, Volume 45, Issue 1, pp 58-64
Date: 09 May 2008

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

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Abstract

Motivated by recent studies of gas permeation through polymer networks, we consider a collection of ordinary random walks of fixed length , placed randomly on the bonds of a square lattice. These walks model polymers, each with 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 , the critical “mass” density, defined as the total number of segments divided by total number of bonds in the system, displays a more complex behavior. In particular, for fixed mass densities, the percolation characteristics of the network can change several times, as shorter polymers are linked to form longer ones.