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The effect of defects on the behavior of electrical conductivity in amonolayer produced by the random sequential adsorption of linear $k$-mers(particles occupying $k$ adjacent sites) onto a square lattice is studied bymeans of a Monte Carlo simulation. The $k$-mers are deposited on the substrateuntil a jamming state is reached, i.e. a state where no one additional particlecan be placed because the presented voids are too small or of inappropriateshapes. The presence of defects in the lattice (impurities) and of defects inthe $k$-mers with concentrations of $d_l$ and $d_k$, respectively, is assumed.The defects in the lattice are distributed randomly before deposition and theselattice sites are forbidden for the deposition of $k$-mers. The defects on the$k$-mers are distributed randomly. The sites filled with $k$-mers have highelectrical conductivity whereas the empty sites, and the sites filled by eithertypes of defect have a low electrical conductivity, i.e., a high-contrast isassumed. We examined isotropic (both the possible orientations of a particleare equiprobable) and anisotropic (all particles are aligned along one givendirection, $y$) deposition. To calculate the effective electrical conductivity,the monolayer was presented as a random resistor network (RRN) and theFrank--Lobb algorithm was used. The effects of the concentrations of defects$d_l$ and $d_k$ on the electrical conductivity for the values of $k = 2^n$,where $n =1,2,\dots, 5$, were studied. Increase of both the $d_l$ and $d_k$parameters values resulted in decreases in the value of $\sigma$ and thesuppression of percolation. Moreover, for anisotropic deposition the electricalconductivity along the $y$ direction was noticeably larger than in theperpendicular direction, $x$. Phase diagrams in the ($d_l, d_k$)-plane fordifferent values of $k$ were obtained.

physica a statistical mechanics and its applications

Influence of defects on the effective electrical conductivity of a  monolayer produced by random sequential adsorption of linear $k$-mers onto a  square lattice