Bond percolation of polymers

Abstract

We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D square lattice of size $L$ with reflecting boundaries. Through simulations, we find the fraction of configurations displaying {\em no} connected cluster which span from one edge to the opposite edge. From this fraction, we define a critical segment density ${\rho }_c^L(\ell )$ and the associated critical fraction of occupied bonds $p_c^L(\ell )$, so that they can be identified as the percolation threshold in the $L\to \infty$ limit. Whereas $p_c^L(\ell )$ is found to decrease monotonically with $\ell$ for a wide range of polymer lengths, ${\rho }_c^L(\ell )$ is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.

4 pages with 6 figures