PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 100 > pp. 13-26

MICROWAVE MEASUREMENTS OF DIELECTRIC CONSTANTS BY EXPONENTIAL AND LOGARITHMIC MIXTURE EQUATIONS

By J. Sheen, Z.-W. Hong, C.-W. Su, and H.-C. Chen

Full Article PDF (225 KB)

Abstract:
This article reports on a study of the dielectric constants of ceramic dispersions in the polyethylene matrix at microwave frequency. The exponential and logarithmic mixture rules are studied in three ceramic powders of fillers with dielectric constants 10, 20, and 36, respectively. The experimental values of the dielectric constants of the mixtures are compared to those obtained by using different mixing laws. The mixing rules are also adopted to calculate the dielectric constants of pure ceramics from the measured dielectric constants of composites with various concentrations. The theories on errors of calculations are studied. The most adequate mixture equation for measuring the dielectric constants of pure ceramics is suggested.

Citation:
J. Sheen, Z.-W. Hong, C.-W. Su, and H.-C. Chen, " microwave measurements of dielectric constants by exponential and logarithmic mixture equations ," Progress In Electromagnetics Research, Vol. 100, 13-26, 2010.
doi:10.2528/PIER09091706
http://www.jpier.org/PIER/pier.php?paper=09091706

References:
1. Achour, M. E., M. El Malhi, J. L. Miane, F. Carmona, and F. Lahjomri, "Microwave properties of carbon black-epoxy resin composites and their simulation by means of mixture laws," J. of Applied Polymer Science, Vol. 73, 969-973, 1999.
doi:10.1002/(SICI)1097-4628(19990808)73:6<969::AID-APP14>3.0.CO;2-1

2. Van Beek, L. K. H., "Dielectric behavior of heterogeneous systems," Progress in Dielectrics, Vol. 7, 69-114, 1967.

3. Tinga, W. R., W. A. G. Voss, and D. F. Blossey, "Generalized approach to multiphase dielectric mixture theory," J. Appl. Phys., Vol. 44, 3897-3902, 1973.
doi:10.1063/1.1662868

4. Sheen, J., Z. W. Hong, W. Liu, W. L. Mao, and C. A Chen, "Study of dielectric constants of binary composites at microwave frequency by mixture laws derived from three basic particle shapes," European Polymer Journal, Vol. 45, 1316-1321, 2009.
doi:10.1016/j.eurpolymj.2008.08.002

5. Wakino, K., New proposal on mixing rule of the dielectric constant of mixture, IEEE International Symposium on Applications of Ferroelectrics, 33-38, 1994.

6. Stolzle, S., A. Enders, and G. Nimtz, "Numerical simulation of random composite dielectrics," J. Phys. I, Vol. 2, 401-408, France, 1999.
doi:10.1051/jp1:1992153

7. Kim, J. B., T. W. Kim, and C. G. Kim, "Simulation method of complex permittivities of carbon balck/epoxy composites at microwave frequency band," J. of Applied Polymer Science, Vol. 100, 2189-2195, 2006.
doi:10.1002/app.23653

8. Zhou, P., L. Deng, B.-I. Wu, and J. A. Kong, "Influence of scatterer's geometry on power-law formula in random mixing composites," Progress In Electromagnetics Research, Vol. 85, 69-82, 2008.
doi:10.2528/PIER08081705

9. Navid, A. and L. Pilon, "Effect of polarization and morphology on the optical properties of absorbing nanoporous thin films," Thin Solid Films, Vol. 516, 4159-4167, 2008.
doi:10.1016/j.tsf.2007.10.117

10. Xiang, F., H.Wang, and X. Yao, "Preparation and dielectric properties of bismuth-based dielectric/PTFE microwave composites," J. Eur. Ceram. Soc., Vol. 26, 1999-2002, 2006.
doi:10.1016/j.jeurceramsoc.2005.09.048

11. Lichtenecker, K. and K. Rother, "Die herleitung des logarithmischen mischungsgesetzes als allegemeinen prinzipien der staionaren stromung," K. Phys. Zeitschrift, Vol. 32, 255-260, 1931.

12. Ragossnig, H. and A. Feltz, "Characterization of dielectric powders by a new defined form factor," J. Eur. Ceram. Soc., Vol. 18, 429-444, 1998.
doi:10.1016/S0955-2219(97)00146-5

13. Looyenga, H., "Dielectric constants of mixtures," Physica, Vol. 31, 401-406, 1965.
doi:10.1016/0031-8914(65)90045-5

14. 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.

15. Lichtenecker, K., "Die dielektrizitatskonstante naturlicher und kunstlicher mischkorper," K. Phys. Zeitschrift, Vol. 27, 115-158, 1926.

16. Koledintseva, M. Y., J. L. Drewniak, R. E. DuBroff, K. N. Rozanov, and B. Archambeault, "Modeling of shielding composite materials and structures for microwave frequencies," Progress In Electromagnetics Research B, Vol. 15, 197-215, 2009.
doi:10.2528/PIERB09050410

17. Huang, K. and X. Yang, "A method for calculating the effective permittivity of a mixture solution during a chemical reaction by experimental results," Progress In Electromagnetics Research Letters, Vol. 5, 99-107, 2008.
doi:10.2528/PIERL08110403

18. 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

19. Koledintseva, M. Y., R. E. DuBroff, R. W. Schwartz, and J. L. Drewniak, "Double statistical distribution of conductivity and aspect ratio of inclusions in dielectric mixtures at microwave frequencie," Progress In Electromagnetics Research, Vol. 77, 193-214, 2007.
doi:10.2528/PIER07073103

20. Lou, J., T. A. Hatton, and P. E. Laibinis, "Effective dielectric properties of solvent mixtures at microwave frequencies," J. Phys. Chem. A, Vol. 101, 5262-5268, 1997.
doi:10.1021/jp970731u

21. 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

22. 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

23. Wang, H. G. and C. H. Chan, "Mixture effective permittivity simulations using imlmqrf method on preconditioned EFIE," Progress In Electromagnetics Research, Vol. 57, 285-310, 2006.
doi:10.2528/PIER05072603

24. Tinga, W. R., "Mixture laws and microwave-material interactions," Progress In Electromagnetics Research, Vol. 6, 1-40, 1992.

25. Sihvola, A., "Two main avenues leading to the Maxwell garnett mixing rule," Journal of Electromagnetic Waves and Applications, Vol. 15, 715-725, 2001.
doi:10.1163/156939301X00968

26. Pekonen, O., K. KarkkÄainen, A. Sihvola, and K. Nikoskinen, "Numerical testing of dielectric mixing rules by FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 13, 67-87, 1999.
doi:10.1163/156939399X01618

27. Hakki, B. W. and P. D. Coleman, "A dielectric resonator method of measuring inductive capacities in the millimeter range," IRE Trans. Microwave Theory Tech., Vol. 8, 402-410, 1960.
doi:10.1109/TMTT.1960.1124749

28. Sheen, J., "Study of microwave dielectric properties measurements by various resonance techniques," Measurement, Vol. 37, 123-130, 2005.
doi:10.1016/j.measurement.2004.11.006


© Copyright 2014 EMW Publishing. All Rights Reserved