Electrical permittivity and conductivity of carbon black-polyvinyl
chloride composites
K. T. Chung, A. Sabo, and A. P. Pica
RCA 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 were
studied over a wide frequency spectrum (dc, 1.3 GHz). Conductivity of the bulk composites
increases with higher volume fraction of carbon black as expected. However, the functional
dependence of the increasing conductivity with carbon black loading is different below and above
the percolation threshold because ofthe different mechanisms involved. Bulk electric permittivity
increases until the composite percolation is reached and then decreases to zero after fully
connected conductive paths have been established. Such highly loaded composites showed a
metal-like electrical behavior. Different electrical percolation threshold of the composites were
found for different species of carbon black. Carbon blacks with the lowest packing efficiency reach
the percolation threshold with the least volume fraction of carbon black loading. The percolation
behavior ofspherical carbon blacks showed good agreement with Bruggeman's effective-medium
theory in terms of both the percolation threshold and frequency dependence of conductivity at
percolation.
PACS numbers: 72.20. - i
I. INTRODUCTION
The electrical properties of conductor-insulator composite systems have been a subject of both theoretical and
experimental interests for a long time. For the theoretical
aspects of such systems, readers are referred to the summary
by Landauer. 1 Many experimental studies on such systems
were brought about by the increasing use of these materials
in electromagnetic shielding applications. 2-5
Polymer-carbon black composites, such as rubber-carbon black, is one of the most extensively studied systems
because of its wide spread use in the automotive industry.6
However, most of these studies were mainly focused on the
mechanical 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 loading 7
and Sheng, Sichel, Gittleman, and coworkers 8 have investigated the dc resistivity of similar carbon black-PVC systems
in 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 by
Sichel et at. 9
In this report, we will analyze the electrical conductivity and permittivity of carbon black-PVC composites over a
wide frequency spectrum (dc, 1300 MHz). While the compound of PVC used was fixed, the carbon black structures
have been varied drastically with four different species of
commercially available carbon blacks.
The structural dependence of the electrical percolation
threshold and the volumetric conductivity will be discussed
in terms of effective-medium theory and conductive network
considerations.
Even though carbon blacks are not as highly conductive
as some ofthe metallic fillers, they do provide the uniqueness
of being small and inert spherical conductors (150-750 A).
They also aggregate into chain-like structures with different
6867
J. Appl. Phys. 53(10), October 1982
overall aspect ratios. Studies of electrical permittivity and
conductivity on composites with these fillers (especially at
different frequencies) are useful for construction of similar
conductive composites and also provide important data for
comparison with theoretical models for such systems in general. Conductive composites of various kinds are being used
in electromagnetic shieldings 4 ,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 the
different volume fractions of carbon blacks was similar to
that described by Martin et al. 1O In order to evaluate the
effect of the various components on the electrical properties
of 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 were
first dry-blended to form a single batch of PVC formulation.
This batch of PVC compound was then again dry blended
with different weight percents of carbon black. The species
of 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 Haake
Rheometer at 200 °C for approximately 10 min, and then
compression molded into plates approximately 1.5 mm
thick. The plates were molded and annealed under pressure
at 200 °C for approximately 2 min. This ensured an isotropic
composite structure. They were then cooled rapidly
(- 50°C/min) to room temperature.
Samples were prepared by machining the plates into
disks of approximately 6.35-mm diameter. Gold was then
vacuum deposited on the surfaces of the samples for electrical measurements. Four-point probe dc-conductivity mea-
0021-8979/82/106867-13$02.40
© 1982 American Institute of Physics
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surements on the plates were also performed. They showed
no observable deviation from the two-terminal measurement. Thus, data using the two-terminal technique is used
for this report.
A Hewlett Packard Network Analyzer (Model 8505A)
was used for ac-conductivity and permittivity measurement.
In the experimental measurement, the complex composite
conductivity
is defined as
a:
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 the
vacuum permittivity.
