dynamic electromechanical measurements of carbon black

Dynamic Electromechanical Measurements of Carbon Black

Loaded SBR

by

Yawlin Hwang

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and state University

in partial fulfillment of the requirements for the degree of

Master of Science

in

Materials Engineering

APPROVED:

F. William Stephenson

July, 1988

Blacksburg, Virginia

Shinzo Onishi

LO Stt,S~ vr.j~"- . , q¥~

Kqn-c.~

Dynamic Electromechanical Measurements of Carbon Black

Loaded SBR

by

Yawlin Hwang

Larry C. Burton, Chairman

Materials Engineering

(ABSTRACT)

The major objectives of this study were to examine

electrical and electromechanical properties of SBR filled

with carbon black in the 0-70 phr range. The experiments

were divided into four parts: dielectric measurement, loss

modulus and phase angle measurements, temperature rise

measurement during stress cycling, and dynamic conductivity

measurement.

It is established that there are three distinct

conduction regimes existing at carbon black loadings below,

at, and above the percolation threshold. Characteristics of

dielectric dispersion depend strongly on carbon black

loading and frequency. Dielectric and AC conductivity

measurements are shown to provide a nondestructive method to

explore the carbon black network inside the rubber.

Both loss modulus and phase angle are related to

hysteresis properties, and to temperature rise due to

compressive cycling. Measurements o.f these parameters will

be discussed in detail, as functions of carbon black

loading, stress and strain amplitudes, and oscillation

frequency. These and other results can be understood in

terms of the mechanics of the carbon black network.

The variation of conductivity with strain amplitude is

related directly to the interplay between the "persistent"

and "transient" fractions of carbon black network. It is

shown that, owing to its experimental accuracy and great

sensitivity to carbon black network changes, the dynamic

conductivity measurement is preferable to traditional

modulus measurements for determining certain dynamic

properties of carbon black filled rubbers.

Acknowledgements

The author wishes to express his sincere appreciation to

his advisor Dr. L.C. Burton for his guidance, and his

invaluable assistance during the course of his study. Many

thanks also go to the members of his committee, Dr. F.W.

Stephenson, and Dr. S. Onishi for their review and

suggestions.

In addition, the author would like to thank his friends

and fellow officemates C.J. Chen, E. Cole, E. Ellis, P.

Johnson, R. Reddy, S. Sen, Chris Turman, A. Vaseashta, N.

Weaver, I.K. YOo, and T. Zhang, who provided both friendship

and support when he needed them the most.

The U.S. Army Tank and Automotive Command is

acknowledged for providing financial support during the

course of this study.

ACKNOWLEDGEMENTS iv

TABLE OF CONTENTS

1.0 INTRODUCTION •••••••••••••••••••••••••••••••••••••••• 1

2 • 0 LITERA~ REV'IEW ••••••••••••••••••••••••••••••••••• 3

2 • 1 CAR.BON BUCK •••••••••••••••••••••••....••••••.•.•••• 4

2.2 CAR.BON BUCK-POLYMER COMPOUNDS ••.•••••••...•.••••... 4

2.3 EFFECT OF COMPOUND MORPHOLOGY ON ELECTRICAL

CONDUCTIVITY ••••••••••••••••..••••••••.•••••••.•...• 5

2 • 4 CONDUCTION MECHANISMS ••••••••••••..••••••...•.•.••.. 6

2 • 5 AC CONDUCTION •.•••••••••••••••••••••..•••••••••••... 9

2.6 DIELECTRIC PROPERTIES •.•••••••.••••••.•...•••••....• 11

2.7 CHARGE CAR.RIERS IN DIELECTRIC MATERIALS •..•...•••... 16

2.8 DYNAMIC PROPERTIES OF RUBBERS ••••••••.•••••••.•..... 18

2.9 EFFECT OF CAR.BON BUCK ON DYNAMIC PROPERTIES ••••.... 20

2.10 EFFECTS OF CAR.BON BUCK ON HYSTERESIS ••••••••.••••• 23

3.0 EXPERIMENTAL METHODS AND MATERIALS •••••••••••••••••• 24

3 • 1 DIELECTRIC MEASUREMENT ••••.•••••••••.•••••••••.....• 24

3.2 LOSS MODULUS AND PHASE ANGLE MEASUREMENTS •..•••••••. 27

3.3 TEMPERA~ RISE MEASUREMENT ••••••••••••.••••.•..••. 28

3.4 DYNAMIC CONDUCTIVITY MEASUREMENT •••••••••••••••••••• 29

4.0 RESULTS AND DISCUSSION •••••••••••••••••••••••••••••• 30

4.1 DIELECTRIC CONSTANT MEASUREMENT ••••...••••••••••••.. 30

4.2 DIELECTRIC LOSS MEASUREMENT •••••••.••••••••.•••••..• 33

TABLE OF CONTENTS V

4.3 THREE REGIMES OF DIELECTRIC RESPONSE ••••••...••••••. 36

4 • 3 • 1 CONDUCTING REGIME •••.•••••••••••••.••.••••••.•.. 3 6

4 • 3 .2 PERCOLATION REGIME ••••••••.•••••••.••••••••••.•• 40

4.3. 3 DIELECTRIC REGIME ••••••••••••••••••••••••••••••• 44

4.4 AC CONDUCTIVITY MEASUREMENT •••••••••••••••••••••••.• 44

4.5 PHASE ANGLE AND LOSS MODULUS MEASUREMENTS ••••••••••• 51

4.6 HYSTERESIS MEASUREMENT •••••••••••••••...•••••.•••••. 57

4.7 TEMPERATURE RISE MEASUREMENT ••••••••••.•.••••••••... 60

4.8 DYNAMIC CONDUCTIVITY MEASUREMENT .•••••.••••••••••.•• 66

4.9 CONDUCTIVITY EFFECT OF DYNAMIC PROPERTIES OF

CARBON BLACK-FILLED RUBBERS ••••••.•.•••••••••••••••. 72

4.9.1 CORRESPONDENCE BETWEEN CONDUCTIVITY AND MODULUS

CHA.NGES ••••••••••••••••••.•••••••••••••••••••••• 73

4.9.2 EFFECTS OF PERSISTENT AND TRANSIENT STRUCTURES ON

CONDUCTIVITY DURING A CYCLE .••••••.••••••••.•.•• 74

4.9.3 PHYSICAL SIGNIFICANCE OF qmin ..•.•.•••••.••••... 75

4.9.4 CONDUCTIVITY RELAXATION AT LOW STRAIN

AMPLITUDES ••••••••••••••••••••••••••••..••••••.. 79

4.9.5 PHYSICAL SIGNIFICANCE OFAg ••••••••••••••.•.•.•• 79

4.9.6 RELATIONSHIP BETWEEN qo-q. AND Aqm .••••••.••.... 87

4.9.7 EFFECTS OF CHANGING VIBRATION FREQUENCy ••••••••• 90

4.9.8 RISE IN Aq AT HIGH STRAIN AMPLITUDES ••••••..•••• 90

4.9.9 THE ASSYMMETRY IN TIME-CURRENT VARIATION CURVE •• 94

5.0 CONCLUSIONS AND RECOMMENDATIONS ••••••••••••••••••••• 96

5. 1 CONCLUSIONS ••••••••••••••••••••••••.•••••.•.•••••••• 96

TABLE OF CONTENTS vi

5.2 RECOMMENDATIONS FOR FUTURE WORK ..•.••..••••.•..•.... 99

BIBLIOGRAPHY 100

CtJR,R,IctJI.tJM VITAE •••••••••••••••••••••••••••••..••...••• 103

TABLE OF CONTENTS vii

LIST OF ILLUSTRATIONS

Figure 1. Equivalent RC circuit in the contact region of carbon aggregates. (From ref.17) ••••••••. 10

Figure 2. Frequency dependence of E and P in the equivalent circuit of Fig.1. (From ref.17) ••• 12

Figure 3. Frequency dependence of resistivity of rubber loaded with 50 phr carbon black •••••••••••.•• 13

Figure 4. Frequency dependence of dielectric constant of rubber loaded with 50 phr carbon black •••••.• 14

Figure 5. A typical hysteresis loop ( SBR with 40 phr, 8% double strain amplitude in compression under 15% static strain, 1Hz) ••.•••••••••••.••••..• 19

Figure 6. Qualitative interpretation of strain amplitude dependence of E t (From ref. 4) ••••..••••..•••. 21

Figure 7. Frequency dependence of dielectric constant of rubbers loaded with different amounts of carbon black. .•••.•••••.••.•••••.•••••..•.•... 31

Figure 8. The dielectric constant of carbon black filled rubber as a function of carbon black loading (frequency = 10 lCHz). •••••••••••••••••.•••.•• 32

Figure 9. Frequency dependence of dielectric loss of rubbers loaded with different amounts of carbon black. ••••••••••••••••••••••••••••.••• 34

Figure 10. The dielectric loss of carbon black filled rubber as a function of carbon black loading (frequency = 10 lCHz). •••••••••••.•••••.••.•.. 35

Figure 11. The dielectric constant as a function of carbon black loading at a fixed frequency 10 lCHz ••••••••••••••••••••••••••••••••••••••• 37

Figure 12. The dispersion of dielectric constant of compounds with carbon black loading falling in the conducting regime ••••••••..•..••••...• 38

Figure 13. The dispersion of dielectric loss of compounds with carbon black loading falling in the conducting regime. ••.••••.••••••..••••••••••• 39

LIST OF ILLUSTRATIONS viii

Figure 14. The dispersion of dielectric constant of compounds with car~on black loading falling in the percolaton reg~me ••••••.•••••••.••••••••• 41

Figure 15. The dispersion of dielectric loss of compounds with carbon black loading falling in the percolation regime •••••••••••••••••••.••••••• 42

Figure 16. The dispersion of dielectric constant of compounds with carbon black loading falling in the dielectric regime ••••••••••••••••••••• 45

Figure 17. The dispersion of dielectric loss of compounds with carbon black loading falling in the dielectric regime ••••••••••••••••.••••••...• 46

Figure 18. Frequency dependence of conductivity of rubbers loaded with different amounts of carbon black. ....................................... 47

Figure 19. Frequency dependence of conductivity of rubbers with carbon black loading falling in the dielectric regime. • •• 0. . . . • • . . . . . . . . . . . . . . . .. 49

Figure 20. Frequency dependence of conductivity of rubbers with carbon black loading falling in the percolation regime ••••••••••••••••••••••..•.• 50

Figure 21. Frequency dependence of conductivity of rubbers with carbon black loading falling in the conducting regime •••••••.••••••••..•••••• 52

