arXiv subjects

Nikolai I. Lebovka

Publications and source records attributed to Nikolai I. Lebovka.

At least 19 recordsLinked to original sources

arXiv2021

Relaxation of saturated random sequential adsorption packings of discorectangles aligned on a line

Relaxation of the packing of elongated particles (discorectangles) aligned on a line was studied numerically. The aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;50]$. The initial jamming (saturated) state was produced using the basic variant of the random sequential adsorption (RSA) model with random positions and orientations of particles. The relaxation was performed by allowing rotational and translational diffusion motions of the particles wile their centers remained located on the line. The effects of the aspect ratio $\varepsilon$ on the kinetics of relaxation, the orientation order parameter and the distribution function of the distances between nearest-neighbor discorectangles were analyzed. The transport properties of the resulting 1D systems were also analyzed by using the diffusion of a tracer particle (random walker) between the nearest-neighbor discorectangles. In the relaxed states the anomalous diffusion was observed having a hopping exponent $d_w>2$ dependent upon $\varepsilon$.

cond-mat.stat-mech↗

arXiv2021

Confinement effects on the random sequential adsorption packings of elongated particles in a slit

The behavior of a system of two-dimensional elongated particles (discorectangles) packed into a slit between two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, $\varepsilon=l/d$) of the particles was varied within the range $\varepsilon \in [1;32]$ while the distance between the walls was varied within the range $h/d\in [1;80]$. The properties of the deposits when in the jammed state (the coverage, the order parameter, and the long-range (percolation) connectivity between particles) were studied numerically. The values of $\varepsilon$ and $h$ significantly affected the structure of the packings and the percolation connectivity. In particular, the observed nontrivial dependencies of the jamming coverage $φ(\varepsilon)$ or $φ(h)$ were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.

cond-mat.soft↗

arXiv2021

Connectedness percolation in the random sequential adsorption packings of elongated particles

Connectedness percolation phenomena in two-dimensional packings of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption (RSA) off-lattice model with preferential orientations of particles along a given direction. The partial ordering was characterized by order parameter $S$, with $S=0$ for completely disordered films (random orientation of particles) and $S=1$ for completely aligned particles along the horizontal direction $x$. The aspect ratio (length-to-width ratio) for the particles was varied within the range $\varepsilon \in [1;100]$. Analysis of connectivity was performed assuming a core-shell structure of particles. The value of $S$ affected the structure of packings, formation of long-range connectivity and electrical conductivity behavior. The effects were explained accounting for the competition between the particles' orientational degrees of freedom and the excluded volume effects. For aligned deposition, the anisotropy in electrical conductivity was observed and the values along alignment direction, $σ_x$, were larger than the values in perpendicular direction, $σ_y$. The anisotropy in localization of percolation threshold was also observed in finite sized packings, but it disappeared in the limit of infinitely large systems.

cond-mat.dis-nn↗

arXiv2020

"Paris car parking problem" for partially ordered discorectangles on a line

The random sequential adsorption (RSA) of identical elongated particles (discorectangles) on a line ("Paris car parking problem") was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The possible orientations of the discorectanles were restricted between $θ\in [-θ_\text{m}; θ_\text{m}]$ while the aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;100]$. Additionally, the limiting case $\varepsilon=\infty$ (i.e., widthless sticks) was considered. We observed, that the RSA deposition for the problem under consideration was governed by the formation of rarefied holes (containing particles oriented along a line) surrounded by comparatively dense stacks (filled with almost parallel particles oriented in the vertical direction). The kinetics of the changes of the order parameter, and the packing density are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, $φ_\text{j}$, and shifted the cusps in the $φ_\text{j}(\varepsilon)$ dependencies. This can be explained by the effects on the competition between the particles' orientational degrees of freedom and the excluded volume effects.

cond-mat.dis-nn↗

arXiv2020

Random sequential adsorption of partially ordered discorectangles onto a continuous plane

Computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane . The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing density $φ$ found at different values of $S_0$ are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, $φ_\text{j}$, and shifted the cusps in the $φ_\text{j}(\varepsilon)$ dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core---shell structure of particles.

cond-mat.soft↗

arXiv2019

Two-dimensional systems of elongated particles: From diluted to dense

This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the systems with isotropically deposited and aligned particles. Overviews of different analytical and computational methods and main results are presented.

