Study on gamma shielding polymer composites reinforced with different sizes and proportions of tungsten particles using MCNP code

Progress in Nuclear Energy 115 (2019) 91–98

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Study on gamma shielding polymer composites reinforced with different sizes and proportions of tungsten particles using MCNP code

T

Hoda Alavian∗, Hossein Tavakoli-Anbaran Faculty of Physics and Nuclear Engineering, Shahrood University of Technology, Shahrood, P.O. Box 3619995161, Iran

ARTICLE INFO

ABSTRACT

Keywords: Filler proportion Filler size Transmission factor Flux buildup factor MCNP

Metal polymer composites (MPCs) are new category of advanced materials whose effectiveness in the field of radiation protection has been confirmed experimentally and theoretically. By using MCNP code, this paper describes a modified model to study effect of size and proportion of tungsten (W) particles on shielding properties of light density polyethylene (LDPE). Indeed, LDPE/W composite is composed of LDPE as a background in which W particles in different sizes and proportions are distributed. Accordingly, we designed a structure containing W particles in sizes of 100 nm, 1 μm, 10 μm, 100 μm and proportions of 1, 5, 10, 15, 20, 25 wt% inside LDPE matrix. Shielding properties of LDPE reinforced with W particles in terms of size and proportion of W have been discussed. The results showed that transmission factor increases sharply in low energy region up to the maximum, then follows a slow descending trend. It was found that the values of transmission factor decrease with an increase in the proportion of W, as it was observed in all W sizes. Besides, the lower the filler proportion is, the more significant the size effect occurs. To find more, we introduced a formula to compute relative reduction of transmission (RRT) from 1 to 25 wt% at each energy point. The maximum value of RRT occurred at 0.05 MeV which enhanced up to 89% while W proportion increased. Besides, the maximum buildup factor was observed at 0.1 MeV which is lower in LDPE/25 wt% W composites compared to 1 wt% ones. In other word, increasing W proportion up to 25 wt% resulted in decreasing the maximum buildup factors and this reduction was more notable in greater W sizes. Furthermore, it was proved that the filler proportion plays more effective role than the filler size in attenuating gamma rays.

1. Introduction Exposure to hazardous ionizing radiation can take place in a great number of fields such as nuclear power plants, accelerators, industrial dosimetry, research laboratory, agriculture, space technology, medical imaging, radiotherapy, and nuclear medicine (Kerur et al., 2009; Biswas et al., 2016; Ambika et al., 2017; Tarim et al., 2017). The emission of gamma radiation and X-rays almost accompany all types of ionizing radiation. Because they can produced through various processes including radioactive decay in radiation sources, bremsstrahlung caused by accelerated electrons, characteristic X-rays, annihilation, neutron inelastic scattering, and neutron capture (Evans, 1955), which make it extremely important to shield against them. Exploring gamma radiation shielding parameters of new materials has become progressively important in order to determine the most adequate material for protection the environment (Chen et al., 2015; Kaur et al., 2016a; Tekin et al., 2017, 2018a; Dong et al., 2017; Gaikwad et al., 2018, 2018b; Sayyed et al., 2018a, 2018b; Issa et al., 2018, 2019a, 2019b). Generally,

∗

attenuation behavior of gamma rays through a medium can be explained by cross-section of the most probable interactions: photoelectric effect, Compton scattering, and pair production (Evans, 1955). Because of the dependency of their cross-sections on atomic number, high Z materials are widely used in the field of gamma radiation shielding. Although applying lead (Z = 82) in protecting against gamma rays is common (Harish et al., 2009), its toxicity to the environment is a critical issue (Aral et al., 2015). Hence, tungsten (Z = 74) has been utilized as the best alternative to lead (Demier et al., 2017). Metal polymer composites (MPCs) are among the most frequently discussed advanced material utilized in attenuating gamma radiation in recent years. The MPC is basically a combination of metal filler bonding with a polymer matrix (Khan et al., 2016). Improved characteristics of the MPCs are provided as a result of uniformly dispersion of the high Z small sized particles inside the light and flexible polymer matrix. In fact, they meet both advantages; light-weight yet radiation protection effective. Many attempts have been made in order to investigate shielding properties of MPCs in both theoretical (Kim et al., 2014;

Corresponding author. E-mail addresses: [email protected], [email protected] (H. Alavian).

https://doi.org/10.1016/j.pnucene.2019.03.033 Received 29 July 2018; Received in revised form 15 January 2019; Accepted 17 March 2019 0149-1970/ © 2019 Elsevier Ltd. All rights reserved.

