Radiation protection is crucial in various fields due to the harmful effects of radiation. Shielding is used to reduce radiation exposure, but gamma radiation poses challenges due to its high energy and penetration capabilities.

This work investigates the radiation shielding properties of polyvinylidene fluoride (PVDF) samples containing different weight fraction of tungsten carbide (WC), tungsten trioxide (WO_{3}), and tungsten disulfide (WS_{2}). Parameters such as the mass attenuation coefficient (MAC), half-value layer (HVL), mean free path (MFP), effective atomic number (_{eff}), and macroscopic effective removal cross-section for fast neutrons (∑_{R}

Increasing the weight fraction of the additives resulted in higher MAC values, indicating improved radiation shielding. PVDF–_{3} and PVDF–0.20WS_{2}. PVDF–0.20WC also exhibited the highest _{eff} values, while PVDF–0.20WS_{2} showed a slightly higher increase in _{eff} at energies of 0.662 and 1.333 MeV. PVDF–0.20WC has demonstrated the highest ∑_{R}_{2} had the lowest ∑_{R}

Overall, this research provides insights into the radiation shielding properties of PVDF mixtures, with PVDF–

Radiation protection is of utmost importance in various fields due to the harmful effects of radiation. Shielding is considered the most effective method to reduce radiation exposure; however, it presents challenges when dealing with gamma radiation due to its high energy and penetration capabilities. Traditionally, lead has been used for radiation shielding due to its high atomic number [

Smart polymers, also known as intelligent polymers, belong to a class of materials that exhibit reversible and significant changes in response to small variations in environmental conditions. These conditions include electric and magnetic fields, temperature, pH levels, light intensity, ionic factors, and mechanical stresses. These polymers possess the remarkable ability to undergo incremental changes triggered by external stimuli until a specific threshold is reached. Once the stimulus is removed, they can fully recover their original shape [

Among these smart polymers, polyvinylidene fluoride (PVDF) stands out as a notable example. PVDF is a specialized thermoplastic fluoropolymer known for its excellent resistance to solvents, acids, and hydrocarbons [

PVDF-based composites have garnered significant attention due to their exceptional properties, such as lightweight nature, thermal stability, ease of processing, affordability, excellent flexibility, and corrosion resistance [

Hence, PVDF displays promising characteristics for radiation shielding purposes, owing to its resistance properties and high-temperature thresholds. Furthermore, other researchers, such as Alabsy et al. [

Various materials have specific shielding properties that are crucial to determine, such as the linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), mean free path (MFP), and half-value layer (HVL). However, conducting experiments to obtain these properties can be challenging and prone to errors due to insufficient equipment, data processing mistakes, and interference from natural radioactivity. Fortunately, researchers have developed computational software and tools to simulate and calculate these shielding properties accurately. For example, the XCOM software (National Institute of Standards and Technology) [

While past works inadequately investigated the impact of adding Tungsten to PVDF, this study focuses on the effects of adding tungsten carbide (WC), tungsten trioxide (WO_{3}), and tungsten disulfide (WS_{2}) at varying concentrations on the gamma-neutron shielding effectiveness of PVDF. The evaluation of shielding effectiveness involved the utilization of EpiXS, Phy-X, and MCNP simulation tools.

The investigation thoroughly assessed the effect of mixing WC, WO_{3}, and WS_{2} chemical compounds on the radiation shielding properties of PVDF with compositions of C_{2}H_{2}F_{2}. The study employed computational tools, including EpiXS, Phy-X/PSD, and MCNP5. PVDF was mixed with WC, WO_{3}, and WS_{2} chemical compounds according to the following: PVDF–_{3}, and PVDF–_{2}, where (_{R}_{R}_{R}

The following equations represent the shielding parameters’ basic relations. When a material of thickness

where _{0} and _{mass}^{2}/g). The MAC is calculated using

The ratio of the intensity of the transmitted gamma radiation to the intensity of the incident gamma radiation is called the gamma transmission factor (GTF).

