mass attenuation coefficients, effective atomic numbers and effective ...

Radiation Protection Dosimetry (2013), Vol. 153, No. 1, pp. 127– 134 Advance Access publication 29 May 2012

doi:10.1093/rpd/ncs091

NOTE

MASS ATTENUATION COEFFICIENTS, EFFECTIVE ATOMIC NUMBERS AND EFFECTIVE ELECTRON DENSITIES FOR SOME POLYMERS Nil Kucuk1,*, Merve Cakir1 and Nihat Ali Isitman2 1 Department of Physics, Faculty of Arts and Sciences, Uludag University, Gorukle Campus, 16059 Bursa, Turkey 2 Department of Metallurgical and Materials Engineering, Middle East Technical University, TR-06531 Ankara, Turkey

Received February 11 2012, revised May 1 2012, accepted May 3 2012 In this study, the total mass attenuation coefficients (mm) for some homo- and hetero-chain polymers, namely polyamide-6 (PA-6), poly-methyl methacrylate (PMMA), low-density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) were measured at 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV photon energies. The samples were separately irradiated with 241Am, 22Na, 137Cs and 60Co (638 kBq) radioactive gamma sources. The measurements were made by performing transmission experiments with a 200 3200 NaI(Tl) scintillation detector having an energy resolution of 7 % at 662 keV gamma ray from the decay of 137Cs. The effective atomic numbers (Zeff ) and the effective electron densities (Neff ) were determined experimentally and theoretically using the obtained mm values for the investigated samples. Furthermore, Zeff and Neff of each polymer were computed for total photon interaction cross-sections using theoretical data over a wide energy region from 1 keV to 10 MeV. The experimental values of the selected polymers were found to be in good agreement with the theoretical values.

INTRODUCTION Polymers play an important role in primary and secondary protection against gamma radiation, in particular, when a shield material is required to prevent the personnel from being exposed to scattered radiation from materials along the path of the photon source. From a practical point of view, polymers used as the matrix of metal- or metal-oxide-filled polymer composites can provide flexibility, ease of shaping, significant cost effectiveness and stability against chemicals and the environment. In order to interpret the behaviour and performance of polymer composites in radiation shielding applications, it is important to identify their photon energy absorption parameters such as mass attenuation coefficients (mm), effective atomic numbers (Zeff ) and effective electron densities (Neff ). The mm is a measure of probability of interaction that occurs between incident photons and matter in a given mass-per-unit area thickness of the material encountered. It is a basic quantity used in the calculation of photon penetration and energy deposition in biological, shielding and other dosimetric materials(1). The magnitude of mm depends on the incident photon energy, the chemical structure and bonding in the absorbing material and parameters such as thickness and density. Accurate values of mm for gamma rays in several materials are of great

importance for industrial, biological, agricultural and medical studies. Moreover, a number of related parameters can be derived from mm such as the mass energy-absorption coefficient, the total interaction cross-section, the molar extinction coefficient, Zeff and N(2) eff . Zeff represents radiation interaction with matter and is a convenient parameter to consider in designing radiation shields, and computing absorbed dose, energy absorption and build-up factor. Compounds or mixtures can be characterised by Zeff, providing insight about photon interaction processes involving absorption as well as scattering. Many researchers have made extensive Zeff studies on a variety of materials such as dosimetric materials(3 – 5), alloys(6 – 13), semiconductors(14 – 16), superconductors(17 – 21), building materials(22), glasses(23 – 25), steels(26), soils(27), amino acids(1, 28), fatty acids(29 – 31), minerals(32, 33), biological samples(34 – 37), etc.. However, only a limited amount of work has been reported in the literature on Zeff of polymers(38, 39). Therefore, this work concentrates on the calculation and experimental verification of photon absorption characteristics of five different polymers. The mm, Zeff and Neff values were calculated at photon energies in the range 1 keV–10 MeV and results were compared with the measurements obtained at photon energies of 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV.

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N. KUCUK ET AL.

COMPUTATIONAL WORK The computational work of mm, Zeff and Neff for five different polymers is as follows:

Computation of mass attenuation coefficients (mm) If a material of thickness x is placed in the path of a beam of gamma radiations, the intensity of the beam will be attenuated according to the Beer– Lambert’s law: I ¼ I0 emx

Using the mm of a material consisting of different elements, the effective atomic number Zeff can be obtained by the following relation(2):

