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CHAPTER 7
Dielectric Response of Conducting Carbon Black Filled Ethylene Octene Copolymer Microcellular Foam
Chapter 7: Dielectric Response of Conducting Carbon
Black Filled Ethylene Octene Copolymer Microcellular
Foams
7.1 Introduction
Dielectric relaxation spectroscopy is used to evaluate the dielectric response of a material.
Polymer and polymer composites are subjected to dielectric relaxation spectroscopy for a
wide range of time and tempareture to study the important phenomenon occuring in them
such as polarization, molecular mobility, interfacial phenomenon, conductivity,
polymerization, phase changes, crystallization phenomenon basing on molecular motion of
the polymer [286,287,260]. Thus with density reduction with foaming can decrease the
electrical percolation threshold of conductive polymer composites [288-290]. Dielectric
properties of the closed cell microcellular polymers are widely applied in the area of
electrical, transportation, automotive and aerospace etc. The dielectric properties of
microcellular vulcanizates have been studied by several researchers at wide range of
frequency [200-202] in recent years.
This chapter focuses the study of dielectric relaxation behaviour of microcellular vulcanizates
by incorporating an electrically conductive carbon black (0-40 wt %) into ethylene octene
copolymer (EOC). It provides insight to the influence of concentration of conductive carbon
black and blowing agent (density) and tempearature on the dielectric properties of EOC/CB
microcellular vulcanizate such as dielectric permittivity, loss tangent, impedance (both real
and complex part), ac conductivity and percolation threshold.
7.2 Results and discussion
7.2.1 Dielectric relaxation behaviour of microcellular EOC/CB vulcanizates
as function of carbon black concentration.
7.2.1.1 Dielectric permittivity
Figure 7.1 shows the variation of dielectric permittivity ( ') at different CB content with 4 phr
blowing agent loading.It is observed that dielectric permittivity ( ') increases with increase in
the filler content. Dielectric permittivity of unfilled and 20 phr filled EOC vulcanizate shows
frequency independent behaviour. Increasing the carbon black content to 40 phr dielectric
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
108
permittivity reduces significantly with increase in frequency but remains approximately
constant after a crossover frequency (i.e 1MHz).This is attributed to the interfacial
polarization (IP) of the filler [291]. At low frequency more predominant effect of interfacial
polarization (IP) is observed. At low frequency the resulting value of permittivity is the
contribution of all types of polarization.
Figure 7.1 Variation of dielectric permittivity ( ' ) of 4 phr blowing agent loaded EOC/CB
microcellular vulcanizates with frequency for different carbon black concentration at 300C.
Interfacial polarization (IP) occurs in electrically heterogeneous materials (system containing
phases of different specific conductivity) such as composites which is known as the Maxwell-
Wagner-Sillars (MWS) effect [259]. At low frequency range the frequency dependent
behaviour of dielectric permittivity is attributed to MWS effect which is associated with the
entrapment of free charges between insulator/conductor interfaces. The IP causes an
enhancement in due to motion of trapped virtual charges at the interface of components of
a multiphase material of different conductivity [260].
102 103 104 105 106
103
Frequency(Hz)
G4
EB24
EB44
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
109
7.2.1.2 Dielectric loss tangent
Figure 7.2 Variation of dielectric loss tangent (tan ) of 4 phr blowing agent loaded EOC
microcellular vulcanizates with frequency for different carbon black concentration at 300C.
Figure 7.2 shows the variation of dielectric loss tangent with frequency in 4 phr blowing agent
loaded microcellular EOC/CB foamed vulcanizate as a function of carbon black loading.It
shows that increase in carbon black loading increases the value of tan at lower frequencies
whereas the change is marginal at higher frequencies. At lower frequencies the increase in
filler loading leads to higher tan values where as at higher frequencies this effect is marginal.
With increase in filler content from 20 phr to 40 phr the dielectric loss becomes frequency
dependent and decreases by seven fold of magnitude with increase in frequency from 100 to
103 Hz. The extent of distribution and/or dispersion of fillers in polymer matrix strongly
affects dielectric relaxation behaviour. Addition of functional fillers like carbon black leads to
both hydrodynamic and physicochemical interactions between the polymer matrix and the
filler surfaces. Increase in filler loading leads to increased filler-polymer interactions, thereby
the bound rubber (BR) value increases which result strong interphase with the polymer and
thus results in increase in tangent loss (tan ) [291].
