Page 172 - Polymer-based Nanocomposites for Energy and Environmental Applications

146 Polymer-based Nanocomposites for Energy and Environmental Applications

poly(vinylidene fluoride) nano-BaTiO 3 composites was due to the increased electric
displacement of nanoparticles and not due to changes in the crystallinity of the poly-
mer [45]. Nanoparticles are considered to provide higher breakdown strength as they
disrupt the continuity of the path provided to charge carriers. Again, Roy et al.
observed that the introduction of surface-treated and untreated nanosilica to cross-
linked polyethylene leads to a lower dielectric constant compared with the base poly-
mer [179]. Contrarily, higher dielectric constants than predicted were shown in
micron-filled composites by various mixing rules. This enhanced dielectric constants
in microcomposites was attributed to interfacial polarization or the accumulation of
charge in a local environment as they drift through the material. However, micro-
composites possess much lower breakdown strengths compared with the base poly-
mer. Contrarily, nanocomposites showed at least a 15% increase in breakdown
strength compared with the pure polymer at room temperature. It was considered that
the decrease in chain movement of the polymer through physical bonding or confine-
ment enhanced breakdown strength of the nanocomposites, as supported by the elim-
ination of a broad loss peak. The addition of nanofillers confines the chain length of
the polymer and hence reduce Maxwell-Wagner-Sillar-type interfacial polarization.
Such polarization actually arises due to the differences in permittivity of the polymer
and the filler. It indicates that the choice of surface groups influences the interfacial
structure; however, there is still doubt on how interfacial modification influences
dielectric breakdown [13].

5.2.6 Predicting enhanced permittivity of polymer
nanocomposites: Theoretical models

The enhanced permittivity of a polymer nanocomposite depends on the individual per-
mittivities of fillers and polymer matrix along with optimized filler loadings and inter-
actions among them. To obtain improved dielectric constant of the nanocomposites,
various models have been developed. These models have been designed based on cer-
tain assumptions, which in turn give an insight into various properties of the polymer
nanocomposites.

5.2.6.1 Lichtenker’s formula

Eq. (5.13) represents Lichtenker’s formula. It is a logarithmic mixture formula and is
most efficient in calculating the effective permittivity of the polymer nanocomposite
[180-182].
α
ε α ¼ φ ε + φ ε α (5.13)
eff f f m m
ε eff is the effective permittivity of the nanocomposites, ε m and ε f are the dielectric per-
mittivities of the polymer matrix and insulating filler, respectively, and φ f and φ m are
the volume fractions of fillers and matrix, respectively. Here, α varies between 1 and
1 and hence sets upper and lower limits of the permittivity for the mixture.