cond-mat.dis-nn↗

arXiv2019

Aging in two dimensional suspensions of rods as driven by Brownian diffusion

Aging in a two dimensional suspension containing rods was studied by means of kinetic Monte Carlo simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state was produced using a random sequential adsorption model. During the aging, the rods underwent translational and rotational Brownian motions. The simulations were run at different values of number density (the number of rods per unit area), $ρ$, and of the initial orientation order parameter, $S_i$. The rods were assumed to have core---shell structures. The evolutions of both the connectivity and the order parameter in the course of the aging were examined.

cond-mat.stat-mech↗

arXiv2019

Sedimentation of a suspension of rods: Monte Carlo simulation of a continuous two-dimensional problem

The sedimentation of a two dimensional suspension containing rods was studied by means of kinetic Monte Carlo (MC) simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state before sedimentation was produced using a model of random sequential adsorption. During such sedimentation, the rods undergo translational and rotational Brownian motions. The MC simulations were run at different initial number densities (the numbers of rods per unit area), $ρ_i$, and sedimentation rates, $u$. For sediment films, the spatial distributions of the rods, the order parameters and the electrical conductivities were examined. Different types of sedimentation-driven self-assembly and anisotropy of the electrical conductivity were revealed inside the sediment films. This anisotropy can be finely regulated by changes in the values of $ρ_i$ and $u$.

cond-mat.stat-mech↗

arXiv2018

Effect of dispersity of particle length on the electrical conductivity of the two-dimensional systems

By means of computer simulation, we examined effect of dispersity of filler length on electrical conductivity of two-dimensional (2D) composites with rod-like fillers. Continuous approach has been used. Highly conductive zero-width rod-like particles were deposited uniformly with given anisotropy onto a poorly conductive substrate. Length of particles varied according to the lognormal distribution. Our simulation evidenced that slightly disordered systems may have both the high figure of merit, i.e., both high electrical conductivity and the optical transmission simultaneously, and the high electrical anisotropy.

physics.class-ph↗

arXiv2018

Simulation of the electrical conductivity of two-dimensional films with aligned rod-like conductive fillers: effect of the filler length dispersity

Using Monte Carlo simulation, we studied the electrical conductivity of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rod-like fillers (rods). The rods were of various lengths fitting a log-normal distribution. They could be aligned along a direction. Special attention was paid to films having completely aligned rods. The impact of length dispersity and the extent of rod alignment on the insulator-to-conductor phase transition was studied. The greater the length dispersity the smaller the critical concentration. The anisotropy of the electrical conductivity was more pronounced in the vicinity of the phase transition. A finite size effect was found to be significant only in the vicinity of the phase transition.

cond-mat.dis-nn↗

arXiv2018

Anisotropy in electrical conductivity of two-dimensional films containing aligned rodlike particles: continuous and lattice models

Numerical simulations using the Monte Carlo method were performed to study the electrical conductivity of two-dimensional films filled with rodlike particles (rods). The main goal was to investigate the effect of rod alignment on the electrical properties of the films. Both continuous and lattice approaches were used. Intersections of particles were forbidden. Our main findings are (i) both models demonstrate similar behaviors, (ii) at low concentration of rods, both approaches lead to the same dependencies of the electrical conductivity on the concentration of the rods, (iii) the alignment of the rods essentially affects the electrical conductivity, (iv) at some concentrations of partially aligned rods, the films may be conducting only in one direction, (v) the films may simultaneously be both highly transparent and electrically anisotropic.

cond-mat.mes-hall↗

arXiv2018

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

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 ($k_x$- and $k_y$-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, $k_x$- and $k_y$-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 ($k \geq 6$) and moderate packing densities (in the interval $p_{down} < p < p_{up}$, where both the critical packing fractions $p_{down}$ and $p_{up}$ are depended on $k$).

cond-mat.stat-mech↗

arXiv2018

Anisotropy in electrical conductivity and transparency of films of aligned conducting rods

