Percolation and jamming of linear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-mers on a square lattice with defects: Effect of anisotropy

Tarasevich, Yuri Yu.; Burmistrov, Andrei S.; Shinyaeva, Taisiya S.; Laptev, V. V.; Vygornitskii, Nikolai V.; Lebovka, Nikolaï

doi:10.1103/physreve.92.062142

Cited by 7 publications

(3 citation statements)

References 48 publications

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“…In contrast to the statistics for simple particles, the statistics of polyatomic species is strongly influenced by the presence of defects in the system. Hence, several papers have been published on jamming and standard percolation of k-mers on heterogeneous systems [42][43][44][45][46][47][48][49][50][51], where the heterogeneity was simulated by introducing a fraction of imperfect sites/bonds or a fraction of deposited impurities. Despite the apparent simplicity of these heterogeneous systems, a rich variety of behaviours were observed and discussed in terms of the k-mer size and the fraction of defects on the lattice.…”

Section: Introductionmentioning

confidence: 99%

Inverse percolation by removing straight rigid rods from square lattices in the presence of impurities

Ramirez¹,

Centres²,

Ramírez-Pastor³

2019

J. Stat. Mech.

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Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse percolation by removing straight rigid rods from square lattices contaminated with non-conducting impurities. The presence of impurities provides a more realistic approach to the deposited monolayer, which usually presents inhomogeneities due to the irregular arrangement of surface and bulk atoms, the presence of various chemical species, etc. The process starts with an initial configuration, where all lattice sites are occupied by an impurity (with a concentration ) or a conducting particle (with a concentration ). Then, the system is diluted by randomly removing linear k-mers (linear clusters of k consecutive conducting particles) from the lattice. The impurities remain fixed in its position and cannot be removed. The central idea of this paper is based on finding the maximum concentration of conducting sites (minimum concentration of empty sites) for which the connectivity disappears. This particular value of the concentration is called inverse percolation threshold, and determines a well-defined geometrical phase transition in the system. On the other hand, the inverse jamming coverage is the coverage of the limit state, in which no more objects can be removed from the lattice due to the absence of linear clusters of nearest-neighbour sites of appropriate size. The dependence of percolation and jamming thresholds on the concentration of defects was investigated for different values of k, ranging from 1 to 120. The obtained results show that the behaviour of the system is significantly affected by the presence of impurities. In addition, the nature of the jamming and percolation transitions was studied. In the first case, the corresponding spatial correlation length critical exponent was measured, being . This value coincides with previous calculations of this exponent for the standard random sequential adsorption of linear k-mers on square lattices. Critical exponents were also calculated for the percolation phase transition, showing that the universality class corresponding to ordinary percolation is preserved regardless the values of k and considered.

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Section: Introductionmentioning

confidence: 99%

Inverse percolation by removing straight rigid rods from square lattices in the presence of impurities

Ramirez¹,

Centres²,

Ramírez-Pastor³

2019

J. Stat. Mech.

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“…the highest concentration for which the percolation was observed, depends on the object shape. Eect of anisotropy on jamming and percolation for RSA of linear k-mers on a square lattice that contains defects was studied in [32]. The critical concentration of defects was found to decrease with the order parameter determining the degree of anisotropy.…”

Section: Introductionmentioning

confidence: 99%

Percolation in irreversible deposition on a triangular lattice: effects of anisotropy

Lončarević¹,

Budinski-Petković²,

Dujak³

et al. 2020

J. Stat. Mech.

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The percolation properties in anisotropic irreversible deposition of extended objects are studied by Monte Carlo simulations on a triangular lattice. Depositing objects of various shapes and sizes are made by directed self-avoiding walks on the lattice. Anisotropy is introduced by imposing unequal probabilities for placing the objects along different directions of the lattice. The degree of the anisotropy is characterized by the order parameter p determining the probability for deposition in the chosen (horizontal) direction. For each of the other two directions adsorption occurs with probability . It is found that the percolation threshold increases with the degree of anisotropy, having the maximum values for fully oriented objects. Percolation properties of the elongated shapes, such as k-mers, are more affected by the presence of anisotropy than the compact ones. Percolation in anisotropic deposition was also studied for a lattice with point-like defects. For elongated shapes a slight decrease of the percolation threshold with the impurity concentration d can be observed. However, for these shapes, significantly increases with the degree of anisotropy. In the case when depositing objects are triangles, results are qualitatively different. The percolation threshold decreases with d, but is not affected by the presence of anisotropy.

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“…The site percolation problem has also been studied for k-mers on lattices with defective sites [26,27] and bonds [28]. However, in the best knowledge of the authors, there is still a lack of systematic studies on S ∩ B and S ∪ B percolation in the presence of multiple occupation of sites and defects.…”

Section: Introductionmentioning

confidence: 99%

Site-bond percolation of heteronuclear dimers irreversibly deposited on square lattices

2017

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A generalization of the site-bond percolation problem was studied, in which pairs of neighboring sites (site dimers) and bonds are occupied irreversibly, randomly, and independently on homogeneous square surfaces. A dimer is composed of two segments and occupies two adjacent sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Two types of dimers are considered, AA and AB, and the connectivity analysis is carried out by accounting only for the conductive segments (segments type A) in combination with bonds. For the combination of dimers and bonds, two different criteria were analyzed: the union or the intersection between the adsorbed percolating particles and the bonds. By means of numerical simulations and finite-size scaling analysis, the complete phase diagram separating a percolating from a non-percolating region was determined.

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Percolation and jamming of lineark-mers on a square lattice with defects: Effect of anisotropy

Cited by 7 publications

References 48 publications

Inverse percolation by removing straight rigid rods from square lattices in the presence of impurities

Inverse percolation by removing straight rigid rods from square lattices in the presence of impurities

Percolation in irreversible deposition on a triangular lattice: effects of anisotropy

Site-bond percolation of heteronuclear dimers irreversibly deposited on square lattices

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