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Spectral density representation of dielectric mixtures

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Abstract

Dielectric relaxation has attracted lot of interest since the days of J.C. Maxwell. Although relaxation in pure, single materials is a puzzling topic, relaxation in mixtures has its own perplexing sides. However, with the help of spectral density representation, one has the possibility to separate contributions of the constituents and the geometrical composition of the mixture phases. Here, we will present the theory of dielectric mixtures with the spectral density representation. It will be shown that depending on the dielectric properties and geometrical description of the constituents different effective permittivity can be obtained for a chosen pair of mixture components—binary mixtures. The tools presented here can be used to better understand the dielectric properties of materials. The numerical implementations presented for immittance data can be used for various physical properties of heterogeneous materials. For mixtures, they provide great value in (i) designing the permittivity of a mixture composed of substances with known permittivities and geometrical composition (for device and insulation applications), (ii) calculating the permittivity of the second component of a two-component mixture when the permittivities of the mixture and the first component are known (for material and system characterization), and (iii) estimating the morphology of a two-component mixture when the permittivities of the mixture and each of the components are known (for microstructure and structure/property relationships).

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References

  1. J.C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 1, 3rd edn. (Clarendon Press, Oxford, 1891), pp. 450–464, reprint by Dover

    Google Scholar 

  2. J.C.M. Garnett, Philos. Trans. R. Soc. Lond. A 203, 385 (1904)

    Article  ADS  MATH  Google Scholar 

  3. K.W. Wagner, Ann. Phys. 40, 817 (1913)

    Article  MATH  Google Scholar 

  4. K.W. Wagner, Archiv Electrotech II, 371 (1914)

    Article  Google Scholar 

  5. H. Fricke, Phys. Rev. 24, 575 (1924)

    Article  ADS  Google Scholar 

  6. H.H. Lowry, J. Franklin Inst. 203, 413 (1927)

    Article  Google Scholar 

  7. D.A.G. Bruggeman, Ann. Phys. (Leipz.) 24, 636 (1935)

    Article  ADS  Google Scholar 

  8. R. Sillars, J. Inst. Elect. Eng. 80, 378 (1937)

    Google Scholar 

  9. R. Landauer, J. Appl. Phys. 23, 779 (1952)

    Article  ADS  Google Scholar 

  10. H. Fricke, J. Phys. Chem. 57, 934 (1953)

    Article  Google Scholar 

  11. M. Sahimi, Heterogeneous Materials I: Linear Transport and Optical Properties, vol. 22 (Springer, Berlin, 2003)

    MATH  Google Scholar 

  12. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, vol. 16 (Springer, Berlin, 2001)

    Google Scholar 

  13. R. Landauer, in Electrical Transport and Optical Properties of Inhomogeneous Media, ed. by J.C. Garland, D.B. Tanner. AIP Conference Proceedings, vol. 40 (American Institute of Physics, New York, 1978), pp. 2–43

    Google Scholar 

  14. A. Sihvola, Electromagnetic Mixing Formulas and Applications, IEE Electromagnetic Waves Series, vol. 47 (The Institute of Electrical Engineers, London, 1999)

    Book  Google Scholar 

  15. G.W. Milton, The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics, vol. 6 (Cambridge University Press, Cambridge, 2002)

    Book  MATH  Google Scholar 

  16. A. Priou (ed.), Progress in Electromagnetics Research, Dielectric Properties of Heterogeneous Materials (Elsevier, New York, 1992)

    Google Scholar 

  17. P.A.M. Steeman, J. van Turnhout, in Broadband Dielectric Spectroscopy, ed. by F. Kremer, A. Schönhals (Springer, Berlin, 2003), pp. 495–522

    Chapter  Google Scholar 

  18. W.R. Tinga, in Dielectric Properties of Heterogeneous Materials. Progress in Electromagnetic Research, vol. 6 (Elsevier, Amsterdam, 1992), pp. 1–40, Chap. 1

