Low-energy x-ray attenuation characteristics of Rhizophora spp. composites

Low-energy x-ray attenuation characteristics of Rhizophora spp. composites 1 3 corresp first-author Corresponding author: saamdoftt82@gmail.com; Corresponding author: saamdoftt82@gmail.com; saamdoftt82@gmail.com 1 1 corresp mjafri@usm.my mjafri@usm.my mjafri@usm.my 2 3 1 4 School of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia School of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia School of Industrial Technology, Universiti Sains Malaysia, 11800 Penang, Malaysia School of Industrial Technology, Universiti Sains Malaysia, 11800 Penang, Malaysia Advanced Medical and Dental Institute, Universiti Sains Malaysia, 13200 Bertam, Penang, Malaysia Advanced Medical and Dental Institute, Universiti Sains Malaysia, 13200 Bertam, Penang, Malaysia School of Health Sciences, Universiti Sains Malaysia, 16150 Kota Bharu, Kelantan, Malaysia School of Health Sciences, Universiti Sains Malaysia, 16150 Kota Bharu, Kelantan, Malaysia Photon absorption parameters such as mass attenuation coefficients ( <math id="M1"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> ), molar extinction coefficients ( <math id="M2"><mi>ε</mi></math> ), total molecular ( <math id="M3"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> ), atomic ( <math id="M4"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> ) and electronic ( <math id="M5"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> ) cross-sections, half-value layers <math id="M6"><mrow><mrow><mo>(</mo><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow></math> , tenth-value layers ( <math id="M7"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub></mrow></math> ), mean free paths <math id="M8"><mrow><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></mrow></math> , effective atomic numbers ( <math id="M9"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> ), and effective electron densities ( <math id="M10"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> ) were estimated for defatted soy flour (DSF), soy protein concentrate (SPC), and soy protein isolate (SPI)-based Rhizophora spp . particleboard composites substituted with 10 wt% sodium hydroxide (NaOH) and 0, 5, 10, and 15 wt% itaconic acid polyamidoamine-epichlorohydrin (IA-PAE) adhesives. Elemental composition was assessed using ultra-high-resolution field emission scanning electron microscopy-energy dispersive X-ray spectrometry (UHR-FESEM-EDX). The interaction parameters were evaluated for <math id="M11"><mrow><msub><mtext>K</mtext><mrow><mtext>α</mtext><mn>1</mn></mrow></msub></mrow></math> photons at 16.59, 17.46, 21.21, and 25.26 keV, employing a low-energy germanium (LEGe) detector system and an 241 Am <math id="M12"><mi>γ</mi></math> -ray source. X-ray diffraction characterization revealed an amorphous phase in the developed particleboard composites. Samples DSF15′, SPC15′, and SPI15′ exhibited the highest values of <math id="M13"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> , <math id="M14"><mi>ε</mi></math> , <math id="M15"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> , <math id="M16"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> , and <math id="M17"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> among all of the studied particleboard samples, within the range of measured photon energies. In addition, all of the modified samples exhibited lower <math id="M18"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> , <math id="M19"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub></mrow></math> , <math id="M20"><mi>λ</mi></math> , <math id="M21"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> , and <math id="M22"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> than the unmodified samples, with DSF-, SPC-, and SPI/NaOH/ Rhizophora spp ./IA-PAE (15 wt%), indicating insignificant changes. The current results of the particleboard samples’ analysis can be useful for medical radiation applications and shielding research. Photon interaction parameters Shielding DSF-SPC-SPI Particleboards NaOH/IA-PAE 1 Introduction 1 In the fabrication of radiological safety materials, significant attention has been paid to the use of heavy elements, including lead (Pb), tungsten (W), iron (Fe), or mixtures of these substances, and various concrete-based radiation shields [ 1 1 , 2 2 ]. However, much concern has been expressed about the environmental health issues associated with the use of materials made of Pb and Pb-based compounds. The disadvantages include inflexibility, chemical instability, poor physico-mechanical strength and dimensional stability, weight, and the nature of toxicity [ 3 3 ]. Lead dust can become airborne and may be ingested by humans [ 4 4 ]. It