Electrical permittivity and conductivity of carbon black...

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Electrical permittivity and conductivity of carbon black-polyvinylchloride composites

K. T. Chung, A. Sabo, and A. P. PicaRCA Laboratories, Princeton, New Jersey 08540

(Received 29 April 1982; accepted for publication 24 June 1982)

Electrical conductivity and permittivity of carbon black-polyvinyl chloride composites werestudied over a wide frequency spectrum (dc, 1.3 GHz). Conductivity of the bulk compositesincreases with higher volume fraction of carbon black as expected. However, the functionaldependence of the increasing conductivity with carbon black loading is different below and abovethe percolation threshold because ofthe different mechanisms involved. Bulk electric permittivityincreases until the composite percolation is reached and then decreases to zero after fullyconnected conductive paths have been established. Such highly loaded composites showed ametal-like electrical behavior. Different electrical percolation threshold of the composites werefound for different species ofcarbon black. Carbon blacks with the lowest packing efficiency reachthe percolation threshold with the least volume fraction ofcarbon black loading. The percolationbehavior ofspherical carbon blacks showed good agreement with Bruggeman's effective-mediumtheory in terms of both the percolation threshold and frequency dependence of conductivity atpercolation.

PACS numbers: 72.20. - i

I. INTRODUCTION

The electrical properties of conductor-insulator composite systems have been a subject of both theoretical andexperimental interests for a long time. For the theoreticalaspects of such systems, readers are referred to the summaryby Landauer. 1 Many experimental studies on such systemswere brought about by the increasing use of these materialsin electromagnetic shielding applications. 2-5

Polymer-carbon black composites, such as rubber-carbon black, is one of the most extensively studied systemsbecause of its wide spread use in the automotive industry.6However, most of these studies were mainly focused on themechanical aspects of the composites. Carbon black-thermoplastic composite systems are relatively new. Fox has reported conductivity of a carbon black-polyvinyl chloride(PVC) composite as a function of weight percent loading7

and Sheng, Sichel, Gittleman, and coworkers8 have investigated the dc resistivity of similar carbon black-PVC systemsin the low temperature regime and discussed their conduction mechanism. Kawamoto et al. reported some ac-resistivity measurements which can be found in a recent review bySichel et at.9

In this report, we will analyze the electrical conductivity and permittivity of carbon black-PVC composites over awide frequency spectrum (dc, 1300 MHz). While the compound of PVC used was fixed, the carbon black structureshave been varied drastically with four different species ofcommercially available carbon blacks.

The structural dependence of the electrical percolationthreshold and the volumetric conductivity will be discussedin terms ofeffective-medium theory and conductive networkconsiderations.

Even though carbon blacks are not as highly conductiveas some ofthe metallic fillers, they do provide the uniquenessof being small and inert spherical conductors (150-750 A).They also aggregate into chain-like structures with different

overall aspect ratios. Studies of electrical permittivity andconductivity on composites with these fillers (especially atdifferent frequencies) are useful for construction of similarconductive composites and also provide important data forcomparison with theoretical models for such systems in general. Conductive composites of various kinds are being usedin electromagnetic shieldings4

,5 for electrical components,disks for information storage,7 as well as to avoid electrostatic buildup in general.

II. EXPERIMENTAL

The PVC compound (denoted as "A") used to load thedifferent volume fractions of carbon blacks was similar tothat described by Martin et al. 1O In order to evaluate theeffect of the various components on the electrical propertiesof the compound, the simplified version (denoted as "n")was also prepared. The exact formulation is reported elsewhere. 1I

The various components in the PVC compound werefirst dry-blended to form a single batch of PVC formulation.This batch of PVC compound was then again dry blendedwith different weight percents of carbon black. The speciesof carbon blacks included the Regal SRF-S®, Mogul-L®,and XC-72® (Cabot Corp., U.S.A.), and also Ketjen Black®(Akzo Chemie, The Netherlands).

These dry blends were then melt blended in a HaakeRheometer at 200 °C for approximately 10 min, and thencompression molded into plates approximately 1.5 mmthick. The plates were molded and annealed under pressureat 200 °C for approximately 2 min. This ensured an isotropiccomposite structure. They were then cooled rapidly(- 50°C/min) to room temperature.