    Google Scholar 

  19. Y.P. Emets, Y.V. Obnosov, Sov. Phys. Tech. Phys. 35, 907 (1990)

    Google Scholar 

  20. Y.P. Emets, Y.V. Obnosov, Sov. Phys. Dokl. 34, 972 (1989)

    MathSciNet  ADS  Google Scholar 

  21. K. Golden, G. Papanicolaou, Commun. Math. Phys. 90, 473 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  22. H. Looyenga, Physica 31, 401 (1965)

    Article  ADS  Google Scholar 

  23. A. Sihvola, Subsurf. Sensing Technol. Appl. 1, 393 (2000)

    Article  Google Scholar 

  24. C. Brosseau, A. Beroual, Progress. Mater. Sci. 48, 373 (2003)

    Article  Google Scholar 

  25. E. Tuncer, Y.V. Serdyuk, S.M. Gubanski, IEEE Trans. Dielectr. Electr. Insul. 9, 809 (2002)

    Article  Google Scholar 

  26. D.J. Bergman, Phys. Rep. 43, 377 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  27. G.A. Niklasson, C.G. Granqvist, J. Appl. Phys. 55, 3382 (1984)

    Article  ADS  Google Scholar 

  28. G.A. Niklasson, J. Appl. Phys. 57, 157 (1985)

    Article  ADS  Google Scholar 

  29. C. Brosseau, A. Beroual, J. Phys. D, Appl. Phys. 34, 704 (2001)

    Article  ADS  Google Scholar 

  30. A. Boudida, A. Beroual, C. Brosseau, J. Appl. Phys. 88, 7278 (2000)

    Article  ADS  Google Scholar 

  31. C. Brosseau, A. Beroual, Eur. Phys. J. Appl. Phys. 6, 23 (1999)

    Article  ADS  Google Scholar 

  32. B. Sareni, L. Krähenbühl, A. Beroual, A. Nicolas, C. Brosseau, J. Electrost. 40 & 41, 489 (1997)

    Article  Google Scholar 

  33. B. Sareni, L. Krähenbühl, A. Beroual, C. Brosseau, J. Appl. Phys. 81, 2375 (1997)

    Article  ADS  Google Scholar 

  34. D. Gershon, J.P. Calame, A. Birnboim, J. Appl. Phys. 89, 8110 (2001)

    Article  ADS  Google Scholar 

  35. E. Tuncer, B. Nettelblad, S.M. Gubański, J. Appl. Phys. 92, 4612 (2002)

    Article  ADS  Google Scholar 

  36. E. Tuncer, S.M. Gubański, B. Nettelblad, J. Appl. Phys. 89, 8092 (2001)

    Article  ADS  Google Scholar 

  37. E. Tuncer, Ph.D. thesis, Chalmers University of Technology, Gothenburg, Sweden (2001)

  38. C. Brosseau, J. Appl. Phys. 75, 672 (1994)

    Article  ADS  Google Scholar 

  39. J.R. Macdonald, Impedance Spectroscopy: Theory, Experiment and Applications, 2nd edn. (Wiley, New York, 2005), pp. 275–281

