Pertanika 6(3),95-98 (1983)

Determination of Effective Atomic Number of Rubber

ELIAS SAlON, ZAINAL ABIDIN SULAIMAN, ANUAR AHMAD and HUSIN WAGIRAN1

labatan Fizik, Fakulti Sains dan Pengajian A lam Sekitar,Universiti Pertanian Malaysia, Serdang, Selangor, Malaysia.

Key words: Gamma ray attenuation coefficient; effective atomic number; electron density.

RINGKASAN

Kertas ini melaporkan suatu cara mudah untuk menentukan nombor atom berkesan bahan getah.Pekali pengecilan linear sinar gamma bagi getah telah diukur dengan menggunakan pengesan Si(Li) yangmempunyai peleraian tinggi bagi sinar gamma bertenaga rendah dan nombor atom berkesan telah ditentu­kan dengan nisbah fungsi pekali pengecilan sinar gamma pada tenaga yang berbeza. Kajian ini dapat mem­beri panduan untuk memahami mutu getah berdasarkan kepada kandungannya.

SUMMARY

This paper reports a simple technique to determine the effective atomic number of rubber materials.The gamma ray attenuation coefficient of rubber was measured with high energy resolution Si(Li) detectorat low gamma ray energies and the effective atomic number was determined by the functional ratio ofattenuation coefficients at different energies. This study could provide a guide to an understanding of thequality of rubber based on its composition.

INTRODUCTION

The concept of effective atomic number isnot valid over a wide range of gamma ray energies(Jackson, 1982). Nevertheless, over a limited rangeof photon energies it is an important quantitywhich can be used in diagnostic study to analysethe atomic composition of composite materials.The simplest way to determine the effectiveatomic number is by the technique first describeby Spiers (1946) and later by Weber and Van derBerge (1969) based on the linear attenuations ofX-rays in matter. Using a polychromatic X-raybeam they were able to measure the effectiveatomic numbers of some body tissues. The tech­nique was further improved by Rutherford et al.(1976) using a computerised assisted tomography(CAT) EMI scanner developed by Hounsfield(1973) and were able to determine the atomicnumbers and electron densities of brain tissues andtumours. In 1977, White noted that the effectiveatomic numbers are energy dependent and deter­mined the effective atomic numbers of biologicaltissues and their substitutes at different energies.

A similar technique was employed for rubbermaterials, the effective numbers of which areexpected to be very close to those of biologicaltissues. In this work, we used gamma rays ofthree different energies from an 241 Am gammaray source to determine the linear attenuationcoefficients of rubber sheets with different per­centages of carbon content. The effective atomicnumber thus determined is dependent to someextent on the experimental arrangement as wellas the parametrisation described through equa­tions (4) and (5) below. Despite this, the choiceof geometry of the experiments as well as theparameters is such that the effective atomicnumber thus determined is close to the properlyweighted mean atomic number of the samples.

THEORY

The interaction of a gamma ray photonwith matter is largely dependent on its ability totransfer energy in its path through matter. Fol­lowing the interaction processes, the intensity

1 Jabatan Fizik. Fakulti Sains, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia.

Key to authors' names: S. Elias, S. Zainal Abidin, A. Anuar and W. Husin.

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S. ELIAS, S. ZAINAL ABIDIN, A. ANUAR AND W. RUSIN

of the gamma ray photons in a good geometryexperiment is attenuated in accordance with thefollowing relationship.

1=10 expo (-px) (1)

atomic number Z and the effective. number bfatoms per unit volume N. The final equation canbe rewritten as;

-3'30 ~4.47 ~ ~ ~

,u(E) = 28.44E Z N + 0r.(E) Z N +

By making measurements of p at three differentenergies, the effective electron density ZN canthen be evaluated.

where a i is the relative electron fraction of ele­ment i. Therefore, equation (7) can be expressedin the form of

(8)

(7)

(9)

-1'78 ~2.50 ~

3.l8E Z N

1

Z =(L. a. Z!l-l )n-11 1 1

The value of Z could be obtained since thefunctional ratio of p(E2 ) and p(E2 ) would be

p(E2 ) p(E3 )

satisfied only by one real value of Z.

