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arXiv · 1205.6875

Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

D. A. Matoz-Fernandez·D. H. Linares·A. J. Ramirez-Pastor
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Abstract

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length $k$ ($k$-mers) on two-dimensional square lattices. The $k$-mers, containing $k$ identical units (each one occupying a lattice site), were adsorbed at equilibrium on the lattice. The process was monitored by following the probability $R_{L,k}(\theta)$ that a lattice composed of $L \times L$ sites percolates at a concentration $\theta$ of sites occupied by particles of size $k$. A nonmonotonic size dependence was observed for the percolation threshold, which decreases for small particles sizes, goes through a minimum, and finally asymptotically converges towards a definite value for large segments. This striking behavior has been interpreted as a consequence of the isotropic-nematic phase transition occurring in the system for large values of $k$. Finally, the universality class of the model was found to be the same as for the random percolation model.

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BibTeXRIS

D. A. Matoz-Fernandez, D. H. Linares, A. J. Ramirez-Pastor. 2012-05-31. Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions. https://doi.org/10.1140/epjb/e2012-30389-2

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