arXiv subjects

Andrei V. Eserkepov

Publications and source records attributed to Andrei V. Eserkepov.

35 records · Page 2Linked to original sources

arXiv2021

Electrical conductivity of nanoring-based transparent conductive films: A mean-field approach

We have studied the electrical conductivity of nanoring-based, transparent conductive films, these being promising elements for flexible electronic devices. Both the wire resistance and the junction resistance were taken into account. We have calculated the dependency of the electrical conductivity on the number density of the rings. We have proposed a mean-field approach to estimate the dependency of the electrical conductivity on the main parameters. Comparison of direct computations of the electrical conductivity and the estimates provided by the mean-field approach evidenced the applicability of this approach for those cases where the wire resistance dominates over the junction resistance and where both resistances are of the same order. For these two cases, both the direct computations and the mean-field approach evidenced a linear dependence of the electrical conductivity of the films on the number density of the conductive rings. By contrast, the dependence of the electrical conductivity on the number density of the conductive rings is a quadratic when the junction resistance dominates over the wire resistance. In this case, the mean-field approach significantly overestimates the electrical conductivity, since the main assumptions underlying this approach are no longer fulfilled.

cond-mat.stat-mech↗

arXiv2021

Electrical conductivity of nanorod-based transparent electrodes: Comparison of mean-field approaches

We mimic nanorod-based transparent electrodes as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We suppose that the number density (the number of objects per unit area of the surface) of these sticks exceeds the percolation threshold, i.e., the system under consideration is a conductor. We computed the electrical conductivity of random resistor networks vs the number density of conductive fillers for the wire-resistance-dominated case, for the junction-resistance-dominated case, and for an intermediate case. We also offer a consistent continuous variant of the mean-field approach. The results of the RRN computations were compared with this mean-field approach. Our computations suggest that, for a qualitative description of the behavior of the electrical conductivity in relation to the number density of conductive wires, the mean-field approximation can be successfully applied when the number density of the fillers $n > 2n_c$, where $n_c$ is the percolation threshold. However, note the mean-field approach slightly overestimates the electrical conductivity. We demonstrate that this overestimate is caused by the junction potential distribution.

cond-mat.dis-nn↗

arXiv2021

Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm

We mimic random nanowire networks by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. The number density (the number of objects per unit area of the surface) of these sticks is supposed to exceed the percolation threshold, i.e., the system under consideration is a conductor. To identify any current-carrying part (the backbone) of the percolation cluster, we have proposed and implemented a modification of the well-known wall follower algorithm -- one type of maze solving algorithm. The advantage of the modified algorithm is its identification of the whole backbone without visiting all the edges. The complexity of the algorithm depends significantly on the structure of the graph and varies from $O\left(\sqrt{N_\text{V}}\right)$ to $Θ(N_\text{V})$. The algorithm has been applied to backbone identification in networks with different number densities of conducting sticks. We have found that (i) for number densities of sticks above the percolation threshold, the strength of the percolation cluster quickly approaches unity as the number density of the sticks increases; (ii) simultaneously, the percolation cluster becomes identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of degree 1. This behavior is consistent with the presented analytical evaluations.

cond-mat.stat-mech↗

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

Identification of a current-carrying subset of a percolation cluster using a modified wall follower algorithm

We have proposed and implemented a modification of the well-known wall follower algorithm to identify a backbone (a current-carrying part) of the percolation cluster. The advantage of the modified algorithm is identification of the whole backbone without visiting all edges. The algorithm has been applied to backbone identification in networks produced by random deposition of conductive sticks onto an insulating substrate. We have found that (i) for concentrations of sticks above the percolation threshold, the strength of the percolating cluster quickly approaches unity; (ii) simultaneously, the percolation cluster is identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of unit degree.

cond-mat.dis-nn↗

arXiv2020

Characterization of domain formation during random sequential adsorption of stiff linear $k$-mers onto a square lattice

Using computer simulation, we have studied the random sequential adsorption of stiff linear $k$-mers onto a square lattice. Each such particle occupies $k$ adjacent lattice sites. During deposition, the two mutually perpendicular orientations of the particles are equiprobable, hence, a macroscopically isotropic monolayer is formed. However, this monolayer is locally anisotropic, since the deposited particles tend to form domains of particles with the same orientation. Using the "excluded area" concept, we have classified lattice sites into several types and examined how the fraction of each type of lattice site varies as the number of deposited particles increases. The behaviors of these quantities have allowed us to identify the following stages of domain formation (i) the emergence of domain seeds; (ii) the filling of domains; (iii) densification of the domains.

