Jamming and percolation in generalized models of random sequential adsorption 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

Lebovka, Nikolaï; Tarasevich, Yuri Yu.; Dubinin, D O; Laptev, V. V.; Vygornitskii, Nikolai V.

doi:10.1103/physreve.92.062116

Cited by 18 publications

(20 citation statements)

References 33 publications

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“…In recent decades, much attention has been paid to the study of self-assembly in systems of linear k-mers (particles occupying k adjacent adsorption sites) deposited on 2D lattices. A linear k-mer represents the simplest model of an elongated particle with an aspect ratio of k. Computer simulations have been extensively applied to investigate percolation and jamming phenomena for the random sequential absorption (RSA) of k-mers [30][31][32][33][34][35][36][37][38]. Various anomalies in the properties of the systems' dependence on the length of the k-mers have been reported.…”

Section: Introductionmentioning

confidence: 99%

Diffusion-driven self-assembly of rodlike particles: Monte Carlo simulation on a square lattice

et al. 2017

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The diffusion-driven self-assembly of rodlike particles was studied by means of Monte Carlo simulation. The rods were represented as linear k-mers (i.e., particles occupying k adjacent sites). In the initial state, they were deposited onto a two-dimensional square lattice of size L×L up to the jamming concentration using a random sequential adsorption algorithm. The size of the lattice, L, was varied from 128 to 2048, and periodic boundary conditions were applied along both x and y axes, while the length of the k-mers (determining the aspect ratio) was varied from 2 to 12. The k-mers oriented along the x and y directions (k_{x}-mers and k_{y}-mers, respectively) were deposited equiprobably. In the course of the simulation, the numbers of intraspecific and interspecific contacts between the same sort and between different sorts of k-mers, respectively, were calculated. Both the shift ratio of the actual number of shifts along the longitudinal or transverse axes of the k-mers and the electrical conductivity of the system were also examined. For the initial random configuration, quite different self-organization behavior was observed for short and long k-mers. For long k-mers (k≥6), three main stages of diffusion-driven spatial segregation (self-assembly) were identified: the initial stage, reflecting destruction of the jamming state; the intermediate stage, reflecting continuous cluster coarsening and labyrinth pattern formation; and the final stage, reflecting the formation of diagonal stripe domains. Additional examination of two artificially constructed initial configurations showed that this pattern of diagonal stripe domains is an attractor, i.e., any spatial distribution of k-mers tends to transform into diagonal stripes. Nevertheless, the time for relaxation to the steady state essentially increases as the lattice size growth.

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Section: Introductionmentioning

confidence: 99%

Diffusion-driven self-assembly of rodlike particles: Monte Carlo simulation on a square lattice

et al. 2017

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“…For example, with k-mers deposited using the random sequential absorption (RSA) model, the data revealed that the percolation threshold has a minimal value when k ≈ 16 and, probably, percolation is impossible for very long k-mers (k 10 4 ) [36]. Moreover, defects have a drastic influence on the percolation behavior [38] of the system of k-mers and electrical conductivity of a monolayer produced by aligned k-mers [39].…”

Section: Introduction: Electrical Conductivity Of Inhomogeneous Mediamentioning

confidence: 99%

Electrical conductivity of a monolayer produced by random sequential adsorption of lineark-mers onto a square lattice

et al. 2016

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The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent adsorption sites) onto a square lattice was studied by means of computer simulation. Overlapping with pre-deposited k-mers and detachment from the surface were forbidden. The RSA process continued until the saturation jamming limit, pj. The isotropic (equiprobable orientations of k-mers along x and y axes) and anisotropic (all kmers aligned along the y axis) depositions for two different models: of an insulating substrate and conducting k-mers (C-model) and of a conducting substrate and insulating k-mers (I-model) were examined. The Frank-Lobb algorithm was applied to calculate the electrical conductivity in both the x and y directions for different lengths (k = 1 -128) and concentrations (p = 0 -pj) of the k-mers. The 'intrinsic electrical conductivity' and concentration dependence of the relative electrical conductivity Σ(p) (Σ = σ/σm for the C-model and Σ = σm/σ for the I-model, where σm is the electrical conductivity of substrate) in different directions were analyzed. At large values of k the Σ(p) curves became very similar and they almost coincided at k = 128. Moreover, for both models the greater the length of the k-mers the smoother the functions Σxy(p), Σx(p) and Σy(p). For the more practically important C-model, the other interesting findings are (i) for large values of k (k = 64, 128), the values of Σxy and Σy increase rapidly with the initial increase of p from 0 to 0.1; (ii) for k ≥ 16, all the Σxy(p) and Σx(p) curves intersect with each other at the same iso-conductivity points; (iii) for anisotropic deposition, the percolation concentrations are the same in the x and y directions, whereas, at the percolation point the greater the length of the k-mers the larger the anisotropy of the electrical conductivity, i.e., the ratio σy/σx (> 1).

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“…However, in spite of the great progress which has taken place in experimental investigations of the EDSA phenomenon for anisotropic particles, the theory and computer simulations of such processes have never previously been discussed in the literature. In earlier studies computer simulation was extensively applied to investigate percolation, jamming and electrical conductivity of films filled with sticks (continuous problem) [24][25][26] and by k-mers (lattice problem) [27][28][29][30][31][32][33][34][35]. For conducting anisotropic particles, the particular interest lies in the impact of particle aspect ratio on the electrical conductivity and morphology of the films.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulation of evaporation-driven self-assembly in suspensions of colloidal rods

et al. 2016

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The vertical drying of a colloidal film containing rodlike particles was studied by means of kinetic Monte Carlo (MC) simulation. The problem was approached using a two-dimensional square lattice, and the rods were represented as linear k-mers (i.e., particles occupying k adjacent sites). The initial state before drying was produced using a model of random sequential adsorption (RSA) with isotropic orientations of the k-mers (orientation of the k-mers along horizontal x and vertical y directions are equiprobable). In the RSA model, overlapping of the k-mers is forbidden. During the evaporation, an upper interface falls with a linear velocity of u in the vertical direction and the k-mers undergo translation Brownian motion. The MC simulations were run at different initial concentrations, p_{i}, (p_{i}∈[0,p_{j}], where p_{j} is the jamming concentration), lengths of k-mers (k∈[1,12]), and solvent evaporation rates, u. For completely dried films, the spatial distributions of k-mers and their electrical conductivities in both x and y directions were examined. Significant evaporation-driven self-assembly and orientation stratification of the k-mers oriented along the x and y directions were observed. The extent of stratification increased with increasing value of k. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of p_{i}, k, and u.

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Jamming and percolation in generalized models of random sequential adsorption of lineark-mers on a square lattice

Cited by 18 publications

References 33 publications

Diffusion-driven self-assembly of rodlike particles: Monte Carlo simulation on a square lattice

Diffusion-driven self-assembly of rodlike particles: Monte Carlo simulation on a square lattice

Electrical conductivity of a monolayer produced by random sequential adsorption of lineark-mers onto a square lattice

Monte Carlo simulation of evaporation-driven self-assembly in suspensions of colloidal rods

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