Department of Physical Chemistry of Disperse Minerals, F.D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kiev, Ukraine, 03142 and Department of Physics, Taras Shevchenko Kiev National University, Kiev, Ukraine, 01033.
Laboratory of Mathematical Modeling, Astrakhan State University, Astrakhan, Russia, 414056.
Phys Rev E. 2017 May;95(5-1):052130. doi: 10.1103/PhysRevE.95.052130. Epub 2017 May 18.
The diffusion-driven self-assembly of rodlike particles was studied by means of Monte Carlo simulation. The rods were represented as linear k-mers (i.e., particles occupying k adjacent sites). In the initial state, they were deposited onto a two-dimensional square lattice of size L×L up to the jamming concentration using a random sequential adsorption algorithm. The size of the lattice, L, was varied from 128 to 2048, and periodic boundary conditions were applied along both x and y axes, while the length of the k-mers (determining the aspect ratio) was varied from 2 to 12. The k-mers oriented along the x and y directions (k_{x}-mers and k_{y}-mers, respectively) were deposited equiprobably. In the course of the simulation, the numbers of intraspecific and interspecific contacts between the same sort and between different sorts of k-mers, respectively, were calculated. Both the shift ratio of the actual number of shifts along the longitudinal or transverse axes of the k-mers and the electrical conductivity of the system were also examined. For the initial random configuration, quite different self-organization behavior was observed for short and long k-mers. For long k-mers (k≥6), three main stages of diffusion-driven spatial segregation (self-assembly) were identified: the initial stage, reflecting destruction of the jamming state; the intermediate stage, reflecting continuous cluster coarsening and labyrinth pattern formation; and the final stage, reflecting the formation of diagonal stripe domains. Additional examination of two artificially constructed initial configurations showed that this pattern of diagonal stripe domains is an attractor, i.e., any spatial distribution of k-mers tends to transform into diagonal stripes. Nevertheless, the time for relaxation to the steady state essentially increases as the lattice size growth.
采用蒙特卡罗模拟方法研究了棒状颗粒的扩散驱动自组装。棒状颗粒被表示为线性 k- 元（即占据 k 个相邻位置的颗粒）。在初始状态下，它们使用随机顺序吸附算法沉积在二维正方形晶格上，晶格大小为 L×L，直至达到堵塞浓度。晶格的大小 L 从 128 变化到 2048，并且在 x 和 y 轴上都施加了周期性边界条件，而 k- 元的长度（决定纵横比）从 2 变化到 12。沿 x 和 y 方向取向的 k- 元（分别为 k_{x}- 元和 k_{y}- 元）被等概率沉积。在模拟过程中，分别计算了同种 k- 元之间以及不同种 k- 元之间的同种和异种接触的数量。还检查了 k- 元沿其纵向或横向轴的实际位移数的移位比以及系统的电导率。对于初始随机构型，短和长 k- 元表现出非常不同的自组织行为。对于长 k- 元（k≥6），识别出扩散驱动空间分离（自组装）的三个主要阶段：初始阶段，反映堵塞状态的破坏；中间阶段，反映连续的簇粗化和迷宫图案形成；以及最终阶段，反映对角条纹域的形成。对两个人工构造的初始构型的进一步检查表明，这种对角条纹域的模式是一个吸引子，即 k- 元的任何空间分布都倾向于转化为对角条纹。然而，松弛到稳态的时间本质上随着晶格尺寸的增长而增加。