10 4
III. RESULTS AND DISCUSSION
A. Theory: Interfacial polarization and effectivemedium theory
The Maxwell-Wagner-Sillars th eory l2-14 is a classical
theory 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 of
Bruggeman 16 is commonly used in accounting for the electrical properties of a conductor-insulator composite. When
the phases in a binary-phase mixture are spherical, the Bruggeman's theory can be written 1 as
r-------.-----...,....-----,...----~---____,
CT C = 1000.n -I
cm- I
FIG. I(a). Volumetric conductivity of carbon
black-PVC composites as a function ofcarbon
black loading at 915 MHz predicted by Bruggeman's effective medium theory. The parameters used for the calculation are the measured
Ep =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 - '.
10- 6 L-_...l.-_--.l._ _.J......_--I...._ _I-_...l.-_--.l._ _..I...-_--I...._--J
1.0
0.2
0.4
0.6
0.8
o
VOLUME FRACTION OF CARBON BLACK
CTC
= 100 -1000 n- I em-I
l-
z
~ 102
10
FIG. I(b). The corresponding predicted bulk
dielectric constants of carbon black-PVC
composites under the same assumption used
in calculating the volumetric conductivity.
(/)
z
o
u
u
a::
l-
u
ILl
.J
ILl
10
o
a
6868
0.2
0.4
0.6
VOLUME FRACTION OF CARBON
J. Appl. Phys. Vol. 53, NO.1 0, October 1982
1.0
Chung, Saba, and Pica
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~-~
¢c E!
c
+
.I.
)~-~
2E! = - (1 - 'Pc.
€p
m
+
(2)
2E!'
m
where ~, ~, and ~ are the complex dielectric constant of
materials (in this case, carbon black, PVC, and the composite, respectively). If the volume fraction (¢c)' ~(cu), and ~(cu)
are known, the real and imaginary part of €:, as a function of
loading 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 an
conductor-insulator composite system. It was shown that
the 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. The
more conductive spherical dispersions will exhibit higher
maxima 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 some
characteristic 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 bulk
ac-conductivity and dielectric constant at 915 MHz. The
different curves corresponded to the wide range of assumed
carbon black conductivity (O"c = 0.1 to 1000 n -I cm -I).
Theoretically, inside a single spherical carbon black, if
the 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 the
intrinsic conductivity of the specific carbon species. If the
electron transport inside a carbon black (simple or highly
structured) has to jump across adjacent shells of graphitic
planes due to some discontinuity of the graphitic planes in
such particles, the carbon black conductivity might be influenced by the tunneling conductivity between the graphitic
stackings (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 E c / Ep ' the
dielectric 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 the
percolation threshold, metal-like conductive paths will be
established. At such level of loading, the composite will
again be expected to exhibit a single-phase-like behavior in
conductivity and dielectric loss. Additional loading of the
conductive component will simply increase the number of
conductive paths in a geometric manner and thus increase
the bulk conductivity correspondingly.
When the loading of carbon 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 electron
transport may still couple strongly with the molecular and
ionic processes in the insulating matrix such as PVC. Thus,
when the loading increases, the conductivity is increased
mainly by virture of the narrowing of tunneling gaps
between the conductive grains. Thus, one can visualize the
bulk conductivity to be described by functions such as
O"m =f(¢c)e-
X
(3)
(4>c),
wheref(¢c) if a function representing the geometric network
of the conductive path and X (¢ c ) represents the average tunneling gap between the grains of carbon black which is being
reduced with increased loading. For spherical conductors,
when ¢c <1/3, the spatial distance between grains is large so
that tunneling is negligible and thus conduction is mainly
due to the interfacial polarization effect. When ¢c approaches 1/3, the conducting phase becomes connected and
the tunneling term becomes important and enhances the
conductivity 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 matrix
phase and the repulsion between the the particles) and is not
expected to decrease drastically. Thus, one may expect the
tunneling gap X (¢c) to reach a critical value, and the additional conductive particles will only help the conductivity by
geometrically increasing the conductive paths. The conductivity of the composite is expected to increase gradually to
the asymptote when the conductivity of a random closepacked condition is reached.
