Tarasevich Yuri Yu, Burmistrov Andrei S, Shinyaeva Taisiya S, Laptev Valeri V, Vygornitskii Nikolai V, Lebovka Nikolai I
Astrakhan State University, 20a Tatishchev Street, Astrakhan 414056, Russia.
Astrakhan State University, 20a Tatishchev Street, Astrakhan 414056, Russia and Astrakhan State Technical University, 16 Tatishchev Street, Astrakhan 414025, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062142. doi: 10.1103/PhysRevE.92.062142. Epub 2015 Dec 28.
Using the Monte Carlo simulation, we study the percolation and jamming of oriented linear k-mers on a square lattice that contains defects. The point defects with a concentration d are placed randomly and uniformly on the substrate before deposition of the k-mers. The general case of unequal probabilities for orientation of depositing of k-mers along different directions of the lattice is analyzed. Two different relaxation models of deposition that preserve the predetermined order parameter s are used. In the relaxation random sequential adsorption (RRSA) model, the deposition of k-mers is distributed over different sites on the substrate. In the single-cluster relaxation (RSC) model, the single cluster grows by the random accumulation of k-mers on the boundary of the cluster (Eden-like model). For both models, a suppression of growth of the infinite (percolation) cluster at some critical concentration of defects d(c) is observed. In the zero-defect lattices, the jamming concentration p(j) (RRSA model) and the density of single clusters p(s) (RSC model) decrease with increasing length k-mers and with a decrease in the order parameter. For the RRSA model, the value of d(c) decreases for short k-mers (k<16) as the value of s increases. For k=16 and 32, the value of d(c) is almost independent of s. Moreover, for short k-mers, the percolation threshold is almost insensitive to the defect concentration for all values of s. For the RSC model, the growth of clusters with ellipselike shapes is observed for nonzero values of s. The density of the clusters p(s) at the critical concentration of defects d(c) depends in a complex manner on the values of s and k. An interesting finding for disordered systems (s=0) is that the value of p(s) tends towards zero in the limits of the very long k-mers, k→∞, and very small critical concentrations d(c)→0. In this case, the introduction of defects results in a suppression of k-mer stacking and in the formation of empty or loose clusters with very low density. On the other hand, denser clusters are formed for ordered systems with p(s)≈0.065 at s=0.5 and p(s)≈0.38 at s=1.0.
我们使用蒙特卡罗模拟方法，研究了含有缺陷的方形晶格上定向线性k聚体的渗流和堵塞现象。在沉积k聚体之前，将浓度为d的点缺陷随机且均匀地放置在基底上。分析了k聚体沿晶格不同方向沉积时取向概率不相等的一般情况。使用了两种不同的沉积弛豫模型，它们能保持预定的序参量s。在弛豫随机顺序吸附（RRSA）模型中，k聚体的沉积分布在基底的不同位置上。在单簇弛豫（RSC）模型中，单簇通过k聚体在簇边界上的随机积累而生长（类伊登模型）。对于这两种模型，在某个临界缺陷浓度d(c)处都观察到无限（渗流）簇的生长受到抑制。在零缺陷晶格中，堵塞浓度p(j)（RRSA模型）和单簇密度p(s)（RSC模型）随着k聚体长度的增加以及序参量的减小而降低。对于RRSA模型，当s值增加时，短k聚体（k<16）的d(c)值减小。对于k = 16和32，d(c)值几乎与s无关。此外，对于短k聚体，对于所有s值，渗流阈值几乎对缺陷浓度不敏感。对于RSC模型，当s不为零时，观察到椭圆形簇的生长。在临界缺陷浓度d(c)处的簇密度p(s)以复杂的方式依赖于s和k的值。对于无序系统（s = 0），一个有趣的发现是，在非常长的k聚体（k→∞）和非常小的临界浓度d(c)→0的极限情况下，p(s)值趋于零。在这种情况下，缺陷的引入导致k聚体堆积受到抑制，并形成密度非常低的空簇或松散簇。另一方面，对于有序系统，当s = 0.5时，形成密度更大的簇，p(s)≈0.065；当s = 1.0时，p(s)≈0.38。