is not easily excreted from the human body, nor is it biodegradable or biocompatible. The ultimate concern is that of the failure of multiple organs. On the other hand, there are various challenges related to the use of concrete-based materials, arising, e.g., when concrete is heated owing to the radiation energy absorption, which leads to the loss of water and induces significant variability in the concrete chemical composition, deterioration of structural strength, and reduction in its density. In general, materials must have high atomic numbers, and should be sufficiently homogeneous in terms of their density and chemical composition to be applicable for radiation shielding. Therefore, in recent years, the evaluation of specific values of interacting factors of composite materials has been of significant experimental and theoretical interest [ 5 5 ]. Several researchers have adopted various natural (renewables) or synthetic (petroleum-based) composite materials to create novel radiation shielding materials, for substituting lead-containing shields using different techniques [ 5 5 – 7 7 5–7 ]. Owing to their specific characteristics, such as homogeneity, wide range of elemental compositions, non-toxicity, ease of fabrication in different shapes and sizes with no discrepancy in their density, high flexibility, and convenient attenuation coefficients, renewable resources such as wood composites can be used in radiation shielding materials [ 8 8 , 9 9 ]. Rhizophora spp . ( Rh. spp .) wood is particularly interesting owing to its unique physico-mechanical and dimensional stability characteristics, and has found applications in radiation dosimetry [ 8 8 – 10 10 8–10 ]. Typical Rh. spp . wood, with high carbon content followed by oxygen, hydrogen, and other elements, is suitable for use as a particleboard radiation shielding material [ 5 5 , 9 9 , 11 11 ]. Untreated Rh. spp . wood, however, has some drawbacks if it is utilized for radiation protection against ionizing radiation [ 9 9 , 12 12 ]. In several studies, addition of suitable curing agents has been considered, which may enhance the physico-mechanical and radiation shielding characteristics of Rh. spp . [ 8 8 , 10 10 ]. The demand for soy protein-based (defatted soy flour (DSF), soy protein concentrate (SPC), and soy protein isolate (SPI)) materials for various medical health applications continues to increase owing to their advantageous characteristics, such as biodegradability, biocompatibility, and cost-effectiveness [ 8 8 , 13 13 ]. Soy protein composites have been noted for their strong network, high thermal stability, advantageous physico-mechanical parameters, high chemical durability, and good dimensional stability. A recent trend has been to incorporate network modifiers like sodium hydroxide (NaOH) or itaconic acid polyamidoamine-epichlorohydrin (IA-PAE) resin, for overcoming disadvantages such as poor water resistance, high viscosity, low solid content, and low effective atomic number, exhibited by unmodified soy protein composites [ 8 8 , 14 14 , 15 15 ]. NaOH has been recognized as an important denaturing agent that unfurls protein molecules to expose hydrophobic groups, which helps in strengthening the adhesive physico-mechanical characteristics and wood-bonding ability [ 15 15 ]. However, NaOH alone does not provide convenient modifier specifications for photon absorption parameters and requires at least one curing agent, such as IA-PAE resin. IA-PAE, which can be produced from sugars, is a non-toxic compound, and is considered one of the most useful building block chemicals with incomparable multifunctionality. In view of this, the combination of DSF, SPC, SPI, and NaOH/IA-PAE adhesives in terms of shielding X- and <math id="M23"><mi>γ</mi></math> -rays can constitute a novel and alternative candidate material. Therefore, in the present study, the radiation interaction properties of uncured and cured DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards encoded as DSF0, SPC0, SPI0, DSF1, SPC1, SPI1, DSF5, SPC5, SPI5, DSF10, SPC10, SPI10, DSF15, SPC15, SPI15, DSF5′, SPC5′, SPI5′, DSF10′, SPC10′, SPI10′, DSF15′, SPC15′, and SPI15′ for 0, 5, 10, and 15 wt% were experimentally determined for 16.59, 17.46, 21.21, and 25.26 keV photons. Crucial radiation interaction parameters, such as mass attenuation coefficients ( <math id="M24"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> ), molar extinction coefficients ( <math id="M25"><mi>ε</mi></math> ), total molecular ( <math id="M26"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> ), atomic ( <math id="M27"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> ) and electronic ( <math id="M28"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> ) cross-sections, half-value