Jamming and percolation of linear k -mers on honeycomb lattices

Abstract

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.

Percolation of defective dimers irreversibly deposited on honeycomb and triangular lattices

“…In fact, the curve θ T = θ j determines the space of all the allowed values of θ 1 and θ 2 (regions 2, 3, and 4). θ j = 0.90681(5) [43], 0.9142 (12) [31], and 0.864 (7) [32], for square, triangular, and honeycomb lattices, respectively.…”

“…Consequently, the total site coverage θ T ranges from 0 to θ j . In the case of triangular (honeycomb) lattices, the value of the jamming coverage for the conventional dimer filling problem is θ j = 0.9142 (12) [31] [θ j = 0.864 (7) [32]]. In this study, we initially fix the value of θ AB .…”