The effective atomic number had been givenby Spears (1946), Cho et aI. (1975) and White(1977) as

(2)

In the low energy range « 100 keV), theattenuation is mainly due to photoelectric absorp­tion in which the gamma ray photons interactlargely with the innermost electrons of the atomand Compton scattering involving the outerelectrons which can be considered as free electrons.The interaction also includes coherent scatteringbut in the energies considered here the effect ofmolecular binding can be neglected. Thus the totalcross-section can be written as:

where 0i is the atomic cross-section for the re­moval of gamma ray photons from the beam byatoms of type i and Ni is the number of atoms oftype i per unit volume.

where I is the transmitted intensity, 10 is theincident intensity, x is the absorber thickness andp is the linear attenuation coefficient of the absor­bing material. For a compound material, theattenuation coefficient is related to its atomiccomposition and is given by:

The energy E is in keY. Thus equation (3) be­comes

For a composite material two parameters aredefined (Spiers, 1946), namely the effective

-3.30 4·47

p(E)= 28.44E L Zi Ni + 0c(E) L Zi Ni +-1.78 2.50

3.l8E L Zi Ni (6)

EXPER]MENTALPROCEDUREThe linear attenuation coefficients for four

different types of rubber samples were determinedseparately by transmission measurements of acollimated 241 Am source at three energies 17.8 keY,26.4 keY and 59.5 keY. The experimental arrange­ment employed a lithium drifted silicon Si(Li)detector, a preamplifier, an amplifier and a multi­channel analyser (MCA) as shown in Fig. 1. Thecollimator was 5mm in diameter bored througha 5 em X 5 em X 6 cm lead block. The radiationsource was deliberately chosen to be of lowintensity, namely 1.43 X 106 Bq. The countingtime of 5 minutes was used although this couldeasily be increased. In the intensity determination,the· number of counts in the photopeak of thespectrum, was measured at a fixed geometrycorresponding to the source-detector distanceused in the efficiency determination of the detec­tor. When there was no sample between the sourceand the detector, the intensity was taken as theinitial intensity. The experiments were repeatedfor different thicknesses. The rubber sampleswere supplied by the Rubber Research Institute ofMalaysia (RRI) and were in the form of sheet ofthickness 0.240 ± 0.005 cm.

(4)

(5)

P -3·30 4.47

0i (Zi ' E) = 28.44 E Zi

and

The cross-sections in the gamma ray con­sidered here can be expressed in the functionalform of ° = kE- ffi Zn which can be fitted tostandard data for the region of energy and atomicnumber of interest. Using the compiled data byVeigele (1973) and optimizing for carbon, theresulting expressions are;

O(Zi' E) = Oi(Zi' E) + 0c (E)Zi +oi(Zi' E) (3)

where Oi(Zi' E) and 0c(E) -are respectively thephotoelectric and Compton cross-sections forgamma rays of energy E and 0i (Zi' E) is thecontribution from coherent scattering.

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DETERMINATION OF EFFECTIVE ATOMIC NUMBER OF RUBBER

1. VerticalSi (Lil detector2. Preamplifier3. Linear amplifier

4. High voltage5. Multichannel analyzer6. Readcut

Leadhousing

to detector

sample

Fig. '1. Experimental set-up and sample holder.

RESULTS AND DISCUSSION

The linear attenuation coefficients at differentenergies and the effective atomic number of rubbersamples were tabulated in Table 1. The calcula­tions were performeq on the ZENITH data systemof the Physics Department, Universiti PertanianMalaysia.