Figure 22. strain amplitude dependence of phase angle 6 at 1 Hz for rubbers loaded with different amounts of carbon black •••••••••••••••••.•••• 53

Figure 23. The dependence of phase angle 5 upon carbon black loading at a given double strain amplitude of 10% and at a given double stress amplitude of 200 lb. during compressive cycl ing at 1 Hz. ••••••••••••••••.•••••••.•••• 55

Figure 24. The dependence of loss modulus E" upon carbon black loading at a given double strain amplitude of 10% and at a given double stress amplitude of 200 lb. during compressive cycling at 1 Hz •••••••••.•••••••..••••••••••• 56

Figure 25. The dependence of double strain amplitude upon carbon black loading at a given stress amplitude of 200 lb. at 1 Hz •••••••••••..•••• 58

LIST OF ILLUSTRATIONS ix

Figure 26. The dependence of hysteresis loop area upon carbon black loading at a given strain amplitude of 10% and at a given stress amplitude of 200 lb. at 1 Hz ••••••••••••••••• 59

Figure 27. The dependence of Eft x (strain amplitude) 2 upon carbon black loading at a given strain amplitude of 10% and at a given stress amplitude of 200 lb. at 1 Hz •••••••••••••••.• 61

Figure 28. Temperature at the center of specimens of different carbon black content at double strain amplitude of 10%, at 10 Hz •.•••••••••• 62

Figure 29. Temperature at the center of specimens of different carbon black content at double stress amplitude of 200 lb. and at 10 Hz. 63

Figure 30. Dependence of temperature rise on hysteresis loop area at a strain amplitude of 10%, at 10 Hz. ••••••••••••••••••••••••••••••••••••••• 64

Figure 31. Dependence of temperature rise on hysteresis loop area at stress amplitude of 200 lb. at 10 Hz. •••••••••••••••••••••••••••••••••••• 65

Figure 32. Current (top) " and strain vs. time curve at a strain amplitude of 0.02 for specimen of 50 phr carbon black loading at vibration frequency 0 f 1 Hz. ••••••••••••••••••••••••••• 67

Figure 33. Conductivity vs. double strain amplitude at 0.25 Hz for specimen of 40 phr carbon black loading. ••••••••••••••••••••.•••••••••••••••. 68

Figure 34. Conductivity vs. double strain amplitude at 0.25 Hz for specimen of 50 phr carbon black loading. ..••••••••••••••••.••.•••••••••....•• 69

Figure 35. Conductivity vs. double strain amplitude at 0.25 Hz for specimen of 60 phr carbon black loading. •••••••••••••••••••••...••...•.••••.• 70

Figure 36. Conductivity vs. double strain amplitude at 0.25 Hz for specimen of 70 phr carbon black loading. .••.••••••••••.••••••••••.•••••••••.• 71

Figure 37. Carbon black loading dependence of go-~' go' <3C.' and 4gm• •••••••••••••••••••••••••••••.••. 77

LIST OF ILLUSTRATIONS x

Figure 38. Current vs. time curves at increasing amplitudes for specimen of 50 phr carbon black loading at 1 Hz. Upper curve is current; lower curve is strain. Double strain amplitudes (DSA) are given next to figure •••••••.••••••.••••••.••• 80

Figure 39. Normalized conductivity Z as a function of strain amplitude. • ••••••••••••••.•.••••.•...• 88

Figure 40. Variation of Agm with go-~ .•...•••••.....•... 89

Figure 41. Conductivity bandwidth (Ag) vs. DSA for specimen of 40 phr carbon black loading at 0.25 and 1 Hz, respectively .••.•..•.•..•••••• 91

Figure 42. Conductivity bandwidth (4g) vs. DSA for specimen of 50 phr carbon black loading at 0.25 and 1 HZ, respectively •••••••..••••.•.•• 92

Figure 43. Conductivity bandwidth (Ag) vs. DSA for specimen of 70 phr carbon black loading at 0.25 and 1 Hz, respectively •••••.••••••••••.. 93

LIST OF ILLUSTRATIONS xi

LIST OF TABLES

Table 1. Akron sample compositions ••••••.•••.•••..••.••• 25

Table 2. (go-g~~/~~ at different carbon black composl.tl.ons •.••.••.••••••.••..••.••••.•••••••• 78

LIST OF TABLES xii

1.0 INTRODUCTION

Tracked military vehicles such as tanks, armored

personnel carriers and self-propelled artillery make use of

rubber pads on their tracks to damp vibrations and to

prevent unnecessary damage to the road surfaces. These

rubber pads generally consist of a synthetic elastomer, e.g.

styrene-butadiene rubber (SBR), using sulfur as a

crosslinking agent, zinc oxide as an accelerator ,and other

processing aids. Such elastomers must be reinforced by the

addition of fillers such as carbon black.

The united states Army's Tank and Automotive Command

(TACOM) is currently conducting an in-depth study for

improving the field-service life of these tank track

materials. The scope of the work described in this thesis

is designed to assist TACOM in the study of electrical and

dynamic properties of tank track rubber pads. The

objectives are:

1. to determine if AC electrical measurements can be used to

explore the internal structures of carbon black network

within such compounds;

2. to examine the dynamic properties of such compounds by

means of electrical measurements, with carbon black

content as a major variable;

INTRODUCTION 1

3. to make recommendations a) as to the feasibility of

electrical measurements toward improving the reliability

of track pad rubber, and b) for future work.

The main experiments of this research are thus divided

into three parts: measurements of mechanical properties,

electrical properties, and dynamic properties respectively.

The determination of mechanical properties included

measurements of loss modulus, phase angle, hysteresis, and

temperature rise resulting from stress. The determination

of electrical properties included measurements of functional

dependence of electrical conductivity, dielectric constant

and dielectric loss on AC frequencies and carbon black

contents. The determination of dynamic properties included

measurements of conductivity as a function of strain

amplitudes.

Although these measurements are seemingly independent of

each other, they are strongly related qualitatively since

both electrical and mechanical processes involve the carbon

black network within the compounds.

INTRODUCTION 2

2.0 LITERATURE REVIEW

Polymer-carbon black compounds, such as carbon black

filled rubber, are some of the most extensively studied

systems because of their wide use in the automotive

industry. Carbon black has long been used as a reinforcing

agent in elastomers due to its low cost, ready availability,

and reinforcing abilityl. The original purpose of creating

such a compound was to increase the strength and durability

of an elastomer while still retaining sufficient elastomeric

behavior. Rubber tires, for example, are made of a carbon

rubber mixture which gives enhanced wear resistance over

that of rubber alone.

Most of the studies reported in the past were mainly

focussed on mechanical aspects of the compounds, such as

stress and strain relaxations2 ,3, dynamic properties4- 8

etc •• Research related to electrical properties of the

compounds has been focused on the conductivity as a function

of carbon black 10ading9- 12 , conduction mechanisms13- 16 , and

AC electrical properties17 ,18. However, there are

insufficient studies on the correlation between mechanical

and electrical properties of rubber-carbon black compounds.

LITERATURE REVIEW 3

2.1 CARBON BLACK

Carbon black is made up of solid or hollow spheres of

partly graphitized carbon, which are usually formed by

subjecting oil droplets to very high temperatures19 .

Graphitic carbon black is a good electrical conductor with

room temperature bulk resistivities of about 10-3 ohm-cm10 .

Carbon black consists of aggregates20 which are formed by

fusion of particles in the flame. The spheroidal carbon

particles do not have an independent existence in carbon

black. The aggregate is the smallest dispersible entity4.

The aggregates are associated into larger units called

agglomerates and, at normal loadings, a network which can be

completely separated into the constituent aggregates by

deformation of the rubber compound.

2.2 CARBON BLACK - POLYMER COMPOUNDS

The carbon-polymer compounds are formed by dispersing

carbon black into a polymer matrix. The compounding is done

by adding the carbon black to the polymer, mixing at

temperatures above the glass transition temperature and

subjecting the mixture to high shears in an extruder until a

uniform blend is obtained21 •

When carbon black is added to a polymer, the

agglomerates may flocculate under the influence of London-

LITERATURE REVIEW 4

Van der Waals force4 ,22. The tendency of carbon to cluster,

resulting in "structure", depends on the type of carbon

black. For example, hollow carbon spheres form highly

structured compounds, while solid carbon spheres show much

less of a tendency to agglomerate11 • And a network of

interconnected carbon black aggregates can be formed. The

physical properties of carbon-ploymer compounds are affected

mainly by the amount, distribution, and the structure of the

carbon black.

2.3 EFFECT OF COMPOUND MORPHOLOGY ON ELECTRICAL CONDUCTIVITY

The exact morphology of the compound has a profound

effect on the electrical properties. The dependence of the

conductivity on carbon black loading is widely documented11 .

At very low carbon black loading, the conductivity of the

compound is low, characteristic of the polymer. Addition of

carbon black increases the conductivity until a critical

carbon concentration, called "percolation threshold", is

reached at which the conductivity of the compound increases

many orders of magnitude for a small increase in the amount

of carbon black10,11. When more carbon black is added, the

conductivity ultimately saturates at a value characteristic

of the graphitic carbon itself.

The effective medium theory23 predicts a percolation

threshold which depends on particle shape, and occurs at

LITERATURE REVIEW 5

about 33 per cent by volume for spherical conducting

particles. A theoretical discussion of the percolation

problem may be found in the article by Kirkpatrick24 •

The percolation threshold depends on the structure of

the carbon dispersion. It has been shown11 that a compound

made of hollow carbon black spheres has a lower percolation

threshold than a compound made of solid carbon spheres.

This is because these agglomerates can have the same

external dimensions, which are critical for network

formation, at a lower density, due to their porosity.

2.4 CONDUCTION MECHANISMS

Most rubbers have long been appreciated as good

electrical insulators with resistivities in the range of

1013 _1016 ohm-cm25 . Carbon black would be classified as a

moderately good conductor with resistivities in the range of

1-103 ohm-cm. Carbon-polymer compounds are a class of

materials whose electrical properties can cover the range

from insulators to conductors by varying the amount of

carbon black present.

Electrical conductivity of carbon-polymer compounds does

not increase linearly with the volume amount of carbon black

present. The electrical behavior can be divided into three

regimes26 : the dielectric regime, the transition or

percolation regime, and the conducting or metallic regime.

LITERATURE REVIEW 6

The conduction mechanisms in each regime are different.

Considerable experimental efforts have been devoted over

several decades to electrical studies of the mechanisms.

