Frequency Dependence of Polarization

FREQUENCY DEPENDENCE OF POLARIZATION

When an alternating field is applied across the material, the polarisation occurs as a function time.

The polarisation P (t) as a function of time t is given by

P(t) =P [1- e ^(-t/t_r)]

where P - the maximum polarisation which occurs due to the static field applied for a long time

t_r = relaxation time i.e., time taken for a particular polarisation process to take place.

The relaxation time t_r is s measure of the time scale of polarisation process. It is the time taken for a polarisation process to reach 0.63 of the maximum value of polarization

The relaxation times are different for different kinds of polarisation mechanisms.

Frequency Dependence

(i) Electronic polarisation is extremely rapid and is complete at any instant the voltage is applied. Thus, even when the frequency of the applied voltage is very high in the optical range (~ 10¹⁵ Hz), electronic polarisation occurs during every cycle of the applied voltage

(ii) Ionic polarisation is slower and it is due to displacement of ions over a small distance when the field is applied. Since ions are heavier than electron cloud, the time taken for displacement is larger.

The frequency of the applied electrical field with which the ions will be displaced is equal to the frequency of the lattice vibrations (~ 10¹³ Hz). This means that for optical frequency the ions do not respond, as the time required for lattice vibrations is nearly 100 times larger than the period of applied voltage at optical frequencies. Thus, at optical frequencies, there is no ionic polarisation.

If the frequency of the applied voltage is less than 10¹³ Hz ie., infrared range, the ions have enough time to respond during each cycle of the applied field (fig 1.9).

(iii) Orientation polarisation is even slower than ionic polarisation. The relaxation time for orientation polarisation changes with the type of dielectric materials (ie., solids or liquids) used.

The relaxation time for orientation polarisation in a liquid dielectric material is less than in a solid dielectric material ie., the molecules in a liquid easily reorient themselves compared to solids

Orientation polarisation occurs only at electrical frequencies (audio and radio frequency) range (≈ 10⁶ Hz) as shown in figure

(iv) Space charge polarisation is the slowest process since in this case ions have to diffuse (jump) over several interatomic distances.

Space - charge polarisation occurs only at power frequencies (50-60 Hz) as shown in fig.1.9.

Therefore from fig 1.9 it is noted that at low frequencies, all the four types of polarisations present and the value of the total polarisation is very high (maximum). The total polarisation value decreases with the increase in frequency. Hence at high frequencies, the value of the polarisation is very small (minimum)..)

Fig. 1.9 and Table 1.1 explains all the four types of polarization at different frequency ranges.

Table 1.1 Types of polarization and their frequency ranges

Table 1.2 Comparison of various types of polarisation mechanisms