chapter 7 dielectric response of conducting carbon black...

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


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


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


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


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


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


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


115


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


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


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


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.


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].


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


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


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


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.


124


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.


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).


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


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)


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.

chapter 7 dielectric response of conducting carbon black...

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