Iglesias Panuska G A, Centres P M, Ramirez-Pastor A J
Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de los Andes 950, D5700HHW, San Luis, Argentina.
Phys Rev E. 2020 Sep;102(3-1):032123. doi: 10.1103/PhysRevE.102.032123.
Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of elongated objects deposited on two-dimensional honeycomb lattices. The depositing particle is modeled as a linear array of length k (so-called k-mer), maximizing the distance between first and last monomers in the chain. The separation between k-mer units is equal to the lattice constant. Hence, k sites are occupied by a k-mer when adsorbed onto the surface. The adsorption process starts with an initial configuration, where all lattice sites are empty. Then, the sites are occupied following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. Jamming coverage θ_{j,k} and percolation threshold θ_{c,k} were determined for a wide range of values of k (2≤k≤128). The obtained results shows that (i) θ_{j,k} is a decreasing function with increasing k, being θ_{j,k→∞}=0.6007(6) the limit value for infinitely long k-mers; and (ii) θ_{c,k} has a strong dependence on k. It decreases in the range 2≤k<48, goes through a minimum around k=48, and increases smoothly from k=48 up to the largest studied value of k=128. Finally, the precise determination of the critical exponents ν, β, and γ indicates that the model belongs to the same universality class as 2D standard percolation regardless of the value of k considered.
已进行数值模拟和有限尺寸标度分析，以研究沉积在二维蜂窝晶格上的细长物体的堵塞和渗流行为。沉积粒子被建模为长度为k的线性阵列（所谓的k聚体），使链中第一个和最后一个单体之间的距离最大化。k聚体单元之间的间距等于晶格常数。因此，当k聚体吸附到表面时，k个位点被其占据。吸附过程从初始构型开始，此时所有晶格位点都是空的。然后，按照随机顺序吸附机制占据位点。当达到堵塞状态且由于没有合适大小和形状的空位簇而无法再沉积物体时，该过程结束。针对广泛的k值范围（2≤k≤128）确定了堵塞覆盖率θ_{j,k}和渗流阈值θ_{c,k}。所得结果表明：(i) θ_{j,k}是k的递减函数，对于无限长的k聚体，极限值为θ_{j,k→∞}=0.6007(6)；(ii) θ_{c,k}对k有强烈依赖性。它在2≤k<48范围内减小，在k = 48左右达到最小值，然后从k = 48平滑增加到所研究的最大k值128。最后，对临界指数ν、β和γ的精确测定表明，无论考虑的k值如何，该模型都属于与二维标准渗流相同的普适类。
