Bond percolation of polymers

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