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Local porosity theory for the frequency dependent dielectric function of porous rocks and polymer blends

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  • Hilfer, R.
  • Nøst, B.
  • Haslund, E.
  • Kautzsch, Th.
  • Virgin, B.
  • Hansen, B.D.

Abstract

We report preliminary results for the application of local porosity theory to dielectric response measurements on two classes of inhomogeneous systems. One class of systems are mixtures of insulators and conductors realized experimentally as sintered glass bead porous media saturated with salt water. In this case the response arises from the Maxwell-Wagner effect. The second class are mixtures of insulators realized experimentally in polymer blends where the response arises from the relaxation of atomic or molecular dipole moments. For the case of water saturated sintered glass bead systems two-dimensional local porosity distributions have been determined from digital image analysis. These measurements allow for the first time semiquantitative comparisons to previous theoretical approaches and with experiment. The dielectric measurements are used to extract the total fraction of percolating cells in the mixture. For the polymer case we show that recent concentration fluctuation models for the dielectric α-relaxation arise as special cases of local porosity theory. Furthermore it is exemplified how information from static Monte-Carlo simulations of polymer blends may be useful in comparing theoretical calculations to experiment.

Suggested Citation

  • Hilfer, R. & Nøst, B. & Haslund, E. & Kautzsch, Th. & Virgin, B. & Hansen, B.D., 1994. "Local porosity theory for the frequency dependent dielectric function of porous rocks and polymer blends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(1), pages 19-27.
    • Handle: RePEc:eee:phsmap:v:207:y:1994:i:1:p:19-27
    DOI: 10.1016/0378-4371(94)90350-6
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    References listed on IDEAS

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    1. Hilfer, R., 1993. "Local porosity theory for electrical and hydrodynamical transport through porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 406-414.
    2. Boger, F. & Feder, J. & Jøssang, T. & Hilfer, R., 1992. "Microstructural sensitivity of local porosity distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(1), pages 55-70.
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    Cited by:

    1. Hilfer, R. & Rage, T. & Virgin, B., 1997. "Local percolation probabilities for a natural sandstone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(1), pages 105-110.
    2. Biswal, B. & Manwart, C. & Hilfer, R., 1998. "Three-dimensional local porosity analysis of porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(3), pages 221-241.
    3. Biswal, B. & Manwart, C. & Hilfer, R. & Bakke, S. & Øren, P.E., 1999. "Quantitative analysis of experimental and synthetic microstructures for sedimentary rock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 273(3), pages 452-475.
    4. Virgin, B. & Haslund, E. & Hilfer, R., 1996. "Rescaling relations between two-and three-dimensional local porosity distributions for natural and artificial porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 1-20.
    5. Andraud, C. & Beghdadi, A. & Haslund, E. & Hilfer, R. & Lafait, J. & Virgin, B., 1997. "Local entropy characterization of correlated random microstructures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 307-318.

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