Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane

Etienne Fayen, Marianne Impéror-Clerc, Laura Filion, Giuseppe Foffi, Frank Smallenburg*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Hard spheres are one of the most fundamental model systems in soft matter physics, and have been instrumental in shedding light on nearly every aspect of classical condensed matter. Here, we add one more important phase to the list that hard spheres form: quasicrystals. Specifically, we use simulations to show that an extremely simple, purely entropic model system, consisting of two sizes of hard spheres resting on a flat plane, can spontaneously self-assemble into two distinct random-tiling quasicrystal phases. The first quasicrystal is a dodecagonal square-triangle tiling, commonly observed in a large variety of colloidal systems. The second quasicrystal has, to our knowledge, never been observed in either experiments or simulations. It exhibits octagonal symmetry, and consists of three types of tiles: triangles, small squares, and large squares, whose relative concentration can be continuously varied by tuning the number of smaller spheres present in the system. The observed tile composition of the self-assembled quasicrystals agrees very well with the theoretical prediction we obtain by considering the four-dimensional (lifted) representation of the quasicrystal. Both quasicrystal phases form reliably and rapidly over a significant part of parameter space. Our results demonstrate that entropy combined with a set of geometrically compatible, densely packed tiles can be sufficient ingredients for the self-assembly of colloidal quasicrystals.

Original languageEnglish
Pages (from-to)2654-2663
Number of pages10
JournalSoft Matter
Volume19
Issue number14
DOIs
Publication statusPublished - 14 Apr 2023

Bibliographical note

Funding Information:
We thank Thomas Fernique, Jean-François Sadoc, Pavel Kalouguine, Alptuğ Ulugöl, and Anuradha Jagannathan for many useful discussions. EF, GF, and FS acknowledge funding from the Agence Nationale de la Recherche (ANR), grant ANR-18-CE09-0025. LF acknowledges funding from the Netherlands Organisation for Scientific Research (NWO) for a Vidi grant (Grant No. VI.VIDI.192.102). The authors acknowledge the use of the Ceres high-performance computer cluster at the Laboratoire de Physique des Solides to carry out the research reported in this article.

Publisher Copyright:
© 2023 The Royal Society of Chemistry

Funding

We thank Thomas Fernique, Jean-François Sadoc, Pavel Kalouguine, Alptuğ Ulugöl, and Anuradha Jagannathan for many useful discussions. EF, GF, and FS acknowledge funding from the Agence Nationale de la Recherche (ANR), grant ANR-18-CE09-0025. LF acknowledges funding from the Netherlands Organisation for Scientific Research (NWO) for a Vidi grant (Grant No. VI.VIDI.192.102). The authors acknowledge the use of the Ceres high-performance computer cluster at the Laboratoire de Physique des Solides to carry out the research reported in this article.

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