Optimization of electric energy density in epoxy aluminium nanocomposite

INTERNATIONAL Electrical EngineeringELECTRICAL ENGINEERING
International Journal of JOURNAL OF and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME
& TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 4, Issue 1, January- February (2013), pp. 36-45 IJEET
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2012): 3.2031 (Calculated by GISI)
www.jifactor.com ©IAEME

OPTIMIZATION OF ELECTRIC ENERGY DENSITY IN
EPOXY-ALUMINIUM NANOCOMPOSITE AS DIELECTRIC

Siny Paul1, Sindhu T.K2
1
(Department of Electrical and Electronics Engineering, Mar Athanasius College of
Engineering, Kothamangalam, Kerala, India, siny_binoy@yahoo.co.in)
2
(Department of Electrical Engineering, National Institute of Technology Calicut, Kerala,
India, tk_sindhu@nitc.ac.in)

ABSTRACT

Dielectric materials with large permittivity and high breakdown strength are required
for large electric energy storage in capacitors. Polymers of high breakdown strength
combined with nanoparticles of high permittivity substantially enhance the electric energy
density of the resulting nanocomposites. In this paper, epoxy-aluminium nanocomposite is
modeled as a three phase material and the dielectric properties of the nanocomposite are
investigated using this model. Influences of aluminium particle size and filler loading on the
permittivity, breakdown strength and electric energy density of the nanocomposite are
evaluated. Numerical results show a drastic increase in permittivity close to the transition
threshold. As the volume fraction increases, there is reduction in breakdown strength, but the
net effect is a notable increment in energy density. The filler size and concentration
correspond to maximum energy density are evaluated. It is found that inter particle distance
controlling breakdown strength have a significant effect on the electric energy storage.

Keywords : Dielectric permittivity, Energy density, Epoxy, Nanocomposite, Polarization.

1. INTRODUCTION

Polymers have high breakdown strength compared to ceramics but low dielectric
constant in the range of 2-5. While ceramic materials usually have large permittivity, their
applications are limited by their relatively small breakdown strength. Since the electric
energy density in a dielectric material is ½kEb2 where k is the dielectric constant or
permittivity of the material and Eb is the breakdown strength, both large permittivity and high
breakdown strength are required for large electric energy storage. Therefore, it is important to
36

International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –

keep a balance between the contradictory criteria of enhancing dielectric constant while
maintaining high breakdown strength. Numerous efforts have been made in the past few
years to combine the polymers of high breakdown strength with ceramic particles of high
permittivity.
Conductive filler - polymer composite is another approach towards high-k materials,
which is a kind of conductor-insulator composite based on percolation theory [1]. Ultra-high
k can be expected with conductive filler - polymer composites when the concentration of the
conductive filler is approaching the percolation threshold. The minimum volume content of
the conducting filler at which the drastic change in electrical properties begins is referred to
as the percolation threshold [2]. Sometimes the effective k of the metal-insulator composite
could be three or four magnitudes higher than the k of the insulating polymer matrix. And
also this percolative approach requires much lower volume concentration of the filler
compared to traditional approach of high-k particles in a polymer matrix [3]. Therefore, this
material option represents advantageous characteristics over the conventional ceramic-
polymer composites [1,2]. Various conductive fillers, such as silver (Ag), aluminium (Al),
nickel (Ni), carbon black, have been used to prepare the polymer-conductive filler composites
[4-9]. For instance, Z. M. Dang, Y. Shen and C. W. Nan [7] and Jiongxin Lu and C.P.Wong
[1] reported k value of 400 and 2000 in Ni/PVDF composite and Ag flake/epoxy composite
respectively.
2. MODELING OF POLYMER NANOCOMPOSITES
Polymer nanocomposites are defined as polymers in which small amounts of
nanometer size fillers are homogeneously dispersed. The small size of nanoparticles relative
to micron fillers means that there are many more particles and much more interfacial area per
unit volume of filler, when the particles are well dispersed. The polymer nanocomposite is
modeled as a three-phase material, consisting of a polymer matrix (phase 1), an interfacial
phase of fixed thickness l (phase 2), and nanoparticle fillers (phase 3), schematically shown
in Fig.1. The interfacial phase is between polymer matrix and nanoparticles and this can be
viewed as a core-shell type of structure [10].

