Jamming and percolation for deposition ofk2-mers on square lattices: A Monte Carlo simulation study

Abstract

Jamming and percolation of square objects of size k × k (k 2-mers) isotropically deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The k 2-mers were irreversibly deposited into the lattice. Jamming coverage θ j,k was determined for a wide range of k (2 ≤ k ≤ 200). θ j,k exhibits a decreasing behavior with increasing k, being θ j,k→∞ = 0.4285(6) the limit value for large k 2-mer sizes. On the other hand, the obtained results shows that percolation threshold, θ c,k , has a strong dependence on k. It is a decreasing function in the range 2 ≤ k ≤ 18 with a minimum around k = 18 and, for k ≥ 18, it increases smoothly towards a saturation value. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size k considered.

Kinetics of random sequential adsorption of two-dimensional shapes on a one-dimensional line

“…The mean packing fraction at the limit of infinite packing can be estimated by finding the crossing of the CDF's for different packing sizes. This method is especially useful for studying RSA on lattices [30][31][32][33][34][35]. However, in our case, the precision given by 2 is enough due to quite large size of packings used in this study.…”

Random sequential adsorption on Euclidean, fractal, and random lattices

“…Following the scheme given in Eqs. (1)(2)(3)(4)(5), different systems were characterized in previous work from our group: (1) linear k-mers on 1D lattices [45]; (2) linear k-mers on 2D square lattices with and without the presence of impurities [48,49]; (3) linear k-mers on 2D triangular lattices [50]; (4) k × k square tiles (k 2 -mers) on 2D square lattices [27]; (5) linear k-mers on 3D simple cubic lattices [45]; (6) k 2 -mers on 3D simple cubic lattices [51] and (7) k × k × k cubic objects k 3 -mers on 3D simple cubic lattices [52]. In all cases, ν j was determined from Eqs.…”

“…More recently, the exponent ν j was measured for different systems in 1D, 2D and 3D Euclidean lattices [27,[49][50][51][52]. The obtained results reveal a simple dependence of ν j with the dimensionality of the lattice.…”

SuSMoST: Surface Science Modeling and Simulation Toolkit

“…There are lattice models of various degrees of abstraction: Langmuir adsorption model, hard disks, [6,7] dimers, [8][9][10][11] k-mers, [12,13] binary gasses, [14][15][16][17][18] molecules of various symmetry, [19][20][21][22][23] tricarboxylic [24][25][26][27] acids, porphyrins, [28] monoatomic adsobates, [29,30] and so forth. [31,32] In spite of numerous successful applications of lattice models, this kind of simulation is still not a daily tool for surface science researchers.…”

“…Probably this is the reason why contemporary computational studies of surface self-assembly do not refer to available codes, but apparently use inhouse state of art codes. [12,13,20,25]…”