Journal of Mathematical Chemistry

, Volume 45, Issue 1, pp 58–64

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

Original Paper

DOI: 10.1007/s10910-008-9367-6

Cite this article as:
Zia, R.K.P., Wu, Y. & Schmittmann, B. J Math Chem (2009) 45: 58. doi:10.1007/s10910-008-9367-6


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.

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of PhysicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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