(55c) Stable Quasicrystal from Tetrahedron Colloids

The tetrahedral geometry is ubiquitous in natural and synthetic systems. Regular tetrahedra do not tile space, which makes understanding their self-assembly behavior a formidable challenge. Simulations of hard tetrahedra –that is particles with the shape of a regular tetrahedron interacting only by excluded volume interactions– discovered a dodecagonal quasicrystal stabilized by entropy alone [1]. But while this quasicrystal forms robustly and reproducibly in simulation, it competes with periodic approximants and cannot be the thermodynamic ground state in the limit of infinite pressure. In this limit, the densest packing will eventually prevail, which is a simple (in comparison) dimer crystal [2]. After a brief historic review of early research in the Glotzer group on this topic, we advance research on tetrahedron particles in two directions. First, we discuss experimental realizations of phases of tetrahedron from gold nanocrystals where vertex sharpness, surface ligands, and the self-assembly environment play key roles in the formation of the quasicrystal, its approximants, and the dimer crystal [3]. Second, we discuss the growth of tetrahedron nanocrystals by spontaneous symmetry breaking of the cubic crystal lattice to tetrahedron Wulff shape symmetry during the crystallization process. We utilize Monte Carlo and molecular dynamics particles simulations as well as kinetic Monte Carlo modeling. Efficient code optimization and effective graphical visualization are key. As time permits, I will discuss other complex ordering phenomena that were initiated during my time in the Glotzer group and continued thereafter.

[1] A. Haji-Akbari, M. Engel, A.S. Keys, X. Zheng, R.G. Petschek, P. Palffy-Muhoray, S.C. Glotzer, Nature 462 (2009) 773.
[2] E.R. Chen, M. Engel, S.C. Glotzer, D. Comput. Geom. 44 (2010), 253.
[3] Y. Wang, J. Chen, R. Li, A. Götz, D. Drobek, T. Przybilla, S. Hübner, P. Pelz, L. Yang, B. Apeleo Zubiri, E. Spiecker, M. Engel, X. Ye, J. Am. Chem. Soc. 145, 17902 (2023).