Fayen Etienne, Impéror-Clerc Marianne, Filion Laura, Foffi Giuseppe, Smallenburg Frank
Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands.
Soft Matter. 2023 Apr 5;19(14):2654-2663. doi: 10.1039/d3sm00179b.
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.
硬球是软物质物理学中最基本的模型体系之一，在阐明经典凝聚态物质的几乎每个方面都发挥了重要作用。在此，我们在硬球形成的相的列表中又增添了一个重要的相：准晶体。具体而言，我们通过模拟表明，一个极其简单的、纯粹基于熵的模型体系，由放置在平面上的两种尺寸的硬球组成，能够自发地自组装成两种不同的随机平铺准晶相。第一种准晶体是十二边形的正方形 - 三角形平铺，在多种胶体体系中普遍观察到。据我们所知，第二种准晶体在实验或模拟中均未被观察到。它呈现八边形对称性，由三种类型的瓷砖组成：三角形、小正方形和大正方形，通过调整体系中较小球体的数量，其相对浓度可以连续变化。自组装准晶体的观察到的瓷砖组成与我们通过考虑准晶体的四维（提升）表示所获得的理论预测非常吻合。在相当大的参数空间范围内，两种准晶相都能可靠且迅速地形成。我们的结果表明，熵与一组几何上兼容、紧密堆积的瓷砖相结合，足以成为胶体准晶体自组装的要素。
