Percolation of aligned rigid rods on two-dimensional triangular lattices

LONGONE P.; CENTRES, PAULO; RAMIREZ-PASTOR, ANTONIO JOSE

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2019

1539-3755

The percolation behavior of aligned rigid rods of length k (k-mers) on two-dimensional triangularlattices has been studied by numerical simulations and finite-size scaling analysis. The k-mers,containing k identical units (each one occupying a lattice site), were irreversibly deposited alongone of the directions of the lattice. The connectivity analysis was carried out by following theprobability RL,k(p) that a lattice composed of L × L sites percolates at a concentration p of sitesoccupied by particles of size k. The results, obtained for k ranging from 2 to 80, showed thatthe percolation threshold pc(k) exhibits a increasing function when it is plotted as a function ofthe k-mer size. The dependence of pc(k) was determined, being pc(k) = A + B/(C + pk), whereA = pc(k ! 1) = 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 to that observed forsquare lattices, where the percolation threshold decreases with k. In addition, the effect of theanisotropy on the properties of the percolating phase was investigated. The results revealed that,while for finite systems the anisotropy of the deposited layer favors the percolation along the paralleldirection to the alignment axis, in the thermodynamic limit, the value of the percolation thresholdis the same in both parallel and transversal directions. Finally, an exhaustive study of criticalexponents and universality was carried out, showing that the phase transition occurring in thesystem belongs to the standard random percolation universality class regardless of the value of kconsidered.