Page 164 - Polymer-based Nanocomposites for Energy and Environmental Applications

138 Polymer-based Nanocomposites for Energy and Environmental Applications

where P is the polarization caused and E is the applied electric field. The degree of
polarization under the influence of applied field is designated by a term called suscep-
tibility, χ (Eq. 5.5) [137]:

P
χ ¼ ε r 1ð Þ ¼ (5.5)
ε o E

The Clausius-Mossotti equation relates dielectric permittivity and polarizability for
the isotropic nonpolar material (Eq. 5.6) [138]:

ε r 1 Nα
¼ (5.6)
ε r +2 3ε o
where N is the number of atoms or molecules per unit volume and α is the polarizabil-
ity of the material.
Four types of polarizations generally exist in a dielectric material, namely, elec-
tronic, ionic, dipolar, and interfacial polarizations as shown in Fig. 5.2. These polar-
izations have been subdivided into two regimes, i.e., resonance and relaxation
regimes [134,139-143]. Electronic or optical polarization is related with displace-
ment of electron cloud with respect to nucleus in the presence of applied electric
field. Ionic polarization is produced in ionic materials and responds in the infrared
(IR) region. Both the electronic and ionic polarization show resonance at frequen-
cies in the visible and IR range, respectively, and hence classified in the resonance
regime [144].
Since the phenomenon is intramolecular in nature, they are temperature-
independent [138]. To enhance electronic and ionic polarizations, delocalization of
electrons and doping of foreign elements in ionic materials can give fruitful results.
However, delocalization of electrons sets an upper limit for enhancement in dielectric
properties for polymeric materials because it reduces bandgap, and generally, ionic
polarization is only 10%–50% of the electronic polarization [100]. Much higher
dielectric constant of 47 was obtained for dCH 2 (SnF 2 ) 3 d, containing both electronic
and ionic polarization. Replacing carbon with other group 14 elements for a new type
of polymeric material having a structure of dXY 2 d will be a better way to exploit the
electronic and ionic polarizabilities, although chemical stability is a limiting factor.
Here, X designates Si, Ge, and Sn, and Y corresponds to H, F, and Cl, respectively
[145]. As mentioned earlier, the electronic and atomic polarizations respond at higher
frequencies and are instantaneous. It indicates whether the polymer is polar or non-
polar, and the dielectric constant in this region is usually small. So, the orientational
polarization plays a pivotal role in determining effective permittivity of polymeric
dielectrics. The orientation or dipolar polarization exists in polar materials carrying
permanent dipoles such as H 2 O and HCl. As the molecules need energy to overcome
the resistance produced by the surrounding molecules, this phenomenon is
temperature-dependent. When the field is removed, the molecules take time to relax
back to equilibrium. Hence, this type of polarization falls in the relaxation regime and