The effective atomic number of pure rubberwas found to be 4.99 ± 0.04. Since the majorelemental composition of pure rubber is carbonand hydrogen, the effective atomic number isexpected to be less than that of carbon atom(Z = 6). By equation (8) and considering only the

photoelectric absorption effect the calculatedvalue was found to be 4.8. This value was basedon cis-1-4-polyisoprene structure which contri­butes as much as 95 percent of natural rubber. Theeffective atomic number of sulphur vulcanisedrubber is higher at the lower percentage of carboncontent and approaches the atomic number ofcarbon as more carbon is added.

We were unable to make a direct comparisonwith previous results due to the absence ofpublished reports of studies on rubber. All previousdata were concentrated on biological materialsand their substitues such as fats, muscles, bones,water and saline solution. The effective atomic

TABLE 1The linear attenuation coefficients at different energies of gamma rays and

the effective atomic numbers of rubber materials for different percentages of carbon content.

%CarbonSample

Pure rubber

Sulphur

Vulcanised

Rubber

a

25

50

75

Energy (keV) J1 (cm-1 )

17.7 0.388 ± 0.005

26.4 0.188 ± 0.005

59.5 0.096 ± 0.001

17.7 0.794 ± 0.005

26.4 0.348 ± 0.005

59.5 0.168 ± 0.005

17.7 0.740 ± 0.005

26.4 0.318 ± 0.005

59.5 0.136 ± 0.005

17.7 0.706 ± 0.005

26.4 0.284 ± 0.005

59.5 0.116 ± 0.005

97

z

4.99

8.66

7.05

6.62

S. ELIAS, S. ZAINAL ABIDIN, A. ANUAR AND W. HUSIN

number of fats was found to be 5.6 (Spiers, 1946),6.0 (Rutherford et aI., 1976) and 5.95 (White,1977). The higher effective atomic num ber of fatscompared with that of pure rubber is possiblydue to the presence of oxygen.

CONCLUSIONThe effective atomic number of rubber

has been measured using a collimated gamma raytransmission method. Because of its simplicitythis technique offers a good non-destructivemethod in the measurement of effective atomicnumber of composite materials as an indicationof their atomic compositions.

ACKNOWLEDGEMENTThis report is part of a final year B.S. degree

project of the Physics Department, UniversitiPertanian Malaysia. The authors wish to thank thePhysics Department, Universiti Tekno10gi Malaysiafor the use of instruments and discussions. Thecooperation of the Rubber Research Institute insupplying the rubber samples is very much appre­ciated.

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REFERENCES

CHO, Z.H.; TSAI. C.M. and WILSON. G. (1975): Studyof contrast and modulation mechanisms in X-rayPhoton Transverse Axial Transmission Tomography.Phys. Med. BioI. 20,879-889.

HOUNSFIELD. G.N. (1973): Computerized transverseaxial scanning (tomography). Part 1. Description ofsystem. Brit. 1. Radiol. 46, 1016-1022.

JACKSON. D.F. (1982): X-ray attenuation coefficientsfor Elements and Mixtures. Proc. 2nd. Int. Symp.Radn. Phys. and references therein.

RUTHERFORD, R.A.; PULLAN. B.R. and ISHER­WOOD. I. (1976): Measurement of effective atomicnumber and electron density using an EMI scanner.Neuroradiology 11, 15-21.

SPIERS. F.W. (1946): Effective atomic number andenergy absorption in tissues. Brith. 1. Radiol. 19,52-63.

VEIGELE. WM. J. (1973): Photon cross section from0.1 keV to 1 MeV from elements Z = 1 to Z = 94.Atomic Data Tables 5, 51-111.

WEBER. J. and VAN DEN BERGE. (1969): The effectiveatomic number and calculation of the compositionof phantom materials. Brit. 1. Radiol. 49, 378-383.

WHITE. D.R. (1977): An analysis of the X-dependence ofphoton and electron interaction. Phys. Med. BioI.22,219-229.

(Received 13 June, 1983)