Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

Matoz-Fernandez, D. A.; Linares, Daniel; Ramírez-Pastor, A. J.

doi:10.1140/epjb/e2012-30389-2

Cited by 19 publications

(19 citation statements)

References 51 publications

(93 reference statements)

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“…For example, the jamming concentration decreases monotonically when approaching the asymptotic value of p j = 0.66 ± 0.01 at large values of k, and the percolation threshold p c is a nonmonotonic function of the length k, with a minimum at a particular length of the kmers (k ≈ 13) [29,32,37]. Several problems related to the self-organization of k-mers have been previously discussed [43][44][45][46][47][48]. Dynamic Monte Carlo simulations using a deposition-evaporation algorithm for the simulation of dynamic equilibrium of the k-mers have been applied [43].…”

Section: Resultsmentioning

confidence: 94%

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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Section: Resultsmentioning

confidence: 94%

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

et al. 2016

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“…The irreversible RSA process leads to a nonequilibrium state of the system, and further selforganization in the deposited film is possible owing to deposition-evaporation processes or the diffusion motion of the k-mers. Several problems related to such type of self-assembly of k-mers have previously been discussed [39][40][41][42][43][44][45]. Dynamic MC simulations using a deposition-evaporation algorithm for simulation of the dynamic equilibrium of k-mers on square lattices have been applied [39].…”

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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“…This method enables to determine directly the percolation threshold and the jamming threshold (the maximum coverage of the substrate by the objects). Theoretical and simulation studies of other large and regular objects like needles (rods, rectangles, squares) or ellipses show that the percolation depends on their aspect ratio, [ 14,[31][32][33][34][35][36][37][38][39][40][41] although in the case of stiff and elongated objects this dependence is nonmonotonic. One has to remember that in the case of macromolecular chains the deposited objects are large and differ one from another and their size and shapes are widely distributed.…”

Section: Macromolecular Theory and Simulationsmentioning

confidence: 99%

Percolation in Two‐Dimensional Copolymer‐Solvent Systems

Kuriata

Polanowski²,

Sikorski

2016

Macro Theory & Simulations

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In this work, the structure of a strictly 2D dense polymer film for some model copolymer systems: diblock, triblock, and random copolymers is studied. An idealized model of these macromolecular systems is developed where positions of polymer beads are restricted to vertices of a simple cubic lattice and chains are under good solvent conditions (the excluded volume is the only interaction between beads of the chain and solvent molecules). The properties of the system are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local cooperative changes of conformation. Scaling of the chain size is studied and the influence of the polymer concentration on the chain's size and shape is discussed. The differences and similarities in the behavior of the percolation thresholds of one component in chains with different bead sequences are also shown and discussed. The percolation threshold is found to be weakly dependent on the chain length and more sensitive to the total polymer concentration.

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Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

Cited by 19 publications

References 51 publications

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

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

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

Percolation in Two‐Dimensional Copolymer‐Solvent Systems

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