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Materials 2015, 8(10), 6697-6718; doi:10.3390/ma8105334

Modeling Percolation in Polymer Nanocomposites by Stochastic Microstructuring

1
Escuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Campus Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L. 64849, Mexico
2
Centro de Estudios de Energía, Dpto. de Ing. Eléctrica, Tecnologico de Monterrey, Campus Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L. 64849, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Biqiong Chen
Received: 2 July 2015 / Revised: 20 September 2015 / Accepted: 23 September 2015 / Published: 30 September 2015
(This article belongs to the Special Issue Polymer Nanocomposites)

Abstract

A methodology was developed for the prediction of the electrical properties of carbon nanotube-polymer nanocomposites via Monte Carlo computational simulations. A two-dimensional microstructure that takes into account waviness, fiber length and diameter distributions is used as a representative volume element. Fiber interactions in the microstructure are identified and then modeled as an equivalent electrical circuit, assuming one-third metallic and two-thirds semiconductor nanotubes. Tunneling paths in the microstructure are also modeled as electrical resistors, and crossing fibers are accounted for by assuming a contact resistance associated with them. The equivalent resistor network is then converted into a set of linear equations using nodal voltage analysis, which is then solved by means of the Gauss–Jordan elimination method. Nodal voltages are obtained for the microstructure, from which the percolation probability, equivalent resistance and conductivity are calculated. Percolation probability curves and electrical conductivity values are compared to those found in the literature. View Full-Text
Keywords: carbon nanotubes; electrical properties; conductivity; percolation; Monte Carlo; nanocomposites; nodal voltage; simulations carbon nanotubes; electrical properties; conductivity; percolation; Monte Carlo; nanocomposites; nodal voltage; simulations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Soto, M.; Esteva, M.; Martínez-Romero, O.; Baez, J.; Elías-Zúñiga, A. Modeling Percolation in Polymer Nanocomposites by Stochastic Microstructuring. Materials 2015, 8, 6697-6718.

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