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140 Polymer-based Nanocomposites for Energy and Environmental Applications

5.2.3 Types of losses

Complex permittivity, ε*, can be correlated with dielectric permittivity and loss as in
Eq. (5.7):

∗
ε ¼ ε jε 00 (5.7)
0
0
where ε is the real permittivity of the system. These two dielectric parameters can be
further combined for a certain frequency and temperature by the term called loss tan-
gent, tan δ (Eq. 5.8):

ε 00
tan δ ¼ (5.8)
ε 0
For an ideal capacitor, ε is zero, or there are no losses. However, for a real capacitor,
00
two types of losses can be present. First one is frequency-independent ohmic conduc-
tion losses that are generated due to long-range movement of charges, and the second
one is frequency-dependent dielectric loss associated with the absorption of energy to
transfer the charges with the field [137]. In a polymeric material, generally, two types
of dipolar relaxations exist: One is the dipolar segmental relaxation, i.e., associated
with micro-Brownian motion of the whole chain, called as α relaxation, and the other
is dipolar group relaxation, i.e., associated with localized motion of the molecules and
small chain units, called as β- and γ-relaxation (Fig. 5.3) [138,151,152].
The β-relaxation is associated with relaxation of side groups such as dCH 2 Cl and
dCOOC 2 H 5 about the CdC chain conformational shift of cyclic unit that results in
changes in the orientation of polar groups or local motion of the dipolar group across

Fig. 5.3 Schematic of various
types of relaxations at Movement of small kinetic Micro-Brownian motion
different temperatures. units of main chain or the of whole chain (glass
Reprinted with permission side chains transition temperature)
from Prateek Thakur VK, Rotation of side group about
Gupta RK. Recent progress C – C bond, conformational
on ferroelectric polymer- flip of cyclic unit,
based nanocomposites for Dielectric loss Crankshaft rotation
high energy density
capacitors: synthesis,
dielectric properties, and
future aspects. Chem Rev
2016;116:4260 317.
Copyright 2016 American γ β α
Chemical Society.

Temperature