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Bond percolation of polymers

Manoj Gopalakrishnan·Beate Schmittmann·R. K. P. Zia
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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 $ρ_{c}^L(\ell)$ 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, $ρ_{c}^L(\ell)$ is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.

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Manoj Gopalakrishnan, Beate Schmittmann, R. K. P. Zia. 2004-07-16. Bond percolation of polymers. https://arxiv.org/abs/cond-mat/0404266

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