layer (HVL) values <math id="M29"><mrow><mrow><mo>(</mo><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow><mo>)</mo></mrow></mrow></math> , tenth-value layer (TVL) values ( <math id="M30"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub></mrow></math> ), mean free path (MFP) values <math id="M31"><mrow><mrow><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></mrow></math> , effective atomic numbers ( <math id="M32"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> ), and effective electron densities ( <math id="M33"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> ) were evaluated to provide accurate information on the performance of the photon radiation shielding characteristics of various soy protein-based adhesives used in the fields of medical diagnostics and radiation dosimetry. 2 Materials and methods 1 2.1 Fabrication of DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboard samples 2 Rh. spp . trunks, obtained from the Forestry Department of the Mangrove Forest Reserve in Kuala Sepetang, Perak, Malaysia, were utilized as raw materials. DSF, SPC, and SPI in the powder form were procured from Shandong Wonderful Biotech Co., Ltd. (Qingdao, China). Epichlorohydrin (ECH), NaOH, diethylenetriamine (DETA), and methylenesuccinic acid (IA) were supplied by Sigma-Aldrich Co., Ltd. (USA). Presynthesized IA-PAE resin from our previous study with specific characteristics (solid content of 55.96 ± 0.01 wt%, pH of 6.68 at 27.58℃, and apparent viscosity of 100.40 ± 0.25 mPa.s) was employed [ 8 8 ]. The DSF-, SPC-, and SPI-based bio-adhesives were prepared at room temperature by suspending DSF (30 g), SPC (30 g), and SPI (12 g) in distilled water, and were completely stirred at 600 rpm for 0.5 h to ensure good uniformity. The synthesized IA-PAE (0, 5, 10, and 15 wt%) were then added carefully to the slurry containing the adhesive mixtures and mixed for 0.5 h, to build up a series of DSF-, SPC-, and SPI-based adhesives. The resultant DSF-, SPC-, and SPI/IA-PAE mixtures were then alkalized with 2N NaOH (10 wt%) solution to a pH of 11.0, mixed carefully for another 0.5 h to expedite dissolution and hydrolysis, ensuring high bonding strength in the resultant particleboards. The reaction temperature and time depended on the molar ratio of the resins. This indicates that the IA-PAE molecular weight strongly affected the subsequent bonding strength performance of particleboards. Different combinations based on the DSF-, SPC-, and SPI/NaOH/IA-PAE concentrations were then thoroughly mixed with Rh. spp . wood (particle size, <math id="M34"><mo>≤</mo></math> 74 μm) for 10 min, using a rotary mixer machine at 25000 rpm to maintain homogeneity and remove voids. Using a preheated stainless-steel mould with dimensions 30 <math id="M35"><mo>×</mo></math> 30 <math id="M36"><mo>×</mo></math> 1.0 cm 3 , the mixtures were subsequently cold-compressed using a hydraulic press machine (0.49 MPa, 5 min, and 0 ℃). The compressed samples were easily moved onto a hydraulic hot press machine (20 MPa, 20 min, and 180 ℃) and manufactured as particleboards. This was followed by seven days of cooling and storage in an ambient environment, to avoid thermal stress and strain created by heat treatment and degradation of the resin. The pressing process consolidated the particle mats to the required density and thickness and polymerized the individual particle resin systems. The uncured and cured DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboard samples were assigned the following codes: DSF0, SPC0, SPI0, DSF1, SPC1, SPI1, DSF5, SPC5, SPI5, DSF10, SPC10, SPI10, DSF15, SPC15, SPI15, DSF5′, SPC5′, SPI5′, DSF10′, SPC10′, SPI10′, DSF15′, SPC15′, and SPI15′ for 0, 5, 10, and 15 wt%, respectively. The gravimetric approach was used for computing the average mass density of the particleboard samples. 2.2 Characterization of composites and theoretical calculations 2 2.2.1 Field emission scanning electron microscopy (FESEM) characterization 3 The morphological characteristics of DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards were examined using an ultra-high-resolution field emission scanning electron microscope (UHR-FESEM) (model FEI Quanta FEG-650, Netherlands). The samples were 60% gold-coated on the surfaces for 30 s at 45 mA, using a sputtering equipment to prevent charge build-up. The scanning electron microscopy (SEM) images of the particleboard crystallites were acquired at the magnification of up to 1000 <math id="M37"><mo>×</mo></math> , using an accelerating voltage in the 5 – 20 kV range, at a tilt angle of 30 o . 