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Polymer-based nanocomposites 143

5.2.5.1 Lewis’s model

The addition of nanofillers in polymer matrix produces numerous interfaces in
nanometric composites. The nanofiller surface, fully or partially, gets charged due
to the difference in Fermi levels or chemical potential of the nanoparticles and poly-
mer matrix [172]. The matrix, in turn, responds by producing counter charges near the
nanofillers surface [35,141]. Consider if a positively charged particle is present inside
the polymer matrix as shown in Fig. 5.4A.
The nanoparticle surface is proposed to be planar for simplicity. The charged nano-
particle result in redistribution of charges in the matrix due to coulomb attraction,
which forms an electric double layer consisting of a Stern layer and a Gouy-Chapman
diffused layer [168]. The Stern layer or Helmholtz double layer is produced on the
nanoparticle surface due to the adsorption of counterions. The diffused layer is caused
around the Stern layer by the distribution of negative and positive ions. This layer
determines the permittivity of the polymer nanocomposites and becomes more
predominant near percolation threshold of the fillers (Fig. 5.4B; also see
Section 5.2.6.4). Fig. 5.4A represents the electric potential distribution, ψ(r) with
respect to the distance from the nanoparticle surface [173-175]. This behavior has
been observed to satisfy the solutions of Poisson and Boltzmann equations [176].
The combined Poisson-Boltzmann equation can be represented as Eq. (5.9):

Stern layer Diffuse layer + Diffuse layer –

Nanoparticle surface Polymer matrix + –

+
–

+
–
Y s Capacitor plate (positively charged) + Polymer matrix – (negatively charged) Capacitor plate
Y o –
+
Y(r)
+ Nanoparticle –
r
(A) (B)

Fig. 5.4 (A) Diffuse electric double layer produced by a positively charged particle in a
polymer matrix containing mobile ions, along with the resulting electric potential distribution
ψ(r). (B) Conduction via diffuse double layers in a composite system.
Reprinted with permission from Prateek Thakur VK, Gupta RK. Recent progress on
ferroelectric polymer-based nanocomposites for high energy density capacitors: synthesis,
dielectric properties, and future aspects. Chem Rev 2016;116:4260 317. Copyright 2016
American Chemical Society.