Numerical simulations by means of the Monte Carlo method have been performed to study the electrical properties of a two-dimensional composite filled with rodlike particles. The main goal was to study the effect of the alignment of such rods on the anisotropy of its electrical conductivity. A continuous model was used. In this model, the rods have zero-width (i.e. infinite aspect ratio) and they may intersect each other. To involve both the low conductive host matrix, and highly conductive fillers (rods) in the consideration, a discretization algorithm based on the use of a supporting mesh was applied. The discretization is equivalent to the substitution of rods with the polyominoes. Once discretized, the Frank--Lobb algorithm was applied to evaluate the electrical conductivity. Our main findings are (i) the alignment of the rods essentially affects the electrical conductivity and its anisotropy, (ii)the discrete nature of computer simulations is crucial. For slightly disordered system, high electrical anisotropy was observed at small filler content, suggesting a method to enable the production of optically transparent and highly anisotropic conducting films.

cond-mat.stat-mech↗

arXiv2017

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

The vertical drying of a two dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different initial number concentrations (the numbers of sticks per unit area), $p_i$, and solvent evaporation rates, $u$. For completely dried films, the spatial distributions of the sticks, the order parameters and the electrical conductivities of the films in both the horizontal, $x$, and vertical, $y$, directions were examined. Significant evaporation-driven self-assembly and stratification of the sticks in the vertical direction was observed. The extent of stratification increased with increasing values of $u$. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of $p_i$ and $u$.

cond-mat.soft↗

arXiv2017

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

The diffusion-driven self-assembly of rod-like 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 $L\times L$ 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 ($k\geq 6$), 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.

cond-mat.stat-mech↗

arXiv2016

Monte Carlo Simulation of Evaporation Driven Self-Assembly in Suspension of Colloidal Rods

The vertical drying of a colloidal film containing rod-like 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, $p_i$, ($p_i \in [0, p_j]$, where $p_j$ is the jamming concentration), lengths of $k$-mers ($k \in [1, 12]$), 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 $u$.

cond-mat.stat-mech↗

arXiv2016

Electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice

The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear $k$-mers 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 continued until the saturation jamming limit, $p_j$. The isotropic and anisotropic 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$ -- $p_j$) of the $k$-mers. The `intrinsic electrical conductivity' and concentration dependence of the relative electrical conductivity $Σ(p)$ ($Σ=σ/ σ_m$ for the C-model and $Σ=σ_m /σ$ for the I-model, where $σ_m$ 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 $Σ_{xy}(p)$, $Σ_{x}(p)$ and $Σ_{y}(p)$. For the C-model, the other interesting findings are: for large values of $k$ ($k=64, 128$), the values of $Σ_{xy}$ and $Σ_{y}$ increase rapidly with the initial increase of $p$ from 0 to 0.1; for $k \geq 16$, all the $Σ_{xy}(p)$ and $Σ_{x}(p)$ curves intersect with each other at the same iso-conductivity points; 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 $σ_y/σ_x$ ($>1$).

cond-mat.stat-mech↗

arXiv2015

Percolation and jamming of linear $k$-mers on square lattice with defects: effect of anisotropy

We study the percolation and jamming of rods ($k$-mers) on a square lattice that contains defects. The point defects are placed randomly and uniformly on the substrate before deposition of the rods. The general case of unequal probabilities for orientation of depositing of rods along different directions of the lattice is analyzed. Two different models of deposition are used. In the relaxation random sequential adsorption model (RRSA), the deposition of rods is distributed over different sites on the substrate. In the single cluster relaxation model (RSC), the single cluster grows by the random accumulation of rods on the boundary of the cluster. For both models, a suppression of growth of the infinite cluster at some critical concentration of defects $d_c$ is observed. In the zero defect lattices, the jamming concentration $p_j$ (RRSA) and the density of single clusters $p_s$ (RSC) decrease with increasing length rods and with a decrease in the order parameter. For the RRSA model, the value of $d_c$ decreases for short rods as the value of $s$ increases. For longer rods, the value of $d_c$ is almost independent of $s$. Moreover, for short rods, the percolation threshold is almost insensitive to the defect concentration for all values of $s$. For the RSC model, the growth of clusters with ellipse-like shapes is observed for non-zero values of $s$. The density of the clusters $p_s$ at the critical concentration of defects $d_c$ depends in a complex manner on the values of $s$ and $k$. For disordered systems, the value of $p_s$ tends towards zero in the limits of the very long rods and very small critical concentrations $d_c \to 0$. In this case, the introduction of defects results in a suppression of rods stacking and in the formation of `empty' or loose clusters with very low density. On the other hand, denser clusters are formed for ordered systems.

cond-mat.stat-mech↗