102 103 104 105 106
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
102 103 104 105 106-100
0
100
200
300
400
500
600
700
800
900
1000
Frequency(Hz)
EB44
Frequncy(Hz)
G0 EB24
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
110
7.2.1.3 AC conductivity
Figure 7.3 Variation of ac conductivity of 4phr blowing agent loaded EOC foamed
vulcanizates with frequency for different carbon black loading in at 300C.
Figure 7.3 depicts the variation of ac electrical conductivity as a function of frequency with
increase in filler loading in 4 phr blowing agent loaded CB reinforced EOC vulcanizates. The
ac conductivity of foamed vulcanizate increases with increase in frequency irrespective of
carbon black loading. At low CB loadings, the conductivity of the polymer vulcanizate is
slightly greater than that of the insulating polymer i.e EOC as the CB particles are isolated
from each other by the insulating polymer matrix. A strong dispersion of the ac conductivity
is mainly due to wide distribution of hopping rates throughout the vulcanizate as the filler
particles are dispersed heterogeneously in the polymer matrix. The conductivity enhanced to
several orders of magnitude by increasing the carbon black loading to 40 phr. As the filler
incorporation increases filler aggregates come in close contact with each other creating a
continuous conductive path. At a particular concentration of CB loading (20 phr and above),
ac conductivity value increases sharply which may be called as percolation threshold. The
increase in ac conductivity is marginal at low frequency but at higher frequency (above 105
Hz) conductivity increases approximately as a power of frequency [292] for 40 phr carbon
black loaded microcellular vulcanizates.
102 103 104 105 106
10-7
10-6
10-5
10-4
10-3
102 103 104 105 10610-2
10-1
Frequency(Hz)
EB44
Frequency(Hz)
G4EB
24
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
111
7.2.1.4 Percolation
0 10 20 30 4010-5
10-4
10-3
10-2
Filler loading (phr)
0 phr 1 phr 2 phr 4 phr
Figure 7.4 Variation in ac conductivity with CB for different blowing agent loading in
microcellular EOC vulcanizates at 1 MHz.
Increase in carbon black concentration establishes close cotanct between the filler aggregates
forming continous path through the matrix for the travel of electrons. Percolation limit is
indicated by a sharp increase in conductivity at a particular carbon black loading. The entire
region which shows the sharp increase in conductivity is termed percolation region. In this
region due to increased filler loading the gap between the carbon black aggregates becomes
short and electrons a transmitted in the short gap easily. In this system percolation occurs
above 20 phr loading of the filler. For conductive carbon black reinforced polymer
vulcanizates, percolation limit has been observed at 20 phr filler loading. Unlike conventional
carbon black the low surface area, high structure and more oxygen containing chemical group
of conductive carbon black promotes the conductive carbon black reinforced EOC
microcellular vulcanizates to achieve percolation limit at low filler loading [202]. According
to Medalia [272] tunnelling of electrons causes percolation and the distance between the
carbon black aggregate controls the conductivity of the composite. The variation of
conductivity with filler loading can be divided into two parts. Part I (0-20 phr) is known as
�inductive region� whereas part II (20-40phr) known as �percolation region� [22]. Inductive
region shows small increase in conductivity with increase in filler loading due to
transportation of less number of charged particles through the polymer matrix and absence of
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
112
continuous conductive path. But percolation region shows a sharp increase in conductivity as
the higher concentration of carbon black forms continuous conductive path in the polymer
matrix. Figure 7.4 also shows that the percolation limit occurs above 20 phr carbon black
filler loading irrespective of blowing agent loading. Both geometry of the filler and
processing of the materials affect the conductivity of polymer composites [274].
7.2.2 Dielectric relaxation behaviour of microcellular EOC/CB vulcanizates
as function of blowing agent concentration.