¼ I0 e

mm d

Zeff ¼

ð5Þ

where st and se is the total atomic cross-section and the total electric cross-section, respectively. The total atomic cross-sections ðst Þ can be obtained using the following relation(43):

st ¼

ð2Þ

where d (g cm22) is the mass thickness of the sample (the mass per unit area). The total mm values for different polymers are obtained by the following rule of mixture equation: X Wi ðmm Þi ð3Þ ðmm Þpolymer ¼

st se

1 ðmm Þpolymer P NA i Wi =Ai

ð6Þ

where NA is the Avogadro’s number. The total electric cross-section ðse Þ is given by the following formula(2):

se ¼

1 X fi Ai ðmm Þi N A i Zi

ð7Þ

i

where Wi is the fractional atomic mass of the elements and (mm)i is the mass attenuation coefficient for the individual elements in the polymer. This well-known mixture rule is valid with the assumption that the effects of molecular binding and the chemical and crystalline environment are negligible. For materials composed of multi-elements, the fraction by atomic mass is given by ni Ai Wi ¼ P j nj Aj

where fi is the number fraction of atoms of element i and Zi is the atomic number of the ith element in the mixture or compound. Computation of effective electron densities (Neff ) The effective electron density (Neff ) can be calculated using the following expression: Neff ¼

ð4Þ

where Ai is the atomic weight of the ith element and ni is the number of formula units. The mm values for elements (Z¼1–92) and some additional substances of dosimetric interest can be found in the tabulation by Hubbell and Seltzer(40) for a wide energy range of 1 keV–20 MeV. Instead of interpolating tabulated values and using the mixture rule, some computer programs such as WinXcom or its predecessor XCOM is definitely less-time consuming. The XCOM program was originally developed by Berger and Hubbell(41) for calculating mass attenuation coefficients or photon interaction cross-sections for any element, compound or mixture in the energy range 1 keV–100 GeV. Later,

X ðmm Þpolymer NA Zeff ni ¼ Ai se i

ð8Þ

EXPERIMENTAL PROCEDURE Mass absorption coefficients of polyamide-6 (PA-6), poly-methyl methacrylate (PMMA), low-density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) were determined by transmission experiments schematically shown in Figure 1. The structural (monomer) units and densities of the polymers are given in Table 1. The samples were separately irradiated with 241 Am (59.5 keV), 137Cs (661.6 keV), 22Na (511 and 1274.5 keV) and 60Co (1173.2 and 1332.5 keV) cylindrical radioactive gamma sources. Each source

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I ¼ I0 e

Computation of effective atomic numbers (Zeff )

ð1Þ

where I0 and I are the un-attenuated and attenuated photon intensities, respectively, and m (cm21) is the linear attenuation coefficient of the material. A more convenient parameter coefficient characterising a given material is the density-independent mass attenuation coefficient [mm ¼ m/r (cm2 g21)]. ðm=rÞrx

this well-known and widely used program was enhanced and transformed to the Windows platform by Gerward et al. under the name WinXcom(42). All computations in the present work have been carried out using the WinXcom program.

EFFECT OF RADIATION ON SOME POLYMERS

has an activity of 638 kBq. For detection purposes, a 200 200 cylindrical NaI(Tl) detector was used having an energy resolution of 7% at 662 keV gamma ray from the decay of 137Cs, connected to a multi channel analyzer system (Canberra Series 40 MCA). The detector was placed in a step-down shield made from Pb to minimise the detection of any radiation coming directly from the source and scattered from the surroundings. The distance between source and detector was kept fixed at 50 mm. The polymer samples were placed one by one between the source and detector. The transmitted spectra were recorded by the MCA during sufficient time for the desired precision and accuracy of the results. The peak areas were calculated from the spectra recorded for each polymer. The mm values of the polymers were also determined by measuring the gamma attenuation through a known thickness of the polymer for 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV gamma rays. The measurements were repeated five times for each energy value and arithmetic mean values were reported. RESULTS AND DISCUSSIONS The mm values for all the selected polymers were calculated at photon energies of 1 keV–10 MeV. The results were compared with the measurements for the photon energies of 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV. This is depicted in Figure 2 where theoretical and experimental results are in good agreement for all studied polymers. Figure 2 shows that mm values are large and show a decreasing trend with strong energy dependence in the low incident photon energy range of 1– 30 keV. In the intermediate (30 keV–1 MeV) and high (1– 10 MeV)

Table 1. The monomer units and densities of polymers. Polymers

Monomers r (g cm23)

Polyamide-6 (PA-6) Poly-methyl methacrylate (PMMA) Low-density polyethylene (LDPE) Polypropylene (PP) Polystyrene (PS)

