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The work describes the framework that allows performing a computer simulation of complex random networks of conducting nanotubes embedded in the dielectric medium. The representative volume element filled with a large number of interconnected nanotubes is modeled and the tunneling conduction mechanism between adjacent tubes is considered. The principal goal is to develop a computational approach for the three­dimensional multielement structure simulation, which will be relatively simple, yet capable of producing realistic results. The connectivity formation processes among nanotubes in random nanotube networks are studied using the elements of graph theory. All stages of the modeling process are discussed in details. The system conductivity model with taking into account the tunnel effect and intrinsic nanotube conductivities is formulated. The random resistor model is used to calculate the total equivalent conductivity of the network. The results of the computer experiments on electrical conductivity simulations for different systems are presented. The dependencies of the electrical conductivity of nanotube networks in the insulating medium on the concentration of nanotubes, geometric parameters and properties of tunneling conductivity between individual tubes are investigated. It is found that the percolation threshold corresponds to the nanotube loading of 0.5 % when the aspect ratio of nanotubes is 160. Non­linear dependence between the aspect ratio and the percolation threshold was established. The analysis of computational complexity and calculation time is performed for quad­core computing systems. Computer experiments carried out in a systematic fashion within the proposed framework can be useful when designing novel CNT­polymer composites for state of the art electronic applications. By following the predictions of the proposed model, tailoring of electrical properties of such composites can be made easier when adjusting the parameters of nanotubes and their concentration during the fabrication of the nanocomposite samples.

Modeling and quantitative analysis of connectivity and conductivity in random networks of nanotubes