CONICET | Buscador de Institutos y Recursos Humanos

Numerical simulations and finite-size scaling analysis have beencarried out to study the problem of inverse percolation by removing straightrigid rods from square lattices contaminated with non-conducting impurities.The presence of impurities provides a more realistic approach to the depositedmonolayer, which usually presents inhomogeneities due to the irregulararrangement of surface and bulk atoms, the presence of various chemicalspecies, etc. The process starts with an initial configuration, where all latticesites are occupied by an impurity (with a concentration ) or a conductingparticle (with a concentration 1 − ). Then, the system is diluted by randomlyremoving linear k-mers (linear clusters of k consecutive conducting particles)from the lattice. The impurities remain fixed in its position and cannot beremoved. The central idea of this paper is based on finding the maximumconcentration of conducting sites (minimum concentration of empty sites) forwhich the connectivity disappears. This particular value of the concentration iscalled inverse percolation threshold, and determines a well-defined geometricalphase transition in the system. On the other hand, the inverse jamming coverageis the coverage of the limit state, in which no more objects can be removedfrom the lattice due to the absence of linear clusters of nearest-neighbour sitesof appropriate size. The dependence of percolation and jamming thresholds onthe concentration of defects was investigated for dierent values of k, rangingfrom 1 to 120. The obtained results show that the behaviour of the systemis significantly aected by the presence of impurities. In addition, the nature of the jamming and percolation transitions was studied. In the first case, thecorresponding spatial correlation length critical exponent j was measured,being j 1. This value coincides with previous calculations of this exponent forthe standard random sequential adsorption of linear k-mers on square lattices.Critical exponents were also calculated for the percolation phase transition,showing that the universality class corresponding to ordinary percolation ispreserved regardless the values of k and considered.