Bond percolation of polymers

Original · EN

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 ρcˡ(ℓ) and the associated critical fraction of occupied bonds pcˡ(ℓ), so that they can be identified as the percolation threshold in the L → ∞ limit. Whereas pcˡ(ℓ) is found to decrease monotonically with ℓ for a wide range of polymer lengths, ρcˡ(ℓ) is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.