2.2.2 X-ray diffraction (XRD) characterization 3 A Bruker D8 Advance XRD system was used for examining the crystalline structure of the particleboard samples. The samples were hydraulically pressed onto a sample holder into a circular disc (diameter, 2.5 cm). The XRD analysis pattern were run in a 2 <math id="M38"><mi>θ</mi></math> scan, with the angle in the 5 o – 80 o range, with Cu- <math id="M39"><mrow><msub><mtext>K</mtext><mrow><mtext>α</mtext><mn>1</mn></mrow></msub></mrow></math> ( <math id="M40"><mi>λ</mi></math> = 0.15406 nm) as a target at 40 kV P and 40 mA, at a scanning rate of 2 o /min. All of the particleboard samples’ data were analyzed using EVA 5+ software. 2.2.3 Mass attenuation and molar extinction coefficients 3 The mass attenuation coefficient ( <math id="M41"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> , cm 2 /g) quantifies the probability of the photon interaction with a particleboard sample. It is an essential parameter for deriving other photon interaction related quantities, such as <math id="M42"><mi>ε</mi></math> , <math id="M43"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> , <math id="M44"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> , <math id="M45"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> , <math id="M46"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> , <math id="M47"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub></mrow></math> , <math id="M48"><mi>λ</mi></math> , <math id="M49"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> , and <math id="M50"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> . The measurements were performed using an X-ray attenuation setup fitted with a low-energy germanium (LEGe) detector system and other associated equipment, such as a multichannel analyzer (MCA-3 series), spectroscopy amplifier, high-voltage supply, a particleboard sample as the absorber, a radioactive source, a Pb shield, and a Pb collimator. The full width half maximum (FWHM) of the detector was 0.4 keV for 59.54 keV photons from an Am-241 source with the strength 3.7 <math id="M51"><mo>×</mo></math> 10 9 Bq. The active crystal area and the diameter of the detector were 2 cm 2 and 1.6 cm, respectively, and the detector was kept at the liquid nitrogen temperature (–196 ℃) during the experiments. X-ray fluorescence (XRF) photons from four metal plates (niobium, molybdenum, palladium, and stannum) were used for obtaining <math id="M52"><mrow><msub><mtext>K</mtext><mrow><mtext>α</mtext><mn>1</mn></mrow></msub></mrow></math> photons with energies ranging from 16.59 keV to 25.26 keV. The distances between the particleboard samples–metal target plates and particleboard samples–detector were fixed at 7 cm and 8.9 cm, respectively, and the diameter of the Pb collimator was 0.3 cm. To reach statistical accuracy, each particleboard sample was assessed by collecting the spectra for a period of 0.6 <math id="M53"><mo>×</mo></math> 10 3 s with observed dead time for all channels ranging from 31.82% to 34.07%. In addition, to eliminate the background and scattered photons, all of the measurements were performed inside a heavily shielded setup. The experimental measurements were repeated three times to determine the values of the selected parameters. The experimental setup is shown schematically in Fig. 1 Fig. 1 . Data collection and evaluation was performed using MAESTRO (an MCA emulation software program by ORTEC). According to the well-known Beer-Lambert law, a parallel beam of monoenergetic X- and <math id="M54"><mi>γ</mi></math> -ray photons is attenuated in matter according to the following exponential attenuation relation [ 8 8 , 16 16 ]: <math display="block" id="M55"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub><mo>=</mo><mfrac><mi>μ</mi><mi>ρ</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>ρ</mi><mi>x</mi></mrow></mfrac><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>I</mi><mtext>o</mtext></msub></mrow><mrow><msub><mi>I</mi><mtext>t</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mo> </mo><mo>,</mo></mrow></math> where, <math id="M56"><mrow><msub><mi>I</mi><mtext>o</mtext></msub></mrow></math> and <math id="M57"><mrow><msub><mi>I</mi><mtext>t</mtext></msub></mrow></math> indicate the incident intensity and transmitted intensity of the photons, respectively, while <math id="M58"><mi>ρ</mi></math> and <math id="M59"><mi>x</mi></math> denote the density and physical thickness of the particleboard samples. In the case of a multi-element material (i.e., a chemical compound or a homogeneous mixture) constituting the sample, <math id="M60"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> can be obtained from the weighted sum of the contributions of individual atoms as in Eq. (2) [ 17 17 ]: <math display="block" id="M61"><mrow><msub><mrow><mrow><mo>(</mo><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow><mo>)</mo></mrow></mrow><mrow><mtext>DSF</mtext><mo>−</mo><mtext>SPC</mtext><mo>−</mo><mtext>SPI composite</mtext></mrow></msub><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></munderover><mrow><mo>{</mo><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></msub><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mo>.