Simulation of the Electrical Conductivity in Systems of Carbon Nanotubes
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tion of the Electrical Conductivity in Systems of Carbon Nanotubes P. A. Likhomanovaa, * and K. Yu. Khromova aNational
Resarch Center “Kurchatov Institute,” Moscow, 123182 Russia *e-mail: [email protected]
Received January 20, 2020; revised February 17, 2020; accepted February 19, 2020
Abstract—A simple and efficient method for calculating the conductivity of systems of carbon nanotubes forming a random resistor circuit in the case where the percolation threshold is reached in the system is proposed in this paper. This method uses the recursive removal of the dead-end branches of a cluster, which is necessary to determine the elements of the percolation cluster participating in the system’s conductivity. The calculated conductivities presented in this paper are obtained using Monte Carlo simulation. In the future, the developed method can be used to calculate the conductivity of polymer–carbon nanocomposites. Keywords: conductivity, carbon nanotubes, polymers, Monte Carlo simulation, percolation cluster, Kirchhoff’s law, nanocomposite materials DOI: 10.1134/S102745102005033X
INTRODUCTION Polymer materials have unique properties that are attractive for applications; they include small weights, high strength, ability to resist aggressive chemical media, and the simplicity of processing. However, polymers are predominantly insulators. If the conductivities of traditional polymers could be increased significantly in some way, this would offer great prospects for the use of such materials in many new spheres, where their application is still limited. Such spheres include the production of organic photocells, photodiodes, and chemical and biological sensors [1]. Over the last three decades, after the development of reliable methods for producing carbon nanoobjects, such as carbon nanotubes and carbon graphene-like nanoflakes, the efforts of researchers have been concentrated on obtaining conducting polymer-based nanocomposites by means of the dispersion of carbon fillers. The conductivity of polymer—carbon nanocomposites depends on many factors, including the type of polymer, the filler density, the technique for preparing the nanocomposites, and the type and geometry of the intersection of carbon nanotubes (CNTs). The dependence on a large number of parameters leads to the fact that the nanocomposite conductivity varies within very large limits [2]. Under these conditions, experimental studies aimed at searching for nanocomposites with optimal properties can be very time consuming and expensive, and, consequently, the importance of
quantitative and predictive simulation of the characteristics of the nanocomposite increases. Simulating the conductivities of carbon nanocomposites is a multiscale problem which includes determination of the spatial position of the polymer near the nanoobject contacts, calculation of the contact resistance of the intersections of nanoobjects filled with polymers, solution of the percolation problem, and calculation of the composite conductivity. In this paper, we concentrate on study
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