Polarization types and orientational polarization

Polarization in a dielectric is of four types:

1. Electronic: shift of electron cloud relative to nucleus; all materials; $\alpha_e = 4\pi\varepsilon_0R^3$.
2. Ionic: relative shift of positive and negative ions in ionic crystals (NaCl).
3. Orientational (dipolar): alignment of permanent dipoles of polar molecules (H₂O, HCl).
4. Interfacial (space-charge): accumulation of charges at grain boundaries and electrodes.

Orientation polarization

• Polar molecules have a permanent dipole moment $p_0$. Without a field they point randomly due to thermal motion, so the net polarization is zero.
• An applied field exerts a torque $\tau = p_0E\sin\theta$ that tends to align them; collisions (heat) oppose alignment.

  E = 0:   / \ | - \ /    random, P = 0
  E -> :   -> / -> -> \   partial alignment, P > 0

• Energy of a dipole at angle $\theta$: $U = -p_0E\cos\theta$. With the Boltzmann distribution, the average is $\langle\cos\theta\rangle = L(x) \approx \dfrac{p_0E}{3kT}$ for $p_0E \ll kT$.
• Average dipole moment and polarizability:

$$p_{av} = \frac{p_0^2E}{3kT}, \qquad \alpha_d = \frac{p_0^2}{3kT}$$

• Features: strongly temperature dependent ($\propto 1/T$); slow, so it disappears above about $10^{9}$–$10^{11}$ Hz; large in water ($\varepsilon_r \approx 80$); causes dielectric loss near its relaxation frequency.