Three distinct physical processes are proposed to control

electron transport in conductor-filled systems. These are

1. Percolative transport27 ;

2. Electron tunneling10 ,15,16,27;

3. Electron hopping1S ,27,2S.

Microscopic conduction within the conductor-filler

particles is controlled principally by ohmic conduction;

between them, it is dominated by quantum mechanical

tunneling or conduction through the polymer. Long-range

macroscopic effects, however, are governed by percolation

phenomena.

Percolation theory27 predicts a filler concentration

threshold where the compound makes a transition between

tunneling (or polymer transport) and conductor-filler ohmic

conduction. When the concentration of the carbon is beyond

this percolation point, the carbon chains form a continuous

network, and the resulting conductivity is graphitic in

nature. As the concentration is decreased to below the

percolation point, conduction depends on electron tunneling

through the insulating polymer-filled gaps between carbon

aggregates. The tunneling may be either of the normal

quantum mechanical type or of a novel sort introduced by

sheng10 • The latter mechanism incorporates the former, but

LITERATURE REVIEW 7

the energy of a tunneling electron is augmented, i.e., the

tunneling barriers between aggregates are lowered and

narrowed by thermally activated voltage fluctuations across

the gaps. The gaps between carbon aggregates actually

control the conductivity rather than the black itself.

Hopping electrons are characterized by the fact that

they spend most of the time in localized sites but can make

a thermally-assisted hopping transition over a potential

barrier to neighboring localized sites28 . The probability

of electron hopping transition is dependent upon the

combined effect of the distance between two aggregates and

the potential barrier height which has to be overcome. It

was shown26 that, when the distance is greater than looA,

electron tunneling becomes negligible and the electron

hopping mechanism is dominant; when less than IOOA, the

fluctuation-induced tunneling is the dominant conduction

mechanism at room temperature, which requires negligible

activation energy. In general, at normal loadings and

normal temperatures, the dominant mechanism of DC conduction

is either tunneling through the gap, assisted by thermal

fluctuations, or thermal activation of electrons over the

potential barrier of the gap. These two mechanisms may be

experimentally indistinguishablel8 •

LITERATURE REVIEW 8

2.5 AC CONDUCTION

The carbon black aggregates are dispersed in the rubber

so that a conductive network is formed. Electrically, the

carbon black filled rubber is a network of a large number of

RC circuits randomly interconnected with each other.

However, for simplicity we assume that the whole body of the

filled rubber can be represented by a single RC circuit

shown in Figure 117. Kawamot017 showed that this simple RC

circuit can be used in modelling the results of AC

measurements. It will be shown later that this model can

only be successfully applied when the loading of conductive

fillers is near or above the percolation threshold.

According to Kawamoto's model17 , "there are two

electrical current components competing with each other in a

contact region between carbon aggregates: one is a

conduction current through an internal contact resistance

Rc; the other is a displacement current through a contact

capacitance Cc. RA represents the resistance within the

carbon aggregates." The contact resistance in this model is

due to a tunneling effect, or an ohmic contact effect, or to

other sources.

At low frequencies, the net resistance is equal to

RA+RC; at high frequencies, the net resistance is equal to

RA since the impedance of Cc at high frequencies is

considered to be negligibly small compared to RC and RA.

LITERATURE REVIEW 9

CARBON AGGREGATE

.-- ....... .JIII". ,

/' , CCNTACT I REGION .-.-1 RC

\

CARBON AGGREGATE

cc } Rubber I Medium

Figure' 1. Equivalent RC circuit in the contact region of

carbon aggregates. (From ref.17)

LITERATURE REVIEW 10

Based on this model, a theoretically estimated curve is

drawn in Figure 2, showing the dependence of resistivity and

dielectric constant upon frequency. The resistivity

saturates at PL(=PA+fL) at low frequencies, decreases with

frequency, and stays at FH(=fA) at high frequencies. The

dielectric constant stays at a high plateau at low

frequencies, and drops by a factor of w2 at high

frequencies, where w is the angular frequency. Figures 3

and 4 show the experimental results of the variation of

resistivity and dielectric constant, respectively, with

frequency at the loading of 50 . parts per hundred rubber

(phr), both of which are quite consistent with the picture

given above except that the dielectric constant drops at

high frequencies by a factor of w1 . 2 rather than w2 .

2.6 DIELECTRIC PROPERTIES29

According to Maxwell's equations, the current in the

frequency domain can be defined in terms of direct

conduction current and displacement current:

I (w) = UoECw) + iwD(w)

= { Uo + iWEo[E' (w) -iE"(w)]}E(w)

= { Uo + EoWE"(W) + iWEoE' (w) } E (w) (2.1)

in-phase out-of-phase

The E'(W) gives the component of displacement current, which


r .C CC

'cL= (1 + RAlRC)2

~ ~ .IJ .IJ -,... -,... PL fA + Pc > > = • .-4 .,... .IJ .IJ

fH fA fJl +J = -.-4 -,... fJl ~ OJ ~ OJ

Slt (lIRA) 2

w2cc

Frequency, w

Figure" 2. Frequency dependence of Eand f in the

equivalent circuit of Fig.l. (From ref.17)


-a o I S .d o -

lEt4~ ________________________________________________ -,

• 59 phI'

~ lI+3 .~

> .~

+J til .~

til OJ ~

lE.2+-____ ~~~~~~--~~nn~~~nn~_r~Tnnr_._r~ntl 1£+2

(Hz)

Figure" 3. Frequency dependence of resistivity of rubber

loaded with 50 phr carbon black.


• 51, ..

Frequency (Hz)

Figure'4. Frequency dependence of dielectric constant of

rubber loaded with 50 phr carbon black.


is out-of-phase with the driving field, and therefore does

not contribute to power loss, while the E" (w) gives the

component of current in-phase with the driving field, and

therefore contributes to power loss. For this reason we

refer to E"(W) as the "dielectric loss".

The frequency-domain dielectric induction Dew) can thus

be expressed as

D(w) = EoE*(W)E(W) = Eo[E'(W) -iE"(W)]E(w) (2.2)

where E* (w) is the complex dielectric constant. The real

part of D(w) represents the component of the total induced

charge at the electrodes which is in phase with the driving

field E(w) at the frequency w, and this component includes

the free space contribution since there is no loss

associated with free space. The imaginary part of Dew),

E"(W), gives the component of the total induced charge which

is out of phase with the driving field E(w).

Since dielectric measurements are concerned with the

movement of charge, i.e., with the electric current, it

follows from eqn.(l) that the DC conductivity uo must appear

in the result. It was shown that no instrument can

distinguish between true dielectric response which does not

include Uo and the effective dielectric response which does.

If we take into account this effective dielectric response,

eqn.(l) can be written as


lew) = iWEoE*(W)E(W) (2.3)

where E* (w) denotes the effective dielectric constant as

measured by the instrument and is expressed as

E* (w) = E I (w) - i{E" (w) + [Uo/W]} (2.4)

As can be seen from this equation, the DC conductivity makes

a contribution to the apparent dielectric loss, which

diverges towards zero frequency, while it does not

contribute to the real part of complex dielectric constant.

A behavior in which E" (w) 0( l/w while E' (w) ......,. constant as w

-+0 is, therefore, conclusive evidence that the dominant

process is direct current conduction in the material in

question in the relevant frequency range.

2.7 CHARGE CARRIERS IN DIELECTRIC MATERIALS30

The dielectric effects of free charge carriers only

become significant at frequencies of the order of the

reciprocal collision time, which fall in the 10-100 GHz

range. Thus the dielectric effects of free charge carriers

are negligible in the frequency range in which we are

predominantly concerned with (100Hz-40MHz). However, these

free charge carriers may give rise to such a high DC


conductivity that dielectric effects may not be easily

measurable. On the other hand, low-frequency dielectric

responses may be expected from any localized charge carriers

that may be present in a semiconducting materials,

especially in conditions where the effects of the free

charge carriers are not dominant.

Within the carbon-polymer compound the normal concept of

band conduction by free electrons does not apply since the

electrons become "localized" and move by tunneling or

hopping between localized sites. If these sites form a

continuous connected network, the charges may be capable of

traversing the entire physical dimensions of the compound

and, therefore, give rise to direct current conduction that

would be indistinguishable from free electron conduction

were it not for a much lower mobility. It is inevitable

that there exist "easier" and "more difficult" paths for

tunneling or hopping, and that electrons execute many

reciprocating transitions between pairs of sites linked by

easy transitions before making "forward" jumps to other

sites involving more difficult transitions. The point to

note here is that the dielectric properties are determined

by the easiest transitions, while the conducting properties

are determined by the most difficult transitions which limit

the free percolation of charges from one electrode to the

other.


2.8 DYNAMIC PROPERTIES OF RUBBERS

The term. "dynamic properties" as applied to elastomers

refers to the response to periodic or transient forces which

do not cause failure or appreciable fatigue during the

investigation. The dynamic properties of rubber are altered

tremendously by the addition of a filler, e.g. carbon black.

The dynamic properties of rubber are best visualized in

terms of a specimen undergoing uniform sinusoidal

deformation. It is convenient to consider the dynamic

properties of rubbers in terms of their elastic and viscous

moduli. A useful description4 of the dynamic properties is

given by

where E* = E' = E" =

It is also

angle, by

E* = E' + iE"

dynamic, or

elastic, or

viscous, or

convenient

tanS =

complex, modulus

in-phase, modulus

out-of-phase, loss modulus.

to define the phase angle,

Elt E'

(2.5)

or loss

(2.6)

If the stress is plotted against strain, rather than time, a

hysteresis loop is obtained, as shown in Figure 5, for a

Fort Belvoir sample. The maximum strain and stress,


STRAIN

Figure 5. A typical hysteresis loop (SBR with 40 phr, 8%

double strain amplitude in compression under 15%

static strain, 1Hz)


represented by segments BF and AB, can be measured and

converted to dynamic parameters by definition

and

= AB/An, BF/Lo

CD sinS =_ ........ -AB

where Ao = area of the hysteresis loop

and Lo = thickness of the specimen.

(2.7)

(2.8)

The area inside the loop represents the mechanical work

which is not recovered as such during a cycle but instead is

converted to heat. For sinusoidal deformation, the heat H

generated by hysteresis is given by H = 11' e 2E", which is

proportional to the area of the hysteresis loop, where E is

the strain amplitude and E" is the loss modulus.

2 .9 EFFECT OF CARBON BLACK ON DYNAMIC PROPERTIES

The principal effects of carbon black on the dynamic

properties of rubber have long been established4 : (a) an

increase in elastic modulus E' (over the pure gum value);

(b) an increase in phase angle; (c) dependence of E' on

strain amplitude (not found with pure gum).