Samples were prepared by machining the plates intodisks of approximately 6.35-mm diameter. Gold was thenvacuum deposited on the surfaces of the samples for electrical measurements. Four-point probe dc-conductivity mea-

6867 J. Appl. Phys. 53(10), October 1982 0021-8979/82/106867-13$02.40 © 1982 American Institute of Physics 6867


surements on the plates were also performed. They showedno observable deviation from the two-terminal measurement. Thus, data using the two-terminal technique is usedfor this report.

A Hewlett Packard Network Analyzer (Model 8505A)was used for ac-conductivity and permittivity measurement.In the experimental measurement, the complex compositeconductivity a: is defined as

a: (CiJ) = 0"m(CiJ) + jCiJEoEm(CiJ), (I)

where O"m(CiJ) is the real part of the composite conductivity,Em (CiJ) is the dielectric constant at frequency CiJ, and Eo is thevacuum permittivity.

III. RESULTS AND DISCUSSIONA. Theory: Interfacial polarization and effectivemedium theory

The Maxwell-Wagner-Sillars theory l2-14 is a classicaltheory used to explain the dielectric-loss due to the interfacial polarization of two-phase system when the volume fraction ofthe dispersion is small. 15 When the loading ofconductor increases, the symmetric effective-medium theory ofBruggeman16 is commonly used in accounting for the electrical properties of a conductor-insulator composite. Whenthe phases in a binary-phase mixture are spherical, the Bruggeman's theory can be written 1 as

10 4 r-------.-----...,....-----,...----~---____,

CTC =1000.n-I cm- I

FIG. I(a). Volumetric conductivity of carbonblack-PVC composites as a function ofcarbonblack loading at 915 MHz predicted by Bruggeman's effective medium theory. The parameters used for the calculation are the measuredEp =3.0,ap =50XIO- 6 n-'cm-';Ec isassumed to be zero while ac is assumed to possess values of 0.1 to 1000 n -, cm - '.

1.00.2 0.4 0.6 0.8

VOLUME FRACTION OF CARBON BLACK

10-6 L-_...l.-_--.l.__.J......_--I....__I-_...l.-_--.l.__..I...-_--I...._--J

o

CTC = 100 -1000 n- I em-I

10

lz~ 102(/)

zouua::luILl.JILl

o

a

10

0.2 0.4 0.6

VOLUME FRACTION OF CARBON

1.0

FIG. I(b). The corresponding predicted bulkdielectric constants of carbon black-PVCcomposites under the same assumption usedin calculating the volumetric conductivity.

6868 J. Appl. Phys. Vol. 53, NO.1 0, October 1982 Chung, Saba, and Pica 6868


~-~ .I. )~-~ (2)¢c E! 2E! = - (1 - 'Pc. 2E!'

c + m €p + m

where ~, ~, and~ are the complex dielectric constant ofmaterials (in this case, carbon black, PVC, and the composite, respectively). Ifthe volume fraction (¢c)' ~(cu), and ~(cu)

are known, the real and imaginary part of€:, as a function ofloading can be readily calculated from Eq. (2).

It is intrinsic in the formulation that such a three-dimensional random system exhibit its electrical percolation(insulator-metal transition) at the volume fraction of onethird. Springett l7 applied such theory to account for the frequency dependence in a dielectric constant and loss in anconductor-insulator composite system. It was shown thatthe bulk composite dielectric constant reached maximum at¢c = 1/3. The magnitude of ~ax depends on both the frequency as well as €~ and €; of the components involved. Themore conductive spherical dispersions will exhibit highermaxima in €m at the percolation threshold. It was also demonstrated that, at percolation, both the conductivity and dielectric constants exhibit a sigmoidal-shape change at somecharacteristic frequency (cu c )' which is a function of the complex dielectric constants (€~ and €;) of the components.

We use Eq. (2) to calculate the volume fraction dependence in the complex dielectric constant of carbon blackPVC composite. Figures l(a) and 1(b) are the plots ofthe bulkac-conductivity and dielectric constant at 915 MHz. Thedifferent curves corresponded to the wide range of assumedcarbon black conductivity (O"c = 0.1 to 1000 n -I cm -I).

Theoretically, inside a single spherical carbon black, ifthe outer shell is graphitic and continuous, then the conductivity of the carbon will be similar to those ofa perfect graphite (0"11 ~3X 104n -I cm- I

). However, the various deviations from a perfect graphitic structure will affect theintrinsic conductivity of the specific carbon species. If theelectron transport inside a carbon black (simple or highlystructured) has to jump across adjacent shells of graphiticplanes due to some discontinuity of the graphitic planes insuch particles, the carbon black conductivity might be in

fluenced by the tunneling conductivity between the graphiticstackings (0"1~ 1.0 n - I cm- I, depending on the d()()2 spacing of the carbon black).

