We study the electrical conductivity of three-dimensional (3D) nanocomposite with incorporated random carbon nanotubes (CNT). Large length of the remote nanotubes generates a lot of intersections that induce rather small percolating threshold of the global conductivity in this medium. We simulate such a system by random cylinders placed in a percolating parallelepiped with the use of Monte Carlo method. Conductivity of such structure is associated with the critical phenomena, where the main transition parameter is dened by the value of the percolation threshold. We calculate the minimal percolating threshold and determine the functional form of the conductivity by the global optimization technique. Such an approach allows studying the details of the electrical conductivity in nanocomposites even at signicant level of the percolating fluctuations.
2. Berhan, L. and A. M. Sastry, "Modeling percolation in high-aspect-ratio fiber systems. I. Soft-core versus hard-core models," Phys. Rev. E, Vol. 75, 1-8, 2007.
3. Eletskii, A. V., A. A. Knizhnik, B. V. Potapkin, and J. M. Kenny, "Electrical characteristics of carbon nanotube-doped composites," Physics --- Uspekhi, Vol. 58, 225-270, 2015.
4. Foygel, M., R. D. Morris, D. Anez, S. French, and V. L. Sobolev, "Theoretical and computational studies of carbon nanotube composites and suspensions:Electrical and thermal conductivity," Phys. Rev. B, Vol. 71, 104201.1-104201.8, 2005.
5. Ma, H. M. and X.-L. Gao, "A three-dimensional Monte Carlo model for electrically conductive polymer matrix composites filled with curved fibers," Polymer, Vol. 49, 4230-4238, 2008.
6. Gu, H., J. Wang, and C. Yu, "Three-dimensional modeling of percolation behavior of electrical conductivity in segregated network polymer nanocomposites using Monte Carlo method," Advances in Materials, Vol. 5, 1-8, 2016.
7. Lin, K. C., D. Lee, L. An, and H. J. Young, "Finite-size scaling features of electric conductivity percolation in nanocomposites," Nanoscience and Nanoengineering, Vol. 1, 15-22, 2013.
8. Ning, H., M. Zen, Y. Cheng, and Y. Go, "The electrical properties of polymernanocomposites with carbon nanotubefillers," Nanotechnology, Vol. 19, 215701, 2008.
9. Sagalianov, I., L. Vovchenko, L. Matzui, and O. Lazarenko, "Synergistic enhancement of the percolation threshold in hybrid polymeric nanocomposites based on carbon nanotubes and graphite nanoplatelets," Nanoscale Research Letters, Vol. 12, No. 140, 2017.
10. Wang, X., Q. Li, J. Xie, Z. Jin, J. Wang, and Y. Li, "Fabrication of ultralong and electrically uniform single-walled carbon nanotubes on clean substrates," Nano Lett., Vol. 9, 3137-3141, 2009.
11. Attiya, A. M., "Lower frequency limit of carbon nanotube antenna," Progress In Electromagnetics Research, Vol. 94, 419-433, 2009.
12. Aidi, M. and T. Aguili, "Electromagnetic modeling of coupled carbon nanotube dipole antennas based on integral equations system," Progress In Electromagnetics Research M, Vol. 40, 179-183, 2014.
13. Mikki, S. M. and A. A. Kishk, "Derivation of the carbon nanotube susceptibility tensor using lattice dynamics formalism," Progress In Electromagnetics Research B, Vol. 9, 1-26, 2008.
14. Bychanok, D., G. Gorokhov, D. Meisak, P. Kuzhir, S. A. Maksimenko, Y. Wang, Z. Han, X. Gao, and H. Yue, "Design of carbon nanotube-based broadband radar absorber for ka-band frequency range," Progress In Electromagnetics Research M, Vol. 53, 9-16, 2017.
15. Dai, Q., H. Butt, R. Rajasekharan, T. D. Wilkinson, and G. A. J. Amaratunga, "Fabrication of carbon nanotubes on inter-digitated metal electrode for switchable nanophotonic devices," Progress In Electromagnetics Research, Vol. 127, 65-77, 2012.
16. Savi, P., M. Yasir, M. Giorcelli, and A. Tagliaferro, "The effect of carbon nanotubes concentration on complex permittivity of nanocomposites," Progress In Electromagnetics Research M, Vol. 55, 203-209, 2017.
17. Grimmett, G., Percolation and Disordered Systems, Springer-Verlag, Berlin, 1997.
18. Hesselbo, B. and R. B. Stinchcombe, "Monte Carlo simulation and global optimization without parameters," Phys. Rev. Lett., Vol. 74, 2151-2155, 1995.
19. Lagarias, J. C., J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the nelder-mead simplex method in low dimensions," SIAM Journal of Optimization, Vol. 9, 112-147, 1998.
20. Press, W. H., S. A. Teukovsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++, Cambridge University Press, Cambridge, 2002.
21. McCaffrey, J. D., "Amoeba method optimization using C#," Microsofts MSDN Magazine, Vol. 28, No. 6, 2013, Availabe at: https://msdn.microsoft.com/en-us/magazine/dn201752.aspx.