through cooperative self-assembly

“…The attractive interaction between TJPs and CSs could be accomplished by depletion, hydrophobic, hydrogen bonding, or electrostatic interactions. 17,26,45,[88][89][90][91][92] The colloidal cubic diamond can be readily obtained by removing the TJP templates consisting of different materials after drying of the crystals. 17,26 Therefore, it is foreseen that our proposed strategy will open up vast opportunities to create other 3D low-coordinated open lattices for a wide range of photonic applications.…”

Programming patchy particles to form three-dimensional dodecagonal quasicrystals

“…We have now very recently achieved this for icosahedral quasicrystals, where the target quasicrystalline structures were generated by projection from six-dimensional cubic lattices. 27 Generating appropriate target structures for other axial quasicrystals, however, may be challenging. In this study, the task was made easier first because we chose the simplest way one could conceive of making a 3D axial quasicrystal, namely, by a simple stacking of two-dimensional quasicrystalline layers.…”

“…49 For this system, the inter-vertex binding is quite flexible, but we have also proposed an approach in which a helix bundle extends from each vertex to provide more directional and torsionally specific interactions between the DNA origami. 27 The sequences of the single strands that allow inter-origami binding can be tuned to provide the requisite specificity, and it would be relatively straightforward to choose the type of polyhedron and tune their edge lengths to match the geometry of the patchy particle. As the origami particles would have a well-defined maximum number of binding partners, they would be more appropriate for realizing the ternary quasicrystal.…”

“…[11][12][13][14][15][16][17][18] For ultrasoft potentials (i.e., particles without a hard repulsive core), it can be shown more rigorously that quasicrystals with a particular symmetry can be favored when the ratio of two inverse length scales in the Fourier transform of the potential has a specific value. [19][20][21] Simulation examples that are exceptions to this "two-lengthscale" stabilization mechanism include quasicrystals formed from hard particles (tetrahedra 22,23 and triangular bipyramids 24 can form dodecagonal quasicrystals) and from "patchy" particles with directional bonding; [25][26][27] the latter are the focus of this paper. In particular, two-dimensional patchy particles with five and seven regularly arranged patches have been found to form dodecagonal quasicrystals that are square-triangle tilings where the bonds are equally likely to be oriented along 12 equivalent directions.…”

Finite Assembly of Three‐Dimensional DNA Hierarchical Nanoarchitectures through Orthogonal and Directional Bonding

“…On the contrary, building orthogonal interactions would make it feasible to organize arbitrary numbers of units into finite assemblies at will [8] . On the other hand, the conformations of hierarchical assemblies are decided by both of the building block and the bonding directions [9] . Specifically, the bonding direction between two units determines their relative orientations.…”