Electric polarization definition

Polarization of molecules in the electric field

Electric polarization arises when a non-polar substance placed between two parallel plates with an applied electric field. The electric field tends to attract the negatively charged towards the positive plate and positive charge towards a negative plate.

Thus under this condition, there will be observed an electrical distortion on the molecule. Such type of distortion in a molecule is called the electric polarization.

But the polarization disappears as soon as the field is withdrawn and the molecule comes back to its original state.

Induced polarization of polar molecules

Let induced polarization = Pi and induced dipole moment = µi.

The induced dipole moment or simply the induced moment directly proportional to the strength of the electric field applied(F).

∴ μi ∝ F

But when F is very low, otherwise, hyperpolarization may occur among the polar molecules.

μi = αi F
where αi = proportionality constant.

This constant is called induced polarizability constant of the molecule.

Thus the definition of induced polarization, the amount of induced moment in the molecule when the unit electric field strength applied.

Unit and dimension of polarizability

From the definition, we can prove that the polarization has the dimension of the volume.

    \[ \alpha _{i}=\frac{\mu _{i}}{F} \]

    \[ \therefore dimension\, of\, \alpha _{i}=\frac{dimension\, of\, \mu _{i}}{dimension\, of\, F} \]

Unit of dipole moment= esu × cm and force = esu cm-2, obtained from Coulomb’s law.

    \[ \therefore unit\, of\, \alpha _{i} =\frac{esu\times cm}{esu\times cm^{-2}}=cm^{3} \]

Thus it can also be shown that, αi = r3 where r = radius of the molecule assuming it to have a spherical shape.

The polarizability of the atom increases with the increasing atomic size, atomic number, and ionization energy. Thus atom behaves like a dipole and this dipole moment induced by the applied electric field.

Clausius mossotti equation

Mossotti derived a relation between the polarizability and the dielectric constant of the non-polar medium between two plates from electromagnetic theory.

    \[ \boxed{P_{i}=\left ( \frac{D-1}{D+2} \right )\times \frac{M}{\rho }=\frac{4}{3}\pi \, N_{0}\, \alpha _{i}} \]

where N0 = Avogadro number,
M = molar mass,
ρ = density of the medium,
and αi = polarizability constant.

Induced polarizability constant and given when the distortion produced in the 1 mole of the substance by a unit electric field. Thus it is a constant value for a given molecule and independent of temperature.

    \[ D=dielctric\, constant=\frac{C}{C_{0}} \]

where C = capacitance of the condenser containing the substance and C0 in the vacuum. Thus D is the dimensionless quantity and it is unity for vacuum. Other substances value of D greater than unity.

So the induced dipole moment of the substance calculated by measuring dielectric constant, density (ρ) and molar mass (M) of the substance.

Debye equation for molar polarizability

For the polar molecules like methyl chloride, water, hydrogen fluoride, etc, the molar polarization not constant. It decreases with increasing temperature.

Thus the Clausius Mossotti equation fails very badly for the polarity of the bond. The reason for the failure put forward by P Debye.

According to him, when an electric field applied between two parallel plates containing polar gaseous molecules, two effects will occur.

  1. Induced polarization
  2. Orientation polarization

Induced polarization tends to increase the induced moment among the molecules which discuss broadly before.

electric polarization of polar molecule
Electric polarization of the molecule

Definition of orientation polarization

When an electric field produces on the polar molecules, the dipolar molecules tend to orient in the direction of the field. This is called orientation polarization. It expresses as

    \[ P_{o}=\frac{4}{3}\, \pi \, N_{0}\, \alpha _{o} \]

where α₀ = orientation polarisability.

Debye calculated the value of α₀ = μ²/3KT. Thus considering the two tendencies

  1. polar molecules tend to orient in the direction of the applied field (applied)
  2. thermal orientation tends to destroy the alignment of the molecules.

Total electric polarization

The definition of total electric polarization,

Pt = Pi + Po

    \[ \therefore \left ( \frac{D-1}{D+2} \right )\frac{M}{\rho }=\frac{4}{3}\, \pi \, N_{0}\, \alpha _{i}\, +\frac{4}{3}\, \pi N_{0}\left ( \frac{\mu ^{2}}{3kT} \right ) \]

Polarizability temperature dependence

A polar chemical bond fixed and unable to orient in the fixed direction. Thus orientation polarization equal to zero. Hence for the condensed system where strong intermolecular forces prevent the free rotation of the molecules. But at very high temperatures tending to infinity.

1/T = 0 and Pt = 0
∴ Pt = Pi

Thus at high temperatures, the polar molecules rotate at such high speed that orientation polarization vanishes.