Progress in Nuclear Energy 115 (2019) 91–98

H. Alavian and H. Tavakoli-Anbaran

Azman et al., 2016) and experimental (Harish et al., 2009, 2012; Nambiar et al., 2013; Ambika et al., 2017; Chang et al., 2015; Ersoz et al., 2016) fields. Monte Carlo simulation is normally applied to test material effectiveness in radiation shielding before utilizing in practical implementations. MCNP is a popular Monte Carlo code widely used for the simulation of physical interactions between radiation and matter (Pelowitz, 2008). First theoretical calculations on shielding effectiveness of MPCs by using MCNP code were conducted in 2009 by a group of researchers from South Korea (Kim et al., 2009). In a major advance in 2014, they estimated transmission rate of gamma rays through micro- and nano-W dispersed polymer composites experimentally and theoretically. The results showed the nano-W composites increased attenuation up to 75% for 0.3 MeV incident photons compared to the micro-structured counterparts (Kim et al., 2014). Most of the literature on the shielding applications of MPCs has been focused on the effect of filler size on attenuating gamma radiation. It is believe that the nanosized filler can effectively increase the ability of composites to absorb and scatter photons because they disperse perfectly uniform within the polymer matrix as compared to micro filled composites (Harish et al., 2009, 2012; Kim et al., 2014; Azman et al., 2016). A growing body of studies has examined the filler size effect theoretically by using Monte Carlo method, yet there are some lesser-known areas. Evaluating the effect of filler proportion in polymeric matrix is one of these areas due to the role of density, chemical composition, and thickness of the absorbing material in attenuating gamma radiation (Degrelle et al., 2016). This paper describes a modified approach to consider effect of filler size (100 μm, 10 μm, 1 μm, and 100 nm) and proportion (1, 5, 10, 15, 20, and 25 wt%) on radiation protection ability of well-dispersed LDPE/W composites, simultaneously. The effect of W size and its proportion on shielding properties in terms of mass attenuation coefficient (μρ), mean free path (MFP), transmission factor (T), and buildup factor (B) in a wide energy range (0.015–15 MeV) has been investigated and discussed in detail.

2.2. MCNP simulation In this project, in order to study the shielding properties of LDPE polymer composite reinforced by micro- and nano- W particles against gamma radiation, MCNP has been hired. MCNP is a noted three-dimensional Monte Carlo code which utilizes extended nuclear crosssection libraries to model the interaction of radiation with materials (Pelowitz, 2008). The lattice (LAT) and universe (U) cards of MCNP have been used to define a polymer matrix homogeneously doped by a metal filler. In 2009, Kim et al. introduced a model involved in studying the effect of filler size on radiation attenuation (see Kim et al. (2009) for more details). The model assumed a slab subdivided into N number of cubes as a matrix and perfect spheres located in the center of each cubes as a filler whose lattice length and sphere diameter correspond to the medium concentration. Several studies, in last decade, have used the model to explore effectiveness of reinforced structures against radiation (Chen et al., 2015; Tekin et al., 2016a, 2016b; 2018a; Soltani et al., 2016). The sum of cube and sphere inside, the simplest repeating unit in the matrix, is called ‘unit cell’. In one hand, if the filler diameter in the model changes regardless to medium concentration, less packed structures is resulted parallel to belittling the size of sphere because the contribution of polymer becomes larger and uniformity of distribution decreases. Consequently, it is necessary to take the filler proportion into account. On the other hand, in experimental designs, proportion of filler in a composite are also studied, e.g. (Nambiar et al., 2013) which is not currently available in theoretical studies except for a few cases (Kim et al., 2009; Kim et al., 2014). To clarify the details, we describe an optimized model in which cube length concomitantly changes with sphere diameter resulting in more uniformly distributed filler within matrix. This model is applicable in cases studying different filler sizes and proportions simultaneously. In fact, we consider a unit cubic cell fell into two parts including a centered sphere and its surrounded space whose proportion are ωf and 1-ωf, respectively. The volume of sphere 4 which defined as 3 R3 has contribution of Vf in volume of unit cell (Vt = 1) that is determined by following relation;

2. Model and method

Vf =

2.1. Characteristics of LDPE/W composite

=

n i

1 ( i / i)

(1)

where ωi and ρi are weight fraction and mass density of ith component (filler and matrix) in the composite, respectively (Agarwal and Broutman, 1990). The description of composites, weight fractions, densities, and elemental compositions are given in Table 1.

