Vol.3, No.12, 1034-1039 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.312129
Frequency dependence of the electrical conductivity
and dielectric constants of polycarbonate (Makrofol-E)
film under the effects of γ-radiation
Soad Fares (s.fares)
National Center for Radiation Research and Technology (NCRRT), AEA, Nasr City, Egypt;
Received 20 September 2011; revised 22 October 2011; accepted 2 November 2011.
ABSTRACT
Irradiation effects of γ-radiation on the physical
and electrical properties of polycarbonate (Ma-
krofol-E) film has been studied to be able to
investigate the dielectric response of irradiated
polymers for a wide range of fluence and fre-
quency. The dielectric constant (ε') The loss
tangent (tanδ), dielectric loss factor (ε''), the a.c
electrical conductivity (σ) and the relaxation
time (τ), were measured in the frequency range
from (40) Hz to (4) MHz. These samples were
irradiated by means of γ-rays from 10 up to 200
KGy. The change in different properties as a
function of absorbed dose was studied. Degra-
dation of the polymers leading to amorphisation
was observed by increasing the absorbed γ-
dose. The induced changes in the electrical
conductivity due to γ-rays irradiation of Makro-
fol-E provide a better method for γ-dose meas-
urements. A semi-empirical equation was de-
veloped to use Makrofol-E as a dielectric do-
simeter. Furthermore, Makrofol-E has much
greater resistance to radiation damage; the at-
tained results suggested strongly the applica-
bility of Makrofol-E to be used in medical prod-
ucts applications.
Keywords: Gamma-Ray; Dose-Response; PC
Polycarbonate; Makrofol-E Chain Scission; Cross
Linking; a.c Electrical Conductivity; Dielectric
Constant and Dielectric Loss
1. INTRODUCTION
Polymeric materials are unique because of the range
of structural forms that can synthesized and the way in
which changes can be made in the structure in local or
general way. Polymer composites have steadily gained
growing importance during the past decade. Appreciable
gain in the knowledge of the structure of such materials
has been accomplished through electrical conductivity
measurements. Also external parameters, such as the
effect of γ-radiation, play a role in the electrical behavior
of such polymer [1].
The irradiation of polymeric materials with ionizing
radiation (gamma rays, X rays, accelerated electrons, ion
beams) leads to the formation of very reactive interme-
diates products (excited states, ions and free radicals),
which result in rearrangements and/or formation of new
bonds. The effects of these reactions are formation of
oxidized products, grafts, scission of main chain (degra-
dation) or cross-linking. Often the two processes (deg-
radation-cross-linking) occur simultaneously, and the
outcome of the process is determined by a competition
between the reactions [2,3]. Oxidation and degradation
occur gradually with increasing irradiation dose.
Different polymers have different responses to radia-
tion, which are intrinsically related to the chemical
structures of the polymers. Polymers with more hydro-
gen atoms on side (e.g., polyethylene) tend to cross-link
with radiation. Polymers with a methyl group (e.g.,
polypropylene), disubstitutions (e.g., polymethacrylate)
and per-halogen substitutions (e.g., polytetrafluoroeth-
lene) would more likely undergo degradation with radia-
tion. Aromatic polymers with benzene rings either in the
main chain or on the side (e.g., polycarbonate) are usu-
ally radiation resistant [4]. Polycarbonate (PC) is a well-
known engineering thermoplastic with an excellent bal-
ance of optical, physical, mechanical, and processing
characteristics [5]. Polycarbonate detectors are used as a
particle track detector for neutrons and alpha particles
detection [6,7]. Moreover, radiation effects on dielectric
properties are of particular interest to science and tech-
nology and they have many applications in modern en-
gineering [8-11], and the effect of ion irradiation on the
dielectric properties of polymers has been also studied
earlier [12-14].
It is well known that irradiation enhance the electrical

