Maxwell–Wagner–Sillars polarization

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]

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]