Table 1 Description of LDPE/W composites. Composition description

Density (g/cm3)

Elemental composition (ele.: weight fraction)

99 wt% 95 wt% 90 wt% 85 wt% 80 wt% 75 wt%

0.954 0.992 1.044 1.102 1.167 1.239

W: W: W: W: W: W:

LDPE: LDPE: LDPE: LDPE: LDPE: LDPE:

1 wt% W 5 wt% W 10 wt% W 15 wt% W 20 wt% W 25 wt% W

0.062; 0.257; 0.422; 0.537; 0.622; 0.687;

C: C: C: C: C: C:

0.804; 0.637; 0.495; 0.397; 0.324; 0.268;

H: H: H: H: H: H:

+ (1

f )/ M

(2)

where ρf and ρM (g/cm3) are the mass density of filler and matrix (Wong and Bollampally, 1999). Taking the fractional volume of filler (Vf) into consideration, length of subdivided cubes were determined. Fig. 1 compares cross-section of designed structure when proportion of components (matrix and filler) are the same and filler diameter takes two different size. Accordingly, we have designed a model assumed each W particle of 100 nm, 1 μm, 10 μm, and 100 μm diameter as a sphere into a cube which its length was determined in line with the proportion of filler in the matrix. In addition, W particles were considered in LDPE matrix in proportions of 1, 5, 10, 15, 20, and 25 wt%. The formed repeated structure were totally fit inside a 20 × 20 × 2 cm3 slab, so given number of W particles have been added inside LDPE matrix. Table 2 describes the unite cell length (a), and number of unit cells inside the slab (N) in different sizes and proportions of filler. The slab with regular lattice structure has been considered between a source and detection area centered at the origin. A point isotropic source has been considered with photon energy in a wide range of 0.015–15 MeV which commonly used in photon calculations by the ANSI/American National Standard (ANS) standards. In fact, a monoenergetic gamma rays source of energy E (E = 0.015, 0.05, 0.1, 0.5, 1, 2, 5, 8, 10, and 15 MeV) has been defined at 10 cm in the left side of the sample. Considering illustrated conditions resulted in 250 calculations. To acquire photon flux amounts in the detection area (0.5 cm radius sphere), point flux tally F5 has been used which is a kind of variance reduction techniques. Simulation processes were run until the relative

The present study investigated the effects of W particles with density of 19.25 g/cm3 (AZoMaterial, 2002) in reinforcing the gamma shielding properties of LDPE marix with density of 0.945 g/cm3 (Peacock, 2000). According to weight fraction of elements, density of the composites (ρc) was calculated on the basis of the following relation; c

f/ f f/ f

0.134 0.106 0.083 0.066 0.054 0.045

92

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Fig. 1. Particulate model when filler size is larger in (a) compared to (b) while filler proportion is same.

Compton scattering process with cross-section proportional to Z/E cause to a photon scattering. Photon is scattered from a nearby free atomic electron, resulting in an attenuated photon and a scattered electron carrying the energy lost by the photon. In high energy region, dominant process is pair-production effect in which photon creates an electron-positron pair and then disappears. The pair production crosssection strongly depends on atomic number as Z2 and is also proportional to the incident photon energy as logE (Singh et al., 2014; Oto et al., 2017; Dong et al., 2017). Therefore, the higher the atomic number of medium is, the greater the probability of interactions. High Z materials make the most appropriate photon shielding consequently the best protection would be achieved. However, choosing the proper materials for making an effective protective shield against photons requires more precise investigations on shielding properties. Thereupon, in the present work, we have studied shielding properties including mass attenuation coefficient (μρ), mean free path (MFP), transmission factor (T), and buildup factor (B) of LDPE doped by different percentages of micro- and nano- W particles. Generally accepted WinXCom database (Berger and Hubbell, 1999) has been used to calculate mass attenuation coefficient (μρ) of composite on the basis of following relation;