It is interesting also, to note that, for a fixed Ec / Ep ' thedielectric maxima (~ax) at percolation reaches an asymptotic value of around 300 for o"c > loon -I cm- I

• However,

when the loading of the conductive component exceeds thepercolation threshold, metal-like conductive paths will beestablished. At such level of loading, the composite willagain be expected to exhibit a single-phase-like behavior inconductivity and dielectric loss. Additional loading of theconductive component will simply increase the number ofconductive paths in a geometric manner and thus increasethe bulk conductivity correspondingly.

When the loading ofcarbon black is below the percolation threshold, the conductivity between the grains of carbon black is expected to be primarily via hopping and tunneling mechanisms. In this mode of conduction, the electrontransport may still couple strongly with the molecular andionic processes in the insulating matrix such as PVC. Thus,when the loading increases, the conductivity is increasedmainly by virture of the narrowing of tunneling gapsbetween the conductive grains. Thus, one can visualize thebulk conductivity to be described by functions such as

O"m =f(¢c)e- X(4>c), (3)

wheref(¢c) ifa function representing the geometric networkof the conductive path and X (¢c ) represents the average tunneling gap between the grains ofcarbon black which is beingreduced with increased loading. For spherical conductors,when ¢c <1/3, the spatial distance between grains is large sothat tunneling is negligible and thus conduction is mainlydue to the interfacial polarization effect. When ¢c approaches 1/3, the conducting phase becomes connected andthe tunneling term becomes important and enhances theconductivity in an exponential manner.

When the loading exceeds the percolation threshold,the gap between the grains might be governed by the interparticle interaction (cohesion by the continuous matrixphase and the repulsion between the the particles) and is notexpected to decrease drastically. Thus, one may expect thetunneling gap X (¢c) to reach a critical value, and the additional conductive particles will only help the conductivity bygeometrically increasing the conductive paths. The conductivity of the composite is expected to increase gradually tothe asymptote when the conductivity of a random closepacked condition is reached.

B. Morphology of carbon black: Packing efficiency andpercolation threshold

The SRF-S@ and Mogul-L@ carbon blacks are known

TABLE I. Summary of the essential features in the carbon blacks used for this study.

SRF-sCijCarbon black structures

Mogul-Ull XC-72@ Ketjen Black")

Aspect ratio(structure)

Primary particlesize

Microstructure

spherical

600 A.

graphite

spherical

240 A.

graphitic

medium

300 A.

graphiticplanesshared withneighboringparticles

high

300 A.

graphiticplanesshared withneighboringparticles

6869 J. Appl. Phys. Vol. 53, NO.1 0, October 1982 Chung, Sabo, and Pica 6869


to be spherical in shape and do not exhibit any aggregatestructure. Because of the high conductivity of the constituent graphitic planes, they can be considered as a sphericalconductor for all intents and purposes. The average particlesize of SRF-S® and Mogul-L® are 600 and 240 A, respectively.I8

Ketjen Black® structures and their composites withrubber have been studied by Verhelst et al. 19 It is well established that they form extended structures with the graphiticplanes shared by the neighboring primary spherical units of- 300 Adiameter. 13 XC-72® , on the other hand, is knownto be a medium-structure carbon black, with approximately

300 A diameter, primary particle.Transmission electron microscope (TEM) lattice imag

ing of the various carbon black species20 seems to indicatethat the graphitic shells are continuous. In the case of highlyextended (high structure) carbon blacks, the graphitic planesactually extended into and were shared by neighboringspherical units. 20 This fact was also demonstrated in KetjenBlack. 19 Thus one can reasonably assume the conductivity ofcarbon black to be that of the graphitic plane. In fact, it hasbeen demonstrated that compressed carbon black shows abulk conductivity as high as 22 n -I em- 1.19

Both XC-72 and Ketjen Black have been studied byVerhelst et al. 19 They showed these carbon blacks to possessrelatively high surface areas when compared with those ofspherical simple carbon blacks. However, for the purpose ofvisualizing the physical concept, it is easier to consider thehigh structure carbon to be a chain with characteristic aspectratio (average chain length of persistent structure/diameterof primary carbon black). The relative aspect ratios of theaggregate structures determine the packing efficiency. 2 I Theessential features of the carbon blacks used for this study are

