Abstract

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]. Here, we advance research on tetrahedron particles in two directions. First, we demonstrate that the quasicrystal is thermodynamically stable at intermediate density [3]. Using a pattern recognition algorithm applied to particle trajectories during quasicrystal growth, we analyse phason strain to follow the evolution of quasiperiodic order. Our results demonstrate that soft-matter quasicrystals dominated by entropy can be thermodynamically stable and grown with high structural quality––just like their more common alloy quasicrystal counterparts. Second, we discuss experimental realizations of phases of tetrahedron colloids where vertex sharpness, surface ligands, and the self-assembly environment play key roles in the formation of the quasicrystal and the dimer crystal [4]. We fully resolve the complex three-dimensional structure of the quasicrystal by a combination of electron microscopy, tomography, and synchrotron X-ray scattering. Our findings demonstrate the predictive power of computer simulations as well as the importance of accurate control over nanocrystal attributes and the assembly method to realize increasingly complex nanopolyhedron supracrystals. [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] K. Je, S. Lee, E.G. Teich, M. Engel, S.C. Glotzer, Proc. Natl. Acad. Sci. 118 (2021) e2011799118. [4] 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, JACS , in press (2023).