volume | PIER Journals

Abstract

To apply the power-law to random mixing composites, the power parameter α is defined as the mean depolarization factor along the external field. The formula of α is derived from the effective medium theory and beta function distribution assumption to study the geometrical influence of scatterers. According to the simulation, we prove that α = 1/3 is fit to the composites of randomly distributed spherical dielectric scatterers, whereas α = 1/2 to the flake-like or cylindrical shaped scatterers. This law can be applied to both dilute and dense condition describing the effective permittivity of random mixing composites and extended to aligned cases, which are meaningful to practical applications.

1. Jackson, J. D., Classical Electrodynamics, John Wiley & Sons Inc., 1974.

2. Kanaun, S. K. and D. Jeulin, "The influence of spatial distributions of inhomogeneities on effective dielectric properties of composite materials (effective field approach) ," Progress In Electromagnetics Research, Vol. 22, 51-84, 1999.
doi:10.2528/PIER98080703 Google Scholar

3. Koledintseva, M. Y., R. E. DuBroff, and R. W. Schwartz, "A Maxwell Garnett model for dielectric mixtures containing conducting particles at optical frequencies," Progress In Electromagnetics Research, Vol. 63, 223-242, 2006.
doi:10.2528/PIER06052601 Google Scholar

4. Koledintseva, M. Y., S. K. R. Chandra, R. E. DuBroff, and R. W. Schwartz, "Modeling of dielectric mixtures containing conducting inclusions with statistically distributed aspect ratio," Progress In Electromagnetics Research, Vol. 66, 213-228, 2006.
doi:10.2528/PIER06110903 Google Scholar

5. Sihvola, A., "Metamaterials and depolarization factors," Progress In Electromagnetics Research, Vol. 51, 65-82, 2005.
doi:10.2528/PIER04021001 Google Scholar

6. Mclachlan, D. S., A. Priou, I. Chenerie, E. Issac, and F. Henry, "Modeling the permittivity of composite materials with a general effective medium equation," Journal of Electromagnetic Waves and Applications, Vol. 6, No. 9, 1099-1131, 1992. Google Scholar

7. Zhuck, N. P., K. Schuemann, and S. N. Shulga, "Effective permittivity of a statistically inhomogeneous medium with strong permittivity fluctuations," Progress In Electromagnetics Research, Vol. 44, 169-195, 2004.
doi:10.2528/PIER03033001 Google Scholar

8. Sihvola, A., "Mixing rules with complex dielectric coefficients," Subsurface Sensing Technologies and Applications, Vol. 1, 393-415, 2000.
doi:10.1023/A:1026511515005 Google Scholar

9. Lichtenecker, K., "Mischkorpertheori alsWahrscheinlichkeitsproblem," Physik. Zeitschr., Vol. 30, 805-809, 1929. Google Scholar

10. Birchak, J. R., C. G. Gardner, J. E. Hipp, and J. M. Victor, "High dielectric constant microwave probes for sensing soil moisture," Proc. IEEE, Vol. 62, 93-98, 1974.
doi:10.1109/PROC.1974.9388 Google Scholar

11. Lichtenecker, K. and K. Rother, "Die Herleitung des logarithmischen Mischungs-gesetzes aus allegemeinen Prinzipien der stationaren Stromung," Physik. Zeitschr., Vol. 32, 255-260, 1931. Google Scholar

12. Jacobsen, O. H. and P. Schjonning, "Comparison of TDR calibration functions for soil water determination," Proc. Symp. Time-domain Reflectometry Applications in Soil Science, 25-33, Tjele, Denmark, September 1994. Google Scholar

13. Zakri, T., J. P. Laurent, and M. Vauclin, "Theoretical evidence for ‘Lichtenecker’s mixture formulae’ based on the effective medium theory," J. Phys. D: Appl. Phys., Vol. 31, 1589-1594, 1998.
doi:10.1088/0022-3727/31/13/013 Google Scholar

14. Mourzenko, V. V., J.-F. Thovert, and P. M. Adler, "Percolation of three-dimensional fracture networks with power-law size distribution," Phys. Rev. E, Vol. 72, 036103, 2005.
doi:10.1103/PhysRevE.72.036103 Google Scholar

15. Bogdanov, I. I., V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Effective permeability of fractured porous media with power-law distribution of fracture size," Phys. Rev. E, Vol. 76, 036309, 2007.
doi:10.1103/PhysRevE.76.036309 Google Scholar

16. Sihvola, A., Electromagnetic Mixing Formulas and Applications, Institution of Electrical Engineers, 1999.

17. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, 1941.

18. Landau, L. D. and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Pergamon, 1960.

19. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, 1972.

20. Bruggeman, D. A. G., "Berechnung verschiedener physikalischer konstanten von heterogenen substanzen: 1. Dielektrizitatskonstanten und leitfahigkeiten der mischkorper aus isotropen substanzen," Ann. Phy., Vol. 24, 636-679, 1935.
doi:10.1002/andp.19354160705 Google Scholar

21. Jia, B., W. Lin, and S. Liu, "The study of effective medium parameters for granular media," Progress In Electromagnetics Research, Vol. 8, 89-108, 1994. Google Scholar

22. Chen, X. D., T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E, Vol. 70, 016608, 2004.
doi:10.1103/PhysRevE.70.016608 Google Scholar

23. Jylha, L. and A. H. Sihvola, "Tunability of granular ferroelectric dielectric composites," Progress In Electromagnetics Research, Vol. 78, 189-207, 2008.
doi:10.2528/PIER07081502 Google Scholar

24. Engstrom, C. and D. Sjoberg, "On two numerical methods for homogenization of Maxwell’s equations ," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1845-1856, 2007. Google Scholar

25. Habashy, T. M. and A. Abubakar, "A generalized material averaging formulation for modeling of the electromagnetic fields," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 9, 1145-1159, 2007. Google Scholar

Dr. Pei-Heng Zhou

Dr. Long-Jiang Deng

Dr. Bae-Ian Wu

Professor Jin Au Kong