SRF-S DRY BEAD--"

summarized in Table I.The packing efficiency of the high structure carbons are

expected to decrease and thus lower the electrical percolation threshold volume. Figure 2 is a plot of the bulk volumeoccupied by the various carbon blacks under relatively weakcompression forces. It is obvious that SRF-S packs moreefficiently than XC-72, which is, in turn, more denselypacked than Ketjen Black. This natural packing efficiencydirectly reflects the minimum volume ofcarbon black needed to ensure intimate contact with the neighboring grains.The bulk densities of0.18 g/cc at -400 g/cm2 ofload wouldimply that - 8% by volume is needed to ensure intimatecontact with its neighbors (assuming de = 1.8 g/cc). Similarly, the volume fractions of SRF-S and XC-72 to ensure intimate contact between grains at the same load are - 32% and17%, respectively.

The magnitude of bulk conductivity in any system willbe a function of the number of interparticle junctions informing a metal-like conductive path. A conductive pathformed by a single continuous conductor is obviously moreconductive than the same path formed by small spheres.Thus, it will be expected that the highly structured carbonssuch as Ketjen Black and XC-72 will be more conductivethan the SRF-S and Mogul-L.

The same effect will also be observed for the particlesize difference. For continuous chain-like aggregates withthe same aspect ratio but a smaller size, a larger amount ofthe conductors will be needed to form a continuous conductive path of the same length. The increase injunction pointswill decrease the bulk conductivity correspondingly. Thesame argument will also apply to spherical conductors withdifferent sizes. The conductivity of the composite with thelarger size conductors will be higher.

200 400 600COMPRESSION PRESSURE (llm/cm 2 j

oo

I

KETJEN DRY BEAD

I I

800

FIG. 2. The bulk densities of the various carbon species used in thisstudy when compressed. The bulk density is a measure of thepacking efficiency inachieving a close-contact condition. TheSRF-S spherical carbonblack being more densely packed under thesame load will correspond to larger volumefraction needed toachieve electrical percolation.



100..---------------------------,¢ PVC COMPOUND-A

o PVC COMPOUND- B

10

'eu

b•0)( 1.0

b

FIG. 3(a). The bulk conductivities of PVCcompound "A " and "0" as measured at0.5-1300 MHz.

10,0001,00010 100

f (M Hz)

1.0

0.1 L. -.l ---l. --L. -'-- ---J

0.1

140r------------------- --,

120

o PVC COMPOUND- A

100

¢ PV C COMPOUND- B

80

60

40

20

O~-----1.----___L._. ...L. L_ ._J

0.1 1.0 10 100 1,000 10,000f (MHz)

FIG. 3(b). The bulk dielectric constants of PVC compounds "A" and "0" asmeasured at 0.5-1300MHz.



FIG. 4. The conductivity profiles ofPVC/SRF-S system as afunction of wt. % loading atdifferent frequencies. The dcconductivities are the same asthose measured at 0.5 MHz forweight loadings higher than40%.

10,000

20 %

0%

10%

1,000100101.0

PVC/SRF-S

: : : : : : : ; ~55%50%

45 %6J ~ ft 1\ /l !-:~:=::=::40 %

• • • • • • •35 %

30%

0.1

10

104

1"Eu

1"~

'" :5I0 10)(

10

210

610 ,--------- ----:- -,

510

f ( MHz)

TABLE II. Rule of mixture applied to carbon black-PVC composite withde - 1.80 glccm dp - 1.38 glcc.

C. €* of PVC compoundsFigure 3(a) is a plot of the ac-conductivity of PVC com

pound "A " and compound "B". The conductivity of thesecompounds obviously demonstrated different molecular andionic mobility at a time scale shorter than 100 MHz. SinceTg ofPVC is around 76'C [differential scanning calorimetry(DSC) measurement at a heating rate of 20 'C/min), the observed dielectric loss may be due to the interfacial polarizability of the various components coupled with the molecularand ionic mobility of the different molecules involved. Theincrease in conductivity at higher frequencies (above 100MHz) is not immediately clear. This frequency dependenceis typical for systems with more than one phase. 17 In general,the bulk conductivity tends to decrease with increasing frequency (analog to decreasing temperature) if the conductingmechanism is an activated process.