The elastic modulus curves are represented in idealized

form in Figure 6. The idealized curve is shown as leveling

off at a value ~ at high amplitude, and at G~ at low

amplitude. PayneS attributed the effect of carbon black at

the high amplitude to a combination of a hydrodynamic effect


REGION DUE TO INTERAGGREGATE' INTERACTION

ADDITIONAL CROSS LINKAGE DUE TO FILLER RUBBER LINKAGES

HYDRODYNAMIC EFFECT DUE TO CARBON BLACK

PURE GUM MODULUS

LOG SHEAR STRAIN

Figure" 6. Qualitative interpretation of strain amplitude

dependence of G' (From ref.4)


and additional effective crosslinks due to rubber-filler

bonds. The difference between Go' and G~', which we will

call AG', was attributed to the "structure" of the carbon

black, which results from the interaggregate association by

physical (van der Waals type) forces.

At normal loadings, carbon black aggregates interact to

form a network. The contribution of carbon black to

augmentation of elastic modulus, at any level of strain

amplitude, is due to the remaining throughgoing network,

whose presence appears to be SUbstantiated by electrical

measurement. The network is rigid at very low strain

amplitudes but breaks down completely at extremes of

oscillation, at high amplitudes. The transition from a

network to isolated aggregates is continuous. This accounts

for the amplitude effect, in which the interaggregate

interaction appears to be responsible for in dynamic

measurements. During strain cycling, the aggregate-to

aggregate transient structures are continually being broken

down and reformed. This is a dissipative process which

accounts for hysteresis.

The dynamic properties of carbon black-rubber systems

are mainly ascribed to8 : (a) the structure which results in

the stiffness of the compounds at the lower end of the

strain range; (2) the hydrodynamic effects of the carbon

black particles embedded in the viscoelastic medium, and (3)

adhesion between carbon black and rubber, which is


increasingly important at larger strains. These factors are

clearly interrelated. The amplitude effect on E' was shown

to increase with increasing loading of a given black and

with increasing reinforcing character of the black.

2. 10 EFFECTS OF CARBON BLACK ON HYSTERESIS

Rubber hysteresis is the mechanical energy that is lost

or dissipated as heat during deformation of the material.

It is also an important factor in determining the strength

of carbon black-rubber compounds31 • It has been shown4 that

carbon black type and loading have a pronounced effect on

rubber hysteresis in a wide variety of vulcanized rubber

systems.

Addition of carbon black to the rubber increases the

hysteresis32 • Because carbon black is much stiffer than the

rubber itself, the deformation of a filled compound occurs

essentially only in the rubber phase. The strain in the

rubber phase is thus larger than the overall strain. This

is termed "strain magnification"32 • Hysteresis increases

with increasing deformation; in other words, the strain

amplification by carbon black acts to increase hysteresis.

On the other hand, the carbon black also reduces the volume

of deformable material, in which at least part of the

hysteresis occurs I and in this respect acts to reduce the

hysteresis.


3.0 EXPERIMENTAL METHODS AND MATERIALS

Carbon black filled rubber samples used in this study

were obtained from Akron Rubber Development Laboratory in

Akron, Ohio. Some earlier samples were obtained from Ft.

Belvoir, VA). These samples contain 30, 40, 50, 60, and 70

phr (parts of carbon black per hundred parts of rubber)

carbon black. Sample dimensions were .5" (thickness) x

1.0625" (diameter). Electrical contact was made by

colloidal silver painted on the broad surfaces of the

specimens for electrical measurements. Sample compositions

are listed in Table 1.

The following measurements were made on these samples.

1. Dielectric measurement

2. Loss modulus and phase angle measurements

3. Temperature rise measurement during stress

4. Dynamic conductivity measurement

These experiments are described in more detail in the

following sections.

3.1 DIELECTRIC MEASUREMENT

It has been shown that the admittance representation,

y*, is the natural way of describing physical phenomena in

which two mechanisms exist in parallel, whereby the same

voltage or field drives two components of current through

EXPERIMENTAL AND MATERIALS 24

Table 1. Akron sample compositions

INGREDIENT AK30 AK40 AK50 AKSO AK70 or AK30A or AK40A or AK50A or AK60A or AK70A

RUBBER SBR1500 SBR1500 SBR1500 SBR1500 . SBR1500

CARBON BLACK TYPE N .. 234 N .. 234 N .. 234 N-234 N-234

BLACK QTY. (PPHR) 30 40 50 60 70

ZINC OXIDE (PPHR) 4.0 4.0 .4.0 4.0 4.0

STEARIC ACID 2.0 2.0 2.0 2.0 2.0

SANTOFLEX 13 (AO) 2.0 2.0 2.0 2.0 2.0

AGERITE RESIN (AO) 2.0 2.0 2.0 2.0 2.0

SUNDEX 790 (OIL) 10 10 10 10 10

AMAX (CURATIVE) 1.9 1.9 1.9 1.9 1.9

-SULFUR (CURATIVE) 1.9 1.9 1.9 1.9 1.9

EXPERIMENTAL AND MATERIALS 25

the system33 • A typical example is the presence of a finite

DC conduction mechanism in parallel with the dielectric

polarization which is inevitably present in all materials.

Since the equivalent circuit of the carbon black-rubber

compounds has been assumed to be a resistance in series with

a parallel R-C combination, the admittance is chosen to be

the measured quantity so that the other dielectric functions

(dielectric constant and loss, AC conductivities etc.) can

subsequently be determined by calculation.

The admittance Y* (w) is defined as the ratio of the

current to the voltage, i.e. I(w)/V(w), and can be written

as

Y*(w) = G(w) + iB(w)

= G (w) + i wc' (w)

where G(w) = effective conductance

B(w) = effective susceptance

C· (w) = effective capacitance

w = angular frequency.

The conductivity U(w), dielectric constant

(3.1a)

(3.1b)

E' (w) I and

dielectric loss E" (w) can then be determined through the

measured quantities G and B according to the relationships

given below:

G(w) = U(w) A d

EXPERIMENTAL METHODS AND MATERIALS

(3.2)

26

B(w) w

G(w) w

= C I (w) = E I (w) ~ (3.3)

A = C" (W) = E" (w) cr- (3.4)

where A is the area of the broad surface of the sample, d is

the thickness of the sample, and C"(w) is the imaginary part

of the effetive capacitance.

A Hewlett Packard 4194A Impedance Analyzer was used to

measure the admittance of all samples in the frequency range

of 100Hz to 40MHz.

3 • 2 LOSS MODULUS AND PHASE ANGLE MEASUREMENTS

The dynamic modulus measurements of carbon black-filled

rubber were carried out using the INSTRON 1331 Dynamic

Material Testing Machine. This testing system is capable of

applying loads to the test sample in the range of a few

pounds to ±1000 lb .• Test specimens can be cycled from very

low frequency (0.001 Hz) to frequencies as high as 200 Hz,

and displacement amplitudes range from micro-inches to ±O.S

inches.

A sinusoidal displacement in compression was applied for

all the testings. The testings are two-fold: the

cylindrical specimens of different carbon black contents

were first precompressed to a constant strain of 15% and

allowed to relax for 20 minutes before starting the

EXPERIMENTAL METHODS AND MATERIALS 27

compressive strain cycling of 1 HZ, first at very low strain

amplitude and then at successively increasing amplitudes;

or, similarly, they were first precompressed to a constant

stress of 200 lb prior to a constant stress amplitude (200

lb) cycling of 1 Hz. Dynamic strains and stresses referred

to throughout this thesis are peak-to-peak. In each case, a

hysteresis loop at each amplitude for each sample was

recorded with an X-Y recorder 1 minute after starting. Data

measured were stress and strain. Appropriate geometrical

measurements were then made by ruler on each chart and the

desired calculations were performed by computer in order to

determine the out-of-phase loss modulus E" and phase angle

s.

3.3 TEMPERATURE RISE MEASUREMENT

Temperature increase due to heat generation inside the

sample under cyclic compression was also measured, during

which the vibration frequency was fixed at 10 Hz to simUlate

road conditions. The temperature was measured by a

thermocouple inserted in the center of the specimen. The

tip of the thermocouple was bare, and the output of the

thermocouple was made by a digital readout. Heat radiation

from the surface of the specimen was minimized by inserting

a bakelite plate, 1" diameter and 0.1" thick, on the loading

surface and wrapping glass wool around the side surface of


the specimen. The temperature rise was measured at 23 0 C and

at two testing conditions: 10% dynamic strain at 10 Hz; and

200 lb. dynamic stress amplitude at 10 Hz.

3.4 DYNAMIC CONDUCTIVITY MEASUREMENT

For dynamic conductivity measurement (as a function of

strain amplitude), a sinusoidal displacement in compression

was applied using the INSTRON at room temperature. The

cylindrical specimens of different carbon black compositions

were first precompressed to 15% strain and then allowed to

relax for 20 minutes prior to a compressive cycling of 0.25

Hz. A KEITHLEY 485 Picoammeter was used to measure the

current flow at a constant voltage across the specimens.

Variation of the current with time at different strain

amplitudes was recorded by a chart recorder, first at the

lowest compressive strain cycling (Double strain Amplitude,

DSA = 0.001). Measurements continued with progressively

increasing strain cyclings until DSA=0.2 was reached. Only

the maximum and minimum current values at each strain

amplitude were taken every 5 minutes after each cycling.

These current values were then converted into conductivities

by calculation according to the applied voltage and the

sample geometry.


4.0 RESULTS AND DISCUSSION

4.1 DIELECTRIC CONSTANT MEASUREMENT

Figure 7 is a plot of dielectric constant as a function

of frequency, showing that dielectric constant decreases

with increasing frequency for all compounds, and that the

dispersion becomes more and more pronounced with carbon

black loading. However, as can be seen in Figure 8, the

dielectric constant first. increases with carbon black

loading up to 60 phr, and then decreases with still higher

loading, indicating that the carbon black aggregates are

already well connected in the form of a large number of

conductive paths throughout the composite after carbon black

loading of 60 phr. Since the dielectric constant represents

the ability of storing polarized charges, as the number of

conductive paths builds up, this charge storage ability is

expected to decrease with carbon black loading as a result

of metal-like conduction behavior throughout the solid.