S. Fares / Natural Science 3 (2011) 1034-1039
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conductivity in insulating polymers. This increase in
conductivity is attributing to the amplifications of con-
jugated structure, i.e. fairly great electron freedom. The
irregularity in the polymer chains may also give rise to a
hopping mechanism which will enhance the conductivity.
Among many dielectric of capacitors P. P, PFT films has
greatly reduced the volume of the capacitors because of
its large electric strength together with its low dissipa-
tion factor (tanδ) [15]. The improvement of the dielectric
properties has been investigated by high electron irradia-
tion of these polymers [16].
The influence of radiation on the properties and per-
formance of a polymer differs according to whether the
material degrades or cross-links and this is in turn de-
pends on specific sensitivities or susceptibilities inherent
in the polymer backbone. All materials have been found
to break down at very high radiation doses, however, the
range of doses under which a given polymer will main-
tain its desirable properties depends greatly on the
chemical structure of the polymers. Indeed, below the
destructive level of exposure, radiation treatment can
impart many benefits and enhance properties of com-
mercial value [17-20].
Therefore in the present work I investigated experi-
mentally the radiation induced conductivity (RIC) for
Makrofol-E film—and by gaining sufficient knowledge
about these beneficial radiation, induced effect—which
are suitable for use as sensitive γ-dosimeter. A theoreti-
cal model is suggested to estimating the RIC in insulat-
ing materials.
2. EXPERIMENTAL PROCEDURE
Makrofol-E is a bisphenol-A polycarbonate of chemi-
cal composition (C16H14O3), with an average thickness
of 0.275 mm and the surface area of the sample is (0.612
cm2). Makrofol-E polycarbonate samples were irradiated
with different γ-doses at room temperature in air with
60Co-gamma cell. The applied radiation dose on the
Makrofol-E sample was (10 - 200) KGy. Makrofol poly-
carbonate samples were cut into square pieces and
coated with silver paste to achieve ohmic contacts. The
measurements of dielectric constant (


), dielectric loss
factor (

) and loss tangent tan(δ) before and after being
irradiated were measured using 3531 ZHITESTER (RLC)
digi bridge manufactured by HIOKI, E.E. Corporation,
having a frequency range of (40 Hz) up to (4 MHz) in
the room temperature. The dielectric parameters (


) and
(

) and the electrical conductivity (σ) were evaluate
using the conventional formula discussed [21,22]. These
formulas are:
0
Lc A


  (1)
tan1 Rwc

 (2)
tand





(3)


LAR   (4)
where
ε0: is the Permittivity of free space (= 8.85 × 10–12
F/m), ω: is the circular frequency L and A: are the thick-
ness and cross-sectional area of the samples respectively.
Tan(δ) data were obtained directly from the bridge
and from which (


) and (


) were calculated using Eqs.1
and 3. Measurements of (

) and (


) have been meas-
ured and calculated, so after obtaining these results, they
were applied in Debye, s equation [23].
where


s: is the dielectric constant in static field,



: is the
dielectric constant at the end of the frequency range
(minimum value of


), and τ: is the relaxation time.
Debye, s equation can be modified to give the dielec-
tric parameters in the form of straight line equation.
22
1
s












(5)


22
1
sc




 
  (6)

log loglog






 


 (7)
Eq.7 is more useful for higher frequencies [24]. From
the intercept of the straight line equation, the relaxation
time can be calculated.
3. RESULTS AND DISCUSSION
The various assumption made in our discussion can be
better appreciated by studying the variations of (


) with
frequency for different γ-doses. These variations for
Makrofol-E samples are depicted in Figure 1. Dielectric
constants (


) measurement were performed over fre-
quency rang from (40 Hz) to (4 MHz). Figure 1 shows
three responses frequency bands for Makrofol-E samples.
At all doses, the samples show that in the (0.2 - 1.2 MHz)
frequency range, the (


) slightly decreases as the fre-
quency increases. In the second band (1.2 - 1.7 MHz), it
seems to be (


) sharply increase which is due to the
main relaxation process. The third frequency band (1.7 -
4 MHz) shows that (


