Thermal and electrical behaviour of epox
Thermal and Electrical Behaviour of Epoxy-based
Microcomposites Filled with Al2O3 and SiO2 Particles
Roman Kochetov
Thomas Andritsch
Peter H.F. Morshuis
Johan J. Smit
Delft University of Technology
High Voltage Components & Power Systems
Delft, the Netherlands
[email protected]
Abstract—Epoxy resin is a polar thermosetting polymer that is
widely employed in different branches of industry and everyday
life, due to their stable physical and chemical properties. Of all
the polymer materials currently being used in the electrical
insulation industry, epoxy resin is the most widely used kind,
together with polyethylene and chosen as the base polymer
material in the present study. As a common practice, in order to
obtain materials of the desired thermal, mechanical and electrical
properties, polymers are processed with different types of
inorganic fillers. In this paper, the authors made an attempt to
thoroughly analyze both the thermal and the electrical behaviour
of the created epoxy microcomposites. Epoxy-based composites
containing microparticles of aluminum oxide and silicon dioxide
were prepared by high shear mechanical mixing and ultrasonic
processing to obtain a fine dispersion of the fillers in the matrix.
The incorporation of all filler types led to noticeable
improvement in thermal conductivity compared to the pure
epoxy resin. The thermal conductivity and the relative
permittivity of the composites were greatly influenced by the
filler loading of the inorganic particles. Rules of mixture are used
to predict the thermal conductivity and the relative permittivity
of two-phase composites have been applied to compare
experimental results with theoretical models.
Keywords - microcomposite, epoxy resin, Al2O3, SiO2, thermal
conductivity, relative permittivity
I.
INTRODUCTION
Epoxy resin (ER) is a common electrical insulating
polymer, which is used in high voltage cast resin transformers;
cable joints, terminations and other accessories; rotating
machines; bushings; GIS spacers [1], etc. Polymers used for
electrical insulation are usually reinforced with inorganic
fillers to improve the thermal, electrical and mechanical
properties. In previous studies we investigated the thermal and
electrical properties of nanocomposites containing one or two
types of nanoparticles with a concentration of up to 10 wt.%
[2, 3]. This paper is focused on the study of the same
properties of microcomposites but the concentration of the
filler is much higher – up to 60 percent by weight.
II.
EXPERIMENTAL
A. Sample fabrication
The epoxy resin system used in this study is a
commercially available Araldite CY231 epoxy resin with
This work was performed for the nanoPOWER project, which is supported by
a Dutch government IOP-EMVT grant.
978-1-4244-6300-8/10/$26.00 ©2010 IEEE
anhydride hardener Aradur HY925. The micro aluminum
oxide (Al2O3) and silicon dioxide (SiO2) particles have an
average particle size of 4 and 20 μm, respectively.
Epoxy composites containing Al2O3 or SiO2 microparticles
were fabricated in six steps:
1) Mixing the epoxy resin, hardener and filler by
conventional mechanical high shear stirring;
2) Degassing;
3) Mixing in an ultrasonic bath at 42 kHz;
4) Casting into the molds;
5) Curing for 3 hours at 140 oC;
6) Postcuring for 3 days at 140 oC.
Several types of alumina and silica microcomposites were
fabricated with a fillgrade up to 60 percent by weight. The
samples for thermal conductivity were prepared as plates with
dimensions of 110×70×3 mm. For dielectric spectroscopy
analysis the samples were prepared as discs with a diameter of
40 mm and a thickness between 0.4 - 0.7 mm.
Table I lists the set of materials used in this study.
B. Thermal conductivity and dielectric spectroscopy
measurements
The thermal conductivity measurements were realized with
a THASYS system, produced by Hukseflux Thermal Sensors.
This system performs a direct measurement which allows the
TABLE I.