7.2.2.1 Dielectric permittivity
Figure 7.5 and Figure 7.6 show the variation of the dielectric permittivity with frequency as a
function of the blowing agent (ADC) in unfilled and 40 phr carbon black reinforced EOC
foams respectively. It is observed that the dielectric constant reduces with frequency. But with
increase in blowing agent concentration the dielectric constant increases. It is observed that
the decrease in dielectric permittivity with increase in frequency is marginal in case of
unfilled vulcanizates but is more prominent in case of 40 phr carbon black filled vulcanizates.
However, with increase in blowing agent the dielectric permittivity increases for both unfilled
as well as carbon black filled microcellular foam.
Figure 7.5 Variation of the dielectric permittivity with frequency as a function of the blowing
agent in unfilled EOC microcellular vulcanizates at 300C.
102 103 104 105 106102
103
Frequency(Hz)
G0
G1
G2
G4
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
113
Figure 7.6 Variation of the dielectric permittivity with frequency as a function of the blowing
agent in 40 phr carbon black filled EOC microcellular vulcanizates at 300C.
Figure 7.7 Variation of dielectric permittivity with relative density ( r) of 40 phr carbon black
loaded EOC microcellular vulcanizates at 300C.
Variation of dielectric permittivity with relative density ( r) at different frequencies are shown
in figure 7.7. An inverse relationship exists between dielectric permittivity and relative
density of foamed EOC-CB vulcanizates. Moreover dielectric permittivity increases with
102 103 104 105 1060
1000
2000
3000
4000
5000
Frequency(Hz)
EB40
EB41EB
42EB
44
0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.420
1000
2000
3000
4000
5000
Relative density ( f/ s)
102 Hz 103 Hz 104 Hz
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
114
decrease in relative density. Figure 7.8 depicts the variation of dielectric permittivity of solid
and foamed EOC/CB vulcanizates with carbon black loading at 100 Hz frequency. The
dielectric permittivity of both foamed and solid EOC vulcanizate increases significantly with
increase in the carbon black content. It is found that the dielectric permittivity of foamed
vulcanizates are 2 to 3 times higher than their solid counter parts. For example, the ' value of
solid vulcanizate of 20 phr increases from 281.8 to 976.5 on foaming. The higher permittivity
of the foamed vulcanizates can be attributed to the enhanced interfacial polarization [290]
through (a) localization of the carbon black particles by creation of the gaseous phase (b)
decreased in-plane orientation by foaming which increased the CB orientation in thickness
direction and (c) decrease in CB-to CB distance caused by biaxial stretching of the matrix
during cell growth. All these might have contributed to the formation of more effective
capacity between adjacent CB within a thin layer of matrix in-between.
Figure 7.8 Variation of dielectric permittivity of solid and foamed EOC foamed vulcanizates
with carbon black loading at 100 Hz frequency and 300C.
Higher permittivity with foaming has also been reported with PP/carbon fiber composite foam
[290]. To achieve a desired value of dielectric permittivity significantly less carbon content is
needed for foamed vulcanizates in comparision to the solid vulcanizates. For example to get
dielectric permittivity ( ') of 750, 24.3 phr and 10.2 phr carbon black is needed for the solid
and foamed EOC vulcanizate. Therefore foamed vulcanizates require 58.04 % less carbon
black than the corresponding solid vulcanizates to achieve the desired dielectric permittivity.
The foamed EOC/CB vulcanizates possesses high dielectric permittivity at higher carbon
black loading and proved to be suitable to be used as dielectric material.
0 10 20 30 400
1000
2000
3000
4000
5000
6000
Carbon black content (phr)
FoamSolid
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
115
7.2.2.2 Dielectric loss tangent
Figure 7.9 and 7.10 shows the dielectric loss tangent (tan ) as a function of blowing agent
loading in unfilled and 40phr CB filled EOC vulcanizates at 300C.
Figure 7.9 Dielectric loss tangents (tan ) as a function of blowing agent loading in unfilled
EOC foamed vulcanizates at 300C.
