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

@article{Zia2009PercolationOA, 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}, year={2009}, volume={45}, pages={58-64} }

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…

## 8 Citations

### Percolation in two-dimensional systems containing cyclic chains

- Materials Science
- 2012

The structure of the system consisting of adsorbed cyclic polymer chains and solvent molecules was studied. Our main aim was to check how the percolation threshold in such a system was related to the…

### Percolation in polymer-solvent systems: a Monte Carlo study.

- Materials ScienceThe Journal of chemical physics
- 2009

It was shown that the percolation threshold decreased strongly with the chain length, which is closely connected to changes in chains' structure with the decreasing polymer concentration.

### The structure of percolated polymer systems: a computer simulation study

- Materials ScienceJournal of molecular modeling
- 2011

The scaling behavior and the structure of the percolation clusters are presented and discussed and the properties of the model system across the entire range of polymer concentrations were determined by Monte Carlo simulations employing a cooperative motion algorithm.

### Monte carlo study of the percolation in two-dimensional polymer systems

- Materials ScienceJournal of Molecular Modeling
- 2013

It was shown that the RSA method gave considerably lower thresholds for longer chains, which can be explained by a different pool of chain conformations used in the calculations in both methods under consideration.

### Numerical study for the percolation threshold and transport properties of porous composites comprising non-centrosymmetrical superovoidal pores

- Materials Science
- 2020

### Anisotropic Percolating Pathways in the Thin Films of Polymeric PEDT/PSS Complex and their Relation to the Electrical Conductivity as Revealed by the Mesoscale Simulation

- Physics
- 2010

The MesoDyn simulation code supplemented with the percolation and cluster analysis concepts has been used to generate the subcritical percolating networks of PEDT beads of the coarse-grained PEDT/PSS…

### Effects of the pore shape polydispersity on the percolation threshold and diffusivity of porous composites: Theoretical and numerical studies

- Materials SciencePowder Technology
- 2021

## References

SHOWING 1-10 OF 16 REFERENCES

### Gas permeation through a polymer network

- Physics
- 2005

We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modelled as non-interacting random walks on the bonds…

### Bond percolation of polymers

- Mathematics
- 2004

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…

### Two-dimensional polymer networks near percolation

- Materials Science
- 2007

We report an extensive finite-size study of polymer networks near the percolation threshold, using numerical techniques. The polymers are modeled by random walks occupying the bonds of a…

### Percolation properties of random ellipses.

- MathematicsPhysical review. A, General physics
- 1988

The percolation concentration for identical ellipses with aspect ratio b/a in a two-dimensional plane where both the centers and orientations are random is computed and an interpolation formula appears superior to all these effective-medium theories.

### Repeated bond traversal probabilities for the simple random walk

- Mathematics
- 2002

We consider the average number Bm(t) of bonds traversed exactly m times by a t step simple random walk. We determine Bm(t) explicitly in the scaling limit t → ∞ with m/√t fixed in dimension d = 1 and…

### Effects of Cooling Rate and Physical Aging on the Gas Transport Properties in Polycarbonate

- Materials Science
- 2003

The gas transport properties of bisphenol A polycarbonate films were examined as a function of the cooling rate during film processing and subsequent physical aging. Interpretation of the permeation…

### Study of the shape of random walks. II. Inertia moment ratios and the two-dimensional asphericity

- Physics, Mathematics
- 1995

A study of some features of the quantities used to describe the shape of random walks, focusing on the probability distribution of the asphericity of discrete random walks in two dimensions, is…

### Analytical approximation of the two-dimensional percolation threshold for fields of overlapping ellipses.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

An analyticalpercolation approach capable of identifying the percolation point in two-phase materials containing generalized ellipses of uniform shape and size is derived and verified and the dependence ofPercolation on the particle aspect ratio is explored.

### Percolation processes

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1957

ABSTRACT The previous paper (1) omitted the proof of the theorem on the connective constant of a crystal. This paper supplies the proof. For ease of reference, we first recall the relevant…

### The physics of amorphous solids

- Materials Science
- 1983

The Formation of Amorphous Solids Amorphous Morphology: The Geometry and Topology of Disorder Chalcogenide Glasses and Organic Polymers The Percolation Model Localization Delocalization Transitions…