C6H11ON C5H8O2 C2H4 C3H6 C2H3

1.14 1.18 0.91 –0.93 0.855 1.045

energy regions, mm values show less energy-dependent behaviour and gradually decrease with increasing incident photon energy. Figure 3 shows the incident photon energy dependence of measured mm values for all studied polymers. Standard deviation of the maximum errors in the measured values is calculated to be ,2%. The total experimental uncertainty of the mm values are mainly due to counting statistics, thickness measurements, the evaluation of peak areas, scattered photons reaching the detector. It can be stated that mm depends on photon energy as the partial photon –matter interactions such as photoelectric absorption, Compton scattering and pair production in nuclear and electric fields differ with incident photon energy. Due to predominant photoelectric absorption, mm values show strong incident photon energy dependence in the low-energy range since mm is inversely proportional (1/E 3.5 dependence) to incident energy. The differences observed in mm values for polymers in the lowenergy region can be attributed to dominating photoelectric absorption since photoelectric crosssection is strongly dependent (Z 4 or Z 5 dependence) on atomic number of constituent elements(38, 44).

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Figure 1. The schematic arrangement of the experimental setup. This figure appears in colour in the online version of Radiation Protection Dosimetry.

N. KUCUK ET AL.

Figure 3. Measured mass attenuation coefficients of polymers at 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV. This figure appears in colour in the online version of Radiation Protection Dosimetry.

Compton (inelastic) scattering starts to predominate over the photoelectric absorption process when the incident photon energy exceeds around 30 keV up to around 1 MeV. In this intermediate energy range, no significant differences in the behaviour of different polymers is observed since composition effects play a less significant role in Compton scattering (linear Z dependence) relative to photoelectric absorption. In the high-energy region, pair production processes in nuclear and electric fields come into prominence after certain thresholds above 1 MeV are exceeded,

and therefore energy dependence of mm changes its slope relative to the intermediate energy region. The Zeff values for all the selected polymers have been calculated at photon energies in the range 1 keV–10 MeV using Eq. (5) and the results have been plotted in Figure 4 where good agreement was obtained between theoretical results and measurements performed at the photon energies of 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV. The Zeff values show a gradual increase at around 30 keV due to a change in the partial photon interaction

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Figure 2. The calculated mass attenuation coefficients of polymers within the 1 keV–10 MeV photon energy range and comparison with the measurements. This figure appears in colour in the online version of Radiation Protection Dosimetry.


Figure 5. The effective electron density of polymers as a function of photon energy. This figure appears in colour in the online version of Radiation Protection Dosimetry.

mechanism and remain almost constant up to the incident photon energy of 10 MeV. The selected polymers are made up of different constituent elements (1H, 6C, 7N and 8O) with different weight fractions (as shown by the monomer units in Table 1) and hence possess different Zeff values except for LDPE and PP, for which the same mm value has been observed throughout the investigated energy range. As expected, the Zeff values of polymers lie within the range of atomic numbers of their constituent elements (1 , Zeff , 8). The Neff values for the studied selected polymers in the photon energy range of 1 keV–10 MeV have been calculated using Eq. (8) and experimental results showed good agreement with theoretical

values (Figure 5). There are slight differences in Neff values for different polymers where a higher value of electron density would indicate an increased probability of photon –electron energy transfer and energy deposition into the material. The Neff values show similar photon energy dependence to what has been observed for Zeff. This is confirmed in Figure 6 showing correlation of Zeff and Neff obtained from theoretical calculation and experimental results. CONCLUSION It can be concluded from this work that the mm, the Zeff and the Neff depend on photon energies and chemical composition of investigated polymers.

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Figure 4. The effective atomic number of polymers as a function of photon energy. This figure appears in colour in the online version of Radiation Protection Dosimetry.

N. KUCUK ET AL.

Good agreement was observed between theoretical calculations and experimental results. The photon energy and compositional dependence of mm is remarkable in the low incident energy range due to predominant photoelectric absorption mechanism. Compositional effects and incident photon energy dependencies are reduced in the intermediate-tohigh-energy range since Compton scattering and pair production processes start to dominate the photon absorption process, respectively. Among the investigated polymers, photon absorption effectivity increases in the order PMMA . PA6 . PS . LDPE ffi PP. PP and LDPE demonstrate poor photon absorption characteristics (low mm and Zeff ) and are prone to degradation upon exposure due to significant photon –electron energy transfer (high Neff ) making them least likely to be used as the matrix material of polymer composites for gamma radiation shielding applications. On the other hand, PA-6 and PMMA have good photon absorption characteristics (high mm and Zeff, low Neff ) in addition to their better mechanical and thermal properties. Our future work will focus on the calculation of energy absorption and exposure build-up factors in an attempt to evaluate different polymers for radiation shielding purposes.

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FUNDING This work was supported by the Commission of Scientific Research Projects of Uludag University, Project Number UAP(F)-2010/28. 132

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