Percolation of aligned rigid rods on two-dimensional triangular lattices

P. M. CENTRES; A. J. RAMIREZ-PASTOR; P. LONGONE

Physical Review E

American Physical Society

Año: 2019 vol. 100 p. 1 - 11

2470-0045

The percolation behavior of aligned rigid rods of length k (k-mers) on two-dimensional triangular latticeshas been studied by numerical simulations and finite-size scaling analysis. The k-mers, containing k identicalunits (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice.The connectivity analysis was carried out by following the probability RL,k (p) that a lattice composed of L × Lsites percolates at a concentration p of sites occupied by particles of size k. The results, obtained for k rangingfrom 2 to 80, showed that the percolation threshold pc (k) exhibits a increasing function when it is plotted as afunction of the k-mer size. The dependence of pc (k) was determined, being pc (k) = A + B/(C + √k), whereA = pc (k → ∞) = 0.582(9) is the value of the percolation threshold by infinitely long k-mers, B =−0.47(0.21), and C = 5.79(2.18). This behavior is completely different from that observed for square lattices,where the percolation threshold decreases with k. In addition, the effect of the anisotropy on the properties ofthe percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of thedeposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamiclimit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally,an exhaustive study of critical exponents and universality was carried out, showing that the phase transitionoccurring in the system belongs to the standard random percolation universality class regardless of the value ofk considered