Figure 3(b) is a plot of the dielectric constants of the

Xc (weight fraction %)"

51015202530354045505560

tPc (volume fraction %)

3.97.8

11.915.320.424.729.233.838.543.448.453.5

6872 J. Appl. Phys. Vol. 53, No. 10, October 1982 Chung, Sabo. and Pica 6872


same compounds from 0.5 to 1300 MHz. The dielectric constant approaches 3.0 from 200 MHz up. This dielectric constant is typical for organic polymers, and simply reflects theelectronic polarizability of the molecules. The extremelyhigh dielectric constant at lower frequencies for compound"A "when compared with "B "is a direct result ofthe interfacial polarizability of the various additives in the PVC matrix.For a pure PVC (or any polymers with Tg above room temperature) the dielectric constant is typically 3.0 for this frequency range.

The dielectric constant and conductivity of compound"A " will be used in the theoretical correlation with the measured experimental results in Sees. III F and III G.

D. PVC-spherical carbon black systems

Figure 4 is a plot of the volumetric conductivity as afunction offrequency for the loaded PVC/SRF-S compositesystem. The data are labelled in weight fractions (xe), but canbe readily converted into volume fraction by the rule of mixture

(4)

_I_=~+I-Xe (5)dm de dp

where de> dp ' and dm are the specific densities of carbonblack, PVC, and the composite, respectively. The implicitassumption is that there are only two phase existing in thecomposite (carbon black and PVC without voids).

The density of the PVC compound is approximately1.38 glee, and the carbon black densities in PVC are-1.80 ± 0.05 glee, depending on the perfection of the crystallites in the carbon black. The weight and volume fractionconversion is shown in Table II.

For the composite with relatively low carbon blackloading (below 20%), the composite conductivity demonstrated the polarization coupling between the conductorsand the continuous PVC matrix. Increase in carbon blackloading enhances the conductivity as expected. In the higher-frequency region (above 100 MHz), the conductivity in-

106~ -,

o 0 o o o 0 o

~50%s

10

FIG. 5. The conductivity profiles of PVC/Mogul-L systemas a function of wI. % loadingat different frequencies. Similar to PVC/SRF-S, the dc conductivities are the same asthose measured at 0.5 MHz forweight loadings higher than40%.

10,000

45%

0%

10%

32.5%

20%

30%

40%

PVC/M OGUL-

1,00010010

f (MHz)

1.0

210

10

1.0'------....J...---__J....- ---L.. ..l....- .....J

0.1

'eu 4~ 10

CD

bx

63

10

6873 J. Appl. Phys. Vol. 53. NO.1 0, October 1982 Chung, Saba, and Pica 6873


creases as a function offrequency similar to that of the PVCcompound. With further increase in loading (40-55%), thefrequency dependence in conductivity decreases and showeda near constant conductivity for frequency below 100 MHz.At the highest loading level (50-55%), the frequency dependence of conductivity is inverted and showed a decrease inthe electronic transport from 100 to 1300 MHz.

The reason for the frequency dependent inversion inconductivity is not completely clear. A possible explanationis that at such high loading, the composite behaves like asingle-phase conductor. The metal-like conduction pathsseem to decouple the carbon black (conductive phase) for thematrix and the frequency dependence in conductivity is simply reflecting the property of scattering within the carbonblacks.

The bulk dielectric constants of the composite at theseloadings (50-55%) were found to be zero. In this case, a zero

dielectrtic constant would simply imply that conductionprocess dominated and the sample was unable to store thepolarized charges. As will be demonstrated in the later section, the percolation of the spherical carbon black systemsoccurred at around 40% by weight (- 34% by volume).Thus at 50% by weight, the carbon black particles are already well connected in the form ofconductive network withnegligible interparticle gap. The zero electric permittivity inthe measurements is a result of the conductor-like conduction with the applied measuring electric field. The absolutevolumetric conductivity reaches as high as 0.50 n - I cm- I.

Another similar system of carbon black-PVC composite will be that of PVC/Mogul-L system. As previously described, the only difference in the two carbon blacks is theparticle size (240 A instead of600 A). Figure 5 is a plot of theac-conductivity as a function of frequency. Similar to thePVC/SRF-S system, the lower-frequency data for the low

PVCI XC-72

10

106

: ; : : : ~5%v....

30%

!S

~ ~ ~ ~ ~ tF ~~25%

1020%

15%

104

-'"'j100/.E FIG. 6. The conductiv-

() ity profiles of PVC/

~ 103 XC-72 system as a func-

btion of wt. % loading atdifferent frequencies.The bulk dc conductiv-

X ities are the same asthose measured at 0.5

to 5%MHz at weight load-

2ings higherthan 15%.