The increase in dielectric constant during dielectric

and percolation regimes can be understood as due to the

reduction in distance between aggregates which serve as the

electrodes of a capacitor, since capacitance increases as

the distance between electrodes decreases. After carbon

black loading reaches the percolation threshold (at about 25

phr), a pronounced increase in dielectric constant follows

RESULTS AND DISCUSSION 30

..., s:: tU ..., f/) s:: o u u .~

J..f ..., U QJ ,.... QJ .~

C

11+

.... t 1 •• _

A 3 .. .. • 5 .. ...

A 11._ A 15._ o •• IIP o 7 •• _

lE •• I+-----~~--~~~~ __ ~Mnw__r~nT~--~~nnr_,_rTnmm 11+a

Frequency (Hz)

Figure 7. Frequency dependence of dielectric constant of

rubbers loaded with different amount of carbon

black.


lE5

- at 10KHz .~ lE4 ~--+J • s::

R:J +J til

lE3 s:: 0 0

0 -..... ~

1E2 / +J 0 OJ .-t OJ .....

/-Cl lEI /'-

-------lEO

0 10 ro :xl 40 00 00 70 Carbon Black Content (phr)

Figure 8. The dielectric constant of carbon black-filled

rubber as a function of carbon black loading

(frequency = 10KHz).


due to the combination of two major effects: one is the

increase in the number of "capacitors" within the compound

(i.e. number of contacts between aggregates); the other is

the reduction in distance between aggregates. This simple

geometrical model of dielectric response can be applied to

carbon black-rubber compounds falling in dielectric and

percolation regimes, while the "true" dielectric response

will not be easily measurable for compounds in metallic

regime owing to the presence of high direct current

conduction, which will be discussed later. An electrical

percolation can be observed in Figure 7 at the loading of 25

phr, below which the dielectric constant only shows slight,

nearly frequency-independent, dispersion with frequency.

4.2 DIELECTRIC LOSS MEASUREMENT

The frequency dependence of dielectric loss of all

compounds is plotted in Figure 9, showing that the

dielectric loss is nearly frequency-independent for

compounds of low carbon black loading «25 phr), with only a

tiny loss peak observed in the frequency range 10-100KHz.

However, the dispersion becomes more and more pronounced

with increasing carbon black loading (>25 phr).

Figure 10 shows that the dielectric loss increases with

carbon black loading and an electrical percolation can also

be observed at a loading of 25 phr carbon black.


.... I Z .... A 31 ... I 5 ....

A 11 ... A Z5", o 41._ o ., ....

ll-a+--r~~~--~~~~-r~~~~~~nn~~~Tn~~~~nm 11+2

Frequency (Hz)

Figure 9. Frequency dependence of dielectric loss of

rubbers loaded with different amount of carbon

black.


lE6~-------------------------------------

lE5 - at 10KHz

!!! lE4 /-v, lE3

:0; lE2, /-lEI ..

QJ ...... /-.~ lEO _

Q IE-I __ ./

-lE-2

~.

~. -----.

lE-3~-----~-------~I-------~----------~----~I-------~I~-----~I----~ o 10 40 50 70 00 Carbon Black Content (phr)

Figure 10. The dielectric loss of carbon black-filled

rubber as a function of carbon black loading

(frequency = 10 KHz).


4 • 3 THREE REGIMES OF DIELECTRIC RESPONSE

The existence of an electrical threshold in the above

measurements suggests35 that different physical mechanisms

of dielectric response are involved below and above the

threshold, which will be discussed later. Therefore,

according to Figure 7, three different regimes are defined26

and replotted in Figure 11: these are the dielectric regime,

percolation regime, and conducting regime.

4.3 • 1 CONDUCTING REGIME

In this regime the volume fraction of carbon black is so

large(>40 phr) that the carbon black aggregates touch each

other and a continuous conductive network is formed, in

which the electrons move freely along conductive paths as in

a metal. The dielectric dispersion of compounds with

different carbon black loading falling in the conducting

regime is plotted in Figures 12 and 13, respectively. As

can be seen in these figures, no loss peaks are observable

within the whole measuring frequency range and instead, the

dielectric loss rises towards low frequencies steeply,

following a power law relation, eqn (2.4), with n = 1, while

the dielectric constant approaches a constant value towards

low frequencies. This phenomenon is due to the presence of

DC conductivity, which gives a contribution of the form


lE5 IEQ

• Dielectric <> conductivity .,.-----<> lEa n constant ~7~:;> -2~ 0

lE4 I :s I

g, +J 1E7 ~ r:: I <> • 0 CO I rt +J I

..... ttl I lEa < r:: I ..... 0 lE3 rt 0

:~: '<

0 DIELECTRIC CONDUCTING 1E5 >C 0.-1 $..4 REGIME REGIME .... +J lE2 ;f~

0 0 1&1

I Q) ....

I""'i .... Q)

OM ~<> H~ -Q • H 1E3 0

lEI 2~1 ~ ~ ::r Ef I

-/ I ~ 1E2 0

~:::::~. ~ Ef -I <> .... tEO IEl

0 10 ro 3J 40 50 00 70 00

Carbon Black Content (phr)

Figure 11. The dielectric constant as a function of carbon

black loading at a fixed frequency 10 KHz.


o 41,_ I 5.'_ 07. , ..

11.1+---------____ ~~~~~""W_~~~mT~~TTnnr_~rTnm~ 11+2

Frequency (Hz)

Figure 12. The dispersion of dielectric constant of

compounds with carbon black loading falling in

the conducting regime.


lit

D .... I 5 •• _

0.,1.-

11+1+-~~~~--~~~~-r"~mr~~~nnr-~TTTnnr~-rTTnm lit a

Frequency (Hz)

Figure 13. The dispersion of dielectric loss of compounds

with carbon black loading falling in the

conducting regime.


uo/w, from eqn (2.4),to the dielectric loss, while making no

contribution to the dielectric constant.

Since a large number of conductive paths exist between

electrodes in this regime, most electrons are considered as

free charge carriers, which gives rise to high DC

conductivity and makes the dielectric effect not measurable.

It was shown30 that the dielectric effect of free electrons

will only become significant at frequencies of the order of

the reciprocal collision time, which fall in the 10-100GHz

range, far beyond our measuring frequency range «100MHz).

4.3.2 PERCOLATION REGIME

within this regime, the inversion between conducting and

dielectric structures takes place, where some of the carbon

black aggregates begin to touch each other and a few

conductive paths are formed. Most of the aggregates remain

separated from each other but the gap width is greatly

reduced.

As can be seen in Figures 14 and 15, the dispersions of

both dielectric constant and dielectric loss rise towards

low frequencies. This simultaneous presence of strong low

frequency dispersions of both dielectric constant and loss

is a result of "genuine" dielectric phenomena. Since most

electrons are localized within carbon aggregates in this

regime, the effects of free electrons, causing high DC


..JJ s:: ItS ..JJ OJ s:: o o o ..... ,.... ..JJ o Q) M Q) ..... o

1 •• ~ ____________________________________________________ ~

It, 2S ... , 31 ...

Frequency (Hz)



the percolation regime.


Frequency (Hz)

A as •• A 31 ...

Figure 15. The disp~rsion of dielectric loss of compounds


percolation regime.


conductivity, are not dominant, so that the dielectric

effect of localized electrons may be measurable.

Fluctuation-induced electron tunneling10 ,15,16 has been

shown to be the dominant conduction mechanism in the

percolation regime where the average gap width (the distance

between aggregates) is not too large. Since this tunneling

current is strongly gap width-dependent, and the gap width

varies within the compounds, the probability of tunneling

transitions between aggregates thus varies, resulting in

both easy paths and more difficult ones for tunneling.

Under the applied AC electric field, the fluctuation-induced

tunneling transitions between carbon black aggregates will

be executed through the easiest paths many times in both

directions, while the more difficult transition paths will

be traversed less frequently 30. Therefore, these tunneling

electrons show both a "dielectric" property and

simultaneously a "conducting" property. The dielectric

effect is determined by the dipole-like motion with

tunneling electrons jumping back and forth between carbon

aggregates, while the conducting effect is determined by the

free electron-like behavior with tunneling electrons

traversing over many aggregates. The DC conducting property

will not be dominant until the conducting regime is reached,

where the free percolation between electrodes takes place.


4.3.3 DIELECTRIC REGIME

The structure of carbon black aggregates in this regime

is an inversion of that of the conducting regime, in which

the small, isolated carbon black aggregates are well

dispersed in the rubber continuum. The gap width between

two aggregates is so large that the dominant conduction

mechanism is considered to be electron hopping transition

between aggregates (i. e. thermally activated transport of

electrons over a potential barrier) rather than electron

tunneling.

As can be seen in Figures 16 and 17, the dispersions of

both dielectric constant and dielectric loss are nearly

frequency-independent, which is usually found experimentally

in very low loss materials.

4.4 AC CONDUCTIVITY MEASUR.EMENT

Figure 18 is a plot of the frequency dependence of

conductivity of all compounds, showing that the conductivity

generally increases with increasing frequency. However, the

extent of dispersion is different for each compound,

decreasing with increasing carbon black loading. An

electrical threshold is observable from this figure,

occurring at approximately the weight fraction of 25 phr

carbon black, below which the variation of conductivity with


1 •• 1 __ ------------------------------------------------~

• I •••. ... II •.•••

.... Illl'_ I Z ....

... "· ... u ...... ........

---

Frequency (Hz)



the dielectric regime.


til til

S o ..... .... +J o Q) ,..... Q) ..... c

lE.l~ ______________________________________________ ~

11:.

.... 4 II p_ I 21 ,hit

II ..... II •• un •••• 111. II Ill. . ....

Frequency (Hz)

Figure 17. The dispersion of dielectric loss of compounds


dielectric regime.


-~ I

~ o -

.... • 21 P_ A 31 ... • 51 Phi'

Frequency (Hz)

A 1 .... A 25 Phi' 0 .... 07 ....

Figure" 18. Frequency dependence of conductivity of rubbers

loaded with different amount of carbon black.


with frequency goes approximately as wn , with n=l (as shown

in Figure 19). This can be expressed as

(4.1)

where U(w) = AC conductivity at frequency w

w = angular frequency of alternating electric field

Uo = conductivity at zero frequency, i.e. DC

conductivity

It has been shown36 that, when the exponent n falls in

the range 0.6<n<1, the above power law relation implies the

presence of hopping conduction by electrons in the

dielectric regime. Furthermore, it was shown37 that this

power law relation with exponent n ~lose to or equal to 1

implies the frequency independence of dielectric loss, which

is quite consistent with the results for compounds of low

carbon black loading as can be seen in Figure 17, where all

show a tiny shallow loss peak superimposed on an almost

constant background extending over many decades of

frequency.