) sharply decrease with the fre-
quency, which is attributed due to the dielectric disper-
sion. As evident from the graph, the dielectric constants
remain almost constant up to 1.2 MHz and then decreases
at higher frequencies. At lower frequencies the motion
of the free charge carriers is constant and thus the di-
electric constant is constant. As the frequency increases,
the charge carriers migrate through the dielectric and get
trapped against a defect site and induce an opposite

S. Fares / Natural Science 3 (2011) 1034-1039 1036
Figure 1. Frequency dependence of the dielectric constant of
Makrofol-E samples at different radiation doses.
charge in its vicinity, as a result of which motion of
charge carriers is slowed down and the value of dielec-
tric constant decreases.
On the other hand, at all the frequency ranges, sig-
nificant changes have been observed in dielectric re-
sponse of Makrofol-E PC after irradiation, the (


) in-
crease by increasing the absorbed dose (10 - 200 KGY),
which is confirmed in Figure 2. Which shows the di-
electric constant versus log(f). The increasing of (


) as
the γ-doses increase may be attributed due to the oxida-
tive degradation and for the presence of oxygen in air
during irradiation.
The variation of dielectric loss factor (

) with fre-
quency at different γ-doses has been measured. These
variations for Makrofol-E samples are depicted in Fig-
ure 3. Which shows that more than one note relaxation
processes occur. At all, it is interesting to find that, the
increase of γ-dose decreases only the height of these
relaxation processes without any shift or effect on the
value of the relaxation time. Figure 3 shows the varia-
tion of (

) all over the frequency ranges. (


) rapidly
decreases in the frequency range (0.7 - 1.2) MHz for
Makrofol-E sample, (

) increases rapidly in high fre-
quency range with a wide band width, which is attribut-
able to Debye dielectric relaxation, due to a dipole rota-
tions caused by movements of the main backbone.
The variation of (

) all over the frequency ranges
shows that more than one relaxation process occurs. The
relaxation times data obtained from the analysis using
Eq.7 are listed in Table 1. From these calculations, it is
notice that, the parameters present of three relaxation
regions were defined as they lie within experimental
measurements. The three dielectric relaxation regions
(which lie approximately at resonance frequencies f
c =
0.5 MHz, fc = 1.77 MHz and fc = 2.93 MHz) are found to
be present for all investigated samples. On the other
Figure 2. Dielectric constant as a function of Log (Frequency)
for different gamma doses Makrofol-E samples.
Figure 3. Frequency dependence of the dielectric loss of
Makrofol-E samples at different radiation doses.
Table 1. Relaxation data of Macrofol-E film.
Dielectric
Relaxation
Region
fc MHz 1

 1

 τ Sec
1st 0.5 34.15 0.215 9.5 × 10–9
2nd 1.77 35.14 0.485 4.7 × 10–9
3rd 2.93 31.84 0.875 7.9 × 10–9
hand, Figure 4 illustrates the plot of

log




 ver-
sus


log



 of the Macrofol-E control sample, from
which the value of the mean relaxation time τ was ob-
tained, from the linear fitting equation, to be (τ = 2.1 ×
10–7 sec.).
Furthermore, it was noticed a small and activated phe-
nomena at low frequencies (1750 KHz) for Makrofol-E
sample, due to local motion of pieces of the polymer
backbone in agreement with the observations of Mary. C.
Wintersgill et al. [25], while the high peak is due to heat

S. Fares / Natural Science 3 (2011) 1034-1039
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Figure 4. Dielectric relaxation time for the Makrofol-E control
sample.
distortion, which appears at (2.8 MHz) [26,27]. In all
samples, the values of dielectric loss (

