Maxwell–Wagner–Sillars polarization

In dielectric spectroscopy, large frequency dependent contributions to the dielectric response, especially at low frequencies, may come from build-ups of charge.

This, so-called 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 $\epsilon '_{1},\epsilon '_{2}$ and its conductivity $\sigma _{1},\sigma _{2}$. The relaxation time is then: $\tau _{{MW}}=\epsilon _{0}{\frac {\epsilon _{1}+\epsilon _{2}}{\sigma _{1}+\sigma _{2}}}$ Importantly this shows that an inhomogeneous material may have frequency dependent response, even though none of the individual inhomogeneities severally are frequency dependent.

A more sophisticated model for treating interfacial polarization was developed by Maxwell, and later generalized by Wagner ^[3] and Sillars.^[4] Maxwell considered a spherical particle with a dielectric permittivity $\epsilon '_{2}$ and radius $R$ suspended in an infinite medium characterized by $\epsilon _{1}$. Certain European text books will represent the $\epsilon _{1}$ 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

Debye relaxation Dielectric dispersion Dielectric function Dipole Permittivity

Ellipsometry Linear response function Kramers–Kronig relation Green–Kubo relations