cond-mat.stat-mech↗

arXiv2019

Percolation thresholds for discorectangles: numerical estimation for a range of aspect ratios

Using Monte Carlo simulation, we have studied the percolation of discorectangles. Also known as stadiums or two-dimensional spherocylinders, a discorectangle is a rectangle with semicircles at a pair of opposite sides. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits. We found: (i) for the two marginal aspect ratios $\varepsilon = 1$ (disc) and $\varepsilon \to \infty$ (stick) the percolation thresholds coincide with known values within the statistical error; (ii) for intermediate values of $\varepsilon$ the percolation threshold lies between the percolation thresholds for ellipses and rectangles and approaches the latter as the aspect ratio increases.

cond-mat.dis-nn↗

arXiv2019

Effect of tunneling on the electrical conductivity of nanowire-based films: computer simulation within a core--shell model

We have studied the electrical conductivity of two-dimensional nanowire networks. An analytical evaluation of the contribution of tunneling to their electrical conductivity suggests that it is proportional to the square of the wire concentration. Using computer simulation, three kinds of resistance were taken into account, viz., (i) the resistance of the wires, (ii) the wire---wire junction resistance, and (iii) the tunnel resistance between wires. We found that the percolation threshold decreased due to tunneling. However, tunneling had negligible effect on the electrical conductance of dense nanowire networks.

cond-mat.mes-hall↗

arXiv2019

Transparent electrodes with nanorings: a computational point of view

Four samples of transparent conductive films with different numbers of silver nanorings per unit area were produced. The sheet resistance, transparency, and haze were measured for each sample. Using Monte Carlo simulation, we studied the electrical conductivity of random resistor networks produced by the random deposition of the conducting rings onto the substrate. Both systems of equal-sized rings, and systems with rings of different sizes were simulated. Our simulations demonstrated the linear dependence of the electrical conductivity on the number of rings per unit area. Size dispersity decreased the percolation threshold, but without having any other significant effect on the behavior of the electrical conductance. Analytical estimations obtained for dense systems of equal-sized conductive rings were consistent with the simulations.

cond-mat.stat-mech↗

arXiv2019

Electrical conductance of two-dimensional composites with embedded rodlike fillers: an analytical consideration and comparison of two computational approaches

Using Monte Carlo simulation, we studied the electrical conductance of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rodlike fillers (rods). The rods were of various lengths, obeying a log-normal distribution. They were allowed to be aligned along a given direction. The impacts of length dispersity and the extent of rod alignment on the insulator-to-conductor phase transition were studied. Two alternative computational approaches were compared. Within Model I, the films were transformed into resistor networks with regular structures and randomly distributed conductances. Within Model II, the films were transformed into resistor networks with irregular structures but with equal conductivities of the conductors. Comparison of the models evidenced similar behavior in both models when the concentration of fillers exceeded the percolation threshold. Some analytical results were obtained: (i) the relationship between the number of fillers per unit area and the transmittance of the film within Model I, (ii) the electrical conductance of the film for dense networks within Model II.

cond-mat.soft↗

arXiv2018

Percolation of sticks: effect of stick alignment and length dispersity

Using Monte Carlo simulation, we studied the percolation of sticks, i.e. zero-width rods, on a plane paying special attention to the effects of stick alignment and their length dispersity. The stick lengths were distributed in accordance with log-normal distributions, providing a constant mean length with different widths of distribution. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits for all values of the parameters. Greater alignment of the sticks led to increases in the percolation threshold while an increase in length dispersity decreased the percolation threshold. A fitting formula has been proposed for the dependency of the percolation threshold both on stick alignment and on length dispersity.

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

Monte Carlo simulation of entropy-driven pattern formation in two-dimensional system of rectangular particles

We simulated random walk of rectangular particles on a square lattice with periodic boundary conditions. Two kind of particles were investigated, viz., so-called `blind' and `myopic' particles. We found that steady state patterns occurred only for some values of the ratio $L_x/L_y$ where $L_x$ and $Ly$ are the linear sizes of the system and only for `needles', i.e., the particles of size $1 \times k$. Different patterns were observed for `blind' and `myopic' particles.

cond-mat.stat-mech↗

arXiv2018

Characterisation of diffusion-driven self-organisation of rodlike particles by means of entropy of generalised two-dimensional words

The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random walk of rectangular particles in a discrete two-dimensional space can lead to their self-organisation. We propose a technique for calculating the entropy characteristics of a two-dimensional system in a discrete two-dimensional space consisting of rectangular particles of two mutually perpendicular orientations, and a change in these characteristics for a random walk of particles is investigated.

cond-mat.stat-mech↗

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

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↗