With increase in blowing agent concentration i.e 1 to 4 phr, the relative densities of the
foamed vulcanizates reduces due to increase in number of cells in the vulcanizate. From the
figure it can be observed that at low frequency loss tangent values of both unfilled and 40 phr
CB loaded vulcanizate decreases with increase in blowing agent loading or decrease in
relative densities, which indicates the decrease in the loss behavior of the vulcanizates,
whereas at high frequencies marginal effect is observed. From the figure it can be observed
that solid vulcanizate has low loss tangent values than microcellular vulcanizates. Increase in
blowing agent concentration increases the amount of decomposed gas as well as gas pressure
inside the cells. The increased gas pressure retain the cell membrane in a strained condition.
This increase in strain to some extent increases the tan value [202]. However at lower
blowing agent loading i.e 1 to 4 phr the gas in the closed cell has less contribution.
102 103 104 105 1060.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Frequency (Hz)
G0 G1 G2 G4
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
116
Figure 7.10 Dielectric loss tangents (tan ) as a function of blowing agent loading in 40 phr
carbon black filled EOC foamed vulcanizates at 300C.
7.2.2.3 Nyquist plot
Figure 7.11 Representation of the electrical behavior of the microcellular foam by means of
an equivalent circuit.
The dispersion of the carbon black in the microcellular EOC matrix is represented by means
of a simple diagram model and an equivalent circuit (CQR) (CR) is designed to simulate the
electrical behavior of the microcellular foam as show in the Figure 7.11. The experimental
102 103 104 105 106
0
500
1000
1500
2000
Frequency(Hz)
EB40
EB41
EB42
EB44
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
117
complex impedance plots were compared with model fitted plots obtained by taking an
equivalent circuit of (CQR) (CR) (using commercially available SIMPWIN version 2).
Figure 7.12 shows Nyquist plot (Z vs. Z ) of carbon black reinforced EOC foams as a
function of blowing agent (ADC) with reference to an equivalent circuit of (CQR) (CR). The
(CQR) and (CR) are in parallel combination in an equivalent circuit for Debye-type response,
where Q is known as constant phase element (CPE). The admittance (Y) of CPE is defined as:
Y (CPE) =A0 (j ) n = A n + j B n [7.1]
Where A =Ao Cos (n /2) and B =Ao Sin (n /2).
The value of A0 and n are temperature dependent but frequency independent. A0 signifies
magnitude of the dispersion, and 0 n 1. For an ideal capacitor n=1 and for ideal resistor n=0
[293]. From these model fitted curves, the values of Rb (bulk resistance), Rgb (grain boundary
resistance), bulk capacitance (Cb) and grain boundary capacitance (Cgb) at 300C temperatures
were calculated and compared with experimental values (Table 7.1).Table 7.1 describes the
comparison of bulk (grain) and grain boundary resistance of microcellular foam at different
blowing agent loading with reference to an equivalent circuit of (CQR) (CR).
Table7.1 Comparison of bulk (grain) and grain boundary resistance of EOC/CB microcellular
vulcanizates at different blowing agent loading.
Sample Cb (F) Q n Rb ( ) Cgb (nF) Rgb ( )
Experimental
EB41 5.697x10-12 2.853x10-9 0.71 827 0.712 653.0
EB42 1.544x10-10 3.385x10-9 0.73 2210 0.210 388.9
EB44 8.460x10-11 2.965x10-9 0.58 2190 10.21 119.6
Calculated from model fit curve
EB41 2.521x10-12 2.853x10-8 0.71 827 0.712 653.1
EB42 1.544x10-10 3.385x10-9 0.73 2210 0.210 388.9
EB44 8.460x10-11 2.965x10-9 0.58 2190 10.22 119.7
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
118
The least Rb and Cb values are obtained in case of 1phr blowing agent loaded microcellular
vulcanizates when it follows (CQR) (CR) circuit. Debye-type of relaxation with single
relaxation time instead of distribution of relaxation time in the materials is interpreted by a
semi-circle arc having centre on Z�axis [294]. The value of bulk and grain boundary
contributions of the electrical properties of the material are provided by the intercept of each
semi-circle on real part of Z axis.
Figure 7.12 Nyquist plot (Z vs. Z ) of 40 phr carbon black reinforced EOC foams as a
function of blowing agent.
