截断三角形双锥的堆积与自组装
Packing and Self-assembly of Truncated Triangular Bipyramids
摘要：
受多面纳米和胶体颗粒合成的突破以及它们的包装的理论和计算研究的启发，我们研究了一个截短的三角形双金字塔家族。我们报告密集的周期性填充与小单位细胞，通过数值和分析优化。最大堆积分数$ϕ_{\max}$随截断参数$t$连续变化。八个不同的包装被确定的基础上，在$ϕ_{\max}(t)$的一阶和二阶导数的不连续性。这些填充物在基本域（晶胞）中的颗粒数量和颗粒之间的接触类型方面不同。特别是，我们报告了两个包装与四个粒子在单位细胞的$ϕ_{\max}(t)$和$ϕ'_{\max}(t)$是连续的和不连续的发生在第二导数。在我们对含有2048个粒子的较大盒子进行的自组装模拟中，发现八个包装中只有一个可以组装。此外，先前报道的没有截短的三角双锥的简并准晶[{http：//prl.aps.org/abstract/PRL/v107/i21/e215702}{Haji-Akbari \emph{et al.}，\emph{Phys. Rev. Lett.} \textbf{107}：215702（2011）}]在高达0.45的截短下组装。的自组装倾向的结构中形成的热力学极限的解释使用的粒子的等周商和配位数在无序流体和组装结构。
英文摘要：
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 [{http://prl.aps.org/abstract/PRL/v107/i21/e215702}{Haji-Akbari \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{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.
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