Designing quasicrystalline ground states of colloids: An inverse statistical-mechanics approach

准晶是一种具有旋转对称性但缺乏周期性的材料。准晶自1982年被发现以来，不仅因其表面摩擦小、硬度高等复杂的材料性质而引起了科学界的极大关注，而且还导致了物理、化学和数学科学家之间许多卓有成效的交叉学科的相互作用。到目前为止，几乎所有观察到的准晶都存在于金属合金中。同时，由胶体或聚合物胶束组成的软准晶是最近研究的焦点。研究胶体准晶的一大优点是可以直接观察到单个粒子的位置，例如使用视频显微镜。重要的是，胶体准晶稳定性的理论解释或自组装过程的预测到目前为止仍然是一个具有挑战性的任务。究竟需要什么分子内力才能获得本征的(不是外界诱导的)准晶，这仍然是一个悬而未决的问题。手头的项目声称通过研究准晶的基态稳定性来弥合这一差距。特别是，计划应用逆统计力学技术来构建相互作用势，使势能最小化，从而自发地在零温度下导致准晶有序。这些结果不仅将启发准晶的稳定性，也将有助于从根本上理解准晶体系中结构与分子内相互作用之间的关系。除此之外，该项目将通过调整实验相互作用势来实现胶体实验中的准晶自组装，以适应我们的发现。此外，在本项目的后期阶段，准晶中的空间有序度将利用多粒子系统中的局域密度涨落的概念来量化。因此，可以对准晶系统的空间有序性和内部性质之间的关系做出陈述，例如旋转对称性或无公度长度尺度。

Quasicrystals are materials possessing rotational symmetry but lacking periodicity. Since their discovery in 1982, quasicrystals have not only drawn big attention in the scientific community due to their sophisticated material properties such as low surface friction and high rigidity, they have also led to many fruitful interdisciplinary interactions between scientist from physics, chemistry and mathematics. Almost all observed quasicrystals are found in metallic alloys so far. Meanwhile, soft quasicrystals built with colloids or polymer micelles constituents are in the focus of recent studies. A big advantage of studying colloidal quasicrystals is that individual particle positions are directly observable, e.g., by using video-microscopy. Importantly, a theoretical explanation of the stability or a prediction of the self-assembly process of colloidal quasicrystals remains a challenging task to date. It is still an open question which intramolecular forces are needed to obtain an intrinsic (not induced from outside) quasicrystal. The project at hand claims to close this gap by investigating the ground-state stability of quasicrystals. Particularly, it is planned to apply the inverse statistical-mechanical techniques to construct interaction potentials that minimise the potential energy, and hence, that spontaneously lead to quasicrystalline ordering at zero temperature. The results will not only enlighten the stability of quasicrystals, they will also essentially contribute to the fundamental understanding of the relation between the structure and the intramolecular interactions in a quasicrystalline system. Beyond that, this project will open the way of enabling quasicrystalline self-assembly in colloid experiments by tailoring the experimental interaction potentials toward our findings. Moreover, in a late stage of this project, the degree of spatial order in quasicrystals shall be quantified by using the concepts of the local density fluctuations in many-particle systems. As a consequence, statements can be made about the relation between the spatial order and the internal properties, such as rotational symmetries or incommensurate length scales of a quasicrystalline system.