View source for 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|date=January 2018}}, and later generalized by Wagner <ref>Wagner KW (1914) Arch Elektrotech 2:371; {{doi|10.1007/BF01657322}}</ref> and Sillars.<ref>Sillars RW (1937) [http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5317372 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 ==
<References/>

== See also ==
{{colbegin}}
* [[Debye relaxation]]
* [[Dielectric dispersion]]
* [[Dielectric function]]
* [[Dielectrophoresis]]
* [[Dipole]]
* [[Permittivity]]
* [[Ellipsometry]]
*[[Linear response function]]
*[[Kramers–Kronig relation]]
*[[Green–Kubo relations]]
{{colend}}

{{DEFAULTSORT:Maxwell-Wagner-Sillars polarization}}
[[Category:Spectroscopy]]
[[Category:Electric and magnetic fields in matter]]