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 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] It is named after the works of James Clerk Maxwell (1891), Karl Willy Wagner (1914) and R. W. Sillars (1937).[2]

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.[3]

Models

The simplest model for describing an inhomogeneous structure is a double layer arrangement, where each layer is characterized by its permittivity ${\displaystyle \epsilon '_{1},\epsilon '_{2}}$ and its conductivity ${\displaystyle \sigma _{1},\sigma _{2}}$. The relaxation time for such an arrangement is given by ${\displaystyle \tau _{MW}=\epsilon _{0}{\frac {\epsilon _{1}+\epsilon _{2}}{\sigma _{1}+\sigma _{2}}}}$. 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 [4] and Sillars.[5] Maxwell considered a spherical particle with a dielectric permittivity ${\displaystyle \epsilon '_{2}}$ and radius ${\displaystyle R}$ suspended in an infinite medium characterized by ${\displaystyle \epsilon _{1}}$. Certain European text books will represent the ${\displaystyle \epsilon _{1}}$ constant with the Greek letter ω (Omega), sometimes referred to as Doyle's constant.[6]

References

1. Kremer F., & Schönhals A. (eds.): Broadband Dielectric Spectroscopy. – Springer-Verlag, 2003, ISBN 978-3-540-43407-8.
2. Xia, Xiaodong; Zhong, Zheng; Weng, George J. (2017-06-01). "Maxwell–Wagner–Sillars mechanism in the frequency dependence of electrical conductivity and dielectric permittivity of graphene-polymer nanocomposites". Mechanics of Materials. 109: 42–50. doi:10.1016/j.mechmat.2017.03.014. ISSN 0167-6636.
3. Kremer F., & Schönhals A. (eds.): Broadband Dielectric Spectroscopy. – Springer-Verlag, 2003, ISBN 978-3-540-43407-8.
4. Wagner KW (1914) Arch Elektrotech 2:371; doi:10.1007/BF01657322
5. Sillars RW (1937) J Inst Elect Eng 80:378
6. G.McGuinness, Polymer Physics, Oxford University Press, p211

See also

• Debye relaxation
• Dielectric dispersion
• Dielectric function
• Dielectrophoresis
• Dipole
• Permittivity
• Ellipsometry
• Linear response function
• Kramers–Kronig relation
• Green–Kubo relations