Percolation in Two‐Dimensional Copolymer‐Solvent Systems

Kuriata, Aleksander; Polanowski, Piotr; Sikorski, Andrzej

doi:10.1002/mats.201500095

Cited by 4 publications

(5 citation statements)

References 66 publications

(150 reference statements)

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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 (see, e.g., [15,16,17] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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Pattern formation in a two-dimensional two-species diffusion model with anisotropic nonlinear diffusivities: a lattice approach

Tarasevich¹,

Laptev²,

Burmistrov³

et al. 2017

J. Stat. Mech.

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Diffusion in a two-species two-dimensional system has been simulated using a lattice approach. Rodlike particles were considered as linear k-mers of two mutually perpendicular orientations (k x -and k y -mers) on a square lattice. These k xand k y -mers were treated as species of two kinds. A random sequential adsorption model was used to produce an initial homogeneous distribution of k-mers. The concentration of k-mers, p, was varied in the range from 0.1 to the jamming concentration, p j . By means of the Monte Carlo technique, translational diffusion of the k-mers was simulated as a random walk, while rotational diffusion was ignored. We demonstrated that the diffusion coefficients are strongly anisotropic and nonlinearly concentration-dependent. For sufficiently large concentrations (packing densities) and k ≥ 6, the system tends toward a well-organized steady state. Boundary conditions predetermine the final state of the system. When periodic boundary conditions are applied along both directions of the square lattice, the system tends to a steady state in the form of diagonal stripes. The formation of stripe domains takes longer time the larger the lattice size, and is observed only for concentrations above a particular critical value. When insulating (zero flux) boundary conditions are applied along both directions of the square lattice, each kind of k-mer tries to completely occupy a half of the lattice divided by a diagonal, e.g., k x -mers locate in the upper left corner, while the k y -mers are situated in the lower right corner ("yin-yang" pattern). From time to time, regions built of k x -and k y -mers exchange their locations through irregular patterns. When mixed boundary conditions are used (periodic boundary conditions are applied along one direction whereas insulating boundary conditions are applied along the other one), the system still tends to form the stripes, but they are unstable and change their spatial orientation.

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Section: Introductionmentioning

confidence: 99%

“…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 (see, e.g. [15][16][17] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Pattern formation in a two-dimensional two-species diffusion model with anisotropic nonlinear diffusivities: a lattice approach

Tarasevich¹,

Laptev²,

Burmistrov³

et al. 2017

J. Stat. Mech.

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“…[26] The percolation threshold in two-dimensional macromolecular systems has recently been extensively studied. [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] The influence of the chain length on the threshold has also been determined: the threshold decreases rapidly for short chains but then the decrease becomes slower. [29,31,35,39] It has also been suggested that the threshold strongly depends on the structure of macromolecules expressed in terms of local polymer density.…”

Section: Introductionmentioning

confidence: 99%

Percolation in Polydisperse Polymer Systems: A Computer Simulation Study

Agajew

Sikorski

2022

Macro Theory & Simulations

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The structure of polymer chains at interfaces still is not fully understood. A coarse-grained lattice model is used to study the structure of macromolecules strongly adsorbed on a flat surface. As a result, the polymers are strictly two-dimensional. Chains are flexible and athermal. A dynamic Monte Carlo algorithm consisting of local and non-local modification of chains' conformations is employed. The scaling behavior of chains' size is found to be similar to monodisperse systems. It is also shown that the introduction of polydispersity increases values of the percolation threshold, especially for longer chains. The influence of the type of polydispersity on the percolation threshold in two-dimensional polymer films is found to be significant.

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“…In recent decades, much attention has been paid to the study of 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 hard-core (completely rigid) rod-like particle with an aspect ratio of k. Computer simulations have been extensively applied to investigate percolation and jamming phenomena for the random sequential adsorption (RSA) [10] of k-mers (see, e.g., [11,12,13] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Impact of packing fraction on diffusion-driven pattern formation in a two-dimensional system of rod-like particles

Tarasevich

Laptev

Chirkova

et al. 2018

J. Phys.: Conf. Ser.

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Pattern formation in a two-dimensional system of rod-like particles has been simulated using a lattice approach. Rod-like particles were modelled as linear k-mers of two mutually perpendicular orientations (kx-and ky-mers) on a square lattice with periodic boundary conditions (torus). Two kinds of random sequential adsorption model were used to produce the initial homogeneous and isotropic distribution of k-mers with different values of packing fraction. By means of the Monte Carlo technique, translational diffusion of the k-mers was simulated as a random walk, while rotational diffusion was ignored, so, kx-and ky-mers were considered as individual species. The system tends toward a well-organized nonequilibrium steady state in the form of diagonal stripes for the relatively long k-mer (k ≥ 6) and moderate packing densities (in the interval p down < p < pup, where both the critical packing fractions p down and pup are depended on k).

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Percolation in Two‐Dimensional Copolymer‐Solvent Systems

Cited by 4 publications

References 66 publications

Pattern formation in a two-dimensional two-species diffusion model with anisotropic nonlinear diffusivities: a lattice approach

Pattern formation in a two-dimensional two-species diffusion model with anisotropic nonlinear diffusivities: a lattice approach

Percolation in Polydisperse Polymer Systems: A Computer Simulation Study

Impact of packing fraction on diffusion-driven pattern formation in a two-dimensional system of rod-like particles

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