By using long-range interacting polygons, we experimentally probe the coupling between particle shape and long-range interaction. For two typical space-filling polygons, square and triangle, we find two types of coupling modes that predominantly control the structure formation. Specifically, the rotational ordering of squares brings a lattice deformation that produces a hexagonal-to-rhombic transition in the high-density regime, whereas the alignment of triangles introduces a large geometric frustration that causes an order-to-disorder transition. Moreover, the two coupling modes lead to small and large "internal roughness" of the two systems, and thus predominantly control their structure relaxations. Our study thus provides a physical picture to the coupling between long-range interaction effect and short-range shape effect in the high-density regime unexplored before.

中文翻译：

---

高密度体系中粒子形状与长程相互作用的耦合

通过使用远程交互多边形，我们通过实验探索了粒子形状和远程交互之间的耦合。对于两个典型的空间填充多边形，正方形和三角形，我们发现了两种主要控制结构形成的耦合模式。具体来说，正方形的旋转排序带来了晶格变形，在高密度区域产生六边形到菱形的转变，而三角形的排列引入了大的几何挫折，导致有序到无序的转变。此外，两种耦合模式导致两个系统的“内部粗糙度”大小不同，从而主要控制它们的结构松弛。