100%

0.1 1.0 10 100 1,000 10,000

f (M Hz )

6874 J. Appl. Phys. Vol. 53, No. 10, October 1982 Chung, Sabo. and Pica 6874


levels of loading (below 20%) showed a strong fluctuationdue to the strong coupling with the PVC matrix.

The inversion in the frequency dependence of conductivity also occurred at 45% by weight loading. As will beclear in Sec. III F, the percolation thresholds for these twocarbon blacks are almost identical.

The absolute volumetric conductivity of PVC/MogulL system is lower than that of PVC/SRF-S system for thesame volume fraction of carbon black loading. This is expected from the earlier discussion of the increased junctionpoints between particles for the same length of connectedcarbon black chains.

It should be noted that the conductivity changes from45-50% loading are rather dramatic for both SRF-S andMogul-L systems (see Figs. 4 and 5). However, when the

carbon black-PVC composite showed a metal-like behaviorin conductivity at the highest loading, the magnitude of volumetric conductivity approached each other (see also Fig.10).

E. PVC-complex carbon black systems

The frequency dependence in conductivity for the various weight percent loading ofcarbon black for PVC/XC-72composite is shown in Fig. 6. The dependence is qualitativelysimilar to those observed for the spherical carbon blacks.The major difference is that the percolation threshold isreached at -15% by weight of loading rather than -40%in the simple carbon blacks.

It is clear from the packing efficiency consideration thatthis chain-like structured carbon black will form a connect-

PVC-KETJEN BLACK

10>

I

Eu

~CD

bX

410

10

1.00.1

• •

1.0

• • •

10

• • •

100

• •• 9 %

6%

1,000 10,000

FIG. 7. The measuredconductivity profiles ofPVC/Ketjen Black system as a function ofWI. % loading at different frequencies. Thebulk dc conductivitiesare the same as thosemeasured at O. 5 MHz atweight loading higherthan 9%. Bulk conductivity higher than 1.0n - I cm - I have beenachieved with loadingshigher than 21%.

6875

f ( MHz)

J. Appl. Phys. Vol. 53, No. 10, October 1982 Chung, Sabo, and Pica 6875


50r---,-----.------r----r------.---~

FIG. 8. Carbon black-PVC composite dielectic constants at 915 MHz as a functionofwt. % loading. Ketjen Black shows percolation at around 8%, both SRF-S andMogul-L show percolation at 40% whileXC-72 shows percolation at intermediateloading of -15%.

6040 50

(WEIGHT %)

PVC915 MHz40

SRF-S;I/\~

Y3r 120 KETJEN XC-72 IlL / I

I /. I /10 / ~~ fiOGUL-L

~ / \ ¥~. - .

0+ ""-o 10 20

CARBON BLACK

30

EIII

ed network at much lower loading. Since the shape of theaggregates depart from the simple spherical structure (thusdifferent depolarization factor), the effective-medium theoryin its present form will not be able to account for their electrical properties.

Similar observations can be made on the PVC/Ketjenblack system. It is clear from the packing efficiency consideration that the percolation threshold volume will be lowestfor the highly structured Ketjen Black. Figure 7 is a plot of

the frequency dependent conductivity with different weightpercent of carbon black loading.

The frequency dependence is, again, qualitatively similar to the previous carbon blacks considered. However, theelectrical percolation as demonstrated by the frequency independence in conductivity is at - 9% by weight ofloading.

The magnitude of bulk conductivity reaches as high as- 1.2 {J - I cm- 1 for the highest loading levels (24%). Thehigh conductivity of PVC/Ketjen Black system agrees well

FIG. 9. A comparison of the percolation behavior between the theoretical and experimental dielectric constant results for thespherical carbon black system. The unfilledcircles represent the experimental data forPVC/SRF-S System, and the continuouscurves represent the prediction of Eq. (2) withU c = 0.5 and 1.0.a -I cm -I, respectively.

1.00.2 0.4 0.6

VOLUME FRACTION OF CARBON

40,......--...----.----..----,--r---r---.----..----,-----,

~ 30z«~(J)

zo<.>

<.>a::~<.>w...JW

o

6876 J. Appl. Phys. Vol. 53, NO.1 0, October 1982 Chung, Sabo. and Pica 6876


tion due to the strong coupling with the PVC matrix at thelower frequency. It is obvious that Mogul-L and SRF-S seemto peak at approximately Xc = 42% or approximately 35%by volume. This is very close to the percolation predicted byBruggeman's effective-medium theory. Figure 9 shows theagreement between the theory and experimental data forPVC/SRF-S system.

