Electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice

Abstract

The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear $k$-mers onto a square lattice was studied by means of computer simulation. Overlapping with pre-deposited $k$-mers and detachment from the surface were forbidden. The RSA continued until the saturation jamming limit, $p_j$. The isotropic and anisotropic depositions for two different models: of an insulating substrate and conducting $k$-mers (C-model) and of a conducting substrate and insulating $k$-mers (I-model) were examined. The Frank-Lobb algorithm was applied to calculate the electrical conductivity in both the $x$ and $y$ directions for different lengths ($k=1$ -- $128$) and concentrations ($p=0$ -- $p_j$) of the $k$-mers. The `intrinsic electrical conductivity' and concentration dependence of the relative electrical conductivity $\Sigma (p)$ ($\Sigma =\sigma /{\sigma }_m$ for the C-model and $\Sigma ={\sigma }_m/\sigma$ for the I-model, where ${\sigma }_m$ is the electrical conductivity of substrate) in different directions were analyzed. At large values of $k$ the $\Sigma (p)$ curves became very similar and they almost coincided at $k=128$. Moreover, for both models the greater the length of the $k$-mers the smoother the functions ${\Sigma }_{xy}(p)$, ${\Sigma }_x(p)$ and ${\Sigma }_y(p)$. For the C-model, the other interesting findings are: for large values of $k$ ($k=64,128$), the values of ${\Sigma }_{xy}$ and ${\Sigma }_y$ increase rapidly with the initial increase of $p$ from 0 to 0.1; for $k\ge 16$, all the ${\Sigma }_{xy}(p)$ and ${\Sigma }_x(p)$ curves intersect with each other at the same iso-conductivity points; for anisotropic deposition, the percolation concentrations are the same in the $x$ and $y$ directions, whereas, at the percolation point the greater the length of the $k$-mers the larger the anisotropy of the electrical conductivity, i.e., the ratio ${\sigma }_y/{\sigma }_x$ ($>1$).

arXiv comment11 pages, 12 figures, 2 tables, 44 references, submitted to Phys.Rev.E

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• Diffusion-driven self-assembly of rod-like particles: Monte Carlo simulation on a square lattice
• Anisotropy in electrical conductivity of two-dimensional films containing aligned rodlike particles: continuous and lattice models
• Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice
• Percolation phase transition by removal of $k^2$-mers from fully occupied lattices
• Connectedness percolation in the random sequential adsorption packings of elongated particles
• Percolation of aligned rigid rods on two-dimensional triangular lattices
• Two-step percolation in aggregating systems
• Effect of dispersity of particle length on the electrical conductivity of the two-dimensional systems