The mixture rule gives the MAC for multi-element materials and is given in _{i}^{th} element. As shown, _{mass}_{mass}_{i}

The HVL and MFP can be calculated using the following expressions:

The fast neutrons macroscopic effective removal cross-section (∑_{R}

where ^{i}^{3}) and ^{th} constituent. The partial density _{i}^{th} constituent (compound or simple element) can be calculated using:

where the _{i}_{s}

The quantity

The equations provided in _{R}

where _{i}

Here, _{A}_{i}

To validate the obtained results, the Windows-based application fast software EpiXS, based on EPICS2017 of ENDF/B-VIII and EPDL97 of ENDF/B-VI.8 photo atomic libraries [

To evaluate the material’s efficacy in shielding against gamma radiation, the MCNP5 program was employed to compute the GTF and dose rate (mSv/hr). This analysis was specifically performed for pure PVDF and PVDF–^{8} disintegrations per second. The simulation was executed nine times to obtain GTF, both before and after incorporating the four layers of pure PVDF samples and four layers only of PVDF–0.20WC, to observe the cumulative GTF after adding each layer. The uncertainties obtained from MCNP5 were found to be less than 4%, indicating the reliability of the results. The tally F4 and the flux-to-dose rate conversion factor sets are for use on the DE and DF tally cards to convert from calculated particle flux to the dose equivalent rate. The dose equivalent rate was obtained before utilizing the samples and after the S_{5} samples in both cases of pure PVDF and PVDF–

The radiation MAC for PVDF samples with different weight fraction of WC, WO_{3}, and WS_{2} were calculated using Phy-X/PSD and EpiXS simulations at energies of 0.0595, 0.662, and 1.333 MeV. The results are presented in _{1} represents the pure PVDF samples and S_{2}, S_{3}, S_{4}, and S_{5} refer to the additive rates of WC, WO_{3}, and WS_{2}, respectively, at 5%, 10%, 15%, and 20%. The MAC values obtained by the Phy-X/PSD and EpiXS simulations show good agreement, and the relative percentage difference (RPD%) was calculated using the following formula:

The obtained results demonstrate that the maximum RPD% for MAC calculations at 0.0595, 0.662, and 1.333 MeV for all samples with WC additives are 1.31%, 0.25%, and 0.36%, respectively. Furthermore, for samples with WO_{3} additives, the maximum RPD% values were found to be 1.26%, 0.26%, and 0.36% at the respective energy levels. Similarly, in the case of samples with WS_{2} additives, the maximum RPD% values were observed to be 1.20%, 0.25%, and 0.18% for the corresponding energies.

_{3}, and WS_{2} as a function of photon energy. Overall, it was observed that the MAC decreases as the photon energy increases. Additionally, higher concentrations of WC, WO_{3}, and WS_{2} in PVDF samples led to increased MAC values at 0.0595 and 0.662 MeV. The percentage changes were calculated relative to the MAC value of the pure PVDF sample, using the following formula:

where _{x}_{2} to _{5} based on _{3}, the percentage changes in MAC values at 0.0595 MeV varied from 74.77% to 299.05%, while the change at 0.662 MeV ranged from 1.16% to 4.27%. The percentage changes in MAC values at 1.333 MeV for WO_{3} were negative, ranging from −0.18% to −0.54% (_{2}, the percentage changes in MAC values at 0.0595 MeV were between 71.42% and 285.58%, while at 0.662 MeV they ranged from 1.03% to 4.01%. The percentage changes at 1.333 MeV were negative, with values between −0.18% and −0.36% (_{3}, and WS_{2} with PVDF leads to an increase in MAC values at 0.0595 and 0.662 MeV, indicating improved radiation shielding properties (_{3}, and WS_{2} concentrations. Comparing the percentage changes, it can be observed that the MAC values in PVDF mixed with WC show higher increases compared to WO_{3} and WS_{2}. This suggests that PVDF mixed with WC exhibits the best radiation shielding properties among the three additives. For enhanced shielding effectiveness, increasing the content of WO_{3} and WS_{2} in the PVDF mixture would be necessary.

The simulated results obtained using the Phy-X/PSD software for MAC have been presented in

_{3} and PVDF–0.20WS_{2} samples, signifying enhanced shielding properties. _{3} shows the second-lowest MFP only at 0.0595 MeV, while PVDF–0.20WS_{2} exhibits the second-lowest MFP values solely at 0.662 and 1.333 MeV. Notably, in the case of PVDF–0.20WC, the MFP undergoes a percentage change at the selected energy points. It decreases to 91.38% at 0.0595 MeV, 62.74% at 0.662 MeV, and 60.66% at 1.333 MeV, indicating a substantial reduction in the average collision distance and highlighting the improved shielding efficiency of the PVDF–0.20WC sample.