B. Morphology of carbon black: Packing efficiency and
percolation 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-sCij
Carbon black structures
Mogul-Ull
XC-72@
Ketjen Black")
Aspect ratio
(structure)
spherical
spherical
medium
high
Primary particle
size
600 A.
240 A.
300 A.
300 A.
Microstructure
graphite
graphitic
graphitic
planes
shared with
neighboring
particles
graphitic
planes
shared with
neighboring
particles
6869
J. Appl. Phys. Vol. 53, NO.1 0, October 1982
Chung, Sabo, and Pica
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to be spherical in shape and do not exhibit any aggregate
structure. Because of the high conductivity of the constituent graphitic planes, they can be considered as a spherical
conductor for all intents and purposes. The average particle
size of SRF-S® and Mogul-L ® are 600 and 240 A, respectively.I8
Ketjen Black® structures and their composites with
rubber have been studied by Verhelst et al. 19 It is well established that they form extended structures with the graphitic
planes shared by the neighboring primary spherical units of
- 300 Adiameter. 13 XC-72® , on the other hand, is known
to be a medium-structure carbon black, with approximately
300 A diameter, primary particle.
Transmission electron microscope (TEM) lattice imaging of the various carbon black species 20 seems to indicate
that the graphitic shells are continuous. In the case of highly
extended (high structure) carbon blacks, the graphitic planes
actually extended into and were shared by neighboring
spherical units. 20 This fact was also demonstrated in Ketjen
Black. 19 Thus one can reasonably assume the conductivity of
carbon black to be that of the graphitic plane. In fact, it has
been demonstrated that compressed carbon black shows a
bulk conductivity as high as 22 n -I em - 1.19
Both XC-72 and Ketjen Black have been studied by
Verhelst et al. 19 They showed these carbon blacks to possess
relatively high surface areas when compared with those of
spherical simple carbon blacks. However, for the purpose of
visualizing the physical concept, it is easier to consider the
high structure carbon to be a chain with characteristic aspect
ratio (average chain length of persistent structure/diameter
of primary carbon black). The relative aspect ratios of the
2
aggregate structures determine the packing efficiency. I The
essential features of the carbon blacks used for this study are
SRF-S
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 volume
occupied by the various carbon blacks under relatively weak
compression forces. It is obvious that SRF-S packs more
efficiently than XC-72, which is, in turn, more densely
packed than Ketjen Black. This natural packing efficiency
directly reflects the minimum volume of carbon black needed to ensure intimate contact with the neighboring grains.
The bulk densities of 0.18 g/cc at -400 g/cm 2 ofload would
imply that - 8% by volume is needed to ensure intimate
contact 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% and
17%, respectively.
The magnitude of bulk conductivity in any system will
be a function of the number of interparticle junctions in
forming a metal-like conductive path. A conductive path
formed by a single continuous conductor is obviously more
conductive than the same path formed by small spheres.
Thus, it will be expected that the highly structured carbons
such as Ketjen Black and XC-72 will be more conductive
than the SRF-S and Mogul-L.
The same effect will also be observed for the particle
size difference. For continuous chain-like aggregates with
the same aspect ratio but a smaller size, a larger amount of
the conductors will be needed to form a continuous conductive path of the same length. The increase injunction points
will decrease the bulk conductivity correspondingly. The
same argument will also apply to spherical conductors with
different sizes. The conductivity of the composite with the
larger size conductors will be higher.
DRY BEAD
--"
KETJEN
o
6870
200
DRY BEAD
I
I
o
400
COMPRESSION PRESSURE (llm/cm 2 j
J. Appl. Phys. Vol. 53, NO.1 0, October 1982
FIG. 2. The bulk densities of the various carbon species used in this
study
when
compressed. The bulk density is a measure of the
packing efficiency in
achieving a close-contact condition. The
SRF-S spherical carbon
black being more densely packed under the
same load will correspond to larger volume
fraction needed to
achieve electrical percolation.