Specimen
Neat ER
ER-Al2O3-5
ER-Al2O3-10
ER-Al2O3-20
ER-Al2O3-30
ER-Al2O3-40
ER-Al2O3-50
ER-Al2O3-60
ER-SiO2-20
ER-SiO2-40
ER-SiO2-60
SPECIMENS STUDIED
Nanofiller
Neat Epoxy Resin system
Epoxy system + 5wt.% Al2O3
Epoxy system + 10wt.% Al2O3
Epoxy system + 20wt.% Al2O3
Epoxy system + 30wt.% Al2O3
Epoxy system + 40wt.% Al2O3
Epoxy system + 50wt.% Al2O3
Epoxy system + 60wt.% Al2O3
Epoxy system + 20wt.% SiO2
Epoxy system + 40wt.% SiO2
Epoxy system + 60wt.% SiO2
determination of the absolute value of the thermal
conductivity. With a combination of a thin heater, two samples
of similar thickness and two heat sinks it is possible to
generate a homogeneous thermal field with a well defined heat
flux through the samples.
A straightforward calculation of the thermal conductivity
was made using the following equation:
λ=
Φ ⋅ H eff
ΔT
,
(1)
where λ is thermal conductivity, Φ is the heat flux derived
from the heated power, H eff is the effective sample thickness
and ΔT is the differential temperature across the samples.
The thermal conductivity data represent the average value
for the thermal conductivity of both samples. The
measurements are performed in a climate chamber at 18 °C to
avoid any influence due to changes of the ambient temperature
during measurement. The accuracy of the measurements is
6%. Each data point corresponds to an average value of 4
measurements.
The real part of the permittivity ε ′ (relative permittivity)
was determined by dielectric spectroscopy (DS) using a
Novocontrol ALPHA-A analyzer in combination with a ZGS
active sample cell. All samples were measured in the
frequency range of 10-2 - 107 Hz and at temperatures between 20 ºC and 120 ºC.
III.
microparticles. The epoxy is a thermal barrier for heat
propagation, while the filler material transmits the heat much
faster. Since the particles of Al2O3 are smaller than SiO2, more
phonons are scattered on the boundary, which in turn results in
a lower heat transmission of the compound.
Two theoretical models were used to predict thermal
conductivity of the binary system – parallel model (2) and
geometric model (3):
RESULTS AND DISCUSSIONS
A. Thermal Conductivity
The thermal conductivity of the ER-Al2O3 and ER-SiO2
composites as a function of the filler concentration is shown in
Fig. 1. With an increase of the filler content, the thermal
conductivity increases gradually. Neat epoxy shows a weak
thermal conductivity because of its relatively low atomic
density [4]. The thermal conductivity of the polymer matrix
can be increased while leaving the dielectric properties intact
by addition of an inorganic filler, which has a higher thermal
conductivity while still being an electrical insulator. Values of
the thermal conductivities of neat epoxy and composites filled
with Al2O3 and SiO2 are presented in Table II. The addition of
Al2O3 resulted in a steady increase of the thermal conductivity
by about 300% at the weight fraction of 60%. Adding 60 wt.%
SiO2 filler improves the thermal conductivity by about 340%
however.
The possible explanation for the higher thermal
conductivity of ER-SiO2 compounds compared to ER-Al2O3
ones could be the larger particle size of silica. The size of the
particles plays an important role in the heat transfer between
polymer matrix and the incorporated filler. The addition of
fillers with a higher thermal conductivity than ER improves
the heat transfer. But the resulting values are much lower than
the values of bulk crystalline silica or alumina would suggest.
Phonons, which are responsible for heat conduction in
dielectric materials, are scattering at the interface between
dissimilar materials and the heat dissipates on the surface of
λc = φ ⋅ λ f + (1 − φ ) ⋅ λm ,
φ
(1−φ )
λc = λ f ⋅ λm
(2)
,
(3)
where λc , λ f and λm are the thermal conductivities of
composite, filler and matrix, respectively, and φ is the volume
fraction of the filler content.