The effective atomic number (_{eff}) was determined for the PVDF samples, as shown in _{eff} concerning photon energy at a range of 0.001 to 15,000 MeV for the PVDF–0.20WC, PVDF–0.20WO_{3}, and PVDF–0.20WS_{2} samples. The _{eff} values at energy points of 0.0595, 0.662, and 1.333 MeV were specifically examined and compared to the initial value of the pure PVDF sample (_{eff} were observed at the specified energy points of 0.0595, 0.662, and 1.333 MeV for each mixture. For PVDF–0.20WC, the percentage changes in _{eff} were 315.17%, 26.80%, and 20.69%, respectively. Similarly, for PVDF–0.20WO_{3}, the percentage changes in _{eff} were 273.66%, 23.77%, and 18.68%. Furthermore, for PVDF–0.20WS_{2}, the percentage increases in _{eff} were 262.92%, 25.13%, and 20.31%. Based on the aforementioned findings, it is evident that the PVDF–0.20WC sample exhibits the highest radiation shielding potential among the PVDF mixtures with different additives, namely PVDF–0.20WO_{3} and PVDF–0.20WS_{2}. This implies that the inclusion of WC in the PVDF matrix results in enhanced shielding properties than those obtained with WO_{3} and WS_{2}. Furthermore, it is worth noting that the percentage increase in _{eff} values for the PVDF–0.20WS_{2} composite is slightly higher than that of the PVDF–0.20WO_{3} sample, only at energy points of 0.662 and 1.333 MeV. This indicates that, specifically at these energy levels, PVDF–0.20WS_{2} offers a marginally greater improvement in radiation shielding effectiveness compared to PVDF–0.20WO_{3}.

The simulation of ∑_{R}_{R}_{R}

In general, ^{2}>0.99) between the weight fraction in the mixtures and the neutron shielding properties. Generally, an increase in ∑_{R}_{3}, and PVDF–_{2} samples. Significantly, PVDF–0.20WC exhibits the highest ∑_{R}^{−1}, showing a percentage change of 116.09% compared to the pure PVDF sample. On the other hand, the PVDF–0.20WS_{2} sample demonstrates the lowest ∑_{R}^{−1} among all the samples (

In addition, in

In addition to the simulation using Phy-X/PSD software, the calculation of ∑_{R}_{R}

The evaluation of the samples was performed using MCNP5, which allowed for the determination of the energy distribution of radiation pulses in a detector before and after adding the layers of pure PVDF and PVDF–

The GTF at the end of each layer was obtained for both pure PVDF and PVDF–

In terms of the dose equivalent rate, the results indicated a decrease from 0.0127 mSv/hr for pure PVDF to 0.0044 mSv/hr and a further decrease to 0.0016 mSv/hr for the PVDF–

In this research study, the Phy-X/PSD software was employed to calculate various important parameters including the MAC, HVL, MFP, _{eff}, and ∑_{R}_{3}, and PVDF–_{2} samples, where _{3}, and PVDF–0.20WS_{2} samples to determine their HVL, MFP, _{eff}, and ∑_{R}_{3}, and WS_{2} increase in PVDF, there is a corresponding increase in the MAC values. This increase in MAC values suggests an improvement in the radiation shielding properties of the PVDF samples. Notably, the percentage change in the MAC values of PVDF–_{3} and PVDF–_{2}. Based on these findings, it can be concluded that PVDF mixed with WC demonstrates the most effective radiation shielding properties among the studied additives. MFP results provide additional insights into the shielding properties of the mixture materials. In the case of the PVDF–0.20WC sample, the MFP values were found to be the lowest among the studied samples. This indicates that PVDF–0.20WC has enhanced shielding properties compared to PVDF–0.20WO_{3} and PVDF–0.20WS_{2}. However, it’s worth noting that the PVDF–0.20WO_{3} sample exhibited the second-lowest MFP value only at an energy of 0.0595 MeV. Similarly, the PVDF–0.20WS_{2} sample showed the second-lowest MFP values specifically at energies of 0.662 and 1.333 MeV. The _{eff} results indicate that the PVDF–0.20WC sample exhibits the highest values among the studied samples. Additionally, the percentage increase in _{eff} values for the PVDF–0.20WS_{2} sample is slightly higher than that of the PVDF–0.20WO_{3} sample, specifically at energy points of 0.662 and 1.333 MeV. This suggests that, at these particular energy levels, PVDF–0.20WS_{2} offers a slightly greater improvement in radiation shielding effectiveness compared to PVDF–0.20WO_{3}. The ∑_{R}_{3}, and PVDF–_{2} samples increases, there is an observed increase in ∑_{R}_{R}_{2} sample demonstrated the lowest ∑_{R}

No potential conflict of interest relevant to this article was reported.