I
600
800
Chung, Sabo, and Pica
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100..---------------------------,
¢
PVC COMPOUND-A
o
PVC
COMPOUND- B
10
'eu
FIG. 3(a). The bulk conductivities of PVC
compound "A " and "0" as measured at
0.5-1300 MHz.
b
•0
)(
1.0
b
0.1 L.
0.1
-.l
1.0
---l.
10
f
--L.
-'--
100
1,000
---J
10,000
(M Hz)
140 r - - - - - - - - - - - - - - - - - - -
--,
120
o
PVC COMPOUND- A
¢
PV C COMPOUND- B
100
80
FIG. 3(b). The bulk dielectric constants of PVC compounds "A" and "0" as
measured at 0.5-1300
MHz.
60
40
20
O~-----1.----___L._.
0.1
6871
1.0
10
f
...L.
100
L_
1,000
._J
10,000
(MHz)
J. Appl. Phys. Vol. 53, NO.1 0, October 1982
Chung, Sabo, and Pica
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6
10 , - - - - - - - - -
:: : : : : :
----:-
-,
PVC/SRF-S
; ~55%
50%
5
10
45 %
6J
~
ft
• • •
1\
/l
!-:~:=::=::40 %
• • •
•
4
35 %
10
1"
E
30%
u
1"
~
'"0
I
FIG. 4. The conductivity profiles ofPVC/SRF-S system as a
function of wt. % loading at
different frequencies. The dc
conductivities are the same as
those measured at 0.5 MHz for
weight loadings higher than
40%.
:5
10
)(
20 %
10
10%
2
10
0%
10
0.1
1.0
10
100
1,000
10,000
f ( MHz)
C. €* of PVC compounds
Figure 3(a) is a plot of the ac-conductivity of PVC compound "A " and compound "B". The conductivity of these
compounds obviously demonstrated different molecular and
ionic mobility at a time scale shorter than 100 MHz. Since
Tg of PVC 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 molecular
and ionic mobility of the different molecules involved. The
increase in conductivity at higher frequencies (above 100
MHz) is not immediately clear. This frequency dependence
is 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 conducting
mechanism is an activated process.
Figure 3(b) is a plot of the dielectric constants of the
6872
J. Appl. Phys. Vol. 53, No. 10, October 1982
TABLE II. Rule of mixture applied to carbon black-PVC composite with
de - 1.80 glccm dp - 1.38 glcc.
Xc (weight fraction %)"
5
10
15
20
25
30
35
40
45
50
55
60
tPc
(volume fraction %)
3.9
7.8
11.9
15.3
20.4
24.7
29.2
33.8
38.5
43.4
48.4
53.5
Chung, Sabo. and Pica
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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 the
electronic polarizability of the molecules. The extremely
high 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 a
function offrequency for the loaded PVC/SRF-S composite
system. The data are labelled in weight fractions (xe), but can
be readily converted into volume fraction by the rule of mixture
(4)
_I_=~+I-Xe
dm
de
(5)
dp
where de> d p ' and d m are the specific densities of carbon
black, PVC, and the composite, respectively. The implicit
assumption is that there are only two phase existing in the
composite (carbon black and PVC without voids).
The density of the PVC compound is approximately
1.38 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 fraction
conversion is shown in Table II.
For the composite with relatively low carbon black
loading (below 20%), the composite conductivity demonstrated the polarization coupling between the conductors
and the continuous PVC matrix. Increase in carbon black
loading enhances the conductivity as expected. In the higher-frequency region (above 100 MHz), the conductivity in-
-,
106~
o
0
o
o
o
0
s
o
~50%
10
45%
'eu
40%
4
~ 10
CD
b
x
FIG. 5. The conductivity profiles of PVC/Mogul-L system
as a function of wI. % loading
at different frequencies. Similar to PVC/SRF-S, the dc conductivities are the same as
those measured at 0.5 MHz for
weight loadings higher than
40%.
32.5%
6
3
30%
10
20%
2
10%
10
0%
10
PVC/M OGUL-
1.0'------....J...---_ _J....0.1
1.0
f
6873
---L..