Table 2 Characteristics of composite matrix in different sizes and proportions of filler. W size

W proportion (%)

Unite cell length (a, cm)

Number of unit cells in slab (N)

100 μm

1 5 10 15 20 25

10.185 × 10−2 5.874 × 10−2 4.587 × 10−2 3.934 × 10−2 3.508 × 10−2 3.191 × 10−2

757,169 3,946,466 8,290,670 13,139,579 18,523,899 24,627,508

10 μm

1 5 10 15 20 25

10.185 × 10−3 5.874 × 10−3 4.587 × 10−3 3.934 × 10−3 3.508 × 10−3 3.191 × 10−3

757,169,925 3,946,466,186 8,290,670,922 13,139,579,287 18,523,899,882 24,627,508,927

1 μm

1 5 10 15 20 25

10.185 × 10−4 5.874 × 10−4 4.587 × 10−4 3.934 × 10−4 3.508 × 10−4 3.191 × 10−4

757,169,925,967 3,946,466,186,184 8,290,670,922,544 13,139,579,287,095 18,523,899,882,952 24,627,508,927,471

100 nm

1 5 10 15 20 25

10.185 × 10−5 5.874 × 10−5 4.587 × 10−5 3.934 × 10−5 3.508 × 10−5 3.191 × 10−5

757,169,925,967,710 3,946,466,186,184,408 8,290,670,922,544,406 13,139,579,287,095,701 18,523,899,882,952,107 24,627,508,927,471,986

µ =

i (µ ) i i

(3)

where ω and μρ are fractional weight and mass attenuation coefficient of ith component of composite (Kaur et al., 2016b). Mean free path (MFP) is regarded as the average distance between two consecutive interactions of photon with material leading to reduced intensity of incident photon beam by a factor of 1/e (Singh et al., 2003). In addition, the linear attenuation coefficient (μ) which describes gamma rays absorbed or scattered per unit thickness of the material is obtained by multiplying mass attenuation coefficient and density of the material and measured in (cm−1). Thus, the MFP is simply calculated by inversing the total linear attenuation coefficient (Kaur et al., 2016b);

standard deviations has been observed less than 0.01. The MCNP calculations were completed by using Intel® Core™ i5-3337U CPU 1.80 GHz computer hardware. 2.3. Theory

MFP =

When a photon with energy of E is traveling through a medium with atomic number of Z, two events may happen: first, it penetrates without interacting; second, it undergoes different interactions including photoelectric absorption, Compton scattering, and pair-production effect which leads to absorption or attenuation (Evans, 1955). On the basis of the behavior of gamma radiation in the matter, the energy range can be divided into three regions. In low energy region, the photoelectric effect is dominant process and its cross-section is proportional to incident photon energy and atomic number as Z4−5/E7/2. In photoelectric effect, photon is absorbed by transferring all its energy to an electron placed in the inner atomic shells. In intermediate energy region, dominance of

1 µ

(4)

Transmission factor (T) is a ratio of transmitted photons in presence of W filler in LDPE matrix (IW/LDPE) to those passed through LDPE sample (ILDPE), which is indicated by relation (5);

T=

ILDPE / W ILDPE

(5)

Looking at the Lambert-Beer law, intensity of transmitted photons (I) through a medium when I0 shows intensity of incident photons depends on linear attenuation coefficient (μ, in cm−1) of the medium and its thickness (x, in cm). 93

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(6)

I = I0 exp ( µx )

In fact, the law is valid until three conditions are met: (i) monochromatic gamma rays, (ii) thin absorbing material, and (iii) narrow beam geometry (Singh and Badiger, 2013). The law would be invalid, providing any of the above conditions is not in the agreement. A correction factor, called ‘buildup factor’, is introduced to modify the law. (7)

I = I0 Bexp ( µx )

Buildup factor (B) which considers the influence of any scattered and secondarygamma rays in the medium, is defined as a ratio of total transmitted photons reached to detection area (It) to those passed through sample to detection area without interaction (Iu);

B=

It Iu

(8)