Table 7.1 describes the comparison of bulk (grain) and grain boundary resistance of
microcellular foam at different blowing agent loading with reference to an equivalent circuit
of (CQR) (CR). The total impedance of the cell, Z can be expressed as the series of
combinations of resistors Rb and capacitors Cb [295]. When the conducting filler loading is
increased from 0 to 40 phr, the centre of the semi-circle arc found to be fall in real impedance
axis. It can be explained on the basis of aggregation of carbon black particles to form
secondary structure to form aggregates [268]. The gaps between the carbon black aggregate
controls the electron conduction via non-ohmic contacts between the carbon black aggregates.
The shift in the centre of the semi-circle is the measure of the gap between the aggregates of
carbon black particulates. With increase in the filler loading, the Rb values decrease and the
centre of the semicircle decreases.
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
119
7.2.2.4 Real and complex part of the impedance
Figure 7.13 The variation in the Z and Z with frequency as a function of blowing agent in
40 phr carbon black reinforced EOC microcellular vulcanizate.
Figure 7.13 shows the variation in the Z and Z with frequency as a function of blowing
agent in 40 phr carbon black reinforced microcellular foams. Z and Z values found to be
increasing only upto 2 phr ADC-21. But with increase in frequency the value of Z� decreases
around 105Hz. The Similar observations are seen for complex impedance (Z ) in the region of
105-106 Hz, where there is a sudden increase. This variation may be due to the secondary
relaxations of the polymer chains of the microcellular vulcanizate. The interfacial region
between the polymer peaks in the field of particulate multi-polymeric systems undergoes
relaxation which gives rise to additional damping peak in the complex impedance [296-298].
The effect of variation of blowing agent loading is marginal on the frequency associated with
damping peak. Additional damping peak is observed in the frequency range of 105-106 Hz
irrespective of blowing agent loading. The mean relaxation time of the process is associated
with the above frequency range and signifies the molecular motion which is affected by some
parameters such as thermal treatment, composition, and mixing with other substances
[299].The polymer-filler interactions, degree of crosslinking, the properties of the interphase
region [300], or microheterogeneity [301] affect the variation in peak intensity with the
blowing agent concentration. However the physical cause of this deviation is under varying
arguments [302, 303].
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
120
7.2.2.5 AC conductivity
Figure 7.14 and 7.15 show the effect of variation of blowing agent loading on the ac
conductivity of unfilled and carbon black filled microcellular EOC foams. It is observed from
the figure that irrespective of blowing agent concentration there is increase in ac conductivity
with increase in the frequency for all the foamed vulcanizates. Increase in blowing agent
loading increases the conductivity of the unfilled and carbon black filled vulcanizates. This
increase in ac conductivity is observed upto 3MHz and then remains almost constant for all
the loadings of ADC in case of both unfilled and filled microcellular vulcanizates.
Figure 7.14 Variation in ac conductivity ( ac) with frequency as a function of blowing agent
loading for unfilled EOC foamed vulcanizates.
Reinforced microcellular vulcanizates consists three phases such as polymer matrix, the filler
and the air enclosed inside the cells of the vulcanizates. So the actual electrical transport
mechanism through the heterogeneous structure could not be discovered yet. The dielectric
properties of polymer composites depend primarily on distribution of filler particles in the
polymer matrix, which is called mesostructure [269]. Figure 7.16 represents the variation of
ac conductivity of unfilled and conductive carbon black filled foams with relative density. It is
observed that ac conductivity increases with decrease in the relative density ( r) of the foamed
vulcanizates. The vulcanizate with highest loading of carbon black (i.e 40 phr) and blowing
agent (i.e 4 phr) shows maximum ac conductivity (1.92x10-2 S/m) possesses least relative
density (0.24).Moreover the vulcanizate with 40 phr carbon black and 4 phr blowing agent,
foamed and expanded effectively to provide highest value of ac conductivity.
102 103 104 105 106
10-7
10-6
10-5
10-4
10-3
Frequency(Hz)
G0G1G2G4
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
121
Figure 7.15 Variation in ac conductivity ( ac) with frequency as a function of blowing agent
loading for 40 phr carbon black filled EOC foamed vulcanizates.