10
100
..l....-
1,000
.....J
10,000
(MHz)
J. Appl. Phys. Vol. 53. NO.1 0, October 1982
Chung, Saba, and Pica
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creases as a function offrequency similar to that of the PVC
compound. With further increase in loading (40-55%), the
frequency dependence in conductivity decreases and showed
a 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 in
the electronic transport from 100 to 1300 MHz.
The reason for the frequency dependent inversion in
conductivity is not completely clear. A possible explanation
is that at such high loading, the composite behaves like a
single-phase conductor. The metal-like conduction paths
seem to decouple the carbon black (conductive phase) for the
matrix and the frequency dependence in conductivity is simply reflecting the property of scattering within the carbon
blacks.
The bulk dielectric constants of the composite at these
loadings (50-55%) were found to be zero. In this case, a zero
:; : : :
6
10
v
....
dielectrtic constant would simply imply that conduction
process dominated and the sample was unable to store the
polarized charges. As will be demonstrated in the later section, the percolation of the spherical carbon black systems
occurred 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 with
negligible interparticle gap. The zero electric permittivity in
the measurements is a result of the conductor-like conduction with the applied measuring electric field. The absolute
volumetric 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 the
particle size (240 A instead of 600 A). Figure 5 is a plot of the
ac-conductivity as a function of frequency. Similar to the
PVC/SRF-S system, the lower-frequency data for the low
~5%
30%
!S
~ ~ ~
10
~
~
tF
~
~25%
20%
15%
4
10
-
'"'j
100/.
E
FIG. 6. The conductivity profiles of PVC/
XC-72 system as a function of wt. % loading at
different frequencies.
The bulk dc conductivities are the same as
those measured at 0.5
MHz at weight loadings higherthan 15%.
()
~
b
3
10
X
to
5%
2
10
0%
10
PVCI XC-72
0.1
10
1.0
f
6874
100
1,000
10,000
(M Hz )
J. Appl. Phys. Vol. 53, No. 10, October 1982
Chung, Sabo. and Pica
6874
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levels of loading (below 20%) showed a strong fluctuation
due 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 be
clear in Sec. III F, the percolation thresholds for these two
carbon blacks are almost identical.
The absolute volumetric conductivity of PVC/MogulL system is lower than that of PVC/SRF-S system for the
same volume fraction of carbon black loading. This is expected from the earlier discussion of the increased junction
points between particles for the same length of connected
carbon black chains.
It should be noted that the conductivity changes from
45-50% loading are rather dramatic for both SRF-S and
Mogul-L systems (see Figs. 4 and 5). However, when the
carbon black-PVC composite showed a metal-like behavior
in 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-72
composite is shown in Fig. 6. The dependence is qualitatively
similar to those observed for the spherical carbon blacks.
The major difference is that the percolation threshold is
reached at -15% by weight of loading rather than -40%
in the simple carbon blacks.
It is clear from the packing efficiency consideration that
this chain-like structured carbon black will form a connect-
PVC-KETJEN BLACK
10>
•
•
•
•
•
•
•
•
•
••
9 %
FIG. 7. The measured
conductivity profiles of
PVC/Ketjen Black system as a function of
WI. % loading at different frequencies. The
bulk dc conductivities
are the same as those
measured at O. 5 MHz at
weight loading higher
than 9%. Bulk conductivity higher than 1.0
n - I cm - I have been
achieved with loadings
higher than 21%.
I
E
u
~
4
10
6%
CD
b
X
10
1.0
0.1
1.0
10
f (
6875
100
1,000
10,000
MHz)
J. Appl. Phys. Vol. 53, No. 10, October 1982
Chung, Sabo, and Pica
6875
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50 r---,-----.------r----r------.---~
PVC
915 MHz
40
SRF-S;I/\~
30
Y
E
III
20
KETJEN
I
10
/
~ /
~.
IlL /
XC-72
~~
1
I
I /
/.
fiOGUL-L
.