(Tsoulfanidis and Landsberger, 2010). The current study, examines a situation in which monenergetic photons are emitted by a point isotropic source toward a slab subdivided to cubic unit cells. Each cell includes a centered sphere as W particles and the surrounded space as LDPE matrix, as well. When a photon enters to a cell, the relative probability of interactions determine it collides with the filler particle, the matrix, or passes without interacting. If photon experiences an interaction, it may be absorbed or scattered. In case it scattered, it may undergoes consecutive scatterings in the cell or adjacent one until it is eventually absorbed or escaped out of the medium. Finally, the flux of photons reached to detection area is used to study the shielding properties. In order to calculate the shielding parameters, when the gamma rays with energy of E are emitted, total energy range is divided in such a way that length of each interval is 0.001. Total value of tally is estimated as the flux of total photons detected in desired point (It) and the value recorded in (E−0.001,E) step is considered as the flux of photons that reach the point of detection without interaction (Iu).

Fig. 2. Variation of mass attenuation coefficient (cm2/g) of WinXCOM as a function of photon energy for LDPE/W composites.

for LDPE samples doped by different percentages of W particles were determined using WinXCom and MCNP simulation for 10 different energies from 0.015 to 15 MeV. The proportion of W in LDPE matrix have been defined as 1, 5, 10, 15, 20, and 25 wt%, respectively. First, the values of mass attenuation coefficient (μρ) for LDPE/W composites were calculated by WinXCom code (Fig. 2). The results showed that the mass attenuation coefficients follow different behaviors grouped into three energy regions: in the low energies (below 0.5 MeV for W), a sharp decrease of μρ can be explained by the dominance of photoelectric effect (σPh∼E−7/2); in the intermediate energies (0.5–7 MeV for W), μρ shows slighter decrease with the increasing incident energy due to the dominance of Compton scattering process (σcom∼E−1); in the high energies (above 7 MeV for W), pair production process is responsible for the dominance of absorption over scattering and hence, a relatively constant behavior (σpp∼logE). In addition, the results indicated that the μρ increased with increasing the proportion of W in LDPE samples, as it can be explained on the basis of Z-dependence cross-section of different photon interaction processes. From Fig. 3 it is clearly observed that the variation of mean free path (MFP) definitely depends on the proportion of W in LDPE matrix, so that higher percentage of W means higher probability of photon interaction and therefore, shorter distance travelled by the photon between two consecutive events. Fig. 4 shows transmission factor (T) which has been calculated by dividing photon flux passed through LDPE/W by that through LDPE sample. The transmission factors increase sharply while the incident photons energy increase up to 1 MeV and then, the upward trend continues quieter to the maximum value in the intermediate energy region. Hereafter, a slight descending part down to the higher energies. It seems to be due to the fact that the dominance of photoelectric

3. Validation of simulation In order to verify the validation of our simulation, the linear attenuation coefficients (μ) of LDPE doped by different percentage of W have been determined for gamma rays of 60Co with average energy of 1.25 MeV and compared with experimental data from other previous works (Kim et al., 2014; Azeez et al., 2014; Chang et al., 2015). It is apparent from Table 3 that there is a fairly good agreement between MCNP and experimental data. The relative deviation (δ(%)=((μExpμMCNP)/μExp) × 100) in the range of ∼1.5%–∼9.5% showed that the modeled MCNP simulation geometry has been confirmed as a standard input for the definition of filler particles inside a uniformly dispersed arrangement. 4. Results and discussion The shielding properties including mass attenuation coefficient (μρ), mean free path (MFP), transmission factor (T), and buildup factor (B)

Table 3 MCNP and experimental data comparison for μ (cm−1) of LDPE/W composites for W size of 300 nm (Kim et al., 2014a), 6 μm (Azeez et al., 2014), and 12 μm (Chang et al., 2015). Composition

LDPE: LDPE: LDPE: LDPE: LDPE: LDPE: LDPE:

7.5 wt% W 15 wt% W 30 wt% W 50 wt% W 60 wt% W 70 wt% W 80 wt% W

300 nm

6 μm

MCNP

Exp

δ (%)

0.063 0.068

0.061 0.067

3.279 1.496

12 μm

MCNP

Exp

δ (%)

