Quasicrystal formation in binary soft matter mixtures

A Scacchi,W R C Somerville,D M A Buzza,A J Archer

doi:10.1103/physrevresearch.2.032043

A Scacchi, W R C Somerville + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.2.032043

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Abstract

Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with integral equation theory. Quasicrystal formation requires particle ordering with two characteristic lengthscales in certain particular ratios. How the lengthscales are related to the form of the pair interactions is reasonably well understood for one component systems, but less is known for mixtures. In our model mixture of big and small colloids confined to an interface, the two lengthscales stem from the range of the interactions between pairs of big particles and from the cross big-small interactions, respectively. The small-small lengthscale is not significant. Our strategy for finding quasicrystals involves tuning locations of maxima in the dispersion relation, or equivalently in the liquid state partial static structure factors.

Highlights

Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals
How the length scales are related to the form of the pair interactions is reasonably well understood for one-component systems, but less is known for mixtures
In our model mixture of big and small colloids confined to an interface, the two length scales stem from the range of the interactions between pairs of big particles and from the cross big-small interactions, respectively

Summary

Quasicrystal formation in binary soft matter mixtures

These are best seen by considering the particle pair interaction potentials and pair correlation functions in Fourier space, where one observes that there are two characteristic peaks at wave numbers k1 and k2, with the ratio k1/k2 taking certain special values which are geometric in origin [1,2,3,4,5,6,7,8,9,10,11]; e.g., for two-dimensional (2D) dodecagonal QCs, k1/k2 = 2 cos(π /12) ≈ 1.93 These features manifest in the dispersion relation ω(k), which characterizes the growth or decay of density modulations with wave number k in the liquid state. The three-step strategy we follow and advocate here, which works for the colloidal mixture model considered below and

Published by the American Physical Society

Increasing J

The growth or decay of small amplitude density perturbations