Frequency dependence of the electrical conductivity and dielectric constants of polycarbonate (Makrofol-E) film under the effects of γ-radiation

doi:10.4236/ns.2011.312129

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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; [email protected]

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:

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.





















(5)

















  (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:

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:

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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