0.098 0.127

0.104 0.137

5.769 7.299

0.194 0.262

0.206 0.274

5.825 4.379

94

MCNP

Exp

δ (%)

0.691 0.766 0.830 0.877

0.73 0.81 0.89 0.97

5.342 5.432 6.742 9.588

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area, therefore, enhanced transmission factors. In the high energy region, the increased absorption rate due to the pair production process cause a nearly insignificant decrease in transmission factors. The variation observed in transmission factors follows similar trend with respect to all W size and proportion while lower transmission rate is determined for the 100 nm size of W in proportion of 25 wt%. In lower filler proportion, better attenuation is observed in smaller sizes while in higher filler proportion the transmission factor is relatively the same in all filler sizes. Once the size of W particles was increased, the transmission factor became larger. For example, the variation of the transmission rate in 15 MeV is in the range of ∼0.7–0.9 in lower filler proportion whereas it is only ∼0.55–0.6 in higher filler proportion. In fact, the difference between the transmission factors of the 1 and 25 wt % proportion of W particles is less significant in smaller sizes. The 100 nm sized filler means more homogeneous distributed structure which shows lower transmission factors because of the increased number of W particles whose makes the probability of interaction between radiations with W particles greater than that with LDPE matrix. Relative reduction in transmission (RRT) while the proportion of W particles raise from 1 to 25 wt% have been calculated by using the relation (9),

Fig. 3. Variation of mean free path (MFP) of WinXCOM as a function of photon energy for LDPE/W composites.

absorption in the low energy region help in reducing photon flux in the detection area and transmission factors, as well. Further, in the intermediate energy region, an increase in the probability of Compton scattering of photons gives rise to enhanced photon flux in the detection

RRT =

T25% T1% × 100 T1%

(9)

which T25% and T1% are transmission factors when the proportion of W particles is 25 and 1 wt%, respectively. Evaluating the quantity for all

Fig. 4. Photon transmission factor of LDPE/W composites for particle size (a) 100 μm, (b) 10 μm, (c) 1 μm, (d) 100 nm calculated by MCNP code. 95

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Fig. 5. Photon flux buildup factor of LDPE/W composites for particle size (a) 100 μm, (b) 10 μm, (c) 1 μm, (d) 100 nm calculated by MCNP code.

W particle sizes suggests that the maximum values of RRT occurred in the low energy region (0.05 MeV) most probably due to the higher atomic number of samples. The maximum RRT have been determined as 82.8%, 84.2%, 85.3%, and 89.6% for the filler size of 100 nm, 1 μm, 10 μm, and 100 μm, respectively. Flux buildup factor (B) as a ratio of all photons reached to detection point by photons that passed the sample without interaction was calculated for all W filler sizes and proportions which is shown in Fig. 5. It can be clearly seen from Fig. 5 that the flux buildup factor strongly increase up to a maximum value at 0.1 MeV, then start decreasing. The dominance of photoelectric effect results in maximum absorption rate by the sample in the lower energy region. In the higher energy region, similarly, pair production as another photon absorption process is dominant. The dominance of absorption over scattering leads to less photon reached to detection point consequently lower flux buildup factor. In the intermediate energy region, the dominance of Compton scattering only help degradation of photon energy due to the scattering. This process results in the longer existence of the photon, the higher probability of photon to escape from the sample, and consequently the larger value of flux buildup factor. It is obvious that the flux buildup factors change in a wide range from 1 to 11.5 approximately. According to the findings, it is possible to demonstrate that the maximum values of flux buildup factor decrease with increasing in filler proportion for all micro- and nano-structured composites. Although, this decrease happens slower in smaller sized samples. This effect can be observed by