However, for compounds with carbon black loading falling

in the percolation regime, a flattening of the frequency

dependence of the AC conductivity towards the lower end of

the frequency range begins to be discernible, as can be seen

in Figure 20, but complete saturation of the low-frequency

conductivity is absent in this figure.


r-4 I -a o I

~ o ........

.... A II, .. • ZI ...

Frequency (Hz)

Figure 19. Frequency dependence of conductivity of rubbers


dielectric regime.


A 25 ,b .& 3 ....

r-f I -~ 0 I ~

..c:: 0 -

r-f r-f I 0 r-f

>< >. .IJ of""4

> of""4 .IJ 0 ::s "0 c 0 U

1 ..

Frequency (Hz)



percolation regime.


As shown in Figure 21, the low-frequency conductivity in

the conducting regime becomes more and more slowly varying

with increasing carbon black loading and finally saturates

to a nearly frequency independent DC conductivity, where the

final value depends on the amount of loading. The power law

relation of eqn (4.1) becomes more difficult to define when

DC conductivity is dominant. Since the frequency dependence

of conductivity in the conducting regime is fairly weak, the

dielectric loss of corresponding compound will show strong

frequency dependence within the entire frequency range,

which is evident from Figures 21 and 13. In another words,

once DC conduction is the dominant process in the material,

the dielectric loss diverges towards zero frequency, while

leaving the dielectric constant almost independent of

frequency.

4.5 PHASE ANGLE AND LOSS MODULUS MEASUREMENT

Figure 22 shows the dependence of phase angle 5 on

strain amplitude for rubbers of different carbon black

contents. The phase angle increases with increasing strain

and passes through a maximum, and then decreases somewhat at

still higher amplitudes. However, at the highest amplitude,

5' generally remains considerably higher than its value at

very low amplitudes, and in fact may not be much below its

maximum value.


-a o I a .!: o -

I+&~r-------------------------------------------------~ D.p. I 5 •• 11P 07. ,lIP

Frequency (HZ)



conducting regime.


z • 31 ..... I ..... A 51 ,b,

16 o 'I.b A 71 .....

-OJ Q) Q)

~ tTt OJ

'tS 1 ....... Q)

r-I tl' s:: < Q) OJ «:S ,

..c: flt

Double strain Amplitude

Figure 22. strain amplitude dependence of phase angle

at 1 Hz for rubbers loaded with different amount

of carbon black.


At constant strain cycling, sin6 (or 6) is a direct

measure of the hysteresis (mechanical work which is not

recovered as such during a cycle but instead is converted to

heat). It is assumed that hysteresis results from breakdown

and reformation of interaggregate bonds8 • At low amplitudes

there is little breakdown of interaggregate bonds, therefore

small 6' results. At intermediate amplitudes considerable

breakdown and reformation of bonds takes place; thus 5 is

high. At high amplitudes, less reformation of

interaggregate bonds takes place than at intermediate

amplitudes because the structure, or network, is broken down

so extensively that reformation of the structure is less

complete over the cycle time.

Figure 23 shows the phase angle plotted against the

carbon black content at double strain amplitude of 10%, and

double stress amplitude of 200 lb., respectively. It can be

seen that during compressive cycling, the greater the

concentration of carbon black, the greater the phase angle

at a given strain.

Figure 24 shows the loss modulus E" plotted against

carbon black content at double strain amplitude of 0.1 and

at double stress amplitude of 200 lb., respectively. These

will hereafter be referred to simply as "strain amplitude"

and "stress amplitude" respectively. Both curves show that

the loss modulus E" increases with increasing carbon black


I;~------------------~-------------------------------, • Stp.i ..... 11t ... = 1.1 [J StN.. _I i t.... = 2. 1 ••

-Ul Q) '1~ Q) J.4 t:l' Q) 't1 -Q)

...-i t:l' ~ < Q) 1 Ul n:s .t: Cot

s+--------r------~~------~------_r--------~------; 2


Figure 23. The dependence of phase angle' upon carbon black

loading at a given double strain amplitude of 10%

and at a given double stress amplitude of 200 lb.

during compressive cycling at 1 Hz.


D St •• i. 1.,litu" = 1.1 .. ItN55 1.,lit ... = 2. I ••

z:s


Figure 24. The dependence of loss modulus En upon carbon

black loading at a given double strain amplitude

of 10% and at a given double stress amplitude of

200 lb. during compressive cycling at 1 Hz.


content. since hysteresis is produced by internal friction

under compressive cycling, the addition of carbon black to a

rubber increases the internal friction, or hysteresis, by an

amount depending on the loading of carbon black.

4.6 HYSTERESIS MEASUREMENT

Figure 25 shows the strain amplitude decreasing with

increasing carbon black content at stress amplitude of 200

lb., which can be understood by the fact that the greater

the concentration of carbon black, the harder is the filled

rubber. According to H = 1r € 2E", the hysteresis is

proportional to the product of loss modulus En times the

square of strain amplitude,

area of the hysteresis loop.

which is proportional to the

Figure 26 shows the results of

such area measurement plotted against carbon black content

at the strain amplitude of 0.1 and at stress amplitude of

200 lb., respectively. For strain ampl i tude of o. 1, loop

area increases with increasing carbon black content while,

for stress amplitude of 200 lb., it is almost independent of

the carbon black content. This could be because of the

mutual cancellation between the increase in E" and

corresponding decrease in E at constant stress cycling. E"

plotted against carbon black content at strain amplitude of


·M;~ __________________________________________________ -,

• 5 tftSS .'" Ii tad. = 211 lit .

• 117 Q) 'tj ~ .JJ or-i r-f .11 a. S ~

$:! 0r-i

.15 «1 }..f +J (I)

Q) r-f ..Q ~ 0 0

.83

.• +-------~--------~------_r--------r_------_r------_, 5 ,


Figure 25. The dependence of double strain amplitude upon

carbon black loading at a given stress amplitude

of 200 lb. at 1 Hz.


lZ~ ____________________________________________________ ~

• St •• in AM,litude = 1.1 , StNSS A..,litad. = 211 1 ••

to •• ev ~

Ie:(

s::l. 0 0 ~

(/) ·M til ev ~ ev 4J (J]

>t ::z::


Figure 26. The dependence of hysteresis loop area upon

carbon black loading at a given strain amplitude

of 10% and at a given stress amplitude of 200 lb.

at 1 Hz.


0.1 and at stress amplitude of 200 lb. is shown in Figure

27. The trend is generally the same as that seen in Figure

26.

4. 7 TEMPERATURE RISE MEASUREMENT

Figure 28 shows the temperature at the center of the

specimens of different carbon black contents, with strain

amplitude of 10% at a frequency of 10 Hz. As can be

expected from Figures 26 and 27, the temperature rise is

higher in rubbers of high carbon black loading than in those

of low carbon black loading at a given strain amplitude.

Figure 29 shows the temperature at the center of the

specimens of different carbon black contents, with stress

amplitude of 200 lb. and a frequency of 10 Hz. The

temperature rise in these specimens is about the same, which

can be explained by the nearly equal areas of the hysteresis

loops of specimens of different carbon black contents, as

also seen in Figures 26 and 27.

According to Figures 28 and 29, the temperature rise is

proportional to the time for several minutes (5 to 10

minutes) after starting, while the nearly adiabatic

condition is maintained at the initial stage. Temperature

then remains constant due to the balance between internal

heat generation and heat radiation.

Figures 30 and 31 show the temperature rise plotted


l' • St •• in AMPlit ... = 1.1 .& St .. ss AMPlita.e = 2. 1 ••

N 12 -,c( til Q

- , ><

--riI

Ul , ::1

.....t ::1 ttj 0 ~

Ul 3 , -' Ul 0 ~ -'

""' ...::I

-


Figure 27. The dependence of E" x (strain amplitude)2 upon

carbon black loading at a given strain amplitude

of 10% and at a given stress amplitude of 200 lb.

at 1 Hz.


-() o -

T~ __________________________________________________ ~

o 31'. 141,. rJ 51 ,lIP "I,. IJ. 71 ,lIP

Time (minutes)

Figure 28. Temperature at the center of specimens of

different carbon black content at double strain

amplitude of 10% and at 10 Hz.


-CJ 0 -

Q) J..t ::s +J ctS J..t Q)

~ Q) 8

41

o 31.hI' • 41.hI' (] 5 •• hI' .. 6 •• hI' Il 7 •• hI'

Time (minutes)

Figure 29. Temperature at the center of specimens of

different carbon black content at double stress

amplitude of 200 lb. and at 10 Hz.


41

, 31 ,hi' [] 41 ,hi' • 51 ,hi'

35. o 'I, .. I 7. 'hP 0 • -U

0 -8 3e. -CI OJ Ul • • .-4 ~

OJ 15. J..f ::J +J (tj

J..f OJ D 0.. ~ Z8 OJ 8

lS+---------~--------_r--------_,----------r_------__; I 31 6 ,. 121 151

Hysteresis Loop Area

Figure 30. Dependence of temperature rise on hysteresis

loop area at a strain amplitude of 10% and at

10 Hz.


Z8

, 31, .. o 41 p. I 51 p. o '1'_

IS I 71' .. -CJ 0 -E-t

I .cf OJ ••• D Ul 1. 0 ...... ~

OJ J...f ::1 +J CU J...f OJ p.. ,. J:t OJ

E-t

I+------------T------------T-----------~----------__; • 1\1 ZI 31

Hysteresis Loop Area

Figure 31. Dependence of temperature rise on hysteresis

loop area at stress amplitude of 200 lb. and at

10 Hz.


against the corresponding hysteresis loop area for rubbers

of different carbon black contents at strain amplitude of

0.1 and stress amplitude of 200 lb. respectively. Under

constant strain cycling, hysteresis is only a function of

loss modulus, which increases with increasing carbon black

content, as shown in Figure 24. Since heat generation is

proportional to hysteresis, temperature rise within the

specimen is therefore expected to increase with increasing

carbon black content, which can be confirmed from Figure 30.

However, under constant stress cycling, hysteresis is shown

to be nearly independent of carbon black content. (Figure

26) • Thus, the temperature rise in rubbers of different

carbon black contents at a given stress amplitude is

expected to be nearly constant, at 11±10 C in this case, as

shown in Figure 31.

