Percolation of polyatomic species on a square lattice

Cornette, V.; Ramírez-Pastor, A. J.; Nieto, F.

doi:10.1140/epjb/e2003-00358-1

Cited by 96 publications

(151 citation statements)

References 33 publications

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“…Longone et al [9] studied the deposition of aligned rigid rods of length k up to 12 and found that the percolation threshold for completely ordered deposition decreases if the length of the rods increases, which is similar to the case with disordered deposition [8].…”

Section: One Can Easily Calculatementioning

confidence: 75%

“…Conjectures for the percolation threshold and jamming concentration tend towards constants as the length of the k-mers increases, based on the simulations for relatively short k-mers [3,5,6,8,9]. However, this conjecture seems to become invalid when considering the results of computer-based experiments with larger kmers [4,7,11].…”

Section: Discussionmentioning

confidence: 99%

“…Cornette et al studied the percolation of linear segments of size k and k-mers of different structures (k varies up to 15) on a square lattice and reported that the percolation threshold exponentially decreases with the length of the rods [8]. The percolation threshold as a function of k for linear segments is fitted by…”

Section: One Can Easily Calculatementioning

confidence: 99%

“…For uniformity, hereinafter we will use the term k-mer. Many important findings regarding percolation and jamming of completely disordered k-mers [3][4][5][6][7][8] or partially aligned k-mers [9][10][11][12] have been reported over the last two decades.…”

Section: Introductionmentioning

confidence: 99%

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Impact of defects on percolation in random sequential adsorption of lineark-mers on square lattices

et al. 2015

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The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models, L d and K d , are analyzed. In the L d model, it is assumed that the initial square lattice is non-ideal and some fraction of sites, d, is occupied by non-conducting point defects (impurities). In the K d model, the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers, d, consists of defects, i.e., are non-conducting. The length of the k-mers, k, varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependencies of the percolation threshold concentration of the conducting sites, pc, vs the concentration of defects, d, were analyzed for different values of k. Above some critical concentration of defects, dm, percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of dm are well fitted by the functions dm ∝ k −α m − k −α (α = 1.28 ± 0.01, km = 5900 ± 500) and dm ∝ log(km/k) (km = 4700 ± 1000 ), for the L d and K d models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k 6 × 10 3 .

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Section: One Can Easily Calculatementioning

confidence: 75%

Section: Discussionmentioning

confidence: 99%

Section: One Can Easily Calculatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impact of defects on percolation in random sequential adsorption of lineark-mers on square lattices

et al. 2015

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“…As for cases of continuum percolation models, a simulation study showed 10) that even simpler size distributions (Gaussian, uniform, and log-normal distributions of particles, regardless of their conductivity) shows a clearly nontrivial effect. Even in simpler models, 11,12) for example, conductor sites arranged in length X bars aligned vertically or horizontally in square lattice, 13) can exhibit quite complex effects and there actually is an optimum value of X, beyond which the effect on p c is inversed.…”

Section: Introductionmentioning

confidence: 99%

Controlling the Percolation Threshold of Conductor-Insulator Composites in a 2D Triangular Lattice by Introducing Binary Size Distributions of Conductor Particles

2012

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When one attempts to modulate and control the characteristics of composite materials, the mathematical threshold of the percolation transition dictates the modulation limit. Using a series of computer simulations, we have been investigating the dependence of the percolation threshold on particle size distributions. However, one of the other factors that can deeply affect percolation behavior, the design of lattice, is always fixed to simple square or cubic lattices. This report presents the first calculation of a percolation threshold in a 2D triangular lattice with binary size distributions of conductor particles. Although a small quantitative difference was found, the results qualitatively matched to the results already reported for 2D square lattices, thus confirming our previous finding: the introduction of large conductor particles increases the percolation threshold in 2D.

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Percolation in Two‐Dimensional Copolymer Systems

Polanowski

Wawrzyńska

Sikorski

2013

Macro Theory & Simulations

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The aim of the study is the investigation of the percolation phenomena in some model copolymer systems. Diblock, triblock, random copolymers, and a blend of homopolymers are studied. For this purpose, we developed an idealized model of polymeric systems. The positions of polymer segments are restricted to vertices of a simple cubic lattice. The chains are at good solvent conditions – the excluded volume is the only interaction between the segments of the chain. The properties of the model chains are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The differences and similarities in the percolation behavior are shown and discussed. The percolation threshold is found to be very weakly dependent on the chain length, however, it appears that the main factor that influenced the percolation threshold is the screening effect of other parts of chains.

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Percolation of polyatomic species on a square lattice

Cited by 96 publications

References 33 publications

Impact of defects on percolation in random sequential adsorption of lineark-mers on square lattices

Impact of defects on percolation in random sequential adsorption of lineark-mers on square lattices

Controlling the Percolation Threshold of Conductor-Insulator Composites in a 2D Triangular Lattice by Introducing Binary Size Distributions of Conductor Particles

Percolation in Two‐Dimensional Copolymer Systems

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