Figure 7.16 Variation of ac conductivity of microcellular EOC vulcanizates with relative
density for different carbon black loadings.
102 103 104 105 106
10-2
102 103 104 105 106
10-5
10-4
10-3
10-2
Frequency(Hz)
EB40
Frequency(Hz)
EB41
EB42 EB
44
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
8.0x10-7
1.2x10-6
1.6x10-6
2.0x10-6
2.4x10-6
2.8x10-6
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.2x10-2
1.6x10-2
2.0x10-2
2.4x10-2
Relative density (r)
EB44
Relative density (r)
G4 EB24
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
122
Figure 7.17 Conductivity of 4 phr blowing agent loaded solid and microcellular EOC/CB
vulcanizates at frequency of 100Hz and temperature 300C.
Figure 7.17 represents ac conductivity as a function of conductive carbon black loading for
the solid and foamed EOC/CB vulcanizates. At lower filler loading (i.e.20 phr carbon black)
the increase in ac of solid vulcanizates is marginal (i.e., from 1.17x10-7 to 2.64x10-7 S/m) due
to foaming. But at 40 phr loading, ac increases significantly upto several orders of magnitude
(i.e from 6.17x10-6 to 1.9x10-2 S/m). At a given phr of CB the ac conductivity of foamed
sample is significantly higher than the corresponding solid one. In other words the carbon
black filled foamed vulcanizate provide large value of ac conductivity than their solid
counterparts. In solid vulcanizates, the carbon black particles were randomly distributed and
oriented and thus their alignment was considered isotropic. By introduction of foaming, the
CB particles around each growing cell started to displace depend on the initial relative
location with respect to the cell nucleus. Moreover the spherical growth of the cells exerted
biaxial stretching on the polymer matrix surrounding the cell and thus disturbed the isotropic
alignment of CB particles. This biaxial stretching is proportional to the degree of foaming
blowing agent loading. As the blowing agent loading increases, the degree of foaming
increases which lead to significant alignment of CB particles around the cells. In case of low
relative density (0.24) foam, the CB particles were fully aligned normal to the cell radius due
to excessive biaxial stretching. In other words the alignment reduced from 3-D to 2-D state
[305].
0 5 10 15 20 25 30 35 40 45
10-7
10-6
10-5
10-4
10-3
10-2
Carbon black content (phr)
Foam Solid
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
123
7.2.3 Effect of temperature on dielectric properties of microcellular
EOC/CB vulcanizates
7.2.3.1 Dielectric constant
Figure 7.18 describes the variation of the relative dielectric constant ( r) as a function of
temperature at frequencies 100 Hz, 1026.7Hz and 10542 Hz of the sample EB44. The increase
in temperature leads to sharp decrease in dielectric constant close to the temperature of 550C
which is the melting point of ethylene-octene copolymer and then the effect is marginal with
increase in temperature. Thermal expansion of vulcanizate causes destruction of conductive
channels caused by separation of CB particles which reduces the permittivity.
According to Kohler [276], conductive fillers form a network of conductive chains throughout
the polymer matrix and the conductive filler particles are separated further due to heating,
thereby increasing the resistance and decreasing the dielectric constant. At higher temperature
i.e above 550C NTC phenomenon (negative temperature coefficient) takes place by drifting of
charge carriers over larger distances [305, 306].
Figure 7.18 Variation of dielectric constant ( r ) as a function of temperature at frequencies
100 Hz, 1026.7Hz and 10542 Hz of the sample EB44.
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
124
7.2.3.2 Dielectric loss tangent
The tan values were significantly decreased with frequency. The values of tan were found
to be between 734.4 to 2081.6, 58.5 to 208 and 7.08 to 25.1 respectively (at frequency 102Hz,
103Hz and 103 Hz) in the temperature range of 300C to 1000C. The sharp increase in the value
of tan at above 700C temperature may be attributed to (a) activation of conducting carbon
black (b) scattering of thermally activated charge carriers (c) some inherent defects in the
sample (d) creation of oxygen ion vacancies during sample preparation. The tan rises at
higher temperature which indicates the dominance of conductivity.