</mo><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub></mrow><mo>}</mo></mrow><mo> </mo><mo> </mo><mo>,</mo></mrow></math> where, <math id="M62"><mrow><msub><mi>n</mi><mi>j</mi></msub></mrow></math> , <math id="M63"><mrow><msub><mi>A</mi><mi>j</mi></msub></mrow></math> , <math id="M64"><mi>ρ</mi></math> , <math id="M65"><mrow><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></munder><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow></math> , and <math id="M66"><mrow><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub></mrow></math> denote the number of atoms, effective atomic weight, density, molecular weight, and mass attenuation coefficient of the j th constituent element ( <math id="M67"><mrow><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>r</mi></mrow></math> ), for a particular photon energy being considered. The overall mass attenuation coefficient ( <math id="M68"><mrow><msub><mi>μ</mi><mrow><mi>m</mi><mrow><mo>(</mo><mrow><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi></mrow><mo>)</mo></mrow></mrow></msub></mrow></math> , cm 2 /g) is the sum of the attenuation coefficients for photoelectric absorption, Compton scattering, and pair production for a given photon energy, and is given as: <math display="block" id="M69"><mrow><msub><mi>μ</mi><mrow><mtext>m</mtext><mrow><mo>(</mo><mrow><mtext>total</mtext></mrow><mo>)</mo></mrow></mrow></msub><mo>=</mo><msub><mi>μ</mi><mrow><mtext>Photoelectric</mtext></mrow></msub><mo>+</mo><msub><mi>μ</mi><mrow><mtext>Compton</mtext></mrow></msub><mo>+</mo><msub><mi>μ</mi><mrow><mtext>pair</mtext><mo>−</mo><mtext>production</mtext></mrow></msub><mo> </mo><mo>.</mo></mrow></math> On the other hand, the molar extinction coefficient ( <math id="M70"><mi>ε</mi></math> , cm 2 /mol) is the attenuation produced by one mole of the substance and can be obtained as follows: <math display="block" id="M71"><mrow><mi>ε</mi><mo>=</mo><msub><mrow><mi>log</mi></mrow><mrow><mn>10</mn></mrow></msub><mi>e</mi><mrow><mo>(</mo><mrow><msub><mi>μ</mi><mtext>m</mtext></msub><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></munder><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow><mo>)</mo></mrow><mo>=</mo><mn>0.434</mn><msub><mi>μ</mi><mtext>m</mtext></msub><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></munder><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub><mo> </mo><mo>.</mo></mrow></math> 2.2.4 Effective atomic number and effective electron density 3 In medical radiation dosimetry, the effective atomic number ( <math id="M72"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> , dimensionless quantity) and effective electron density ( <math id="M73"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> , electron/g) are remarkable parameters used for ascertaining the radiation absorption in human tissues and dosimetric phantoms. The value of <math id="M74"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> informs about the material subjected to radiation, and the <math id="M75"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> values of complex materials are used in the computations of absorbed dose for radiation therapy [ 18 18 ]. The <math id="M76"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> value for the presently studied composite particleboard samples was computed from the respective atomic compositions, as follows: <math display="block" id="M77"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><mfrac><mrow><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mi>A</mi></msub></mrow></mfrac><msubsup><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></msubsup><mrow><mo>{</mo><mrow><msub><mi>f</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub></mrow><mo>}</mo></mrow></mrow><mrow><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mi>A</mi></msub></mrow></mfrac><msubsup><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></msubsup><mrow><mo>{</mo><mrow><mfrac><mrow><msub><mi>f</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow><mrow><msub><mi>Z</mi><mi>j</mi></msub></mrow></mfrac><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub></mrow><mo>}</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><msubsup><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></msubsup><mrow><mo>{</mo><mrow><msub><mi>f</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub></mrow><mo>}</mo></mrow></mrow><mrow><msubsup><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></msubsup><mrow><mo>{</mo><mrow><mfrac><mrow><msub><mi>f</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow><mrow><msub><mi>Z</mi><mi>j</mi></msub></mrow></mfrac><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub></mrow><mo>}</mo></mrow></mrow></mfrac><mo>,</mo></mrow></math> where, <math