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Irina V. Vodolazskaya

Publications and source records attributed to Irina V. Vodolazskaya.

At least 19 recordsLinked to original sources
arXiv2026

Electrical conductivity of crack-template-based transparent conducting films: mean-field approximation, effective-medium theory, and simulation

In this work, crack-template-based transparent conducting films were modeled as networks corresponding to the edges of a two-dimensional Poisson--Voronoi diagram. Two types of networks were considered: the original one, in which the conductance of each edge was inversely proportional to its length, and the effective one, in which all edges had the same conductance obtained from the effective-medium theory. The mean-field approximation was used for analytical evaluation of the electrical conductivity. Direct numerical calculations for the Poisson--Voronoi diagram showed that the mean-field approximation overestimated the effective conductivity of the original network by approximately 13\%, and of the effective network by 79\%. In addition, a honeycomb network with an edge conductance distribution corresponding to the Poisson--Voronoi diagram was studied: for it, the predictions of the effective-medium theory turned out to be more accurate than for the Poisson--Voronoi diagram, which was explained by the greater structural homogeneity of the periodic honeycomb lattice. The results indicate that, when modeling crack-template-based transparent conducting films, the application of the mean-field approximation may lead to significant errors if the resistance of individual conductors is not simply proportional to their length. This possibility is discussed as a motivation for future studies of hierarchical cracks with variable width, which are not directly investigated here.

cond-mat.dis-nn↗
arXiv2025

Electrical conductivity of randomly placed linear wires: a mean field approach

Using the mean-field approximation, a formula for the effective electrical conductivity of a two-dimensional system of randomly arranged conducting sticks with a given orientation distribution was obtained. Both the resistance of the sticks themselves and the resistance of the contacts between them were taken into account. The accuracy in the resulting formula was analyzed. A comparison of the theoretical predictions of mean-field approach with the results of direct electrical conductivity calculations for several model orientation distributions describing systems with crossed sticks demonstrated good agreement. Our study showed that cross-alignment of nanowires should lead to a decreasing in the electrical conductivity compared to electrodes with isotropically arranged nanowires. We suppose that the widely used model with zero-width sticks is quite acceptable for systems of cross-aligned nanowires, but overestimates their connectivity in isotropic systems. Thus, the enhancement of the electrical conductivity of conducting films with cross-aligned nanowires may be due to a significant difference in the network topology.

cond-mat.stat-mech↗
arXiv2025

Simulation of the thermocapillary assembly of a colloidal cluster during the evaporation of a liquid film in an unevenly heated cell

The control of the thermocapillary assembly of colloidal particle clusters is important for a variety of applications, including the creation of photonic crystals for microelectronics and optoelectronics, membrane formation for biotechnology, and surface cleaning for laboratory-on-chip devices. It is important to understand the main mechanisms that influence the formation of such clusters. This article considers a two-dimensional mathematical model describing the transfer of particles by a thermocapillary flow in an unevenly heated cell during the evaporation of a liquid. This gave us the opportunity to study one of the main processes that triggers the formation of a particle cluster. Whether the particle will move with the flow or stop at the heater, becoming the basis for the cluster, is determined by the ratio between gravity and the drag force. The results of numerical calculations show that, for small particle concentrations, their fraction entering the cluster decreases as the volumetric heat flux density $Q$ increases. The reason for this is an increase in the thermocapillary flow with an increase in the volumetric heat flux $Q$. It reduces the probability of particles entering the cluster.

cond-mat.soft↗
arXiv2025

Simulation of charged nanotubes self-assembly during evaporation of a sessile droplet on a substrate

The ability to control the morphology of the nanotube deposit formed during the evaporation of a sessile droplet on a substrate is of theoretical and practical interest. Such deposits are required for various applications including nanotechnology, medicine, biotechnology, and optronics. In the experiment of Zhao et al. [J. Colloid Interface Sci. 440, 68 (2015)], an annular deposit was formed near the contact line. The deposition geometry is caused by the coffee ring effect. This deposit is unusual in its morphology. It changes gradually in space from a disordered structure in the inner part of the ring to an aligned structure of nanotubes close to the periphery. To understand the mechanisms that lead to this, we have developed a mathematical model that takes into account the effects of advection, diffusion, and electrostatic interactions on particle transport. Results of numerical calculations have confirmed that all these factors together have an influence on the formation of such a variable morphology. Qualitative agreement with the experiment is shown for some values of the model parameters.