This article does not contain any studies with human participants or animals performed by any of the authors.

Conceptualization: Aljumaili Z. Methodology: Abu Ghazal A. Data curation: El-Sayed A. Writing - original draft: Abu Ghazal A. Writing - review & editing: Alakash R, Abdel-Rahman H. Approval of final manuscript: all authors.

We would like to express our sincere gratitude and appreciation to all those who have contributed to the completion of this paper. Their support, guidance, and assistance have been invaluable throughout the research process.

The geometry setup of the Monte Carlo N-Particle Transport version 5 (MCNP5) simulation was used for the determination of the gamma transmission factor and dose rate for the four layers of pure polyvinylidene fluoride (PVDF) and four layers of PVDF–0.20WC samples. WC, tungsten carbide.

The relationship between the percentage change of mass attenuation coefficient (MAC) values and the weight fraction of additives (_{3}, (C) PVDF–_{2}, and (D) comparison of MAC values at _{3}, tungsten trioxide; WS_{2}, tungsten disulphide.

The variation of the mass attenuation coefficient (MAC) as a function of gamma-ray energies, covering a range from 0.001 to 15,000 MeV: (A) for polyvinylidene fluoride (PVDF)–_{3}, (C) PVDF–_{2}, and (D) comparison between the MAC values only at _{3}, tungsten trioxide; WS_{2}, tungsten disulphide.

Mean free path (MFP) of the pure polyvinylidene fluoride (PVDF), PVDF–0.20WC, PVDF–0.20WO_{3}, and PVDF–0.20WS_{2} samples as a function of photon energies: (A) at the energy range of 0.001 to 15,000 MeV and (B) specifically focusing on the MFP values at energy points of 0.0595, 0.662, and 1.333 MeV. WC, tungsten carbide; WO_{3}, tungsten trioxide; WS_{2}, tungsten disulphide.

Effective atomic number (_{eff}) results for the pure polyvinylidene fluoride (PVDF), PVDF–0.20WC, PVDF–0.20WO_{3}, and PVDF–0.20WS_{2} as a function of photon energy: (A) for the photon energy at a range of 0.001 to 15,000 MeV and (B) at 0.0595, 0.662, and 1.333 MeV. WC, tungsten carbide; WO_{3}, tungsten trioxide; WS_{2}, tungsten disulphide.

Variation of macroscopic effective removal cross-section for fast neutrons (∑_{R}_{3}, (C) for PVDF–_{2}, and (D) ∑_{R}_{3}, and PVDF–0.20WS_{2} samples. WC, tungsten carbide; WO_{3}, tungsten trioxide; WS_{2}, tungsten disulphide.

Detailed illustration of multilayer samples using Monte Carlo N-Particle Transport version 5 (MCNP5): (A) for polyvinylidene fluoride (PVDF)–

Gamma transmission factor (GTF) results for the multilayer samples simulated using Monte Carlo N-Particle Transport version 5 (MCNP5): (A) two-dimensional representation of the GTF results and (B) three-dimensional representation of the GTF results. PVDF, polyvinylidene fluoride; WC, tungsten carbide.

Variation of Weight Fraction and Densities for WC, WO_{3}, and WS_{2} Additives in PVDF Samples

Code | Sample | Weight fraction (%) | Density (g/cm^{3}) | |
---|---|---|---|---|

| ||||

PVDF | Additive | |||

WC | ||||

S_{1} |
PVDF | 100 | 0 | 1.78 |

S_{2} |
PVDF+0.05WC | 95 | 5 | 2.47 |

S_{3} |
PVDF+0.10WC | 90 | 10 | 3.17 |

S_{4} |
PVDF+0.15WC | 85 | 15 | 3.86 |

S_{5} |
PVDF+0.20WC | 80 | 20 | 4.55 |

| ||||

WO_{3} | ||||

S_{1} |
PVDF | 100 | 0 | 1.78 |

S_{2} |
PVDF+0.05 WO_{3} |
95 | 5 | 2.05 |

S_{3} |
PVDF+0.10 WO_{3} |
90 | 10 | 2.32 |

S_{4} |
PVDF+0.15 WO_{3} |
85 | 15 | 2.59 |

S_{5} |
PVDF+0.20 WO_{3} |
80 | 20 | 2.86 |

| ||||

WS_{2} | ||||

S_{1} |
PVDF | 100 | 0 | 1.78 |

S_{2} |
PVDF+0.05 WS_{2} |
95 | 5 | 2.07 |

S_{3} |
PVDF+0.10 WS_{2} |
90 | 10 | 2.35 |

S_{4} |
PVDF+0.15 WS_{2} |
85 | 15 | 2.64 |

S_{5} |
PVDF+0.20 WS_{2} |
80 | 20 | 2.92 |

WC, tungsten carbide; WO_{3}, tungsten trioxide; WS_{2}, tungsten disulfide; PVDF, polyvinylidene fluoride.

