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 coloids, 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 $\epsilon'_{1,2}$ and its conductivity σ_1,2. 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., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 2002.
2. ^ Kremer F., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 2002.
3. ^ Wagner KW (1914) Arch Elektrotech 2:371; [DOI:10.1007/BF01657322 http://dx.doi.org/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