Dielectric Spectra Analysis: Reliable Parameter Estimation Using Interval Analysis

  • Adrien Brochier
  • Maëlenn Aufray
  • Wulff Possart
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 3)


Dielectric spectra of materials are often difficult to analyze since the common software algorithms and line shape functions do not always provide unambiguous data for the fitted parameters. In this paper, a new algorithm (called S.A.D.E. as SIVIA (Set inversion Via Interval Analysis) Applied to DiElectric spectroscopy), based on a global optimization algorithm which uses interval analysis, is presented. Taking into account the experimental error of each data point in the measured dielectric spectrum, our algorithm provides a confidence interval for every parameter of the dielectric function implemented in the software. This is demonstrated for an epoxy monomer with a sum of Debye relaxators as dielectric line shape function. S.A.D.E. is also able to deliver and guarantee the number of relaxation processes even if they are in part masked by other phenomena like conductivity or electrode polarization.


computer modeling dielectric properties epoxy monomers simulations 



The authors acknowledge Professor Springborg who granted the access to the computing cluster and Michael Bauer for his help in using it. We also thank Luc Jaulin for his most useful advices.Software AvailabilityS.A.D.E. is freely available on the website of M. Aufray ( S.A.D.E. is protected by copyright (c) 2006 Brochier, and is distributed under the terms of the GNU general public license.


  1. 1.
    P. Debye, Polar Molecules (Chemical Catalog, Reprinted by Dover Publications, New York, 1929)Google Scholar
  2. 2.
  3. 3.
    K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941)CrossRefGoogle Scholar
  4. 4.
    K.S. Cole, R.H. Cole, J. Chem. Phys. 10, 98 (1942)CrossRefGoogle Scholar
  5. 5.
    D. Davidson, R.H. Cole, J. Chem. Phys. 18, 1417 (1950)CrossRefGoogle Scholar
  6. 6.
    M. Mangion, M. Wang, G. Johari, J. Polym. Sci. B Polym. Phys. 30(5), 433 (1992), Google Scholar
  7. 7.
    Corezzi, S. Capaccioli, G. Gallone, A. Livi, P. Rolla, J. Phys. Condens. Matter 9, 6199 (1997),
  8. 8.
    N. Axelrod, E. Axelrod, A. Gutina, A. Puzenko, P. Ben Ishai, Y. Feldman, Meas. Sci. Technol. 15, 1 (2004)CrossRefGoogle Scholar
  9. 9.
    F. Stickel, E. Fischer, R. Richert, J. Chem. Phys. 104(5), 2043 (1996)CrossRefGoogle Scholar
  10. 10.
    R.M. Fuoss, J.G. Kirkwood, J. Am. Chem. Soc. 63(2), 385 (1941)CrossRefGoogle Scholar
  11. 11.
    J. Maxwell, A Treatise on Electricity and Magnetism, vol 1. (Dover Publications, New York, 1954)Google Scholar
  12. 12.
    K.W. Wagner, Archiv für Elektrotechnik 2(9), 371 (1914). URL
  13. 13.
    R. Sillars, Proc. Inst. Electr. Eng. 80, 378 (1937)Google Scholar
  14. 14.
    D.W. Marquardt, J. Soc. Ind. Appl. Math. 11(2), 431 (1963)CrossRefGoogle Scholar
  15. 15.
    K. Levenberg, Q. J. Appl. Math. 2, 164 (1944)Google Scholar
  16. 16.
  17. 17.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Adrien Brochier
    • 1
  • Maëlenn Aufray
    • 2
  • Wulff Possart
    • 3
  1. 1.Lehrstuhl Adhesion and Interphases in PolymersUniversität des SaarlandesSaarbrückenGermany
  2. 2.Chair Adhesion and Interphases in PolymersUniversity of SaarlandSaarbrückenGermany
  3. 3.Saarland UniversitySaarbrückenGermany

Personalised recommendations