Fig.1. Schematic diagram of a dielectric nanocomposite consisting of polymer matrix,
nanoparticles, and interfacial phase.

37


There are large interfacial areas in a nanocomposite, which could promote interfacial
exchange coupling through a dipolar interface layer and lead to enhanced polarization and
polarizability in polymer matrix near the interface [11,12]. As a result, enhanced permittivity
can be expected in the polymer matrix near the interfaces. As particle loading increases, the
interaction zones begin to overlap, leading to effective percolation of the interfacial areas at
relatively low loadings. The inclusion of nanoparticles with high dielectric constants
increases the average dielectric constant of a composite. They also produce a highly
inhomogeneous electric field with local hot spots of increased electric field concentration and
reduced dielectric strength, thus reducing the effective breakdown strength of the composite
[10].
According to J.Y.Li et al. [10], the effective permittivity of the nanocomposite can be
expressed as:

k * = k 1 + f 2(k 2 − k 1) a 2 + f 3( k 3 − k 1)a 3 (1)

where k* is the effective relative permittivity of the nanocomposite, k1, k2, k3 are the
relative permittivities of matrix, interphase and nanoparticles respectively. f2 is the volume
fraction of interfacial phase which is given by:

(r + l ) 3 − r 3
f2 = f3 (2)
r3
The interfacial thickness l is governed by exchange constant and permittivity of polymer
and thus it is reasonable to assume that the interfacial phase has fixed thickness independent
of nanoparticle size. f3 is the volume fraction of nanoparticles and r is the nanoparticle
radius. From Eq.(2) it is clear that the interfacial fraction f2 increases substantially when the
nanoparticle size decreases. ar is the electric field concentration factor for corresponding
phase r, which relates the average electric field in phase r to that applied at boundary, E0.
The average electric field in phase r is given by:

E r = ar E0 (3)

For the core-shell type of structure, the electric field concentration factor is given by:

[
ar = 1 − s (kr − k * ) −1 k * + s ]−1
, r = 2,3 (4)

where s is the component of the dielectric Eshelby tensor that is related to the
depolarization factor and for spherical particles s is 1/3. As k* appears on both sides of
Eq.(1), a numerical solution is required. When a2 and a3 are determined from Eq.(4), the
electric field concentration factor a1 can then be determined from the normalization
condition:

38


∑
3
r =1
f r ar = 1 (5)

With the addition of nanoparticles of larger permittivity, the average electric field in
polymer matrix E1 will be enhanced compared to that applied at boundary as:

E1 = a1 E0 (6)

When the field fluctuation is taken into account, electric field in the polymer matrix is
again enhanced to E2 which is given by Eq.(7) as:

2
E2 = E1 + E12 − E1
(7)

2 1 δk * 2
where E 1 = E0 (8)
f1 δk1

Which is the second order moment of electric field in polymer matrix . Accordingly, the
breakdown strength of the composite will be reduced.
This criterion only considers the field fluctuation in the polymer matrix due to the addition
of nanoparticles and ignores the introduction of defects that could reduce breakdown strength
even further. As such, the results can be viewed as an upper bound on the breakdown strength
of the composite.

3. DIELECTRIC CONSTANT OF ALUMINIUM

The present study concentrates mainly on the modeling and evaluation of the
dielectric properties of aluminium–epoxy nanocomposite as a function of composition and
particle size. Relative permittivity of epoxy is around 3.6. But the concept of dielectric
constant for a conducting material is not defined. The dielectric constant is related to the
electronic susceptance in an isotropic material. The susceptance is basically the ratio of
polarization to applied electric field. A conductor have "bound" electrons in that they cannot
leave the entire material, but are free to polarize across the entire length of a conductor. When
an external electric field is applied to a conductor, the entire conductor will be polarized, such
that the polarization causes the electric field inside the conductor to be zero (electrostatic
equilibrium). In a normal dielectric, the bound electrons cannot move as far as in a conductor
and hence they have a much smaller polarization. Hence, the polarization vectors in a
conductor are nearly infinite compared to the polarization vectors of a dielectric. The
susceptance is therefore very large and so is the permittivity. It should be noted that the
concept of permittivity of conductor might be used only to express the effect of the metal
filler on the dielectric constant of the polymer matrix.
For the conventional (micron sized) fillers, based on the Lichtenecker-Rother logarithmic
law [13] of mixing applicable to chaotic or statistical mixtures, the relative permittivity of
the microcomposite is given by:

39


log kc = y p log k p + ym log k m (9)

where kc is the relative permittivity of composite and yp , ym are volume fractions of the two
components having relative permittivities kp and km.
Vishal Singh, A. R. Kulkarni and T. R. Rama Mohan [2] conducted experiments on
aluminium-epoxy microcomposites and evaluated the value of composite permittivity for
different filler loadings. They used Eq.(9) to evaluate permittivity of aluminium (km) as
follows; for each composition point, determined the value of km such that the value of
composite permittivity obtained using the above equation is equal to the experimental value
and then estimated the average of the values of km found at various composition points. The
average value of km was found to be 1145.

4. RESULTS AND DISCUSSIONS

In this work, Al-epoxy nanocomposite is modeled and its permittivity, breakdown
strength and energy density are evaluated. Modeling is done on the assumption that the
dispersed particles are spherical in shape and of uniform size.

3µm
Relative permittivity of the composite

600
20nm
500 60nm
100nm
400

300

200

100

0
0 10 20 30 40 50 60
% volume of Nanoparticles added
Fig.2. Relative permittivity of epoxy-aluminium composites.
(Filler size of 3µm, 20nm, 60nm and 100nm )

Solving equations (1) to (5), substituting 3.6 for k1 and 1145 for k3 which are the relative
permittivities of epoxy and aluminium respectively, the effective permittivity of aluminium-
epoxy nanocomposite for different filler concentration is evaluated and plotted as shown in
Fig.2. Effective permittivity of three different sizes of nanofillers such as 20nm, 60nm and
100nm are evaluated and compared with that of the microcomposite.
It is clear from Fig.2 that the relative permittivity of nanocomposites is very high
compared to relative permittivity of microcomposites. There is a rapid increase in effective
permittivity beyond a threshold in volume fraction. In addition, the interfacial exchange

40


coupling shifts the transition threshold towards lower volume fraction and higher dielectric
constants are obtained for composite with smaller nanoparticles. Nanoparticles can indeed
lead to higher dielectric constant in composites compared to microscale particles. This
permittivity enhancement is attributed to interfacial polarization also referred to as the
Maxwell–Wagner–Sillars (MWS) effect, a phenomenon that appears in heterogeneous media
consisting of phases with different dielectric permittivity and conductivity. This may be due
to the accumulation of charges at the interfaces [2].
Electric field enhancement in polymer matrix is calculated using Eq.(6) and also the
increment in electric field due to field fluctuations is considered to evaluate the breakdown
strength of the composite. DC breakdown strength of pure epoxy is around 60kV/mm [14].
The calculated breakdown strength of the composite as a function of nanoparticle volume
fraction is given in Fig.3. Three cases of aluminium particle size 20nm, 60nm and 100nm are
considered. It is observed that the breakdown strength decreases rapidly with the increase of
nanoparticle volume fraction until the percolation threshold is reached. Beyond the
percolation transition, the breakdown strength rebounds because the field fluctuation is
reduced as nanoparticle fraction increases. As the inter particle distance decreases below the
limit, breakdown strength falls down rapidly. However, the calculated values are the upper
bound on the breakdown strength because the agglomeration of the metal particles and other
defects are likely to reduce the breakdown strength even further.
DC Breakdown Voltage of Composite (KV/mm)

60

20nm
50
60nm
100nm
40

30

20

10

0
0 10 20 30 40 50 60
Fig.3. Breakdown strength of epoxy-aluminium nanocomposites
(Filler size of 20nm, 60nm and 100nm )

The energy density of nanocomposite as a function of volume fraction of nanoparticles is
calculated. It is compared with the energy density of pure epoxy(0.0573J/cm3) and the energy
density increment ratio is plotted as shown in Fig.4. Below percolation transition, the net
energy density is smaller than that of pure polymer matrix. Beyond percolation transition,
energy density rises rapidly, but depends on the reliability of breakdown strength.