4.8 DYNAMIC CONDUCTIVITY MEASUREMENT

For each single sinusoidal cycle, a minimum

conductivity, gmin' was observed at the lowest strain, and a

maximum, gmax, was observed at the highest strain, as

defined in Figure 32. Figures 33-36 show the dependence of

gmax and the gmin upon strain amplitude for specimens of

different carbon black contents, measured at progressively

increasing amplitudes up to 0.2 DSA. In the strain

amplitude range observed (DSA = 0.001-0.2), gmax and gmin


It t

I

t

I mi "-.",t' I

one cycle time

Current

Figure 32. Current (top), and strain vs. time curve at a

strain amplitude of 0.02 for specimen of 50 phr

carbon black loading at vibration frequency of

1 Hz.


12~------------------------------~

..... 11 I

'ii 10 o I a ..c: o -

r-I o ..... ~

>t ..... -..-4 >

-..-4 ..... U ::s '0 c o· u

9

o gmax 6 gmin • 49


Figure 33. Conductivity vs. double strain amplitude at

0.25 Hz for specimen of 40 phr carbon black

loading.


r-t I -~ I

.E o -

to I o r-t

6~-----------------------------------------,

o gmax .4g

5




loading.


2.5---------------------------------------------.

-5 2.0 I J::

.J:: o -~ I o r-I

1.5

o gmax Il. gmin • Ag



loading.


8~---------------------------------.

r-4 7 I

o gmax II gmin • .o.g

-a o I a

..c: o -oe::t' I o r-4

OL---~~~~--~~--~--~--~--~~--~~ 1 E -3 I E-2 f E-l 3E-l




loading.


were shown to alter as follows: At very low amplitudes, a

slow rise in gmin and gmax occurs, and a maximum is reached,

followed by a rapid decrease. At a strain amplitude of

about 0.2, gmin levels off asymptotically to a nearly

constant value. The difference between gmax and gmin (Ag)

was also plotted as a function of strain amplitude in each

figure. As can be seen, A g is low at very low strain

amplitudes, rises to a maximum at about 0.01-0.06 DSA, and

then decreases somewhat at still higher amplitudes. At the

highest amplitude, Ag generally remains higher than its

value at very low amplitudes. However, a considerable

decrease in Ag may be seen at very high amplitudes, as in

Figure 33, approaching or even lower than the value at very

low amplitudes.

4.9 CONDUCTIVITY EFFECT OF DYNAMIC PROPERTIES OF CARBON

BLACK-FILLED RUBBERS

Electrical conductivity is of interest in connection

with dynamic properties since both phenomena involve a

carbon black network. As stated earlier, conductivity is

high within each aggregate, so the resistivity is determined

essentially by the barrier between aggregates. It has been

shown10 that conduction between two aggregates by electron

tunneling does not require "contact" between aggregates, but

only close proximity. Thus, while the "through-going"


conductive paths responsible for conductivity of the

specimen may be equivalent to the network which contributes

to the augmentation of dynamic modulus, the gap width

between aggregates may have a quantitatively different

effect on tunneling versus interaggregate attractive

forces4 • Voet and Cook38 showed that the dynamic modulus is

a higher order function of interaggregate distance and is

more responsive to small chain breakdown than electrical

conductivity. In addition, due to hydrodynamic effects plus

other smaller contributions, the augmentation of the dynamic

modulus may be brought about by isolated aggregates which do

not contribute to conductivity4.

4.9.1 CORRESPONDENCE BETWEEN CONDUCTIVITY AND MODULUS

CHANGES

It has been shown4- 7 ,39 that gmin varies with DSA in

roughly the same manner as elastic modulus E'. However, the

onset of the decrease in gmin with increasing DSA has been

shown to occur at somewhat higher DSA than that of EI, and

that of gmax at still higher DSA, since the conductivity

might not be as sensitive to gap distance as E'.

Also, the A g and loss modulus E" have been shown to

vary in a roughly similar way with increasing DSA38 ,39. ~g

passes through a maximum at about the same DSA as the

maximum of E", where gmin is changing most rapidly, as can


be seen in Figures 33-36.

Since there is a correspondence between conductivity

changes and modulus changes with the strain amplitude of

oscillation, Figures 33-36 can be used to determine the

amplitude dependence of dynamic properties of carbon black

filled rubbers.

4.9.2 EFFECTS OF PERSISTENT AND TRANSIENT STRUCTURES ON

CONDUCTIVITY DURING A CYCLE

It was suggested40 that "there are two distinctly

different physical bases for the formation of the ensemble

of particle chains and networks in dispersed carbon blacks,

commonly referred to as structure. The transient,

reversible structure is formed by interaggregate contacts

caused by a van der Waals type of attraction, while the

persistent, irreversible structure is due to strong

reticulate particle aggregates which appear to be "fused"

together in the formative stage of the carbon black, at

extremely high temperatures in the furnace."

As can be seen in Figure 32, in a specimen subjected to

compressive oscillation about a midpoint, the transient

structure is broken down in a nearly equal amount in the

lower and upper halves of a strain cycle, the extent of

which depends on the applied strain amplitude. The

persistent aggregates which become separated from each other


at the lower half of a cycle, however, will be brought into

proximity with each other in the upper half of a cycle, with

the opportunity of reforming interaggregate contacts,

resulting in the formation of new transient structure.

since the closer proximity between persistent aggregates in

the upper half of a cycle makes the reformation process more

rapid and easier, more reformation is expected at the upper

half of a strain cycle than at the lower half of the strain

cycle. As will be explained later, this reformation process

is more significant at low and intermediate DSA ranges than

at high DSA ranges. Thus, it becomes obvious that

conductivity is higher in the upper half of a cycle than in

the lower half of a cycle.

4.9.3 PHYSICAL SIGNIFICANCE OF gmin

gmin can therefore be used to represent the remaining

carbon black conductive network, which is a combination of

the persistent structure and the remaining transient

structure. From Figures 33-36, the maximum value of gmin

(gO> at low strain amplitudes, and the limiting value of

gmin (g~) at high strain amplitudes, can be determined6 ,39.

Because all the curves exhibit a maximum at low strain

amplitudes, this maximum value of gmin was used to represent

go-

~ represents the minimum conductivity of one cycle, at


very high DSA, caused by the conduction between persistent

aggregates after all the transient structure has been

completely broken down by vibrations. It was shown40 that

extreme amplitudes of oscillation do not give rise to

destruction of persistent carbon black aggregates. Only the

distance between persistent aggregates will be sinusoidally

changed in a single cycle, which will not alter the average

conductivity greatly, but only the minimun and maximum

values of the cycle38 • Since electron tunneling dominates

the conduction mechanism between aggregates, it is obvious

that gmin will approach a limiting value at high strain

amplitudes. With further increase in DSA, the distance

between persistent aggregates will become so large, with no

transient structure connected in-between, that the electron

tunneling effect becomes less and less sensitive to further

changes of interaggregate distance at the lower half of a

strain cycle. However, for the transient structure

breakdown process, the average conductivity is greatly

influenced, decreasing rapidly with strain amplitudes within

the intermediate strain range, until all the transient

structure is broken down.

The difference between go and g~ (i.e., go-g~)

represents the maximum contribution of the transient

structure4 ,6,38,39. Figure 37 shows that go, gee' go-g(t) , and

the maximum of ~g (Agm) all increase rapidly with increasing

carbon black loading, indicating that the amount of both


-a o I a .c: o -

11-

f:J go-g«1 [] go A. gQ) 1 4 gm

~1'r-----'------r-----~-----r----~------r-----------~


Figure 37. Carbon black loading dependence of go-goo' go' g~,

and Agm•


transient and persistent structure greatly increases with

carbon black loading. In addition, go is shown to be around

one to two orders of magnitude greater than gO) for all

specimens. As can be seen in Table 2, the ratio of gO-gm to

gm is decreasing with increasing carbon black loading within

the 40-70 phr range, reflecting that the ratio of the

maximum transient structure to the persistent structure

within a specimen decreases with carbon black loading.

This decrease in go-gcc/9'cc indicates the vast existence of

through-going conductive paths of a persistent nature (i.e.,

with no interaggregate contacts in-between), the number of

which increases rapidly with carbon black loading, thus

reducing the relative amount of transient structure.

Table 2. go-~/~ at different carbon black compositions

carbon black content(phr)

go-9o,/gcc

RESULTS AND DISCUSSION

30 40 50

44.56 167.1 29.3

60

18.7

70

18.3

78

4.9.4 CONDUCTIVITY RELAXATION AT LOW STRAIN AMPLITUDES

At very low strain amplitudes «0.01 DSA), the

reformation is so rapid and easy that a slight breakdown of

the transient structure can be readily mended even at the

lower half of a strain cycle, with a possibility of

connecting a few isolated aggregates to the conductive

network and therefore building more conductive paths. This

"conductivity relaxation" phenomenon results in a slow rise

in conductivity at low strain amplitudes. However, after a

critical DSA (about 0.01) is reached, the rate of

reformation is no longer effective enough to fully mend the

destroyed transient structure, and, thus, conductivity

starts to decrease rapidly with further increase in strain

amplitude.

4.9.5 PHYSICAL SIGNIFICANCE OF 4q

Because of its similarity to the loss modulus E", .4.g

is, likewise, strongly related to the reformation and

breakdown of the carbon black network during each strain

cycle, and may be treated as the electrical equivalent of

the mechanical loss modulus, or hysteresis. Figure 38 shows

a series of pictures of the variation of current with

sinusoidal cycling at increasing strain amplitudes, taken

for a specimen of 50 phr carbon black loading.


0.001

0.002 0.004

Figure 38. CUrrent vs. time curves at increasing amplitudes

for specimen of 50 phr carbon black loading at

1 Hz. Upper curve is current; lower curve is

strain. Double strain amplitudes (DSA) are

given next to figure.


0.005 0.008

0.006 0.009

0.007 0.01

Figure 38 (cont.)


0.012 0.03

0.015 0.04

0.02 0.05

Figure 38 (cont.)


0.06 0.09

0.07 0.1

0.08 0.11

Figure 38 (cont.)


0.12 0.15

1~'J'f~/'-,,/,. (\ r (\ I I I I

I \J \ J \ I

J \ \ I \. I I IV V

~~'v~J'n-I /1 II /1 \ / \ I \ ! \ I \ I \

I \ I \ / \ \ I \ I \ I \ I \ \ . \ , \j ~! \...1

0.13 0.16

0.14 0.17

Figure 38 (cont.)


0.18 0.19

Figure 38 (cent.)


As can be seen, at very low strain amplitudes the

current shows only modest variation during one cycle, since

there is little breakdown of carbon black network and the

reformation is easy, thus resulting in small Ag.