The thermal conductivity values of the bulk Al2O3 and
SiO2 vary in the range 15-40 W/m·K and 1.3-10 W/m·K,
respectively. These values depend on the purity of the
material, crystal structure, way of production and so on. But as
mentioned earlier, the thermal conductivity of powders is
significantly lower than their crystalline counterparts, because
the interface area is much larger, which leads to scattering of
phonons. Therefore we used lower values of the thermal
conductivity for our calculations, namely 10 W/m·K for Al2O3
and 1.2 W/m·K for SiO2.
The measured values of the thermal conductivity are
plotted in Fig. 2 and compared to values that were calculated
using the parallel and geometric mean models.
For Al2O3 composites the measured values and values
estimated by using the geometric mean model correspond
almost completely with each other, throughout the whole
range. The parallel model agrees better with the SiO2
composites for our measured values of the thermal
conductivity for silica powder, which is 1.2 W/m·K. However,
the geometric mean model is fitting the experimental data of
ER-SiO2 samples best with the assumption that the thermal
conductivity of silica is close to 7 W/m·K. According to
literature, the value of a bulk of crystalline silica lies between
1.3 and 10 W/m·K, thus it is possible that the silica used has a
thermal conductivity value of 7 W/m·K.
TABLE II.
Composite
Neat ER
ER-Al2O3-5
ER-Al2O3-10
ER-Al2O3-20
ER-Al2O3-30
ER-Al2O3-40
ER-Al2O3-50
ER-Al2O3-60
ER-SiO2-20
ER-SiO2-40
ER-SiO2-60
THE THERMAL CONDUCTIVITIES OF FABRICATED
COMPOSITES
Volume fraction φ , %
0.016
0.033
0.071
0.117
0.17
0.235
0.316
0.102
0.232
0.405
Experimental
value λ , W/m·K
0.168
0.182
0.197
0.233
0.283
0.361
0.487
0.675
0.251
0.408
0.735
Figure 1. Thermal conductivity of investigated materials as a function of
filler concentration.
B. Dielectric Properties
Fig. 3 shows the relative permittivity at 1.15 MHz as a
function of temperature. A specimen of unfilled epoxy is used
for comparison with the microcomposites. The relative
permittivity ε ′ increases with the increase of both the filler
content and temperature. The raised temperature increases the
kinetic energy, which leads to faster movement of the particles
on the molecular level.
Fig. 4 shows the typical behavior of the relative
permittivity of composites with different particles inside as a
function of frequency. The permittivity of all samples
decreases with increasing frequency in the whole range due to
a reduction in the polarization caused by a dipolar group of the
organic matrix.
The interesting observation evident from Fig. 4b is that the
permittivities of silica-epoxy composites decrease with an
increasing concentration of SiO2, regardless of the fact that
permittivity of the filler is higher than matrix. The relative
.
Figure 2. The experimental and predicted thermal conductivity values for
Al2O3-epoxy (a) and SiO2-epoxy (b) composites at 18 °C.
Figure 3. Relative permittivity of ER-Al2O3 (a) and ER-SiO2 (b) as a
function of temperature.
permittivity of the silica is 4.3-4.7 [5], which is close to the
value of the epoxy, i.e. 3.2-3.3 at 1 MHz. A possible
explanation of this behaviour could be the immobilization of
polymer chains. For a higher amount of filler material the
mobility of the chains would be limited, lowering the effective
relative permittivity.
In case of alumina the permittivity is much higher than that
of ER ( ε ′ of Al2O3 is about 9). The contribution of the
intrinsic permittivity of the filler plays a more important role
in this case than the change of the molecular structure of the
epoxy.
Rules of mixture are often used to predict the dielectric
properties of ceramic composites. The relative permittivity of
a composite at a certain frequency can be calculated using the
following equations [6, 7, 8]:
log ε c = φ ⋅ log ε f + (1 − φ ) ⋅ log ε m ,
⎛2 ε
(1 − φ ) ⋅ ε m ⋅ ⎜ + f
⎝ 3 3ε m
εc =
⎛2 ε
(1 − φ ) ⋅ ⎜ + f
⎝ 3 3ε m
⎞
⎟ +φ ⋅ε f
⎠
,
⎞
⎟ +φ
⎠
(4)
(5)
TABLE III.