-\
¥
0+
o
3r
FIG. 8. Carbon black-PVC composite dielectic constants at 915 MHz as a function
of wt. % loading. Ketjen Black shows percolation at around 8%, both SRF-S and
Mogul-L show percolation at 40% while
XC-72 shows percolation at intermediate
loading of -15%.
10
""20
40
CARBON BLACK
50
60
(WEIGHT %)
ed network at much lower loading. Since the shape of the
aggregates depart from the simple spherical structure (thus
different depolarization factor), the effective-medium theory
in its present form will not be able to account for their electrical properties.
Similar observations can be made on the PVC/Ketjen
black system. It is clear from the packing efficiency consideration that the percolation threshold volume will be lowest
for the highly structured Ketjen Black. Figure 7 is a plot of
the frequency dependent conductivity with different weight
percent of carbon black loading.
The frequency dependence is, again, qualitatively similar to the previous carbon blacks considered. However, the
electrical 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%). The
high conductivity of PVC/Ketjen Black system agrees well
40,......--...----.----..----,--r---r---.----..----,-----,
~
z
30
«
~
(J)
z
o
FIG. 9. A comparison of the percolation behavior between the theoretical and experimental dielectric constant results for the
spherical carbon black system. The unfilled
circles represent the experimental data for
PVC/SRF-S System, and the continuous
curves represent the prediction of Eq. (2) with
U c = 0.5 and 1.0.a - I cm - I , respectively.
<.>
<.>
a::
~
<.>
w
...J
W
o
0.2
0.4
0.6
1.0
VOLUME FRACTION OF CARBON
6876
J. Appl. Phys. Vol. 53, NO.1 0, October 1982
Chung, Sabo. and Pica
6876
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KETJEN
X~-72
.,..6-/1
SRF-S
x
/1,,!J._
1l"
/"
/
I/·
1
/
;
I
/
b
102+~
~.-
~/
I/0
Y
MOGUL-L
./
PVC-CARBON BLACK
915 MHz
10
1~_---:-':--_-L
o
10
tion due to the strong coupling with the PVC matrix at the
lower frequency. It is obvious that Mogul-L and SRF-S seem
to peak at approximately Xc = 42% or approximately 35%
by volume. This is very close to the percolation predicted by
Bruggeman's effective-medium theory. Figure 9 shows the
agreement between the theory and experimental data for
PVC/SRF-S system.
The higher-structure XC-72 showed a peak at approximately 12 to 15% by weight or around 10 to 12% by volume
loading. The highest-structure Ketjen Black showed a peak
at as little loading as 7% by weight loading.
A similar observation on the structural dependence of
percolation 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 very
similar 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 spherical
conductor composite.
_ _--1._ _---'-_ _.....J..._ _...J
20
30
40
50
60
CARBON BLACK LOADING (WEIGHT %)
FIG. 10. PVC carbon composite conductivities at 915 MHz as a function of
wt. % 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 black
structure 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 dielectric
constant at percolation threshold
It is clear from the relationship between the carbon
black structure and the composite percolation threshold
that, in the case of spherical carbon blacks, the agreement
with the Bruggeman's effective-medium theory is extraordinarily good. It will be meaningful to also compare the experimental and theoretical frequency dependent conductivity
and permittivity at percolation threshold. Figures 12(a) and
12(b) are the respective plots of Urn and Em as a function of
frequency as predicted by Eq. (2). The Urn and Em of the
PVC/SRF-S system at 35 and 40% carbon loading were also
plotted for direct comparison.
I
E
(,)
FIG. II. A comparison between experimental
data and theoretical predication on composite
conductivity. The legend is the same as in Fig.
9. The solid lines represent the prediction of
Eq. (2) with U c = 0.5 and 1.0 fJ -I em-I. respectively. The conductivities of PVC/SRF-S
and PVC/Mogul-L system are extremely similar to those predicted in Fig. I for U c = 1.0
fJ - I em-I.