    Google Scholar 

  40. J.R. Macdonald, Braz. J. Phys. 29, 332 (1999)

    Article  Google Scholar 

  41. J.R. Macdonald, J. Appl. Phys. 82, 3962 (1997)

    Article  ADS  Google Scholar 

  42. E. Tuncer, Materials 3, 585 (2010), ISSN 1996-1944, http://www.mdpi.com/1996-1944/3/1/585

    Article  ADS  Google Scholar 

  43. A. Ramos, H. Morgan, N.G. Green, A. Castellanos, J. Phys. D, Appl. Phys. 31, 2338 (1998)

    Article  ADS  Google Scholar 

  44. L.A. Dissado, R.M. Hill, Phys. Rev. B 37, 3434 (1988)

    Article  ADS  Google Scholar 

  45. K.L. Ngai, A.K. Jonscher, C.T. White, Nature 277, 185 (1979)

    Article  ADS  Google Scholar 

  46. A.K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric, London, 1983)

    Google Scholar 

  47. P. Debye, Polar Molecules (Dover Publications, New York, 1945)

    Google Scholar 

  48. L.A. Dissado, R.M. Hill, J. Chem. Soc. Faraday Trans. II 80, 291 (1984)

    Article  Google Scholar 

  49. S. Havriliak, S. Negami, J. Polym. Sci.: Part C 14, 99 (1966)

    Google Scholar 

  50. S. Havriliak, S. Negami, Polymer 8, 161 (1967)

    Article  Google Scholar 

  51. K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941)

    Article  ADS  Google Scholar 

  52. D.W. Davidson, R.H. Cole, J. Chem. Phys. 19, 1484 (1951)

    Article  ADS  Google Scholar 

  53. J.R. Macdonald, J. Non-Cryst. Solids 212, 95 (1997)

    Article  ADS  Google Scholar 

  54. E. Tuncer, J.R. Macdonald, J. Appl. Phys. 99, 074106 (2006)

    Article  ADS  Google Scholar 

  55. E. Tuncer, S.M. Gubański, IEEE Trans. Dielectr. Electr. Insul. 8, 310 (2001)

    Article  Google Scholar 

  56. J.R. Macdonald, E. Tuncer, J. Elctroanal. Chem. 602, 255 (2007)

    Article  Google Scholar 

  57. G.W. Milton, J. Appl. Phys. 52, 5286 (1981)

    Article  ADS  Google Scholar 

  58. D.J. Bergman, Phys. Rev. B 19, 2359 (1979)

    Article  ADS  Google Scholar 

  59. K. Ghosh, R. Fuchs, Phys. Rev. B 38, 5222 (1988)

    Article  ADS  Google Scholar 

  60. E. Tuncer, J. Phys., Condens. Matter 17, L125 (2005), cond-mat/0502580

    Article  ADS  Google Scholar 

  61. R. Fuchs, in Electrical Transport and Optical properties of Inhomogeneous Media, ed. by J.C. Garland, D.B. Tanner. AIP Conference Proceedings, vol. 40 (American Institute of Physics, New York, 1978), pp. 276–281

    Google Scholar 

  62. R. Fuchs, Phys. Rev. B 11, 1732 (1975)

    Article  ADS  Google Scholar 

  63. R. Fuchs, S.H. Liu, Phys. Rev. B 14, 5521 (1976)

    Article  ADS  Google Scholar 

  64. E. Tuncer, S.M. Gubański, in NORD-IS’99 Nordic Insulation Symp. Lyngby Denmark (1999), pp. 223–230

    Google Scholar 

  65. E. Tuncer, arXiv:cond-mat/0107618 (2001)

  66. E. Tuncer, S.M. Gubański, Turk. J. Phys. 26, 1 (2002)

    Google Scholar 

  67. R. Vila, M.J. de Castro, J. Phys. D, Appl. Phys. 25, 1357 (1992)

    Article  ADS  Google Scholar 

  68. A. Mejdoubi, C. Brosseau, Phys. Rev. E 74, 031405 (2006)

    Article  ADS  Google Scholar 

  69. O. Wiener, Der Abhandlungen der Mathematisch-Physischen Klasse der Königl. Sächs. Ges. Wiss. 32, 509 (1912)

    Google Scholar 

  70. E. Tuncer, G.A. Niklasson, Opt. Commun. 281, 4374 (2008)

    Article  ADS  Google Scholar 

  71. E. Tuncer, J. Phys. D, Appl. Phys. 38, 223 (2005)

    Article  ADS  Google Scholar 

  72. E. Tuncer, Phys. Rev. B 71, 012101 (2005), cond-mat/0403243

    Article  ADS  Google Scholar 

  73. H.A. Kramer, Nature (London) 117, 775 (1926)

    Google Scholar 

  74. G.W. Milton, D.J. Eyre, J.V. Mantese, Phys. Rev. Lett. 79, 3062 (1997)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Dielectrics & Electrophysics Lab, GE Global Research Center, Niskayuna, NY, 12309, USA

    Enis Tuncer

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  1. Enis Tuncer
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Correspondence to Enis Tuncer.

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The manuscript is dedicated to Professor Reimund Gerhard for his kindness, fruitful discussion and guidance in my research and professional life.

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Tuncer, E. Spectral density representation of dielectric mixtures. Appl. Phys. A 107, 575–582 (2012). https://doi.org/10.1007/s00339-012-6832-7

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