双分散球体随机停放的四面体胶体团簇
Tetrahedral colloidal clusters from random parking of bidisperse spheres
摘要：
使用实验和模拟，我们研究了胶体球不可逆地粘在或“停”在更小的球体上时形成的簇。我们使用带相反电荷的粒子或用互补DNA序列标记的粒子，并且我们改变大球体半径与小球体半径的比率$α$。一旦结合，大的球体不能重新排列，因此簇不会形成致密或对称的堆积。然而，这种随机聚集过程产生了一个显着狭窄的集群分布与近90%的四面体在$α=2.45$。在$α=2.41$的模拟中，四面体的高产率达到100%，这不仅仅是因为填充约束，还因为存在一个长时间的下限，我们称之为“最小停车”数。我们推导出这个下限从解决方案的经典数学问题的球形覆盖，我们表明，有一个临界尺寸比$α_c=(1+\sqrt{2})\approx 2.41$，接近观察到的最大产量点，其中下限等于上限设置包装约束。随机聚集过程中临界值的出现提供了一种强大的方法来组装均匀的簇，用于各种应用，包括超材料。
英文摘要：
Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to -- or "park" on -- smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio $α$ of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at $α=2.45$. The high yield of tetrahedra, which reaches 100% in simulations at $α=2.41$, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the "minimum parking" number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio $α_c=(1+\sqrt{2})\approx 2.41$, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.
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