THE EXPERIMENTAL AND CALCULATED VALUES OF
RELATIVE PERMITTIVITY
Composite
Volume
fraction φ , %
ER-Al2O3-10
ER-Al2O3-20
ER-Al2O3-30
ER-Al2O3-40
ER-Al2O3-50
ER-Al2O3-60
ER-SiO2-20
ER-SiO2-40
ER-SiO2-60
0.033
0.071
0.117
0.17
0.235
0.316
0.102
0.232
0.405
εc = εm +
Experimental
value
εc
3.28
3.55
3.59
3.70
3.94
4.35
3.82
3.63
3.05
2 ⋅φ ⋅ ε m ⋅ ε f
2ε m + (1 − φ ) ⋅ ε f
,
ε c1
ε c2
ε c3
3.31
3.45
3.61
3.82
4.08
4.44
3.31
3.46
3.67
3.32
3.47
3.64
3.86
4.13
4.5
3.32
3.47
3.69
3.33
3.48
3.67
3.91
4.22
4.65
3.48
3.87
4.48
(6)
where ε c , ε f , ε m are the dielectric constant of the composite,
filler and the matrix, respectively, φ is the volume fraction of
the filler.
The experimental values and those calculated using (4)-(6)
are presented in Table III.
As it can be see from the Table III, the calculated values
are close to each other and predict the effective ε c of the ERAl2O3 binary system quite good. As discussed earlier, the ε c
of ER-SiO2 composites becomes lower with addition of the
filler, therefore it cannot be predicted with the rules of
mixture. The lower relative permittivity is an advantage which
is currently exploited in different applications of epoxy with
silica filler. A lower ε ′ means lower capacity which leads to
lower reactive currents.
IV.
Figure 4. Relative permittivity of ER-Al2O3 (a) and ER-SiO2 (b) as a
function of frequency.
CONCLUSIONS
In this paper we investigated the influence of different
types of particles and fillgrades on the thermal conductivity
and dielectric properties of epoxy-based microcomposites.
Major findings from this study are as follows:
• Epoxy-based microcomposites containing Al2O3 and
SiO2 particles were successfully fabricated.
• The highest value of the thermal conductivity was
achieved for ER-SiO2-60 with 0.745 W/m·K, which
means an improvement of 340% compared to the neat
polymer. The addition of 60 wt.% Al2O3 improved the
thermal conductivity by 4 times. The reason for the
higher thermal conductivity of composites filled with
silica is the larger particle size of silica.
• The most interesting behavior of the relative
permittivity was observed for ER-SiO2 compounds.
The relative permittivity of ER-SiO2-60 became lower
than the one of neat epoxy. A possible explanation for
this is an immobilization of polymer chains due to the
filler.
• Different theoretical models were applied to calculate
the thermal conductivity and relative permittivity of
the composites. For Al2O3 composites the geometric
mean model corresponds well, while the parallel
model agrees better with SiO2 composites.
[4]
REFERENCES
[1]
[2]
[3]
T. Shimizu, S. Kinoshita, S. Makishima, J. Sato, O. Sakaguchi,
“Material and Simulation Technology for Solid Insulated Switchgear”,
IEEE 7th International Conference on Properties and Application of
Dielectric Materials (ICPADM), S22-5, pp. 1194-1197, 2003.
R. Kochetov, T. Andritsch, U. Lafont, P.H.F. Morshuis, J.J. Smit, “The
Thermal Conductivity in Epoxy-Aluminum Nitride and EpoxyAluminum Oxide Nanocomposite Systems”, Nordic Insulation
Symposium (Nord-IS09), Gothenburg, Sweden, June 15-17, pp. 27-30,
2009.
