{
  "id": "1607.08385",
  "version": "v1",
  "published": "2016-07-28T09:57:04.000Z",
  "updated": "2016-07-28T09:57:04.000Z",
  "title": "Electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice",
  "authors": [
    "Yuri Yu. Tarasevich",
    "Valeri V. Laptev",
    "Valeria A. Goltseva",
    "Nikolai I. Lebovka"
  ],
  "comment": "11 pages, 12 figures, 2 tables, 44 references, submitted to Phys.Rev.E",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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 $k \\geq 16$, 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 $\\sigma_y/\\sigma_x$ ($>1$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-28T09:57:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43"
    ],
    "keywords": [
      "electrical conductivity",
      "random sequential adsorption",
      "square lattice",
      "anisotropic deposition",
      "large values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}