Page 163 - Polymer-based Nanocomposites for Energy and Environmental Applications

Polymer-based nanocomposites 137

breakdown strengths are the two most basic parameters that influence the energy den-
sity of the polymer nanocomposites. The breakdown strength and the energy density
of linear dielectrics are related as follows (Eq. 5.2) [53,130]:

1 2
Energy density ¼ ε o ε r E b (5.2)
2
where ε r and ε o is the dielectric permittivity of the material and vacuum
(8.85 10 12 F/m), respectively, E b is the breakdown strength of the medium. Break-
down strength is the maximum electric field that can be employed on a dielectric
material without making it conducting. The square relationship between the energy
density and the breakdown strength follows that higher breakdown strength is needed
to obtain higher energy density. Fillers with fair dielectric constant are imperative to
get improved energy density, but its loading cannot be increased beyond a certain limit
that may lead to agglomeration and hence decrease in breakdown strength. Also, a
large difference in the permittivity of the fillers and matrix causes inhomogeneity
in the electric fields of the polymers and fillers and should be hence avoided to
increase the breakdown strength and subsequent energy density [131]. Another crucial
parameter is dielectric loss that occurs due to the rate of energy transfer associated
with molecular collisions under the influence of an electric field.
The dielectric loss can be related to the average dissipated power density inside a
dielectric, i.e., the energy absorbed by the dielectric per unit volume per unit time is
given by Eq. (5.3) [132-134]:

1 00 2
Dissipated power density ¼ ωε o ε E o (5.3)
2
where ε is the imaginary permittivity of the system, ω is the frequency, and E o is the
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electric field applied across the film. It follows that the higher ε for the same ω and
E o , leads to the higher power dissipation in a dielectric material. Commercially, capac-
itors are required to work at high-temperature conditions, and a material with higher
thermal conductivity can give useful results. For example, biaxially oriented polypro-
pylene (BOPP) can be used at temperatures up to 100°C. Certain polymers like poly-
ethylene naphthalate (PEN) (up to 150°C) and polyphenylene sulfide (PPS) (up to
175°C) can work under higher temperatures than BOPP but under higher-cost setup.
Thus, development of higher temperature viable polymer nanocomposites is a
must [135].

5.2.2 Polarization phenomena
Polarization is defined as the total dipole moment in a dielectric per unit volume. It can
be related to dielectric constant according to the following equation [136]:

P ¼ ε r 1ð Þε o E (5.4)