As strain amplitude increases, more and more breakdown

and reformation of a destroyed transient structure take

place, resulting in the increase in Ag, which passes through

a maximum at some strain amplitude in the middle region

where considerable structure breakdown occurs, but

reformation is at a maximum.

At high strain amplitudes (greater than about 0.1), low

values of Ag are observed, owing to the fact that "the

structure is broken down so extensively "that reformation of

structure is very much slower than the cycle time,,4,

indicating that less reformation takes place at high

amplitudes than at intermediate amplitudes.

Therefore, Ag represents not only the electrical

equivalent of the loss modulus but is also a function of the

ratio of the amount of structure reformation to that of

structure breakdown during one cycle. The amount of the

remaining transient structure at certain strain amplitude

can be estimated from the value of gmin-~.


4.9.6 RELATIONSHIP BETWEEN go - qm and Agm

It has been found4 convenient to normalize the data

related to go and g~. The normalized conductivity Z can be

defined at any strain amplitude by

Z = 9Jni n - q", go - gG)

(4.2)

which is a ratio of remaining transient structure to total

transient structure. As can be seen from Figure 39, the

value of DSA required for 50% breakdown of transient

structure increases with increasing loading and the

percentage of the remaining transient structure at certain

DSA also increases wi th carbon black loading. Thus, the

strain work needed to break up the same percentage of the

transient structure will increase with carbon black loading,

reflecting an increasing hysteresis property with carbon

black content.

The relationship between 4gm and go-~ for all

compounds (except 0, 10, 20 and 25 phr, whose resistances

were too high) is found to be linear, as shown in Figure 40,

and can be expressed as

(4.3)

showing that the maximum amount of reformation for all


1

Il 71 ,I.--, A 'I, .. Il 51 ,lIP

.1 I 41 ,lIP o 31, ..

$-4 . 7

0 ...., 0 ., ,

«' r.. N .: "d Q) N

.4 • ....t

,.....j

ro e .3 0 Z

.1

.1

• 11-2


Figure 39. Normalized conductivity Z as a function of

strain amplitude.


D at 1.25 Hs , 11 ... = 1.11

1-12r-rnmm~~~~~mw~Tnmr-rMmnr~~~~~N-~~'---~ 11-11

Figure 40. Variation of 4gm with go-g~·


specimens occurs approximately when one half of the whole

transient structure is broken down, and the occurence of Ag

is, again, found to be almost entirely due to the breakdown

and reformation of transient structure.

4.9.7 EFFECTS OF CHANGING VIBRATION FREQUENCY

Figures 41-43 show the effect of changing the cycle time

(period) on Ag. As can be seen, the strain amplitude at

which the maximum value of A g occurs is shifted towards

lower values with increasing vibration frequency. This is

due to the fact that at lower cycle time (i. e., higher

frequency), less reformation takes place at the same strain

amplitude, resulting in lower strain amplitude at which the

structure breakdown and reformation is at a maximum.

4.9.8 RISE IN q AT HIGH STRAIN AMPLITUDES

It can be seen from Figure 36 that, at strain amplitude

higher than 0.13, an increase in

mainly caused by the increase

approaching a limiting value.

Ag is observed, which is

in gmax' while gmin is

This phenomenon is mostly

observed in specimens of high carbon black loading, in which

a large number of isolated aggregates can be brought into

close proximity at the upper half of a strain cycle after a

critical DSA (here, 0.13) is reached (where most of the


r-I I -~ U I

.a o -

['. I o r-I

5----------------------------------------------~ o at 1 Hz • at 0.25 Hz

4

3

3E-l Double strain Amplitude

Figure 41. Conductivity bandwidth (Ag) vs. DSA for specimen

of 40 phr carbon black loading at 0.25 and 1 Hz,

respectively •

.. RESULTS AND DISCUSSION 91

2.0r------------------M t.8 ~ 0 at 1 Hz I -6 1.6 t

.a o -

to I o

1.4 ~

1.2

M 1.0

• at 0.25 Hz


Figure 42. conductivity bandwidth (A9) vs. DSA for specimen


respectively.


4.0 ------------------,

.-i

~ 3.5 o at 1 Hz • at 0.25 Hz

U • .E 3.0 o - 2.5

(.0

1.5

1.0


Figure 43. Conductivity bandwidth (4g) vs. DSA for specimen


respectively.


transient structure has been broken down). Because the

number of these isolated aggregates is qualitatively

proportional to carbon black loading,

amplitude at which the increase in

the highest strain

gmax starts thus

decreases with increasing carbon black loading. Since the

distance between persistent aggregates is decreasing with

increasing DSA(>0.13), and more isolated aggregates are

brought into close proximity and connected to the conductive

paths, a significant increase in gmax is therefore expected

at high DSA.

4.9.9 THE ASSYMMETRY IN TIME-CURRENT VARIATION CURVE

Also observed from Figures 32 and 38 is a subpeak in the

current-time variation curve. According to Voet and cook38 ,

the observed assymmetry may be caused by a superposition of

longitudinal compression waves(4-second cycle) and shear

waves (2-second cycle) which unavoidably accompany the

longitudinal compression waves through any specimen of

finite thickness, especially for specimens of high loadings

of high structure black. It is expected that the

compression wave simply influences the interaggregate

distance, exactly following the dynamic strain, while the

shear wave mainly causes the transient structure breakdown.

As can be seen, even at the lowest amplitude of 0.001 DSA,

the influence of the 2-second shear wave cycle on the


current is discernible, and is superimposed on the 4-second

compression cycle, resulting in the assymmetry. The extent

of the influence of the shear wave increases with increasing

DSA.


5.0 CONCLUSIONS AND RECOMMENDATIONS

5.1 CONCLUSIONS

(1) The electrical percolation was clearly evident from

both dielectric constant and AC conductivity measurements,

reflecting that there exist different conduction mechanisms

below and above this percolation threshold: when the carbon

black loading is well below the threshold (i. e. in the

dielectric regime), the hopping transition is believed to be

the dominant conduction mechanism; when the carbon black

loading is in the percolation regime, the fluctuation

induced electron tunneling is dominant; when the carbon

black loading is in the conducting regime, DC conduction

between two electrodes becomes dominant.

(2) Since different types of dielectric response are

characterized for rubbers with carbon black loading falling

in the dielectric, percolation and conducting regimes, the

AC conductivity and dielectric constant measurements thus

provide a nondestructive method to investigate the carbon

black network that exists in filled rubbers.

In the dielectric regime, both dielectric constant and

dielectric loss show only slight dispersion with frequency,

while the AC conductivity shows very strong dispersion with

frequencies. In percolation regime, both the dielectric

constant and dielectric loss rise towards low frequencies,

CONCLUSIONS AND RECOMMENDATIONS 96

while a saturation of the frequency dependence of the AC

conductivity towards the lower end of frequency range

becomes discernible. In conducting regime, the dielectic

loss shows strong dispersion in our measuring frequency

range with dielectric constant approaching a constant value

towards low frequencies, while the AC conductivity shows

only very weak dispersion with frequency.

(3) Both loss modulus and phase angle are related to

hysteresis properties of the carbon black-rubber compounds

and are shown to increase with increasing carbon black

content either at a given strain amplitude or at a stress

amplitude. Hysteresis loop area at a given strain amplitude

increases with increasing carbon black content, while that

at a given stress amplitude is nearly independent of carbon

black content. Temperature rise measurements show that the

larger the area of the hysteresis loop, the higher the

temperature rise. Since the temperature rise of a filled

rubber under compressive cycling is directly related to the

hysteresis loop area, the temperature rise is, therefore,

independent of the amount of carbon loading when the

compounds are subjected to a compressive cycling at a given

stress amplitude.

(4) The effect of vibration frequency on g was also

investigated, showing that the strain amplitude at which the

maximum Ag occurs is shifted toward lower values with

increasing vibration frequency.


(5) A rise in Ag at high strain amplitude is observed

for rubbers with high carbon black loading, owing to the

incorporation of many isolated aggregates into the

conductive network and the closer proximity of persistent

aggregates at high strain amplitudes. The highest strain

amplitude at which the increase in Ag starts is expected to

decrease with increasing carbon black loading.

(6) Although the amount of both transient structure and

persistent structure increases rapidly with carbon black

loading, the ratio of the maximum transient structure to

persistent structure, (go-gm)/g~, decreases with increasing

carbon loading, due to the large number of through-going

conductive paths of persistent nature.

(7) The maximum 4g follows a linear relationship with

go-g~ for all carbon black-rubber compounds, reflecting that

the breakdown and reformation of the transient structure is

the only mechanism responsible for the occurrence of 4 g.

(8) Owing to its experimental accuracy and its great

sensitivity to carbon black network changes, the dynamic

conductivity measurement (as a function of dynamic strain

amplitude) can be successfully applied, in preference to

traditional modulus measurements, to determine the dynamic

properties of carbon black-filled rubbers.


5.2 RECOMMENDATIONS FOR FUTURE WORK

(1) The determination of both electrical and mechanical

properties of carbon black-filled rubbers is recommended to

be carried out over a wide temperature range between -30°C

and 50oC.

(2) Appropriate comparisons should be made between the

actual tank track pads with field history and the virgin as

received samples, in their dynamic properties and electrical

properties.


BIBLIOGRAPHY

1. J.A. Manson and L.H. Sperling. Polymer Blends and Composites, chap.10, Plenum Press, N. Y. , (1976) .

2. G.R. Cotten and B.B. Boonstra, J. Appl. Polym. Sci. , vol.9, 3395 (1965).

3. G.B. McKenna and L.J. Zapas, Rubber Chern. Technol. , 54, 718 (1981).

4. A.I. Medalia, Rubber Chem. Technol., 51, 437 (1978).

5. A. Voet and F.R. Cook, Rubber Chem. Technol., 41, 1215, (1968).

6. A.K. Sircar and T.G. Lamond, Rubber Chem. Technol., 48, 79 (1975).

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CURRICULUM VITAE

Yawlin Hwang was born in Taipei, Taiwan, R.O.C. on April

12, 1960. He received his BS degree in Materials Science

and Engineering from National Tsing Hua University in Hsing

Chu, Taiwan in June of 1982. He spent two years on ROTC

program in Taiwan as an Executive Officer in a Coast Guard

Company and was discharged in May of 1984. He then worked

one year in Institute of Materials Science and Engineering,

National Sun Yat-sen University in Kaohsiung, Taiwan, as a

STEM technician. He began work toward his MS degree in

Materials Engineering in Virginia Tech in september of 1986.

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dynamic electromechanical measurements of carbon black

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