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Abstract

Two new equations are developed for effective electrical conductivity of concentrated particulate composites using a differential scheme along with the solution of an infinitely dilute dispersion of particles in a continuous matrix. The proposed equations are evaluated using 16 sets of experimental data on the electrical conductivity of two-phase particulate systems. The following model developed in the paper describes the experimental data very well: (σ/σm)1/3 (σd — σm)/ (σd — σ) = (1 — φ/φm )—αφm ) where σ, σm and σd are electrical conductivities of composite, matrix, and dispersed phase (filler) respectively, φ is volume fraction of filler, φm is the maximum packing volume fraction of filler, and α is a constant of the order of unity. In the special case of α = 1 and φm = 1, this model reduces to the well-known Bruggeman equation for the electrical conductivity of two-phase particulate systems. The predictions of the proposed model are significantly different from the predictions of the existing general effective media (GEM) model.

Keywords

composite two-phase electrical conductivity properties.

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References

Maxwell, J.C. (1881). A Treatise on Electricity and Magnetism, 2nd edn, Vol. 1, p. 435, Clarendon Press, Oxford.

Wagnar, K.W. (1914). Arch Elektrotech. (Berlin), 2: 371.

Wiener, O. (1912). Abh. Math. Phys. Kgl. Sachs, Ges. Wiss., 32: 509.

Bruggeman, D.A.G. (1935). Berechnung verschiedener physikalischer Konstanten von heterogenen substanzen, Ann. Phys. (Leipzig), 24: 636—679.

Meredith, R.E. and Tobias, C.W. (1960). Resistance to Potential Flow Through a Cubical Array of Spheres, J. Appl. Phys., 31: 1270—1273.

Meredith, R.E. and Tobias, C.W. (1962). Conduction in Heterogeneous Systems, In: Advances in Electrochemistry and Electrochemical Engineering, Delahay, P. and Tobias, C.W. (eds), Vol. 2, p. 15, Interscience, New York.

Lord Rayleigh . (1892), Phil. Mag., 34: 481.

Bottcher, C.J.F. (1952). Theory of Electric Polarization, p. 419, Elsevier, New York.

Feitosa, K. , Marze, S. , Saint-Jalmes, A. and Durian, D.J. (2005). Electrical Conductivity of Dispersions: From Dry Foams to Dilute Suspensions, J. Phys.: Condens. Matter, 17: 6301—6305.

10.

Zuzovsky, M. and Brenner, H. (1977). J. Appl. Math. Phys., 28: 979.

11.

Pal, R. ( 1987). Emulsions: Pipeline Flow Behavior, Viscosity Equations, and Flow Measurement, PhD thesis, University of Waterloo , Ontario, Canada.

12.

Clingerman, M.L. , Weber, E.H. , King, J.A. and Schulz, K.H. (2003). Development of an Additive Equation for Predicting the Electrical Conductivity of Carbon-Filled Composites , J. Appl. Poly. Sci., 88: 2280—2299.

13.

Mamunya, Y.P. , Davydenko, V.V. , Pissis, P. and Lebedev, E.V. (2002). Electrical and Thermal Conductivity of Polymers Filled with Metal Powders, Euro- Poly. J., 38: 1887—1897.

14.

Krupa, I. , Novak, I. and Chodak, I. (2004). Electrically and Thermally Conductive Polyethylene/Graphite Composites and Their Mechanical Properties, Syn. Metals, 145: 245—252.

15.

McLachlan, D.S. , Blaszkiewicz, M. and Newnham, R.E. (1990). Electrical Resistivity of Composites, J. Am. Ceram. Soc., 73: 2187—2203.

16.

Peng, H.X. , Fan, Z. and Evans, J.R.G. (2001). Bi-continuous Metal Matrix Composites, Mat. Sci. and Eng. A, 303: 37—45.

17.

Pinto, G. and Maidana, M.B. (2001). Conducting Polymer Composites of Zinc-Filled Nylon 6, J. Appl. Poly. Sci., 82: 1449—1454.

18.

Campo, M.A. , Woo, L.Y. , Mason, T.O. and Garboczi, E.J. (2002). Frequency-Dependent Electrical Mixing Law Behavior in Spherical Particle Composites, J. Electro Ceramics, 9: 49—56.

19.

Weber, L. , Dorn, J. and Mortensen, A. (2003). On the Electrical Conductivity of Metal Matrix Composites containing High Volume Fractions of Non-conducting Inclusions, Acta Materialia, 51: 3199—3211.

20.

da Rocha, S.R.P. , Psathas, P.A. , Klein, E. and Johnston, K.P. (2001). Concentrated CO2-in-Water Emulsions with Nonionic Polymeric Surfactants, J. Colloid & Int. Sci., 239: 241—253.

21.

Dhanuka, V.V. , Dickson, J.L. , Ryoo, W. and Johnston, K.P. (2006). High Internal Phase CO2-in-Water Emulsions Stabilized with a Branched Nonionic Hydrocarbon Surfactant, J. Colloid & Int. Sci., 298: 406—418.

22.

Krieger, I.M. and Dougherty, T.J. (1959). A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres, Trans. Soc. Rheol., 3: 137—152.

23.

McLachlan, D.S. (1987). An Equation for the Conductivity of Binary Mixtures with Anisotropic Grain Structures, J. Phys. C: Solid State Phys., C20: 865—877.

24.

McLachlan, D.S. (1986). Equations for the Conductivity of Macroscopic Mixtures, J. Phys. C: Solid State Phys., C19: 1339—1354.

25.

McLachlan, D.S. (1987). Equation for the Conductivity of Heterogeneous Binary Media, Jpn. J. Appl. Phys., 26: 901—902.

26.

McLachlan, D.S. (1988). Measurement and Analysis of a Model Dual-Conductivity Medium Using a Generalized Effective-Medium Theory , J. Phys. C: Solid State Phys., C21: 1521—1532.

27.

Stauffer, D. and Aharony, A. (1992). Introduction to Percolation Theory, Taylor and Francis, London.