Frequency dependence of polarizability

The total polarizability of a dielectric is $\alpha = \alpha_e + \alpha_i + \alpha_d$ (+ $\alpha_{sc}$ interfacial). Each mechanism needs a certain time to respond. When the applied AC field changes faster than a mechanism can follow, that mechanism drops out, so $\alpha$ (and $\varepsilon_r$) falls in steps as frequency rises.

 alpha (or er)
   ^
   |____
   |    \  interfacial (space charge)
   |     \_______
   |             \   orientational
   |              \________
   |                       \/\  ionic
   |                          \_______
   |                                  \/\ electronic
   |                                     \______
   +----+--------+--------+--------+-------> f (Hz)
       1e2     1e6-1e9   1e13    1e15
       power   radio/MW  infra-   UV/
       freq.             red      optical

Explanation of each region

1. Interfacial (space-charge) polarization: charges drift to grain boundaries and electrodes. Very slow; it follows the field only up to about $10^2$–$10^3$ Hz.
2. Orientational (dipolar) polarization: permanent dipoles rotate. Molecules have inertia and suffer collisions, so they follow the field up to about $10^{6}$–$10^{10}$ Hz (radio/microwave). Above this, $\alpha_d \to 0$.
3. Ionic polarization: positive and negative ions are displaced. Ions are heavy, so a resonance occurs at infrared frequencies (~$10^{13}$ Hz).
4. Electronic polarization: the light electron cloud shifts. It follows the field up to UV/optical frequencies (~$10^{15}$ Hz). Above that, nothing can respond and $\varepsilon_r \to 1$.

Key points

• Near the relaxation frequencies (interfacial and orientational), the fall is smooth and the dielectric loss ($\varepsilon_r''$) shows a peak.
• Near each resonance (ionic, electronic) there is a small rise then a sharp drop, also with a loss peak.
• At optical frequencies only electronic polarization remains, so $\varepsilon_r = n^2$ (n = refractive index). Example: water has $\varepsilon_r \approx 80$ at low frequency but $n^2 \approx 1.77$ at optical frequency, because dipolar polarization has dropped out.