# Two-dimensional polymer networks near percolation

@article{Wu2008TwodimensionalPN, title={Two-dimensional polymer networks near percolation}, author={Yong Wu and Beate Schmittmann and R. K. P. Zia}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2008}, volume={41}, pages={025004} }

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 two-dimensional square lattice. We measure the percolation threshold and critical exponents of the networks for various polymer lengths. We find that the critical occupation probability is a decreasing function of the polymer length, and the percolation of polymers with a fixed polymer length belongs to the…

## 13 Citations

### 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.

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

- Physics
- 2009

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…

### 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…

### 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.

### Critical exponents and universality for the isotropic-nematic phase transition in a system of self-assembled rigid rods on a lattice.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The calculation of the critical exponents and the behavior of Binder cumulants indicate that the universality class of the IN transition changes from two-dimensional Ising-type for monodisperse rods without self-assembly to q=1 Potts- type for self-assembled rods.

### Conformations of a dipolar solute in a Stockmayer solvent channel.

- ChemistryLangmuir : the ACS journal of surfaces and colloids
- 2012

This study studies the redistribution of freely-rotating dipolar solute molecules solvated by a water-like Stockmayer solvent initially adhered to a face-centered cubic substrate and augments the understanding of the evolution of aggregates in biological systems and the design of polymers for self-assembled monolayers for industrial applications.

### Sol–gel transition in solutions of FG-Nups of the nuclear pore complex

- BiologyExtreme Mechanics Letters
- 2018

## References

SHOWING 1-10 OF 24 REFERENCES

### 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…

### 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…

### Critical exponent of percolation conductivity by finite-size scaling

- Physics
- 1983

Calculates the critical exponent of percolation conductivity t for two- and three-dimensional networks by using a finite-size scaling technique. In two dimensions the authors obtain t=1.264+or-0.054,…

### Properties of Granular Percolation in Two Dimensions.

- Physics
- 1997

Percolation process is studied in a model granular system on a square lattice, where grains are grown around seeds up to the n -th neighbors. Critical percolation coverage is shown to oscillate as a…

### Randomly diluted xy and resistor networks near the percolation threshold.

- MathematicsPhysical review. B, Condensed matter
- 1987

The results show conclusively that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, at least in high spatial dimension.

### Percolation by position-space renormalisation group with large cells

- Physics
- 1978

We demonstrate that the critical properties of the percolation model can be obtained with a rather high degree of accuracy by extrapolating to b = a3 a sequence of position-space renormalisation…

### Introduction To Percolation Theory

- Physics
- 1985

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…