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.<ref>Kremer F., & Schönhals A. (eds.): Broadband Dielectric Spectroscopy. – Springer-Verlag, 2003, ISBN 978-3-540-43407-8.</ref>
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.<ref>Kremer F., & Schönhals A. (eds.): Broadband Dielectric Spectroscopy. – Springer-Verlag, 2003, ISBN 978-3-540-43407-8.</ref>
Models
The simplest model for describing an inhomogeneous structure is a double layer arrangement, where each layer is characterized by its permittivity <math>\epsilon'_1,\epsilon'_2</math> and its conductivity <math>\sigma_1,\sigma_2</math>. The relaxation time for such an arrangement is given by <math>\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 <ref>Wagner KW (1914) Arch Elektrotech 2:371; doi:10.1007/BF01657322</ref> and Sillars.<ref>Sillars RW (1937) J Inst Elect Eng 80:378</ref> Maxwell considered a spherical particle with a dielectric permittivity <math>\epsilon'_2</math> and radius <math>R</math> suspended in an infinite medium characterized by <math>\epsilon_1</math>. Certain European text books will represent the <math>\epsilon_1</math> constant with the Greek letter ω (Omega), sometimes referred to as Doyle's constant.<ref>G.McGuinness, Polymer Physics, Oxford University Press, p211</ref>
References
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