41


The microstructure of nanocomposite must be carefully controlled to avoid defects and
ensure uniform dispersion to obtain expected gain in electric energy density. Energy density
attains a maximum value and then reduces due to the rapid reduction in breakdown strength
as the filler concentration increases. The energy density increment ratio plotted in Fig.4
shows that energy density of the composite can be upto 15 - 25 times as that of pure epoxy.
25
20nm
Energy density increment ratio

60nm
20
100nm

15

10

5

0
0 10 20 30 40 50 60
Fig. 4. Energy density increment ratio of epoxy-aluminium nanocomposites

Maximum energy density increment ratio and corresponding percentage volume of fillers
added vs. filler size are shown in Fig.5 and Fig.6 respectively. For composites with smaller
nanoparticles, the maximum energy density is obtained at lower volume fractions.
Maximum Energy density increment ratio

30

25

20

15

10

5

0
0 20 40 60 80 100 120 140
Filler size (nm)
Fig.5. Maximum energy density increment ratio vs. filler size

42


60

% volume of fillers correspond to
50

maximum energy density
40

30

20

10

0
0 20 40 60 80 100 120 140
Filler size (nm)

Fig.6. Percentage volume of nanoparticles added correspond to
maximum energy density vs. filler size.
Uniform dispersion of nanoparticles in nanocomposite materials is required because nanoparticle
agglomeration will lead to undesirable electrical or material properties. Therefore, dispersion of
nanoparticles is an extremely important contributor for achieving improved dielectric properties and
electric energy density.
The inter particle distance D is calculated based on Eq.(10) assuming that the nanofillers are
spherical in shape [15].
1
π  ρ
  100  wt %  ρ m   3 
D=   m
  wt % 1 − 100 1 − ρ   − 1 d
   (10)
 6  ρn
    n  


Where ρm is the specific gravity of matrix, ρn is the specific gravity of filler and d is the diameter
of nanoparticle.

100nm
200
60nm
Interparticle distance (nm)

20nm
150

100

50

0
0 10 20 30 40 50 60

Fig.7. Interparticle distance of epoxy-aluminium nanocomposite.

43


From the plot of inter particle distance (Fig.7), it is observed that maximum energy
density is obtained at the same inter particle distance for each particle size. When the inter
particle distance is reduced below this, breakdown strength of the composite falls down
rapidly. Thus inter particle distance plays an important role in determining the dielectric
properties of nanocomposites.

5. CONCLUSION

Theoretical modeling of epoxy-aluminium nanocomposite shows that the inclusion of
aluminium nanoparticles increases the effective permittivity of the composite. The
permittivity increases rapidly when a particular volume fraction (transition point or threshold)
is reached. It is observed that the breakdown strength decreases rapidly with increase of
nanoparticle volume fraction until the threshold is reached. Beyond the transition, the
breakdown strength rebounds because the field fluctuation is reduced as nanoparticle fraction
increases. But the net effect is a notable increment in energy density. The electric energy
density below transition threshold is low and the net energy density is smaller than that of
pure polymer matrix. Beyond the transition, energy density rises rapidly and reaches a
maximum value and then falls down as the inter particle distance reduces. It is observed that
filler concentration correspond to maximum energy density is shifted towards lower volume
fractions as the size of nanoparticles is reduced. From the simulations it is concluded that an
energy density increment up to 25 times is possible by optimally selecting the filler size and
concentration. Modeling and evaluation of dielectric properties and energy density of the
nanocomposite shows that epoxy-aluminium nanocomposite is a promising candidate
material for high energy density capacitor applications.

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Optimization of electric energy density in epoxy aluminium nanocomposite

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