>-
~
>
~
u
::)
Q
Z
o
u
10- 5 OL--.L-..-....L.---L....--L...---l..----1--L--l.--...l.--...J
O.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
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The experimental conductivities agree with the theoretical prediction reasonably well. The composite conductivity seems to indicate that the carbon conductivity is more
close to I than 3 X 104 {l - I cm - I.
The magnitudes of the experimental composite dielectric constants do not seem to fall within the bounds predicted
by Eq. (2). However, the general frequency dependence of
the experimental results seem to run reasonably parallel to
those 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 of chainlike aggregates structures showed drastically different percolation thresholds. The highest structure carbon black
(Ketjen Black) with lowest packing efficiency reaches its
electrical percolation with the lowest volume fraction loading.
The percolation behavior of spherical carbon blacks
showed good agreement with the Bruggeman's effective-medium theory in terms of both the percolation threshold and
the frequency dependence of conductivity at percolation.
Further loading of carbon black beyond the percolation
threshold yields a single-phase structure with metal-like
electrical properties. This structure can be achieved by loading with both the spherical and aggregate forming carbon
blacks.
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 3 X 104 {l -lcm -1, suggesting that
scattering due to defects within the carbon black grains
hinders 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 different
frequencies. It was also demonstrated that more understand-
I 0 3 ~---------------------------,
2
10
FIG. l2(a). The measured am
as a function of frequency of
PVC/SRF-S composite at
35% (filled circles) and 40%
(filled triangle) by weight of
carbon black loading. The
theoretically predicted frequency dependence of am at
percolation (,pc = 1/3) when
the a c are assumed to be 1.0
11 - I cm - I (unfilled squares)
and 3 X 104 n - I cm - I (filled
squares), respectively. A reasonably
good
agreement
between the measured and calculated data is evident for the
theoretical prediction with
ac-I.On- 1 cm- I .
10
(T
.. .......
(40 o/.Clt.
.
(T
(ac: 1.0 n-1cm· l )
... -10·3I
L
0.1
o-(35%Cl
...L
1.0
J-
.J..
10
100
---l_------'
1000
10,000
( MHz)
6878
J. Appl. Phys. Vol. 53, No. 10, October 1982
Chung, Saba, and Pica
6878
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w
FIG. 12(b). The measured
as a function offrequen·
cy for PVC/SRF·S composite at 35% (unfilled cir·
cles) and 40% (unfilled
triangles) by weight of carbon black loading. The
agreement is not as good as
in the case the bulk conductivity. The unfilled and
filled hexagons represent
the theoretically predicted
results for u = 1.0 and
3X lif n -, em-I, respec·
tively.
Em
e
E
Q,,_
E
".I::.: •.. .t!. ..
I 35%cP---o-- -0- -<>-...:~:..: .t!.." "~".
.
-0-.
".
'n- -0-
10
0.1
1.0
10
f
100
10,000
(M Hz )
ing on the composite structure can be obtained with the combined knowledge of electrical conductivity and permittivity.
Structures of the composites (such as connectivity between
conductive fillers) as inferred from these electrical characteristics are also useful in the understanding of other physical
properties (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", AlP
Conf. Proc. 40, 2 (1978).
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lC. Rajagopal and M. Satyam, J. Appl. Phys. 49,5536 (19781.
4R. M. Simon, Polym Plast. Technol. Eng. 17, 1(19811.
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"E. K. Sichel, J. I. Gittleman, and Ping Sheng, J. of Electron. Mater. (to be
published).
'OC. J. Martin, M. J. Voelker, R. J. Ryan, U. S. Patent 4 228 050 (1980).
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ilK. W. Wagner, Arch. J. Elektrotech. 2, 371 (1914).
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'5L. K. H. Van Beek, Prog. Dielectr. 7, 69 (1967).
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"B. E. Springett, Phys. Rev. Lett. 31, 1463 (1973).
I "Technical booklets on: (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.
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2'J. V. Milewski, Ph.D. thesis, Rutgers University, 1973.
Chung, Saba, and Pica
6879
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