Dimer percolation and jamming on simple cubic lattice

Abstract

We consider site percolation of dimers ("neadles") on simple cubic lattice. The percolation threshold is estimated as p perc c ≈ 0.2555 ± 0.0001. The jamming threshold is estimated as p jamm c = 0.799 ± 0.002. PACS. 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions -05.10.-a Computational methods in statistical physics and nonlinear dynamics -81.20.Fw Sol-gel processing, precipitation

Random sequential adsorption of straight rigid rods on a simple cubic lattice

“…In addition, A 2 = 2.63(5) and A 3 = −5.2(2). • In the case of dimers (k = 2), the value of θ j = 0.918388 (16) obtained in the present paper corrects the value θ j = 0.799(2) calculated by Tarasevich and Cherkasova [29]. This important finding was corroborated by using an independent algorithm developed to measure the coverage as a function of time θ (t).…”

“…2 corrects the previously reported value of θ j = 0.799(2) [29]. Due to the methodology used in this contribution, our estimate of θ j is expected to be more accurate than that reported previously.…”

“…In the line of present work, Tarasevich and Cherkasova examined the percolation and jamming properties of dimers (straight rigid rods with k = 2) on 3D simple cubic lattices and found that θ p = 0.2555(1), θ j = 0.799(2) and θ p /θ j ≈ 0.32 [29]. This value of θ p /θ j differs from the corresponding value obtained for square lattices and small values of k (2 ≤ k ≤ 10), θ p /θ j ≈ 0.62 [16].…”

“…It is quite obvious that the model considered here is highly idealized and is not meant to reproduce a particular experimentally studied system. However the objectives of this work are (1) to introduce a new procedure to calculate jamming properties, which can be widely applied in RSA problems; (2) to evaluate the accuracy and applicability of the new technique; (3) to determine, for the first time, the dependence of the jamming coverage on the size of the deposited k-mers for 3D cubic lattices; (4) to improve previous calculations of θ j for dimers (k = 2) [29]; and (5) to stimulate the development of more sophisticated models which can be able to reproduce concrete experimental systems. With respect to the last point, the 3D adsorption of k-mers layer by layer could be an interesting topic for further research.…”

“…the authors found that the method of filling used in Ref [29]. produces a slightly anisotropic configurations.…”