The higher-structure XC-72 showed a peak at approximately 12 to 15% by weight or around 10 to 12% by volumeloading. The highest-structure Ketjen Black showed a peakat as little loading as 7% by weight loading.

A similar observation on the structural dependence ofpercolation threshold is shown in the plot of composite conductivity as a function of loading (Figure 10). The percolation threshold as indicated by the inflection points are verysimilar to those obtained in the dielectric measurements.Figure 11 is a comparison of experimental data of PVC/SRF-S system with the theoretical prediction for sphericalconductor composite.

PVC-CARBON BLACK915 MHz

10

KETJEN.,..6-/1 X~-72 SRF-S

/1,,!J._ x1l" /" ~.-

/ I/· ~/;1 / I/0 MOGUL-L

I Y/ ./

102+~

b

1~_---:-':--_-L__--1.__---'-__.....J...__...J

o 10 20 30 40 50 60

CARBON BLACK LOADING (WEIGHT %)

FIG. 10. PVC carbon composite conductivities at 915 MHz as a function ofwt. % loadings. Similar to the dielectric constants, the percolation in conductivity depends on the packing efficiency and thus its structure.

with the considerations in Sec. III B.

F. Structural dependence of percolation threshold

In order to reveal the relationship between carbon blackstructure and the electrical percolation threshold, the dielectric constant of the composites at 915 MHz is plotted in Fig.8. The high-frequency data is chosen to avoid the complica-

G. Frequency-dependent conductivity and dielectricconstant at percolation threshold

It is clear from the relationship between the carbonblack structure and the composite percolation thresholdthat, in the case of spherical carbon blacks, the agreementwith the Bruggeman's effective-medium theory is extraordinarily good. It will be meaningful to also compare the experimental and theoretical frequency dependent conductivityand permittivity at percolation threshold. Figures 12(a) and12(b) are the respective plots of Urn and Em as a function offrequency as predicted by Eq. (2). The Urn and Em of thePVC/SRF-S system at 35 and 40% carbon loading were alsoplotted for direct comparison.

I

E(,)

>~

>~u::)QZou

FIG. II. A comparison between experimentaldata and theoretical predication on compositeconductivity. The legend is the same as in Fig.9. The solid lines represent the prediction ofEq. (2) with U c = 0.5 and 1.0 fJ -I em-I. respectively. The conductivities of PVC/SRF-Sand PVC/Mogul-L system are extremely similar to those predicted in Fig. I for U c = 1.0fJ -I em-I.

10-5OL--.L-..-

O....L.---L....--L...---l..----1--L--l.--...l.--...J

.2 0.4 0.6 0.8 1.0

VOLUME FRACTION OF CARBON BLACK

6877 J. Appl. Phys. Vol. 53, NO.1 O. October 1982 Chung, Saba. and Pica 6877


The experimental conductivities agree with the theoretical prediction reasonably well. The composite conductivity seems to indicate that the carbon conductivity is moreclose to I than 3X 104 {l - I cm- I.

The magnitudes of the experimental composite dielectric constants do not seem to fall within the bounds predictedby Eq. (2). However, the general frequency dependence ofthe experimental results seem to run reasonably parallel tothose predicted by effective-medium theory.

IV. CONCLUSION

The electrical conductivity and permittivity of PVCcarbon blacks were studied over a wide frequency spectrum(dc, 1.3 GHz). Carbon blacks with different degrees ofchainlike aggregates structures showed drastically different percolation thresholds. The highest structure carbon black(Ketjen Black) with lowest packing efficiency reaches itselectrical percolation with the lowest volume fraction loading.

The percolation behavior of spherical carbon blacksshowed good agreement with the Bruggeman's effective-medium theory in terms of both the percolation threshold andthe frequency dependence of conductivity at percolation.

Further loading ofcarbon black beyond the percolationthreshold yields a single-phase structure with metal-likeelectrical properties. This structure can be achieved by loading with both the spherical and aggregate forming carbonblacks.

