Physics:Maxwell–Wagner–Sillars polarization

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In dielectric spectroscopy, large frequency dependent contributions to the dielectric response, especially at low frequencies, may come from build-ups of charge. This Maxwell–Wagner–Sillars polarization (or often just Maxwell-Wagner polarization), occurs either at inner dielectric boundary layers on a mesoscopic scale, or at the external electrode-sample interface on a macroscopic scale. In both cases this leads to a separation of charges (such as through a depletion layer). The charges are often separated over a considerable distance (relative to the atomic and molecular sizes), and the contribution to dielectric loss can therefore be orders of magnitude larger than the dielectric response due to molecular fluctuations.[1]

Occurrences

Maxwell-Wagner polarization processes should be taken into account during the investigation of inhomogeneous materials like suspensions or colloids, biological materials, phase separated polymers, blends, and crystalline or liquid crystalline polymers.[2]

Models

The simplest model for describing an inhomogeneous structure is a double layer arrangement, where each layer is characterized by its permittivity [math]\displaystyle{ \epsilon'_1,\epsilon'_2 }[/math] and its conductivity [math]\displaystyle{ \sigma_1,\sigma_2 }[/math]. The relaxation time for such an arrangement is given by [math]\displaystyle{ \tau_{MW}=\epsilon_0\frac{\epsilon_1+\epsilon_2}{\sigma_1+\sigma_2} }[/math]. Importantly, since the materials' conductivities are in general frequency dependent, this shows that the double layer composite generally has a frequency dependent relaxation time even if the individual layers are characterized by frequency independent permittivities.

A more sophisticated model for treating interfacial polarization was developed by Maxwell [citation needed], and later generalized by Wagner [3] and Sillars.[4] Maxwell considered a spherical particle with a dielectric permittivity [math]\displaystyle{ \epsilon'_2 }[/math] and radius [math]\displaystyle{ R }[/math] suspended in an infinite medium characterized by [math]\displaystyle{ \epsilon_1 }[/math]. Certain European text books will represent the [math]\displaystyle{ \epsilon_1 }[/math] constant with the Greek letter ω (Omega), sometimes referred to as Doyle's constant.[5]

References

  1. ↑ Kremer F., & Schönhals A. (eds.): Broadband Dielectric Spectroscopy. – Springer-Verlag, 2003, ISBN:978-3-540-43407-8.
  2. ↑ Kremer F., & Schönhals A. (eds.): Broadband Dielectric Spectroscopy. – Springer-Verlag, 2003, ISBN:978-3-540-43407-8.
  3. ↑ Wagner KW (1914) Arch Elektrotech 2:371; doi:10.1007/BF01657322
  4. ↑ Sillars RW (1937) J Inst Elect Eng 80:378
  5. ↑ G.McGuinness, Polymer Physics, Oxford University Press, p211

See also



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