considering variation in the maximum values of flux buildup factors versus filler proportion increased from 1 to 25 wt% so that the maximum values changes from 11.3 to 6.8 in 100 μm, from 11.3 to 9.1 in 10 μm, from 11.1 to 9.3 in 1 μm, and from 11 to 9.7 in 100 nm. It can be demonstrated by the fact that in the large sized structures the chemical composition has a significant effect on attenuation properties whereas at their small counterparts the effect of chemical composition is less because of the main influence of homogeneity in W particles distribution inside the LDPE matrix. The present findings seem to corroborate the findings of a great deal of the previous works in studying the effect of filler size and proportion on gamma shielding properties of a matrix. Experimental work of Dong et al. (2012) reported a better gamma attenuation of nano-WO3 filled E44 epoxy in comparison with micro size particles in a wide energy range 0.05–1.33 MeV, which was theoretically confirmed by Malekie and Hajiloo (2017). In 2014, Kim et al. indicated that gamma transmittance dependents on the size and proportion of fillers which is more significant at lower energy (∼0.3 MeV). In several research studies, Tekin et al. (2016a, 2016b, 2017, 2018a) reported improved gamma attenuation by increasing particles proportions and decreasing the particle sizes. They reported an increase from 0.06 to 0.19 of mass attenuation coefficients at 0.3 MeV when WO3 is added up to 75% (Tekin et al., 2017). In addition, they showed a 5.5% increase at 2 MeV for using nano-BaSO4 in replace of bulk Pb (Tekin et al., 2016b). In other works, it has been established that applying nano-sized particles give a 96

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higher gamma attenuation than micro-sized counterparts (Azman et al., 2016; Tekin et al., 2016a, 2016b, 2018a). Besides, a good consistency was observed with recent work of Issa et al. (2019b) which calculated gamma buildup factor by G-P method. They showed that there is a maximum in the intermediate energy range which decrease along with increase in the proportion of Pb(NO3)2 particles in PVA.

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5. Conclusion We reported new findings on transmission factor (T) and buildup factor (B) in terms of size and proportion of W filler within LDPE matrix in the energy region of 0.015–15 MeV. The model provided in this work describes more packed structure whose density and uniformity is maintained over changing the filler size and contribution inside the matrix at the same time. Although our study is in agreement with other researches but it includes more details and key results. All in all, summary of the main findings of the study is outlined below: - In the assessment of transmission factor in terms of energy, it is clearly observed that it follows the identical trend in all filler sizes and proportions where a significant increase at low energies and then a slow decrease at intermediate and high energies is perceived. - Increases in the percentage of W particles within the LDPE matrix influenced decrease in the transmission factor which is more significant at low energies. - Decrease in the size of W particles presented a decrease in the values of transmission factor that is more important in lower filler proportion. For example, it is about 0.2 and 0.05 at 15 MeV in 100 μm and 100 nm respectively. - At each energy point, difference between transmission rate in 1 and LDPE/25 wt% W was calculated by a new quantity called “RRT”. Results showed the maximum of RRT were occurred at 0.05 MeV enhanced up to 89% while W proportion increase. - The flux buildup factors found to be maximum at 0.1 MeV, where scattering dominants absorption. The most significant discrepancy in maximum values of flux buildup factor over filler proportion occurs when filler size is larger where the highest and the lowest reduction observed from 11.3 to 6.8 for 100 μm and from 11 to 9.7 for 100 nm. - It was proved that filler proportion is more effective than filler size in attenuating gamma rays. Formatting of funding sources This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.pnucene.2019.03.033. References Agarwal, B.D., Broutman, L.J., 1990. Analysis and Performance of Fiber Composites, second ed. John Wiley and Sons, New York. Ambika, M.R., Nagaiah, N., Suman, S.K., 2017. Role of bismuth oxide as a reinforcer on gamma shielding ability of unsaturated polyester based polymer composites. J. Appl. Polym. Sci. 134, 44657. https://doi.org/10.1002/app.44657. Aral, N., Nergis, F.B., Candan, C., 2015. An alternative X-ray shielding material based on coated textiles. Textil. Res. J. 86, 803–811. https://doi.org/10.1177% 2F0040517515590409. Azeez, A.B., Mohammed, K.S., Abdullah, M.M.A.B., Sandu, A.V., Rahmat, A., Hussin, K., Jamaludin, L., 2014. Replacement of lead by green tungsten-brass composites as a radiation shielding material. Appl. Mech. Mater. 679, 39–44. https://doi.org/10. 4028/www.scientific.net/AMM.679.39. AZoMaterial, 2002. Tungsten (W): properties, applications. available at: https://www. azom.com/article.aspx?ArticleID=1201. Azman, N.Z.N., Musa, N.F.L., Razak, N.N.A.N.A., Ramli, R.M., Mustafa, I.S., Rahman,

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