Lončarević I, Budinski-Petković Lj, Šćepanović J R, Jakšić Z M, Vrhovac S B
Faculty of Engineering, Trg D. Obradovića 6, Novi Sad 21000, Serbia.
Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, Zemun 11080, Belgrade, Serbia.
Phys Rev E. 2020 Jan;101(1-1):012119. doi: 10.1103/PhysRevE.101.012119.
The properties of the random sequential adsorption of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are "lattice animals," made of a certain number of nearest-neighbor sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). We analyzed all lattice animals of size n=1, 2, 3, 4, and 5. A significant number of objects of size n⩾6 were also used to confirm our findings. Approach of the coverage θ(t) to the jamming limit θ_{J} is found to be exponential, θ_{J}-θ(t)∼exp(-t/σ), for all lattice animals. It was shown that the relaxation time σ increases with the number of different orientations m that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them cannot be translated into the other. Our simulations performed for large collections of 3D objects confirmed that σ≅m∈{1,3,4,6,8,12,24}. The presented results suggest that there is no correlation between the number of possible orientations m of the object and the corresponding values of the jamming density θ_{J}. It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.
通过蒙特卡罗模拟对各种形状的物体在简单三维立方晶格上的随机顺序吸附特性进行了数值研究。沉积物体是“晶格动物”，由晶格上一定数量的最近邻位点组成。这项工作的目的是研究形状的几何特性对堵塞密度θ_J和覆盖分数θ(t)的时间演化的影响。我们分析了尺寸为n = 1、2、3、4和5的所有晶格动物。还使用了大量尺寸n⩾6的物体来证实我们的发现。对于所有晶格动物，发现覆盖θ(t)接近堵塞极限θ_J的方式是指数形式的，即θ_J - θ(t)∼exp(-t/σ)。结果表明，弛豫时间σ随着晶格动物放置在立方晶格上时可以采取的不同取向数m的增加而增加。如果晶格动物在晶格上两个随机选择的位置沉积的取向之一不能转换为另一个，则它们是不同的。我们对大量三维物体进行的模拟证实，σ≅m∈{1,3,4,6,8,12,24}。给出的结果表明，物体可能的取向数m与堵塞密度θ_J的相应值之间没有相关性。研究发现，对于足够大的物体，形状的变化对堵塞密度的影响比物体尺寸的增加大得多。
