The AC and DC Conductivity of Nanocomposites

McLachlan, David S.; Sauti, Godfrey

doi:https://doi.org/10.1155/2007/30389

Journal of Nanomaterials

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Modeling and Characterization of the Interaction of Electromagnetic Wave with Nanocomposites and Nanostructured Materials

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Volume 2007 | Article ID 030389 | https://doi.org/10.1155/2007/30389

The AC and DC Conductivity of Nanocomposites

David S. McLachlan^1,2and Godfrey Sauti^1,3

Academic Editor: Christian Brosseau

Received25 Apr 2007

Accepted09 Aug 2007

Published29 Nov 2007

Abstract

The microstructures of binary (conductor-insulator) composites, containing nanoparticles, will usually have one of two basic structures. The first is the matrix structure where the nanoparticles (granules) are embedded in and always coated by the matrix material and there are no particle-particle contacts. The AC and DC conductivity of this microstructure is usually described by the Maxwell-Wagner/Hashin-Shtrikman or Bricklayer model. The second is a percolation structure, which can be thought to be made up by randomly packing the two types of granules (not necessarily the same size) together. In percolation systems, there exits a critical volume fraction below which the electrical properties are dominated by the insulating component and above which the conducting component dominates. Such percolation systems are best analyzed using the two-exponent phenomenological percolation equation (TEPPE). This paper discusses all of the above and addresses the problem of how to distinguish among the microstructures using electrical measurements.

