Jamming and percolation of k ²-mers on simple cubic lattices

Abstract

Jamming and percolation of three-dimensional (3D) k × k × k cubic objects (k 3-mers) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The k 3-mers were irreversibly deposited into the lattice. Jamming coverage θ j,k was determined for a wide range of k (2 ≤ k ≤ 40). θ j,k exhibits a decreasing behavior with increasing k, being θ j,k=∞ = 0.4204(9) the limit value for large k 3-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent νj was measured, being νj ≈ 3/2. On the other hand, the obtained results for the percolation threshold θ p,k showed that θ p,k is an increasing function of k in the range 2 ≤ k ≤ 16. For k ≥ 17, all jammed configurations are non-percolating states, and consequently, the percolation phase transition disappears. The interplay between the percolation and the jamming effects is responsible for the existence of a maximum value of k (in this case, k = 16) from which the percolation phase transition no longer occurs. 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

“…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.…”

Jamming and percolation of linear k -mers on honeycomb lattices

“…3. As periodic boundary conditions are used, the value of the intersection point of the jamming probability curves is W L,k (θ j,k ) ≈ 0.5 [49,52,53]. However, and independently of the considered boundary conditions (open or periodic), the methodology shown in Fig.…”

“…The decreasing behavior of the jamming coverage with the size k towards an asymptotic limit value has been already observed in numerous systems. The cases of linear k-mers on 2D square [8], 2D triangular [20], and 3D cubic lattices [49], k × k tiles on 2D square [55] and 3D cubic lattices [53], and k × k × k cubic objects on 3D cubic lattices [56], are examples of this. However, to the best of our knowledge, the case corresponding to honeycomb lattices has not been reported up to now.…”