cond-mat.soft↗
arXiv2025

Effective medium theory for the electrical conductivity of random metallic nanowire networks

Interest in studying the conductive properties of networks made from randomly distributed nanowires is due to their numerous technological applications. Although the sheet resistance of such networks can be calculated directly, the calculations require many characteristics of the system (distributions of lengths, diameters and resistances of nanowires, distribution of junction resistance), the measurement of which is difficult. Furthermore, such calculations can hardly offer an analytical dependence of the sheet resistance on the basic physical parameters of the systems under consideration. Although various theoretical approaches offer such analytical dependencies, they are often based on more or less reasonable assumptions rather than rigorously proven statements. Here, we offer an approach based on Foster's theorem to reveal a dependence of the sheet resistance of dense nanowire networks on the main parameters of such networks. This theorem offers an additional perspective on the effective medium theory and extends our insight. Since the application of Foster's theorem is particularly effective for regular random resistor networks, we propose a method for regularizing resistor networks corresponding to random nanowire networks. We found an analytical dependence of the effective electrical conductivity on the main parameters of the nanowire network (reduced number density of nanowires, nanowire resistance, and resistance of contacts between nanowires).

cond-mat.dis-nn↗
arXiv2025

Phenomenological model of crack patterns in thin colloidal films undergoing desiccation

A number of geometric and topological properties of samples of crack-template based conductive films are examined to assess the degree to which Voronoi diagrams can successfully model structure and conductivity in such networks. Our analysis suggests that although Poisson--Voronoi diagrams are only partially successful in modeling structural features of real-world crack patterns formed in films undergoing desiccation, such diagrams can nevertheless be useful in situations where topological characteristics are more important than geometric ones. A phenomenological model is proposed that is more accurate at capturing features of the real-world crack patterns.

cond-mat.dis-nn↗
arXiv2025

Electrical conductivity of conductive films based on random metallic nanowire networks

Using computer simulation, we investigated the dependence of the electrical conductivity of random two-dimensional systems of straight nanowires on the main parameters. Both the resistance of the conductors and the resistance of the contacts between them were taken into account. The dependence of the resistance, $R$, between network nodes on the distance between nodes, $r$, is $R(r) = R_\Box/π\ln r + \mathrm{const}$, where $R_\Box$ is the sheet resistance.

cond-mat.dis-nn↗
arXiv2024

Effective medium theory for the electrical conductance of random resistor networks which mimic crack-template-based transparent conductive films

We studied random resistor networks produced with regular structure and random distribution of edge conductances. These networks are intended to mimic crack-template-based transparent conductive films as well some random networks produced using nano-imprinting technology. Applying an effective medium theory, we found out that the electrical conductance of such networks is $\approx 0.5852 \sqrt{n_E}$, where $n_E$ is the number density of conductive edges. This dependence is in agreement with numerical calculations in Voronoi networks, although the effective conductances are approximately 15\% larger.

cond-mat.dis-nn↗
arXiv2023

Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation

We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean space. Such RRNs are isotropic and in average homogeneous, however, local fluctuations of the number of edges per unit area are inevitably. These RRNs may mimic, e.g., crack-template-based transparent conductive films. The RRNs were treated within a mean-field approach (MFA). We found an analytical dependency of the effective electrical conductivity on the number of conductive edges (resistors) per unit area, $n_\text{E}$. The effective electrical conductivity is proportional to $\sqrt{n_\text{E}}$ when $n_\text{E} \gg 1$.

cond-mat.dis-nn↗
arXiv2023

Electrical conductivity of crack-template-based transparent conductive films: A computational point of view

