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

The effect of defects on the behaviour of electrical conductivity, σ, in a monolayer produced by the random sequential adsorption of linear k-mers (particles occupying k adjacent sites) onto a square lattice is studied by means of a Monte Carlo simulation. The k-mers are deposited on the substrate until a jamming state is reached. The presence of defects in the lattice (impurities) and of defects in the k-mers with concentrations of dl and dk, respectively, is assumed. The defects in the lattice are distributed randomly before deposition and these lattice sites are forbidden for the deposition of k-mers. The defects of the k-mers are distributed randomly on the deposited k-mers. The sites filled with k-mers have high electrical conductivity, σk, whereas the empty sites, and the sites filled by either types of defect have a low electrical conductivity, σl, i.e., a high-contrast, σk∕σl≫1, is assumed. We examined isotropic (both the possible x and y orientations of a particle are equiprobable) and anisotropic (all particles are aligned along one given direction, y) deposition. To calculate the effective electrical conductivity, the monolayer was presented as a random resistor network and the Frank-Lobb algorithm was used. The effects of the concentrations of defects dl and dk on the electrical conductivity for the values of k=2n, where n=1,2,…,5, were studied. Increase of both the dl and dk parameters values resulted in decreases in the value of σ and the suppression of percolation. Moreover, for anisotropic deposition the electrical conductivity along the y direction was noticeably larger than in the perpendicular direction, x. Phase diagrams in the (dl,dk)-plane for different values of k were obtained.