The intrinsic conductivity of carbon blacks can be deduced from Bruggeman's effective-medium theory if one assumed its validity. It was found that U c is in the range of 1.0{l - I cm- I rather than 3X 104 {l -lcm-1, suggesting thatscattering due to defects within the carbon black grainshinders the electronic transport seriously. One can also employ such theory with confidence for the prediction of enduse properties, such as effective shielding behavior (a function of bulk conductivity) of similar composites at differentfrequencies. It was also demonstrated that more understand-

I 03 ~---------------------------,

210

10 FIG. l2(a). The measured amas a function of frequency ofPVC/SRF-S composite at35% (filled circles) and 40%(filled triangle) by weight ofcarbon black loading. Thetheoretically predicted frequency dependence of am atpercolation (,pc = 1/3) whenthe ac are assumed to be 1.011 - I cm - I (unfilled squares)and 3X 104 n - I cm - I (filledsquares), respectively. A reasonably good agreementbetween the measured and calculated data is evident for thetheoretical prediction withac-I.On- 1 cm- I

.

(T

(ac: 1.0 n-1cm· l)

--...

.........(T (40 o/.Clt. .

10,0001000100101.0

Io-(35%Cl

10·3L ...L J- .J.. ---l_------'

0.1

( MHz)

6878 J. Appl. Phys. Vol. 53, No. 10, October 1982 Chung, Saba, and Pica 6878


ew

10

Q,,_ ".I::.: •.. .t!. ..

E I 35%cP---o-- -0- -<>-...:~:..:..t!.." "~".-0-. ".'n -0-

E

FIG. 12(b). The measuredEm as a function offrequen·cy for PVC/SRF·S composite at 35% (unfilled cir·cles) and 40% (unfilledtriangles) by weight of carbon black loading. Theagreement is not as good asin the case the bulk conductivity. The unfilled andfilled hexagons representthe theoretically predictedresults for u = 1.0 and3X lif n -, em-I, respec·tively.

0.1 1.0 10

f (M Hz )

100 1000 10,000

ing on the composite structure can be obtained with the combined knowledge ofelectrical conductivity and permittivity.Structures of the composites (such as connectivity betweenconductive fillers) as inferred from these electrical characteristics are also useful in the understanding of other physicalproperties (such as mechanical shape stability, brittleness,etc.).

ACKNOWLEDGMENT

Thanks are due to L. P. Fox, L. A. DiMarco, C. H. Wu,J. I. Gittleman, and C. H. Anderson for valuable discussions.

'R. Landauer, "Electrical Conductivity in Inhomogeneous Media", AlPConf. Proc. 40, 2 (1978).

2F. Bueche, J. Appl. Phys. 44, 532 (19731.lC. Rajagopal and M. Satyam, J. Appl. Phys. 49,5536 (19781.4R. M. Simon, Polym Plast. Technol. Eng. 17, 1(19811.

50. E. Davenport, Polm Plast. Technol. Eng. 17,221 (1981).6J·B Donnet and A. Voet, Carbon Black (Marcel Dekker, New York, 1976).7L. P. Fox, RCA Rev. 39, 116 (19781."E. K. Sichel,J.I. Gittleman, and Ping Sheng, Phys. Rev. B18, 5712(1978)."E. K. Sichel, J. I. Gittleman, and Ping Sheng, J. ofElectron. Mater. (to bepublished).

'OC. J. Martin, M. J. Voelker, R. J. Ryan, U. S. Patent 4 228 050 (1980).1'K. T. Chung and L. A. DiMarco (unpublished).12J. C. Maxwell, Electricity and Magnetism (Oxford University, London,

1892), Vol. I.ilK. W. Wagner, Arch. J. Elektrotech. 2, 371 (1914).'4R. W. Sillars, J. Inst. Electr. Eng. [1889·1940]80, 378(1937).'5L. K. H. Van Beek, Prog. Dielectr. 7, 69 (1967).160. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935)."B. E. Springett, Phys. Rev. Lett. 31, 1463 (1973).I "Technical bookletson: (al Cabot Carbon blacks for ink, paint, plastics, and

paper and (b) carbon blacks for conductive plastics.''''N. F. Verhelst, K. G. Wolthuis, A. Voet, P. Ehrburger, andJ. B. Donnet

RubberChem. Technol. SO, 735 (19771.2°L. L. Ban and W. M. Hess, Petroleum Derived Carbons (American Chemi

cal Society, Washington, D.C., 19761, Vol. 21, p. 358.2'J. V. Milewski, Ph.D. thesis, Rutgers University, 1973.

6879 J. Appl. Phys. Vol. 53, No. 10, October 1982 Chung, Saba, and Pica 6879

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