Crack-template-based transparent conductive films (TCFs) are promising kinds of junction-free, metallic network electrodes that can be used, e.g., for transparent electromagnetic interference (EMI) shielding. Using image processing of published photos of TCFs, we have analyzed the topological and geometrical properties of such crack templates. Additionally, we analyzed the topological and geometrical properties of some computer-generated networks. We computed the electrical conductance of such networks against the number density of their cracks. Comparison of these computations with predictions of the two analytical approaches revealed the proportionality of the electrical conductance to the square root of the number density of the cracks was found, this being consistent with the theoretical predictions.

cond-mat.dis-nn↗
arXiv2023

Percolation and electrical conduction in random systems of curved linear objects on a plane: computer simulations along with a mean-field approach

Using computer simulations, we have studied the percolation and the electrical conductance of two-dimensional, random percolating networks of curved, zero-width metallic nanowires. We mimicked the curved nanowires using circular arcs. The percolation threshold decreased as the aspect ratio of the arcs increased. Comparison with published data on the percolation threshold of symmetric quadratic Bézier curves suggests that, when the percolation of slightly curved wires is simulated, the particular choice of curve to mimic the shape of real-world wires is of little importance. Considering the electrical properties, we took into account both the nanowire resistance per unit length and the junction (nanowire/nanowire contact) resistance. Using a mean-field approximation (MFA), we derived the total electrical conductance of the nanowire-based networks as a function of their geometrical and physical parameters. The MFA predictions have been confirmed by our Monte Carlo numerical simulations. For our random homogeneous and isotropic systems of conductive curved wires, the electric conductance decreased as the wire shape changed from a stick to a ring when the wire length remained fixed.

cond-mat.stat-mech↗
arXiv2022

Random 2D nanowire networks: Finite-size effect and the effect of busbar/nanowire contact resistance on their electrical conductivity

We have studied the resistance of two-dimensional random percolating networks of zero-width metallic nanowires (rings or sticks). We toke into account the nanowire resistance per unit length, the junction (nanowire/nanowire contact) resistance, and the busbar/nanowire contact resistance. Using a mean-field approximation (MFA), we derived the total resistance of the nanoring-based networks as a function of their geometrical and physical parameters. We have proposed a way of accounting for the contribution of the busbar/nanowire contact resistance toward the network resistance. The MFA predictions have been confirmed by our Monte Carlo (MC) numerical simulations. Our study evidenced that the busbar/nanowire contact resistance has a significant effect on the electrical conductivity when the junction resistance dominates over wire resistance.

cond-mat.stat-mech↗
arXiv2022

Electrical conductivity of random metallic nanowire networks: An analytical consideration along with computer simulation

We have proposed an analytical model for the electrical conductivity in random, metallic, nanowire networks. We have mimicked such random nanowire networks as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We studied the electrical conductivity of these RRNs using a mean-field approximation. An analytical dependency of the electrical conductivity on the main physical parameters (the number density and electrical resistances of these wires and of the junctions between them) has been derived. Computer simulations have been performed to validate our theoretical predictions. We computed the electrical conductivity of the RRNs against the number density of the conductive fillers for the junction-resistance-dominated case and for the case where the wire resistance and the junction resistance were equal. The results of the computations were compared with this mean-field approximation. Our computations demonstrated that our analytical expression correctly predicts the electrical conductivity across a wide range of number densities.

cond-mat.stat-mech↗
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↗
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

Circles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes

We consider $N$ circles of equal radii, $r$, having their centers randomly placed within a square domain $\mathcal{D}$ of size $L \times L$ with periodic boundary conditions ($\mathcal{D} \in \mathbb{R}^2$). When two or more circles intersect each other, each circle is divided by the intersection points into several arcs. We found the exact length distribution of the arcs. In the limiting case of dense systems and large size of the domain $\mathcal{D}$ ($L \to \infty$ in such a way that the number of circle per unit area, $n=N/L^2$, is constant), the arc distribution approaches the probability density function (PDF) $f(ψ) = 4 n r^2\exp(-4 n r^2 ψ)$, where $ψ$ is the central angle subtended by the arc. This PDF is then used to estimate the sheet resistance of transparent electrodes based on conductive rings randomly placed onto a transparent insulating film.

cond-mat.stat-mech↗