id="M78"><mrow><msub><mi>f</mi><mi>j</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>n</mi><mi>j</mi></msub></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></msub><msub><mi>n</mi><mi>j</mi></msub></mrow></mfrac></mrow></math> is the fractional abundance of element j relative to the number of atoms, subject to <math id="M79"><mrow><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi><mi>r</mi></munderover><msub><mi>f</mi><mi>j</mi></msub><mo>=</mo><mn>1</mn></mrow></math> , <math id="M80"><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></math> is Avogadro’s constant, and <math id="M81"><mrow><msub><mi>Z</mi><mi>j</mi></msub></mrow></math> is the atomic number. The value of <math id="M82"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> can also be assessed from the percentage elemental compositions of the sample specimens using ultra-high-resolution field emission scanning electron microscope-energy dispersive X-ray (UHR-FESEM-EDX) spectrometry, and is given by Eq. (6) [ 8 8 , 19 19 ]: <math display="block" id="M83"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><msup><mrow><mrow><mo>[</mo><mrow><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mfrac><mrow><msubsup><mi>N</mi><mi>g</mi><mi>j</mi></msubsup></mrow><mrow><msub><mi>N</mi><mi>g</mi></msub></mrow></mfrac><msub><mi>z</mi><mi>j</mi></msub><msup><mrow/><mrow><mn>3.4</mn></mrow></msup></mrow><mo>]</mo></mrow></mrow><mrow><mfrac bevelled="true"><mn>1</mn><mrow><mn>3.4</mn></mrow></mfrac></mrow></msup><mo>=</mo><msup><mrow><mrow><mo>[</mo><mrow><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mfrac><mrow><mfrac bevelled="true"><mrow><msub><mi>ω</mi><mi>j</mi></msub><msub><mi>z</mi><mi>j</mi></msub></mrow><mrow><msub><mi>A</mi><mi>j</mi></msub></mrow></mfrac></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></msub><mrow><mo>(</mo><mrow><mfrac bevelled="true"><mrow><msub><mi>ω</mi><mi>j</mi></msub><msub><mi>z</mi><mi>j</mi></msub></mrow><mrow><msub><mi>A</mi><mi>j</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mfrac><msub><mi>z</mi><mi>j</mi></msub><msup><mrow/><mrow><mn>3.4</mn></mrow></msup></mrow><mo>]</mo></mrow></mrow><mrow><mfrac bevelled="true"><mn>1</mn><mrow><mn>3.4</mn></mrow></mfrac></mrow></msup><mo>,</mo></mrow></math> where, <math id="M84"><mrow><msubsup><mi>N</mi><mi>g</mi><mi>j</mi></msubsup></mrow></math> and <math id="M85"><mrow><msub><mi>ω</mi><mi>j</mi></msub></mrow></math> are the number of electrons per unit volume of the mixture and weight ratio of the j th constituent element. The elemental compositions, along with <math id="M86"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> and respective density values of the investigated uncured and cured DSF-, SPC-, and SPI-based Rh. spp . particleboards are listed in Table 1 Table 1 . <math id="M87"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> is closely related to <math id="M88"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> by Eq. (7) [ 20 20 ]: Note: DSF0/SPC0/SPI0 = Binderless Rh. spp. ; DSF1 = DSF/ Rh. spp. ; SPC1 = SPC/ Rh. spp. ; SPI1 = SPI/ Rh. spp. ; DSF5 = DSF/IA-PAE/ Rh. spp. ; SPC5 = SPC/IA-PAE/ Rh. spp. ; SPI5 = SPI/IA-PAE/ Rh. spp. ; DSF10 = DSF/IA-PAE/ Rh. spp. ; SPC10 = SPC/IA-PAE/ Rh. spp. ; SPI10 = SPI/IA-PAE/ Rh. spp. ; DSF15 = DSF/IA-PAE/ Rh. spp. ; SPC15 = SPC/IA-PAE/ Rh. spp. ; SPI15 = SPI/IA-PAE/ Rh. spp. ; DSF5ʹ = DSF/NaOH/IA-PAE/ Rh. spp. ; SPC5ʹ = SPC/NaOH/IA-PAE/ Rh. spp. ; SPI5ʹ = SPI/NaOH/IA-PAE/ Rh. spp. ; DSF10ʹ = DSF/NaOH/IA-PAE/ Rh. spp. ; SPC10ʹ = SPC/NaOH/IA-PAE/ Rh. spp. ; SPI10ʹ = SPI/NaOH/IA-PAE/ Rh. spp. ; DSF15ʹ = DSF/NaOH/IA-PAE/ Rh. spp .; SPC15ʹ = SPC/NaOH/IA-PAE/ Rh. spp. ; and SPI15ʹ = SPI/NaOH/IA-PAE/ Rh. spp. refer to 0, 5, 10, and 15 wt% IA-PAE, respectively. 1 2 Sample Code 1 2 ρ 14 1 Weight faction of elements in each sample (%) 1 1 H 1 1 C 1 1 O 1 1 N 1 1 Na 1 1 Mg 1 1 P 1 1 S 1 1 Cl 1 1 K 1 1 Ca 1 1 Mn 1 1 Fe 1 1 Zn 1 1 DSF0 1 1 1.04 1 1 - 1 1 53.90 1 1 43.50 1 1 - 1 1 0.54 1 1 - 1 1 - 1 1 0.26 1 1 0.51 1 1 0.49 1 1 0.80 1 1 - 1 1 - 1 1 - 1 1 SPC0 1 1 1.11 1 1 - 1 1 53.74 1 1 44.18 1 1 - 1 1 0.46 1 1 - 1 1 - 1 1 0.05 1 1 0.34 1 1 - 1 1 0.50 1 1 - 1 1 0.73 1 1 - 1 1 SPI0 1 1 1.05 1 1 - 1 1 51.20 1 1 44.34 1 1 4.30 1 1 0.06 1 1 - 1 1 - 1 1 0.07 1 1 0.03 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 DSF1 1 1 1.08 1 1 - 1 1 53.77 1 1 43.43 1 1 2.15 1 1 0.06 1 1 0.04 1 1 - 1 1 - 1 1 0.24 1 1 0.17 1 1 0.14 1 1 - 1 1 - 1 1 - 1 1 SPC1 1 1 1.03 1 1 - 1 1 49.33 1 1 44.21 1 1 5.32 1 1 0.24 1 1 - 1 1 - 1 1 - 1 1 0.42 1 1 0.16 1 1 0.32 1 1 - 1 1 - 1 1 - 1 1 SPI1 1 1 1.07 1 1 - 1 1 48.21 1 1 44.08 1 1 7.13 1 1 - 1 1 0.13 1 1 - 1 1 - 1 1 0.19 1 1 - 1 1 0.25 1 1 - 1 1 - 1 1 - 1 1 DSF5 1 1 1.07 1 1 - 1 1 51.77 1 1 42.25 1 1 5.09 1 1 0.24 1 1 0.05 1 1 - 1 1 0.04 1 1 0.21 1 1 0.15 1 1 0.13 1 1 - 1 1 0.07 1 1 - 1 1 SPC5 1 1 1.09 1 1 - 1 1 51.24 1 1 43.04 1 1 4.43 1 1 0.17 1 1 - 1 1 0.11 1 1 0.10 1 1 0.48 1 1 0.23 1 1 0.20 1 1 - 1 1 - 1 1 - 1 1 SPI5 1 1 1.06 1 1 - 1 1 53.35 1 1 42.52 1 1 3.11 1 1 0.18 1 1 - 1 1 0.25 1 1 0.04 1 1 0.18 1 1 0.22 1 1 0.15 1 1 - 1 1 - 1 1 - 1 1 DSF10 1 1 1.09 1 1 - 1 1 49.62 1 1 45.09 1 1 4.22 1 1 0.18 1 1 0.13 1 1 - 1 1 - 1 1 0.41 1 1 0.14 1 1 0.21 1 1 - 1 1 - 1 1 - 1 1 SPC10 1 1 1.06 1 1 - 1 1 47.15 1 1 44.57 1 1 7.18 1 1 0.23 1 1 - 1 1 - 1 1 - 1 1 0.33 1 1 0.30 1 1 0.24 1 1 - 1 1 - 1 1 - 1 1 SPI10 1 1 1.08 1 1 - 1 1 48.27 1 1 44.30 1 1 5.95 1 1 0.20 1 1 - 1 1 - 1 1 - 1 1 0.38 1 1 0.47 1 1 0.43 1 1 - 1 1 - 1 1 - 1 1 DSF15 1 1 1.01 1 1 - 1 1 47.74 1 1 45.26 1 1 5.74 1 1 0.16 1 1 - 1 1 - 1 1 - 1 1 0.53 1 1 0.15 1 1 0.25 1 1 - 1 1 0.17 1 1 - 1 1 SPC15 1 1 1.01 1 1 - 1 1 46.07 1 1 45.26 1 1 7.24 1 1 0.32 1 1 - 1 1 - 1 1 - 1 1 0.37 1 1 0.23 1 1 0.17 1 1   1 1 0.34 1 1 - 1 1 SPI15 1 1 1.01 1 1 - 1 1 52.42 1 1 45.67 1 1 - 1 1 0.35 1 1 0.15 1 1 - 1 1 - 1 1 0.39 1 1 0.24 1 1 0.40 1 1 - 1 1 0.38 1 1 - 1 1 DSF5ʹ 1 1 1.09 1 1 - 1 1 50.70 1 1 45.92 1 1 2.94 1 1 0.10 1 1 - 1 1 - 1 1 - 1 1 0.13 1 1 - 1 1 0.14 1 1 - 1 1 0.07 1 1 - 1 1 SPC5ʹ 1 1 1.04 1 1 - 1 1 48.89 1 1 44.52 1 1 5.13 1 1 0.40 1 1 - 1 1 - 1 1 - 1 1 0.63 1 1 0.27 1 1 0.12 1 1 - 1 1 0.04 1 1 - 1 1 SPI5ʹ 1 1 1.03 1 1 - 1 1 50.51 1 1 43.33 1 1 5.53 1 1 0.13 1 1 0.04 1 1 - 1 1 0.03 1 1 0.15 1 1 0.05 1 1 0.13 1 1 - 1 1 0.09 1 1 - 1 1 DSF10ʹ 1 1 1.02 1 1 - 1 1 52.95 1 1 43.88 1 1 - 1 1 0.64 1 1 0.23 1 1 0.43 1 1 - 1 1 0.34 1 1 0.49 1 1 0.55 1 1 - 1 1 0.36 1 1 0.03 1 1 SPC10ʹ 1 1 1.03 1 1 - 1 1 53.26 1 1 42.15 1 1 2.49 1 1 0.36 1 1 - 1 1 0.12 1 1 0.20 1 1 0.49 1 1 0.24 1 1 0.20 1 1 - 1 1 0.39 1 1 - 1 1 SPI10ʹ 1 1 1.02 1 1 - 1 1 50.56 1 1 43.53 1 1 3.91 1 1 0.47 1 1 - 1 1 0.09 1 1 0.02 1 1 0.40 1 1 0.16 1 1 0.63 1 1 - 1 1 0.23 1 1 - 1 1 DSF15ʹ 1 1 1.12 1 1 - 1 1 54.39 1 1 43.64 1 1 1.07 1 1 0.09 1 1 0.04 1 1 0.12 1 1 0.05 1 1 0.02 1 1 0.18 1 1 0.14 1 1 0.01 1 1 0.47 1 1 0.09 1 1 SPC15ʹ 1 1 1.12 1 1 - 1 1 53.91 1 1 45.20 1 1 - 1 1 0.20 1 1 0.10 1 1 0.08 1 1 0.03 1 1 0.05 1 1 0.08 1 1 0.05 1 1 0.04 1 1 0.51 1 1 0.05 1 1 SPI15ʹ 1 1 1.11 1 1 - 1 1 54.69 1 1 44.08 1 1 - 1 1 0.22 1 1 0.03 1 1 0.06 1 1 0.07 1 1 0.21 1 1 0.05 1 1 0.20 1 1 0.05 1 1 0.46 1 1 0.07 <math display="block" id="M90"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>J</mi></msub><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow></mfrac><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>J</mi></munder><msub><mi>n</mi><mi>j</mi></msub><mo>=</mo><msub><mi>N</mi><mtext>A</mtext></msub><mfrac><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow><mi>A</mi></mfrac><mo>,</mo></mrow></math> <math display="block" id="M91"><mrow><mi>A</mi><mo>=</mo><mfrac><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>J</mi></msub><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>J</mi></msub><msub><mi>n</mi><mi>j</mi></msub></mrow></mfrac><mo> </mo><mo> </mo><mo>,</mo></mrow></math> <math display="block" id="M92"><mrow><mi>Z</mi><mo>=</mo><mfrac><mrow><msub><mi>n</mi><mi>i</mi></msub><msub><mi>Z</mi><mi>i</mi></msub></mrow><mi>n</mi></mfrac><mo>,</mo></mrow></math> where, <math id="M93"><mi>A</mi></math> and <math id="M94"><mi>Z</mi></math> denote, respectively, the mean atomic weight and atomic number of the composite material. 2.2.5 HVL, TVL, and MFP 3 HVL ( <math id="M95"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> , cm) is one of the most appropriate parameters for estimating the effective attenuating ability of a particleboard material with respect to photons. It can be expressed as the thickness of the material needed for reducing the radiation intensity by 50%, and is given by [ 8 8 , 21 21 ]: <math display="block" id="M96"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>0.693</mn></mrow><mi>μ</mi></mfrac><mo> </mo><mo>.</mo></mrow></math> Similarly, TVL ( <math id="M97"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub></mrow></math> , cm) corresponds to the thickness of the absorber required for attenuating the radiation intensity by 90%, and is given by: <math display="block" id="M98"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>2.303</mn></mrow><mi>μ</mi></mfrac><mo> </mo><mo>.</mo></mrow></math> Likewise, MFP ( <math id="M99"><mi>λ</mi></math> , cm), which plays a critical role in understanding the exponential attenuation of photons, is the mean distance travelled by a photon before it interacts, and is given by Eq. (12): <math display="block" id="M100"><mrow><mi>λ</mi><mo>=</mo><mfrac><mn>1</mn><mi>μ</mi></mfrac><mo>.