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

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.

21 pages, 4 figures

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Cited by in corpus (7)

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• Monte Carlo Simulation of Evaporation Driven Self-Assembly in Suspension of Colloidal Rods
• Jamming and percolation of $k^3$-mers on simple cubic lattices
• Sedimentation of a suspension of rods: Monte Carlo simulation of a continuous two-dimensional problem
• Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem
• Aging in two dimensional suspensions of rods as driven by Brownian diffusion