Stability of Quasicrystals Composed of Soft Isotropic Particles

TL;DR

This paper explains the stability of soft-matter quasicrystals by analyzing a coarse-grained free energy, highlighting the roles of two length scales and entropy-driven interactions, aiding future experimental control.

Contribution

It provides a theoretical and numerical framework for understanding the stability of soft quasicrystals based on pair potential features and entropy effects.

Findings

Stability linked to two natural length scales in pair potential

Effective three-body interactions from entropy contribute to stability

Phase diagram regions for stable soft quasicrystals identified

Abstract

Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate to this day, we argue that the stability of certain soft-matter quasicrystals can be directly explained by examining a coarse-grained free energy for a system of soft isotropic particles. We show, both theoretically and numerically, that the stability can be attributed to the existence of two natural length scales in the pair potential, combined with effective three-body interactions arising from entropy. Our newly gained understanding of the stability of soft quasicrystals allows us to point at their region of stability in the phase diagram, and thereby may help control the self-assembly of quasicrystals and a variety of other desired structures in future experimental realizations.