) are also found
to decrease by increasing the γ-radiation dose. The di-
electric loss is due to the perturbation of the phonon
system by an electric field, the energy transferred to the
phonons dissipated in the form of heat.
The variation of loss tangent (tanδ) with irradiation
dose (KGy) is shown in Figure 5. This figure represent
the loss behavior at low frequency ranges was found to
be appreciable, and no relaxation peaks are observed.
Figure 5 shows a liner decrease in (tanδ) with γ-doses
for the low frequency rang from 525 KHz to 1.2 MHz.
From such plots we can use its liners equation, which
represented by:
34
tan3.6 100.22 10D 

 
where (D) in KGy
It was observed at low frequency regions mentioned
before, as the frequency increases, the tan(δ) decreases
in these regions (at constant γ-dose), which means that,
these samples cannot be used as dielectric in capacitors.
The variation of the impedance with frequency for
different γ-doses is shown in Figure 6 for the samples
under consideration. It can be seen from this curve that
the impedance rapidly decrease by increasing frequency
until 1.5 MHz, above which it remains nearly constant
(1.05 MHz) for Makrofol-E sample The variation of a.c.
conductivity with frequency was found to obey the con-
ventional formula which discussed before [20]. The de-
pendency of conductivity at high frequency is repre-
sented in Figure 7. The increase in conductivity is due
to irradiation which attributed to scission of polymer
chains and as a result of the absence of dispersion in
permittivity of high frequency, suggests that the conduc-
tion mechanism is based on electronic hopping, creating
energetic free electrons, ions and free radicals [28].
The variation in conductivity with γ-radiation dose at
various frequencies for Makrofol-E samples studied
systematically. Figure 8 depict that the change in con-
ductivity, show that a slight increase in conductivity
Figure 5. Loss tangent versus gamma dose for Makrofol-E
samples at different frequency.
Figure 6. Impedance versus frequency for Makrofol-E samples
at different radiation doses.
Figure 7. The a.c Conductivity of the Makrofol-E samples
versus frequency at different radiation doses.

S. Fares / Natural Science 3 (2011) 1034-1039 1038
Figure 8. The a.c Conductivity of the Makrofol-E samples
versus radiation doses at various frequency values.
with radiation dose. Furthermore, a sharp increase in
conductivity was observed within the frequency rang (2 -
3.5) MHz. The increase in conductivity due to irradiation
may be attributed to scissioning of the polymer chains,
resulting in an increase of free radicals, unsaturation, etc.
Further more, Figure 8 depicts a linear relation be-
tween conductivity and radiation dose up to 200 KGy.
The empirical equation satisfied by this relation at fre-
quency (0.6 MHz), represented as:
95
7.25 101.2 10D 

 
where (D) in KGy. Which prove that, the induced
changes in electrical conductivity due to gamma irradia-
tion of Makrofol-E provide a better method for gamma
dose measurements.
4. CONCLUSIONS
Makrofol-E polycarbonate films were irradiated with
γ-radiation to study the modification in dielectric proper-
ties induced by irradiation. Ionizing radiation interacts
with polymers via two primary mechanisms, chain scis-
sion to reduce molecular weight and cross-linking to
generate large polymer networks. Both mechanisms oc-
cur and its effects vary from polymer to polymers and to
some degree from part to part, during irradiation, but one
generally dominates. Our experimental results of elec-
trical properties of the Makrofol-E samples prove that,
the samples vary in sensitivity to radiation. That is mean,
Makrofol-E polymer have much greater resistance to
radiation damage, so we suggest Makrofol-E to be used
in medical products applications. It has been observed
that under γ-irradiation, dielectric constant decreases
with frequency whereas dielectric loss shows random
behavior. It increases up to 2.8 MHz followed by a de-
crease up to 3.5 MHz.
5. ACKNOWLEDGEMENTS
The auther sincerely thanks prof. Dr.A.korna and Dr. S.M.Abdou,
Assi.Prof., for research faciliteis and helpful discussions which enabled
this work to be carried out. This work supported by the Departement of
Radiation Physics, National Center for Radiation Research and Tech-
nology (NCRRT), Cairo, Egypt, is also gratefully acknowledged.
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