7.2.3.3 Complex impedance
Figure 7.19 shows the temperature dependence of complex impedance spectra (Z vs. Z ) plot
known as Nyquist plot) over a wide frequency range (0.1 kHz�5 MHz) of the sample EB44
with 40phr carbon black filler and 4 phr blowing agent loadings. The impedance is
characterized by the appearance of semicircular arcs with its centre on real part of impedance
axis, which are observed in the temperature range of 300C to 1000C (Nyquist plot at 1000C is
not shown in the figure). Most widely accepted approach to interpret the semicircles is single
relaxation time due to presence of Debye type of relaxation in the material [307].
Figure 7.19 The temperature dependence of complex impedance spectra (Z vs. Z ) plot
known as Nyquist plot) over a wide frequency range (0.1 kHz�5 MHz) of the sample EB44
with 40phr carbon black filler and 4 phr blowing agent loading.
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
125
These model fitted curves obtained by taking the equivalent circuit of (CQR) (CR) are used to
calculate the values of Rb (bulk resistance), Rgb (grain boundary resistance), bulk capacitance
(Cb) and grain boundary capacitance (Cgb) at different temperatures and compared with
experimental values (Table 7.2).
Table 7.2 clearly shows increase in temperature increases the values of parameters such as
bulk resistance(Rb) and grain boundary resistance(Rgb) indicating the existence of positive
temperature coefficient of resistance (PTCR) in the material [308], whereas the values bulk
capacitance (Cb) and grain boundary capacitance (Cgb) were found to be reducing with
temperature. A semi-circle arc is obtained with its center on Z axis was observed in the
microcellular foams. The characteristic peak of the semicircles of the impedance spectrum
associated with a unique relaxation frequency, known as resonance frequency (fr) (where r
=2 fr). It can be expressed as
r Rb Cb= r b=1 [7.3]
Thus f r = 1/2 RbCb, [7.4]
Where is the relaxation time.
The relaxation time due to bulk effect ( b) has been calculated using the equation [7.5]
b =1/2 fr
The temperature dependence of the relaxation time for the bulk material was found to be
following the Arrhenius relation:
b= 0 exp (-Ea/Kb T) [7.6]
Where 0 is the pre-exponential factor, Kb is the Boltzmann constant, and T is absolute
temperature.
The variation of ln b of the vulcanizates with the reciprocal of the absolute temperature (1/T)
is represented in figure 7.20.The slope the plot of ln b vs (1/T) is equals to -Ea/KbT, the
activation energy (Ea) was found to be 0.446 eV which is less than the ferroelctrics [309,
310], b values found to be increasing from 300C to 800C and decreasing trend is observed
above 800C (not represented in the figure).
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
126
Figure 7.20 The variation of ln b of the EOC/CB microcellular vulcanizates with the
reciprocal of the absolute temperature (1/T)
Table7.2 Comparison of bulk (grain) and grain boundary resistance and capacitance at
different temperatures of microcellular foam (EB44)
Circuit
Parameters 300C 400C 500C 600C 800C
Experimental Parameters
Cb (F) 8.46x10-11 8.39x10-11 1.52x10-11 9.05x10-17 1.18x10-10
Q 2.96 x10-8 7.80 x10-9 2.13 x10-10 3.10 x10-10 1.44x10-9
n 0.583 0.658 0.954 0.961 0.767
Rb ( ) 2190 2339 4063 8213 12900
Cgb ( nF) 10.21 6.056 0.764 0.250 0.324
Rgb ( ) 1196 1627 1401 9370 5575
(CQR)(CR) model fit parameter
Cb (F) 8.46x10-11 8.39x10-11 1.52x10-11 9.05x10-17 1.17x10-10
Q 2.96 x10-8 7.81 x10-9 2.13 x10-10 3.10 x10-10 1.42x10-9
n 0.583 0.658 0.954 0.961 0.768
Rb ( ) 2190 2339 4064 8213 12910
Cgb (nF) 10.22 6.052 0.764 0.250 0.324
Rgb( ) 1197 1627 1401 9370 5569
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
127
7.2.3.4 DC conductivity
The dc conductivity of the bulk sample was evaluated from the impedance spectrum using the
following relation
dc = t/ARb [7.7]
Where t, A and Rb represent the thickness, area, and bulk resistance of the sample
respectively. The temperature dependence of the dc conductivity of the microcellular polymer
vulcanizate follows the nature of the plot follows the Arrhenius relation
dc= 0 exp (-Ea/KbT) [7.8]
Therefore the plot of ln dc vs (1/T) gives a straight line with slope equal to -Ea/Kb. Figure
7.21 is a plot between ln dc vs (1/T). From the plot it is observed that dc reduces with
increase in temperature. As a result we get positive slope indicating the existence of positive
temperature coefficient of resistance (PTCR) in the foamed vulcanizate [305]. The activation
energy (Ea) of microcellular polymer vulcanizate was found to be 0.363 eV in the temperature
range of 300C to 1000C. The value of Ea is comparable with 0.446 Ev calculated from the
relaxation time plot. This implies that the charge carriers responsible for conduction and
relaxation processes in the sample are almost same in the microcellular polymer foams
obtained from EOC, carbon black as filler and ADC as the blowing agent in the above
temperature range.