R. Kochetov, T. Andritsch, U. Lafont, P.H.F. Morshuis, J.J. Smit,
“Thermal Conductivity of Nano-filled Epoxy Systems”, IEEE
[5]
[6]
[7]
[8]
Conference on Electrical Insulation and Dielectric Phenomena (CEIDP),
Virginia Beach, USA, October 18-21, 2009.
S.L. Shindé, J.S. Goela, High thermal conductivity materials, Springer,
2006.
J. Kriegesmann, Technische Keramische Werkstoffe, Deutsche
Keramische Gesellschaft, 1992.
J.K. Nelson, J.C. Fothergill, “Internal charge behaviour of
nanocomposites”, Nanotechnology 15, pp. 585-595, 2004.
J.I. Hong, P. Winberg, L.S. Schadler, R.W. Siegel, “Dielectric properties
of zinc oxide / low density polyethylene nanocomposites”, Materials
Letters 59, pp. 474-476, 2005.
S-H. Xie, B-K. Zhu, J-B Li, X-Z. Wei, Z-K. Xu, “Preparation and
properties of polyimide / aluminum nitride composites”, Polymer testing
23, pp. 797-804, 2004.
Microcomposites Filled with Al2O3 and SiO2 Particles
Roman Kochetov
Thomas Andritsch
Peter H.F. Morshuis
Johan J. Smit
Delft University of Technology
High Voltage Components & Power Systems
Delft, the Netherlands
[email protected]
Abstract—Epoxy resin is a polar thermosetting polymer that is
widely employed in different branches of industry and everyday
life, due to their stable physical and chemical properties. Of all
the polymer materials currently being used in the electrical
insulation industry, epoxy resin is the most widely used kind,
together with polyethylene and chosen as the base polymer
material in the present study. As a common practice, in order to
obtain materials of the desired thermal, mechanical and electrical
properties, polymers are processed with different types of
inorganic fillers. In this paper, the authors made an attempt to
thoroughly analyze both the thermal and the electrical behaviour
of the created epoxy microcomposites. Epoxy-based composites
containing microparticles of aluminum oxide and silicon dioxide
were prepared by high shear mechanical mixing and ultrasonic
processing to obtain a fine dispersion of the fillers in the matrix.
The incorporation of all filler types led to noticeable
improvement in thermal conductivity compared to the pure
epoxy resin. The thermal conductivity and the relative
permittivity of the composites were greatly influenced by the
filler loading of the inorganic particles. Rules of mixture are used
to predict the thermal conductivity and the relative permittivity
of two-phase composites have been applied to compare
experimental results with theoretical models.
Keywords - microcomposite, epoxy resin, Al2O3, SiO2, thermal
conductivity, relative permittivity
I.
INTRODUCTION
Epoxy resin (ER) is a common electrical insulating
polymer, which is used in high voltage cast resin transformers;
cable joints, terminations and other accessories; rotating
machines; bushings; GIS spacers [1], etc. Polymers used for
electrical insulation are usually reinforced with inorganic
fillers to improve the thermal, electrical and mechanical
properties. In previous studies we investigated the thermal and
electrical properties of nanocomposites containing one or two
types of nanoparticles with a concentration of up to 10 wt.%
[2, 3]. This paper is focused on the study of the same
properties of microcomposites but the concentration of the
filler is much higher – up to 60 percent by weight.
II.
EXPERIMENTAL
A. Sample fabrication
The epoxy resin system used in this study is a
commercially available Araldite CY231 epoxy resin with
This work was performed for the nanoPOWER project, which is supported by
a Dutch government IOP-EMVT grant.
978-1-4244-6300-8/10/$26.00 ©2010 IEEE
anhydride hardener Aradur HY925. The micro aluminum
oxide (Al2O3) and silicon dioxide (SiO2) particles have an
average particle size of 4 and 20 μm, respectively.
Epoxy composites containing Al2O3 or SiO2 microparticles
were fabricated in six steps:
1) Mixing the epoxy resin, hardener and filler by
conventional mechanical high shear stirring;
2) Degassing;
3) Mixing in an ultrasonic bath at 42 kHz;
4) Casting into the molds;
5) Curing for 3 hours at 140 oC;
6) Postcuring for 3 days at 140 oC.
