A hard-sphere quasicrystal stabilized by configurational entropy

TL;DR

This paper demonstrates that configurational entropy stabilizes a dodecagonal quasicrystal in a binary hard-sphere mixture on a plane, with all tilings equally likely, suggesting a route for quasicrystal self-assembly in colloidal systems.

Contribution

It provides the first quantitative evidence that configurational entropy stabilizes a quasicrystal in a simple hard-sphere model, confirming the equal likelihood of tiling realizations.

Findings

Configurational entropy stabilizes the quasicrystal.

All tilings are nearly equally probable with minimal free-energy differences.

The model is suitable for experimental realization of quasicrystal self-assembly.

Abstract

Due to their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001$k_BT$ per particle -- an observation that could be the related to the observation of only random tilings in soft matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is a excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.