Percolation of a collection of finite random walks: a model for gas permeation through thin polymeric membranes

  title={Percolation of a collection of finite random walks: a model for gas permeation through thin polymeric membranes},
  author={R. K. P. Zia and Yong Wu and Beate Schmittmann},
  journal={Journal of Mathematical Chemistry},
Motivated by recent studies of gas permeation through polymer networks, we consider a collection of ordinary random walks of fixed length ℓ, placed randomly on the bonds of a square lattice. These walks model polymers, each with ℓ segments. Using computer simulations, we find the critical concentration of occupied bonds (i.e., the critical occupation probability) for such a network to percolate the system. Though this threshold decreases monotonically with ℓ, the critical “mass” density… 
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