Several types of alumina and silica microcomposites were
fabricated with a fillgrade up to 60 percent by weight. The
samples for thermal conductivity were prepared as plates with
dimensions of 110×70×3 mm. For dielectric spectroscopy
analysis the samples were prepared as discs with a diameter of
40 mm and a thickness between 0.4 - 0.7 mm.
Table I lists the set of materials used in this study.
B. Thermal conductivity and dielectric spectroscopy
measurements
The thermal conductivity measurements were realized with
a THASYS system, produced by Hukseflux Thermal Sensors.
This system performs a direct measurement which allows the
TABLE I.
Specimen
Neat ER
ER-Al2O3-5
ER-Al2O3-10
ER-Al2O3-20
ER-Al2O3-30
ER-Al2O3-40
ER-Al2O3-50
ER-Al2O3-60
ER-SiO2-20
ER-SiO2-40
ER-SiO2-60
SPECIMENS STUDIED
Nanofiller
Neat Epoxy Resin system
Epoxy system + 5wt.% Al2O3
Epoxy system + 10wt.% Al2O3
Epoxy system + 20wt.% Al2O3
Epoxy system + 30wt.% Al2O3
Epoxy system + 40wt.% Al2O3
Epoxy system + 50wt.% Al2O3
Epoxy system + 60wt.% Al2O3
Epoxy system + 20wt.% SiO2
Epoxy system + 40wt.% SiO2
Epoxy system + 60wt.% SiO2
determination of the absolute value of the thermal
conductivity. With a combination of a thin heater, two samples
of similar thickness and two heat sinks it is possible to
generate a homogeneous thermal field with a well defined heat
flux through the samples.
A straightforward calculation of the thermal conductivity
was made using the following equation:
λ=
Φ ⋅ H eff
ΔT
,
(1)
where λ is thermal conductivity, Φ is the heat flux derived
from the heated power, H eff is the effective sample thickness
and ΔT is the differential temperature across the samples.
The thermal conductivity data represent the average value
for the thermal conductivity of both samples. The
measurements are performed in a climate chamber at 18 °C to
avoid any influence due to changes of the ambient temperature
during measurement. The accuracy of the measurements is
6%. Each data point corresponds to an average value of 4
measurements.
The real part of the permittivity ε ′ (relative permittivity)
was determined by dielectric spectroscopy (DS) using a
Novocontrol ALPHA-A analyzer in combination with a ZGS
active sample cell. All samples were measured in the
frequency range of 10-2 - 107 Hz and at temperatures between 20 ºC and 120 ºC.
III.
microparticles. The epoxy is a thermal barrier for heat
propagation, while the filler material transmits the heat much
faster. Since the particles of Al2O3 are smaller than SiO2, more
phonons are scattered on the boundary, which in turn results in
a lower heat transmission of the compound.
Two theoretical models were used to predict thermal
conductivity of the binary system – parallel model (2) and
geometric model (3):
RESULTS AND DISCUSSIONS
A. Thermal Conductivity
The thermal conductivity of the ER-Al2O3 and ER-SiO2
composites as a function of the filler concentration is shown in
Fig. 1. With an increase of the filler content, the thermal
conductivity increases gradually. Neat epoxy shows a weak
thermal conductivity because of its relatively low atomic
density [4]. The thermal conductivity of the polymer matrix
can be increased while leaving the dielectric properties intact
by addition of an inorganic filler, which has a higher thermal
conductivity while still being an electrical insulator. Values of
the thermal conductivities of neat epoxy and composites filled
with Al2O3 and SiO2 are presented in Table II. The addition of
Al2O3 resulted in a steady increase of the thermal conductivity
by about 300% at the weight fraction of 60%. Adding 60 wt.%
SiO2 filler improves the thermal conductivity by about 340%
however.