MAC Values for PVDF Samples Mixed with Different Weight Fraction of WC, WO_{3}, and WS_{2}, Calculated Using Phy-X/PSD and EpiXS

Case | Energy (MeV) | Software | MAC (cm^{2}/g) |
Maximum RPD (%) | ||||
---|---|---|---|---|---|---|---|---|

| ||||||||

S_{1} |
S_{2} |
S_{3} |
S_{4} |
S_{5} | ||||

WC | 0.0595 | Phy-X/PSD | 0.1907 | 0.3594 | 0.5282 | 0.6969 | 0.8656 | 1.31 |

EpiXS | 0.1909 | 0.3567 | 0.5226 | 0.6885 | 0.8543 | |||

0.662 | Phy-X/PSD | 0.0772 | 0.0782 | 0.0792 | 0.0801 | 0.0811 | 0.25 | |

EpiXS | 0.0771 | 0.0781 | 0.0790 | 0.0800 | 0.0810 | |||

1.333 | Phy-X/PSD | 0.0551 | 0.0550 | 0.0549 | 0.0549 | 0.0548 | 0.36 | |

EpiXS | 0.0550 | 0.0549 | 0.0548 | 0.0547 | 0.0547 | |||

| ||||||||

WO_{3} |
0.0595 | Phy-X/PSD | 0.1907 | 0.3333 | 0.4759 | 0.6184 | 0.7610 | 1.26 |

EpiXS | 0.1909 | 0.3310 | 0.4712 | 0.6114 | 0.7515 | |||

0.662 | Phy-X/PSD | 0.0772 | 0.0781 | 0.0789 | 0.0797 | 0.0805 | 0.26 | |

EpiXS | 0.0771 | 0.0779 | 0.0787 | 0.0796 | 0.0804 | |||

1.333 | Phy-X/PSD | 0.0551 | 0.0550 | 0.0550 | 0.0549 | 0.0548 | 0.36 | |

EpiXS | 0.0550 | 0.0549 | 0.0548 | 0.0548 | 0.0547 | |||

| ||||||||

WS_{2} |
0.0595 | Phy-X/PSD | 0.1907 | 0.3269 | 0.4630 | 0.5991 | 0.7353 | 1.20 |

EpiXS | 0.1909 | 0.3248 | 0.4587 | 0.5926 | 0.7265 | |||

0.662 | Phy-X/PSD | 0.0772 | 0.0780 | 0.0788 | 0.0795 | 0.0803 | 0.25 | |

EpiXS | 0.0771 | 0.0779 | 0.0786 | 0.0794 | 0.0802 | |||

1.333 | Phy-X/PSD | 0.0551 | 0.0550 | 0.0550 | 0.0549 | 0.0549 | 0.18 | |

EpiXS | 0.0550 | 0.0549 | 0.0549 | 0.0548 | 0.0548 |

MAC, mass attenuation coefficient; PVDF, polyvinylidene fluoride; WC, tungsten carbide; WO_{3}, tungsten trioxide; WS_{2}, tungsten disulphide; PSD, Photon Shielding and Dosimetry; S, sample number; RPD, relative percentage difference.

Calculated and Simulated Results of ∑_{R}^{−1}) for PVDF–

Sample | Using |
Phy-X/PSD | RPD (%) |
---|---|---|---|

Pure PVDF | 0.105141 | 0.105160 | 0.018061 |

PVDF–0.05WC | 0.140399 | 0.140426 | 0.019173 |

PVDF–0.10WC | 0.172493 | 0.172528 | 0.020378 |

PVDF–0.15WC | 0.201424 | 0.201468 | 0.021689 |

PVDF–0.20WC | 0.227192 | 0.227244 | 0.023119 |

PVDF, polyvinylidene fluoride; WC, tungsten carbide; PSD, Photon Shielding and Dosimetry; RPD, relative percentage difference.