Two-dimensional polymer networks near percolation

We report an extensive finite-size study of polymer networks near the percolation threshold, using numerical techniques. The polymers are modeled by random walks occupying the bonds of a two-dimensional square lattice. We measure the percolation threshold and critical exponents of the networks for various polymer lengths. We find that the critical occupation probability is a decreasing function of the polymer length, and the percolation of polymers with a fixed polymer length belongs to the same universality class as ordinary bond percolation. By adding particles to the lattice cells we can study the diffusion process in polymer networks. Measuring the current near percolation, we observe that its critical exponent is also independent of polymer length.