References

Z. Hashin and S. Shtrikman, “A variational approach to the theory of the effective magnetic permeability of multiphase materials,” Journal of Applied Physics, vol. 33, no. 10, pp. 3125–3131, 1962.
View at: Publisher Site | Google Scholar
D. S. McLachlan, M. Blaszkiewicz, and R. E. Newnham, “Electrical resistivity of composites,” Journal of the American Ceramic Society, vol. 73, no. 8, pp. 2187–2203, 1990.
View at: Publisher Site | Google Scholar
M. Campo, L. Woo, T. Mason, and E. Garboczi, “Frequency-dependent electrical mixing law behavior in spherical particle composites,” Journal of Electroceramics, vol. 9, no. 1, pp. 49–56, 2002.
View at: Publisher Site | Google Scholar
J.-H. Hwang, D. S. Mclachlan, and T. O. Mason, “Brick layer model analysis of nanoscale-to-microscale cerium dioxide,” Journal of Electroceramics, vol. 3, no. 1, pp. 7–16, 1999.
View at: Publisher Site | Google Scholar
D. S. McLachlan, C. Chiteme, W. D. Heiss, and J. Wu, “The correct modelling of the second order terms of the complex AC conductivity results for continuum percolation media, using a single phenomenological equation,” Physica B, vol. 338, no. 1–4, pp. 256–260, 2003.
View at: Publisher Site | Google Scholar
D. S. McLachlan, C. Chiteme, W. D. Heiss, and J. Wu, “Fitting the DC conductivity and first order AC conductivity results for continuum percolation media, using percolation theory and a single phenomenological equation,” Physica B, vol. 338, no. 1–4, pp. 261–265, 2003.
View at: Publisher Site | Google Scholar
J. Wu and D. S. McLachlan, “Percolation exponents and thresholds obtained from the nearly ideal continuum percolation system graphite-boron nitride,” Physical Review B, vol. 56, no. 3, pp. 1236–1248, 1997.
View at: Google Scholar
J. Wu and D. S. McLachlan, “Scaling behaviour of the complex conductivity of graphite-boron nitride systems,” Journal of Physical Review B, vol. 58, no. 22, pp. 14880–14887, 1998.
View at: Publisher Site | Google Scholar
D. S. McLachlan and M. B. Heaney, “Complex ac conductivity of a carbon black composite as a function of frequency, composition, and temperature,” Physical Review B, vol. 60, no. 18, pp. 12746–12751, 1999.
View at: Publisher Site | Google Scholar
D. S. McLachlan, W. D. Heiss, C. Chiteme, and J. Wu, “Analytic scaling functions applicable to dispersion measurements in percolative metal-insulator systems,” Physical Review B, vol. 58, no. 20, pp. 13558–13564, 1998.
View at: Publisher Site | Google Scholar
W. D. Heiss, D. S. McLachlan, and C. Chiteme, “Higher-order effects in the dielectric constant of percolative metal-insulator systems above the critical point,” Physical Review B, vol. 62, no. 7, pp. 4196–4199, 2000.
View at: Publisher Site | Google Scholar
C. Chiteme and D. S. McLachlan, “AC and DC conductivity, magnetoresistance, and scaling in cellular percolation systems,” Physical Review B, vol. 67, no. 2, Article ID 024206, 18 pages, 2003.
View at: Publisher Site | Google Scholar
D. S. McLachlan, G. Sauti, and C. Chiteme, “Static dielectric function and scaling of the ac conductivity for universal and nonuniversal percolation systems,” Physical Review B, vol. 76, no. 1, Article ID 014201, 13 pages, 2007.
View at: Publisher Site | Google Scholar
I. J. Youngs, Electrical percolation and the design of functional electromagnetic materials, M.S. thesis, Electronic and Electrical Engineering, University College, London, UK, 2001.
I. J. Youngs, “Exploring the universal nature of electrical percolation exponents by genetic algorithm fitting with general effective medium theory,” Journal of Physics D, vol. 35, no. 23, pp. 3127–3137, 2002.
View at: Publisher Site | Google Scholar
C. Chiteme, D. S. McLachlan, and G. Sauti, “AC and DC percolative conductivity of magnetite-cellulose acetate composites,” Physical Review B, vol. 75, no. 9, Article ID 094202, 13 pages, 2007.
View at: Publisher Site | Google Scholar
C. Brosseau, “Generalized effective medium theory and dielectric relaxation in particle-filled polymeric resins,” Journal of Applied Physics, vol. 91, no. 5, pp. 3197–3204, 2002.
View at: Publisher Site | Google Scholar
J. P. Clerc, G. Giraud, J. M. Laugier, and J. M. Luck, “The electrical conductivity of binary disordered systems, percolation clusters, fractals and related models,” Advances in Physics, vol. 39, no. 3, pp. 191–309, 1990.
View at: Publisher Site | Google Scholar
D. J. Bergman and D. Stroud, “The physical properties of macroscopically inhomogeneous media,” Solid State Physics, vol. 46, pp. 148–270, 1992.
View at: Google Scholar
C.-W. Nan, “Physics of inhomogeneous inorganic materials,” Progress in Materials Science, vol. 37, pp. 1–116, 1993.
View at: Publisher Site | Google Scholar
D. S. Mclachlan, “Analytical functions for the DC and AC conductivity of conductor-insulator composites,” Journal of Electroceramics, vol. 5, no. 2, pp. 93–110, 2000.
View at: Publisher Site | Google Scholar
D. S. McLachlan, C. Chiteme, C. Park et al., “AC and DC percolative conductivity of single wall carbon nanotube polymer composites,” Journal of Polymer Science Part B, vol. 43, no. 22, pp. 3273–3287, 2005.
View at: Publisher Site | Google Scholar
D. S. McLachlan, R. Rosenbaum, A. Albers et al., “The temperature and volume fraction dependence of the resistivity of granular Al-Ge near the percolation threshold,” Journal of Physics: Condensed Matter, vol. 5, no. 27, pp. 4829–4842, 1993.
View at: Publisher Site | Google Scholar
D. S. McLachlan, J.-H. Hwang, and T. O. Mason, “Evaluating dielectric impedance spectra using effective media theories,” Journal of Electroceramics, vol. 5, no. 1, pp. 37–51, 2000.
View at: Publisher Site | Google Scholar
G. Sauti, Electrical Conductivity and Permittivity of Ceramics and other Composites, M.S. thesis, Physics, University of the Witwatersrand, Johannesburg, South Africa, 2005.
A. K. Jonscher, “The ‘universal’ dielectric response,” Nature, vol. 267, no. 5613, pp. 673–679, 1977.
View at: Publisher Site | Google Scholar
C. León, M. L. Lucía, and J. Santamaría, “Correlated ion hopping in single-crystal yttria-stabilized zirconia,” Physical Review B, vol. 55, no. 2, pp. 882–887, 1997.
View at: Publisher Site | Google Scholar
R. E. Meredith and C. W. Tobias, “Conduction in heterogenous systems,” in Advances in Electrochemistry and Electrochemical Engineering, C. Tobias, Ed., vol. 2, pp. 15–47, John Wiley & Sons, New York, NY, USA, 1962.
View at: Google Scholar
R. Zallen, The Physics of Amorphous Solids, John Wiley & Sons, New York, NY, USA, 1983.
R. P. Kusy, “Influence of particle size ratio on the continuity of aggregates,” Journal of Applied Physics, vol. 48, no. 12, pp. 5301–5305, 1977.
View at: Publisher Site | Google Scholar
I. Balberg, C. H. Anderson, S. Alexander, and N. Wagner, “Excluded volume and its relation to the onset of percolation ,” Physical Review B, vol. 30, no. 7, pp. 3933–3943, 1984.
View at: Publisher Site | Google Scholar
B. I. Halperin, S. Feng, and P. N. Sen, “Differences between Lattice and continuum percolation transport exponents,” Physical Review Letters, vol. 54, no. 22, pp. 2391–2394, 1985.
View at: Publisher Site | Google Scholar
P. M. Kogut and J. P. Straley, “Distribution-induced non-universality of the percolation conductivity exponents,” Journal of Physics C, vol. 12, no. 11, pp. 2151–2159, 1979.
View at: Publisher Site | Google Scholar
S. Feng, B. I. Halperin, and P. N. Sen, “Transport properties of continuum systems near the percolation threshold ,” Physical Review B, vol. 35, no. 1, pp. 197–214, 1987.
View at: Publisher Site | Google Scholar
I. Balberg, “Limits on the continuum-percolation transport exponents,” Physical Review B, vol. 57, no. 21, pp. 13351–13354, 1998.
View at: Publisher Site | Google Scholar
H. E. Stanley, “Cluster shapes at the percolation threshold: and effective cluster dimensionality and its connection with critical-point exponents,” Journal of Physics A, vol. 10, no. 11, pp. L211–L220, 1977.
View at: Publisher Site | Google Scholar
A. Coniglio, “Cluster structure near the percolation threshold,” Journal of Physics A, vol. 15, no. 12, pp. 3829–3844, 1982.
View at: Publisher Site | Google Scholar
I. Balberg, “Tunneling and nonuniversal conductivity in composite materials ,” Physical Review Letters, vol. 59, no. 12, pp. 1305–1308, 1987.
View at: Publisher Site | Google Scholar
G. Sauti and D. S. McLachlan, “Impedance and modulus spectra of the percolation system silicon-polyester resin and their analysis using the two exponent phenomenological percolation equation,” Journal of Materials Science, vol. 42, no. 16, pp. 6477–6488, 2007.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2007 David S. McLachlan and Godfrey Sauti. 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.

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