Figure 7.21 The variation of dcln of the vulcanizates with the reciprocal of the absolute
temperature (1/T)
CHAPTER 7 DIELECTRIC RESPONSE OF CONDUCTING CARBON BLACK FILLED ETHYLENE OCTENE COPOLYMER MICROCELLULAR FOAMS
128
3.5 Conclusions
The dielectric response of Ensaco 250G reinforced EOC microcellular vulcanizates has been
studied as function of filler loading in the frequency range of 102Hz to 5MHz over a wide
temperature range (250C to 1000C). Dielectric constant and ac conductivity increases with
increase in both carbon black and blowing agent loading. The value of r of the conducting
microcellular EOC vulcanizates decreases with rise in temperature up to 600C temperature
and above this temperature there is marginal increase in the dielectric constant. The tan
value increases with carbon black loading and decreases with blowing agent loading due to
less viscoelastic damping. The values of tan at frequency 100Hz, 1026.7Hz and 10542Hz
were found to be between 734.4 to 2081.6, 58.5 to 208 and 7.08 to 25.1 respectively in the
temperature range of 300C to 1000C. The Nyquist plot shows that the bulk resistance reduces
and bulk capacitance increases with increase in carbon black loading respectively in
accordance with resistance-capacitance circuit. Nyquist plot also indicates more lossy
response with increase in blowing agent loading. The experimental complex impedance plots
were compared with model fitted plots obtained by taking an equivalent circuit of (CQR)
(CR). From these model fitted curves, the values of Rb (bulk resistance), Rgb (grain boundary
resistance), bulk capacitance (Cb) and grain boundary capacitance (Cgb) at different
temperatures were calculated and compared with experimental values. Rb and Rgb increases
with rise in, whereas Cb) and Cgb were found to be decreasing. The semi-circles of the
impedance spectrum have a characteristic peak occurring at a unique relaxation frequency(fr),
which is usually referred as resonance frequency (fr) .The relaxation time due to bulk effect
( b) has been calculated using the equations b =1/2 fr. The relaxation time ( b) values were
found to be increasing from 300C to 800C. The dc conductivity ( dc) decreases with rise in
temperature indicating the existence of positive temperature coefficient of resistance (PTCR)
in the material. The activation energy (Ea) calculated from the relaxation time due to bulk
effect ( b) was found to be 0.446 eV, whereas it is found to be 0.363 eV from the dc
conductivity plot in the temperature range of 300C to 1000C. This implies that the charge
carriers responsible for conduction and relaxation processes in the sample are almost same in
the conducting microcellular polymer foams obtained from EOC, carbon black as filler and
ADC as the blowing agent. The ac conductivity shows the frequency dependent
characteristics irrespective of blowing agent loading. AC conductivity increases with increase
in both blowing agent and carbon black loading. The 20 phr of Ensaco 250G loadings was
found to be the percolation limit of EOC polymer matrix.