The possible explanation for the higher thermal
conductivity of ER-SiO2 compounds compared to ER-Al2O3
ones could be the larger particle size of silica. The size of the
particles plays an important role in the heat transfer between
polymer matrix and the incorporated filler. The addition of
fillers with a higher thermal conductivity than ER improves
the heat transfer. But the resulting values are much lower than
the values of bulk crystalline silica or alumina would suggest.
Phonons, which are responsible for heat conduction in
dielectric materials, are scattering at the interface between
dissimilar materials and the heat dissipates on the surface of
λc = φ ⋅ λ f + (1 − φ ) ⋅ λm ,
φ
(1−φ )
λc = λ f ⋅ λm
(2)
,
(3)
where λc , λ f and λm are the thermal conductivities of
composite, filler and matrix, respectively, and φ is the volume
fraction of the filler content.
The thermal conductivity values of the bulk Al2O3 and
SiO2 vary in the range 15-40 W/m·K and 1.3-10 W/m·K,
respectively. These values depend on the purity of the
material, crystal structure, way of production and so on. But as
mentioned earlier, the thermal conductivity of powders is
significantly lower than their crystalline counterparts, because
the interface area is much larger, which leads to scattering of
phonons. Therefore we used lower values of the thermal
conductivity for our calculations, namely 10 W/m·K for Al2O3
and 1.2 W/m·K for SiO2.
The measured values of the thermal conductivity are
plotted in Fig. 2 and compared to values that were calculated
using the parallel and geometric mean models.
For Al2O3 composites the measured values and values
estimated by using the geometric mean model correspond
almost completely with each other, throughout the whole
range. The parallel model agrees better with the SiO2
composites for our measured values of the thermal
conductivity for silica powder, which is 1.2 W/m·K. However,
the geometric mean model is fitting the experimental data of
ER-SiO2 samples best with the assumption that the thermal
conductivity of silica is close to 7 W/m·K. According to
literature, the value of a bulk of crystalline silica lies between
1.3 and 10 W/m·K, thus it is possible that the silica used has a
thermal conductivity value of 7 W/m·K.
TABLE II.
Composite
Neat ER
ER-Al2O3-5
ER-Al2O3-10
ER-Al2O3-20
ER-Al2O3-30
ER-Al2O3-40
ER-Al2O3-50
ER-Al2O3-60
ER-SiO2-20
ER-SiO2-40
ER-SiO2-60
THE THERMAL CONDUCTIVITIES OF FABRICATED
COMPOSITES
Volume fraction φ , %
0.016
0.033
0.071
0.117
0.17
0.235
0.316
0.102
0.232
0.405
Experimental
value λ , W/m·K
0.168
0.182
0.197
0.233
0.283
0.361
0.487
0.675
0.251
0.408
0.735
Figure 1. Thermal conductivity of investigated materials as a function of
filler concentration.
B. Dielectric Properties
Fig. 3 shows the relative permittivity at 1.15 MHz as a
function of temperature. A specimen of unfilled epoxy is used
for comparison with the microcomposites. The relative
permittivity ε ′ increases with the increase of both the filler
content and temperature. The raised temperature increases the
kinetic energy, which leads to faster movement of the particles
on the molecular level.
Fig. 4 shows the typical behavior of the relative
permittivity of composites with different particles inside as a
function of frequency. The permittivity of all samples
decreases with increasing frequency in the whole range due to
a reduction in the polarization caused by a dipolar group of the
organic matrix.
The interesting observation evident from Fig. 4b is that the
permittivities of silica-epoxy composites decrease with an
increasing concentration of SiO2, regardless of the fact that
permittivity of the filler is higher than matrix. The relative
.
Figure 2. The experimental and predicted thermal conductivity values for
Al2O3-epoxy (a) and SiO2-epoxy (b) composites at 18 °C.
Figure 3. Relative permittivity of ER-Al2O3 (a) and ER-SiO2 (b) as a
function of temperature.
permittivity of the silica is 4.3-4.7 [5], which is close to the
value of the epoxy, i.e. 3.2-3.3 at 1 MHz. A possible
explanation of this behaviour could be the immobilization of
polymer chains. For a higher amount of filler material the
mobility of the chains would be limited, lowering the effective
relative permittivity.
