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Numerical simulations and finite-size scaling analysis have been carried outto 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 atequilibrium on the lattice. The process was monitored by following theprobability $R_{L,k}(\theta)$ that a lattice composed of $L \times L$ sitespercolates 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 finallyasymptotically converges towards a definite value for large segments. Thisstriking behavior has been interpreted as a consequence of theisotropic-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 asfor the random percolation model.

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