Abstract
A radically new percolation model for describing the extremal dependence of the degree of reinforcement of polymer/carbon nanotube nanocomposites on the nanofiller content has been proposed. It has been shown that, for this nanofiller, the percolation threshold almost coincides with the aggregation threshold on the concentration scale. From the structural point of view, the extremum of this dependence is caused by the change in the type of the reinforcing component (from interphase regions to the skeleton of carbon nanotubes). From the mathematical point of view, the behavior of the degree of reinforcement is described by the general percolation relationship with replacement of the critical exponents near the percolation threshold. Neither the functionalization of the nanofiller nor the preliminary ultrasound treatment qualitatively change the dependence under study.
Similar content being viewed by others
References
D. Blond, V. Barron, M. Ruether, K. P. Ryan, V. Nicolosi, W. J. Blau, and J. N. Coleman, Adv. Funct. Mater. 16, 1608 (2006).
B. A. Komarov, E. A. Dzhavadyan, V. I. Irzhak, A. G. Ryabenko, V. A. Lesnichaya, G. I. Zvereva, and A. V. Krestinin, Polym. Sci., Ser. A 53 (6), 502 (2011).
Ya. I. Estrin, E. R. Badamshina, A. A. Grishchuk, G. S. Kulagina, V. A. Lesnichaya, Yu. A. Ol’khov, A. G. Ryabenko, and S. N. Sul’yanov, Polym. Sci., Ser. A 54 (4), 290 (2012).
A. N. Bobryshev, V. N. Kozomazov, L. O. Babin, and V. I. Solomatov, Synergetics of Composite Materials (ORIUS, Lipetsk, 1994) [in Russian].
G. V. Kozlov, M. A. Gazaev, V. U. Novikov, and A. K. Mikitaev, Tech. Phys. Lett. 22 (8), 657 (1996).
D. W. Schaefer and R. S. Justice, Macromolecules 40, 8501 (2007).
G. V. Kozlov, Yu. G. Yanovsky, and G. E. Zaikov, Synergetics and Fractal Analysis of Polymer Composites Filled with Short Fibers (Nova Science, New York, 2011).
C. Zhao, G. Hu, R. S. Justice, D. W. Schaefer, S. Zhang, M. Yang, and C. C. Han, Polymer 46, 5125 (2005).
A. K. Mikitaev, G. V. Kozlov, and G. E. Zaikov, Polymer Nanocomposites: The Variety of Structural Forms and Applications (Nauka, Moscow, 2009) [in Russian].
A. L. Svistkov, L. A. Komar, G. Heinrich, and B. Lauke, Polym. Sci., Ser. A 50 (5), 600 (2008).
J. Feder, Fractals (Plenum, New York, 1988; Mir, Moscow, 1991).
B. I. Shklovskii and A. L. Efros, Sov. Phys.—sp. 18 (11), 845 (1975).
M. Foygel, R. D. Morris, D. Anez, S. French, and V. L. Sobolev, Phys. Rev. B: Condens. Matter 71 (10), 104201 (2005).
G. V. Kozlov, Yu. G. Yanovskii, Z. M. Zhirikova, V. Z. Aloev, and Yu. N. Karnet, Mekh. Kompoz. Mater. Konstr. 18, 131 (2012).
B. Bridge, J. Mater. Sci. Lett. 8, 102 (1989).
V. A. Smirnov, E. V. Korolev, and A. I. Al’bakasov, Nanotekhnol. Stroit., No. 4, 17 (2011).
G. V. Kozlov, Z. M. Zhirikova, V. Z. Aloev, and G. E. Zaikov, Chem. Chem. Technol. 8 (1), 57 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.K. Mikitaev, G.V. Kozlov, 2015, published in Fizika Tverdogo Tela, 2015, Vol. 57, No. 5, pp. 961–964.
Rights and permissions
About this article
Cite this article
Mikitaev, A.K., Kozlov, G.V. Description of the degree of reinforcement of polymer/carbon nanotube nanocomposites in the framework of percolation models. Phys. Solid State 57, 974–977 (2015). https://doi.org/10.1134/S1063783415050224
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063783415050224