In case of alumina the permittivity is much higher than that
of ER ( ε ′ of Al2O3 is about 9). The contribution of the
intrinsic permittivity of the filler plays a more important role
in this case than the change of the molecular structure of the
epoxy.
Rules of mixture are often used to predict the dielectric
properties of ceramic composites. The relative permittivity of
a composite at a certain frequency can be calculated using the
following equations [6, 7, 8]:
log ε c = φ ⋅ log ε f + (1 − φ ) ⋅ log ε m ,
⎛2 ε
(1 − φ ) ⋅ ε m ⋅ ⎜ + f
⎝ 3 3ε m
εc =
⎛2 ε
(1 − φ ) ⋅ ⎜ + f
⎝ 3 3ε m
⎞
⎟ +φ ⋅ε f
⎠
,
⎞
⎟ +φ
⎠
(4)
(5)
TABLE III.
THE EXPERIMENTAL AND CALCULATED VALUES OF
RELATIVE PERMITTIVITY
Composite
Volume
fraction φ , %
ER-Al2O3-10
ER-Al2O3-20
ER-Al2O3-30
ER-Al2O3-40
ER-Al2O3-50
ER-Al2O3-60
ER-SiO2-20
ER-SiO2-40
ER-SiO2-60
0.033
0.071
0.117
0.17
0.235
0.316
0.102
0.232
0.405
εc = εm +
Experimental
value
εc
3.28
3.55
3.59
3.70
3.94
4.35
3.82
3.63
3.05
2 ⋅φ ⋅ ε m ⋅ ε f
2ε m + (1 − φ ) ⋅ ε f
,
ε c1
ε c2
ε c3
3.31
3.45
3.61
3.82
4.08
4.44
3.31
3.46
3.67
3.32
3.47
3.64
3.86
4.13
4.5
3.32
3.47
3.69
3.33
3.48
3.67
3.91
4.22
4.65
3.48
3.87
4.48
(6)
where ε c , ε f , ε m are the dielectric constant of the composite,
filler and the matrix, respectively, φ is the volume fraction of
the filler.
The experimental values and those calculated using (4)-(6)
are presented in Table III.
As it can be see from the Table III, the calculated values
are close to each other and predict the effective ε c of the ERAl2O3 binary system quite good. As discussed earlier, the ε c
of ER-SiO2 composites becomes lower with addition of the
filler, therefore it cannot be predicted with the rules of
mixture. The lower relative permittivity is an advantage which
is currently exploited in different applications of epoxy with
silica filler. A lower ε ′ means lower capacity which leads to
lower reactive currents.
IV.
Figure 4. Relative permittivity of ER-Al2O3 (a) and ER-SiO2 (b) as a
function of frequency.
CONCLUSIONS
In this paper we investigated the influence of different
types of particles and fillgrades on the thermal conductivity
and dielectric properties of epoxy-based microcomposites.
Major findings from this study are as follows:
• Epoxy-based microcomposites containing Al2O3 and
SiO2 particles were successfully fabricated.
• The highest value of the thermal conductivity was
achieved for ER-SiO2-60 with 0.745 W/m·K, which
means an improvement of 340% compared to the neat
polymer. The addition of 60 wt.% Al2O3 improved the
thermal conductivity by 4 times. The reason for the
higher thermal conductivity of composites filled with
silica is the larger particle size of silica.
• The most interesting behavior of the relative
permittivity was observed for ER-SiO2 compounds.
The relative permittivity of ER-SiO2-60 became lower
than the one of neat epoxy. A possible explanation for
this is an immobilization of polymer chains due to the
filler.
• Different theoretical models were applied to calculate
the thermal conductivity and relative permittivity of
the composites. For Al2O3 composites the geometric
mean model corresponds well, while the parallel
model agrees better with SiO2 composites.
[4]
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