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Self-assembled configurations are versatile for applications in which liquid-mediated phenomena are employed to ensure that static or mild physical interactions between assembling blocks take advantage of local energy minima. For granular materials, however, a particle’s momentum in air leads to random collisions and the formation of disordered phases, eventually producing jammed configurations when densely packed. Therefore, unlike fluidic self-assembly, the self-assembly of dry particles typically lacks programmability based on density and ordering symmetry and has thus been limited in applications. Here, we present the self-assembly of particles with momentum, yielding regular arrays with programmable density and symmetry. The key is to embed anti-repellent structures, i.e., traps, that can capture kinetic particles individually and then robustly hold them against collisions with other momentum granules during a dynamic assembly procedure. By using anti-repellent traps, physical interactions between neighbouring particles can be inhibited, resolving many phenomena related to the uncertainty of space-sharing events in granular packing. With our self-assembly strategy, highly dense yet unjammed configurations are demonstrated, which conserve the inherent randomness in the location information of each granule in the trap and are useful for robust multilevel authentication systems as unique applications.

自组装构型在依托液体介导现象的应用中具有广泛适用性，这类应用通过利用组装单元间的静态或温和物理相互作用，借助局部能量极小值实现组装过程。但对于颗粒材料而言，空气中颗粒的动量会引发随机碰撞并形成无序相，在密堆积状态下最终会生成堵塞构型。因此，与流体自组装不同，干颗粒的自组装通常不具备基于密度与有序对称性的可编程性，其应用场景因此受到限制。本研究展示了具有动量的颗粒的自组装过程，成功制备出具备可编程密度与对称性的规则阵列。其核心在于引入抗斥结构（即捕集阱），可在动态组装过程中单独捕获运动颗粒，并牢固固定颗粒以抵御其他运动颗粒的碰撞。通过使用抗斥捕集阱，相邻颗粒间的物理相互作用得以被抑制，解决了颗粒堆积中与空间共享事件不确定性相关的诸多问题。依托本研究提出的自组装策略，我们实现了高密却未堵塞的构型，该构型保留了每个捕集阱中颗粒位置信息的固有随机性，可作为独特应用场景用于可靠的多级认证系统。