Speaker
Etienne Fayen (Université Paris-Sud, LPS)
Title
Quasicrystals in binary (non-)additive hard disk mixtures
Abstract
Over the last few decades, soft quasicrystals, whose relevant building blocks are much larger than atoms, have been observed in an impressive variety of systems, such as nanoparticles, colloids, micelles, and block copolymers. These experimental findings suggest that very general principles stabilise quasicrystals in soft matter, although understanding these principles is still a topic of active research.
Here we explore the self-assembly of binary mixtures of non-additive hard disks, a simple 2D model for binary mixtures self-assembling at an interface, where soft quasicrystals are commonly observed. Since interactions are hard, entropy is the only ordering force.
The infinite pressure phase behaviour of this model, which reduces to the geometrical problem of disk packing and entropy arguments, already predicts the stability of dodecagonal quasicrystals, based on random tilings [1]. We show that the quasicrystal stability regions are broadened when the quasi-two dimensional nature of spherical particles at an interface is taken into account through non-additivity [2].
In addition, we explore the direct self-assembly of quasicrystals in this system at finite pressure. Both the expected 12-fold symmetric quasicrystal and a new octagonal quasicrystal were found to spontaneously self-assemble [3]. Finally, we investigate the stability of the dodecagonal quasicrystal using numerical free-energy calculations.
Our results show that in a system as simple as binary non-additive hard disks, quasicrystals of symmetry 12 and 8 can consistently self-assemble, demonstrating that geometrical packing constraints and entropy are sufficient ingredients for the emergence of quasicrystalline order. Given its simplicity and the possibility of experimental realisations in colloid mixtures, the binary hard-disks system provide an ideal base model for studies on quasicrystal stability.
[1] C. N. Likos and C. L. Henley, Philos. Mag. B, 68, 85-113 (1993)
[2] E. Fayen, A. Jagannathan, G. Foffi and F. Smallenburg, J. Chem. Phys. 152, 204901 (2020)
[3] E. Fayen, M. Impéror-Clerc, L. Filion, G. Foffi and F. Smallenburg, arXiv:2202.12726