Phillips Carolyn L, Jankowski Eric, Marval Michelle, Glotzer Sharon C
Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041124. doi: 10.1103/PhysRevE.86.041124. Epub 2012 Oct 15.
We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters (N-clusters) with well-defined structures. We use Brownian dynamics to model the assembly of N-clusters varying in size from two to twelve outer spheres and free energy calculations to predict the expected cluster sizes and shapes as a function of temperature and inner particle diameter. We show that the arrangements of outer spheres at finite temperatures are related to spherical codes, an ideal mathematical sequence of points corresponding to the densest possible sphere packings. We demonstrate that temperature and the ratio of the diameters of the inner and outer spheres dictate cluster morphology. We present a surprising result for the equilibrium structure of a 5-cluster, for which the square pyramid arrangement is preferred over a more symmetric structure. We show this result using Brownian dynamics, a Monte Carlo simulation, and a free energy approximation. Our results suggest a promising way to assemble anisotropic building blocks from constituent colloidal spheres.
我们考虑球体在中心球体表面上由热力学驱动的自组装过程。这种组装过程形成具有明确结构的自限性或终端各向异性簇（N簇）。我们使用布朗动力学对由两个到十二个外层球体组成的不同大小的N簇的组装进行建模，并通过自由能计算来预测预期的簇大小和形状随温度和内部粒子直径的变化情况。我们表明，有限温度下外层球体的排列与球形码有关，球形码是对应于最密集球体堆积的理想数学点序列。我们证明，温度以及内球和外球的直径比决定了簇的形态。我们给出了一个关于5簇平衡结构的惊人结果，对于该结构，方锥排列比更对称的结构更受青睐。我们通过布朗动力学、蒙特卡罗模拟和自由能近似来展示这一结果。我们的结果为从组成胶体球体组装各向异性构建块提供了一种有前景的方法。
