Haji-Akbari Amir, Chen Elizabeth R, Engel Michael, Glotzer Sharon C
Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012127. doi: 10.1103/PhysRevE.88.012127. Epub 2013 Jul 22.
Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic packings with small unit cells that were obtained via numerical and analytical optimization. The maximal packing fraction φ(max) changes continuously with the truncation parameter t. Eight distinct packings are identified based on discontinuities in the first and second derivatives of φ(max)(t). These packings differ in the number of particles in the fundamental domain (unit cell) and the type of contacts between the particles. In particular, we report two packings with four particles in the unit cell for which both φ(max)(t) and φ(max)'(t) are continuous and the discontinuity occurs in the second derivative only. In the self-assembly simulations that we perform for larger boxes with 2048 particles, only one out of eight packings is found to assemble. In addition, the degenerate quasicrystal reported previously for triangular bipyramids without truncation [Haji-Akbari et al., Phys. Rev. Lett. 107, 215702 (2011)] assembles for truncations as high as 0.45. The self-assembly propensities for the structures formed in the thermodynamic limit are explained using the isoperimetric quotient of the particles and the coordination number in the disordered fluid and in the assembled structure.
受多面体纳米颗粒和胶体颗粒合成方面的突破以及它们堆积的理论和计算研究的启发，我们研究了一族截顶三角双棱锥。我们报告了通过数值和解析优化获得的具有小晶胞的密集周期性堆积。最大堆积分数φ(max)随截断参数t连续变化。基于φ(max)(t)的一阶和二阶导数的不连续性，确定了八种不同的堆积。这些堆积在基本区域（晶胞）中的粒子数量以及粒子之间的接触类型上有所不同。特别是，我们报告了两种晶胞中有四个粒子的堆积，对于这两种堆积，φ(max)(t)和φ(max)'(t)都是连续的，只有二阶导数出现不连续性。在我们对含有2048个粒子的更大盒子进行的自组装模拟中，发现八种堆积中只有一种能够组装。此外，先前报道的无截断三角双棱锥的简并准晶体[Haji-Akbari等人，《物理评论快报》107, 215702 (2011)]在截断高达0.45时也能组装。利用粒子的等周商以及无序流体和组装结构中的配位数，解释了在热力学极限下形成的结构的自组装倾向。