</mo></mrow></math> These are the most widely used raw parameters for composite materials that characterize the efficiency of radiation shielding. Particleboard sample materials for incident photons with the lowest values of <math id="M101"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> , <math id="M102"><mrow><msub><mi>X</mi><mrow><mn>1</mn><mo>/</mo><mn>10</mn></mrow></msub></mrow></math> , and <math id="M103"><mi>λ</mi></math> demonstrate good radiation shielding properties and are better suitable for shielding against ionizing radiation for radiation protection applications [ 22 22 ]. 2.2.6 Total molecular, effective atomic, and electronic cross-sections 3 The expressions for the total molecular ( <math id="M104"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> , cm 2 /molecule), effective atomic ( <math id="M105"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> , cm 2 /atom), and electronic ( <math id="M106"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> , cm 2 /electron) cross-sections are given in the following equations [ 23 23 ]: <math display="block" id="M107"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><msub><mrow><mrow><mo>(</mo><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow><mo>)</mo></mrow></mrow><mrow><mtext>DSF</mtext><mo>−</mo><mtext>SPC</mtext><mo>−</mo><mtext>SPI composite</mtext></mrow></msub><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></munder><msub><mi>n</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub><mo>,</mo></mrow></math> <math display="block" id="M108"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></munder><msub><mi>f</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub><mo>=</mo><mfrac><mrow><msub><mrow><mrow><mo>(</mo><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow><mo>)</mo></mrow></mrow><mrow><mtext>DSF</mtext><mo>−</mo><mtext>SPC</mtext><mo>−</mo><mtext>SPI composite</mtext></mrow></msub></mrow><mrow><msub><mi>N</mi><mtext>A</mtext></msub><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></msub><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>ω</mi><mi>j</mi></msub></mrow><mrow><msub><mi>A</mi><mi>j</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></msub><msub><mi>n</mi><mi>j</mi></msub></mrow></mfrac><mo> </mo><mo>,</mo></mrow></math> <math display="block" id="M109"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>j</mi></munder><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>f</mi><mi>j</mi></msub><msub><mi>A</mi><mi>j</mi></msub></mrow><mrow><msub><mi>Z</mi><mi>j</mi></msub></mrow></mfrac></mrow><mo>)</mo></mrow><msub><mrow><mrow><mo>(</mo><mrow><mfrac><mi>μ</mi><mi>ρ</mi></mfrac></mrow><mo>)</mo></mrow></mrow><mi>j</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></mfrac><mo>.</mo></mrow></math> The experimental error associated with the measurement of <math id="M110"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> was estimated using the following relation: <math display="block" id="M111"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>Δ</mi><msub><mi>μ</mi><mtext>m</mtext></msub></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>=</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><msub><mi>ρ</mi><mtext>t</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mrow><mo>[</mo><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>Δ</mi><msub><mi>I</mi><mtext>t</mtext></msub></mrow><mrow><msub><mi>I</mi><mtext>t</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>Δ</mi><msub><mi>I</mi><mtext>o</mtext></msub></mrow><mrow><msub><mi>I</mi><mtext>o</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>ln</mi><mfrac><mrow><mi>Δ</mi><msub><mi>I</mi><mtext>o</mtext></msub></mrow><mrow><msub><mi>I</mi><mtext>t</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>.</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>Δ</mi><msub><mi>ρ</mi><mtext>t</mtext></msub></mrow><mrow><msub><mi>ρ</mi><mtext>t</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mo>]</mo></mrow><mo> </mo><mo>,</mo></mrow></math> where, <math id="M112"><mrow><mi>Δ</mi><msub><mi>I</mi><mtext>t</mtext></msub><mo>,</mo><mo> </mo><mi>Δ</mi><msub><mi>I</mi><mtext>o</mtext></msub></mrow></math> and <math id="M113"><mrow><mi>Δ</mi><msub><mi>ρ</mi><mtext>t</mtext></msub></mrow></math> correspond to the uncertainties (estimated errors) in the intensities <math id="M114"><mrow><msub><mi>I</mi><mtext>t</mtext></msub><mo>,</mo><mo> </mo><msub><mi>I</mi><mtext>o</mtext></msub></mrow></math> and areal density of the composite sample material, respectively. 3 Results and discussion 1 3.1 Analysis of SEM images 2 The micrograph images of the uncured and cured particleboard composites are shown in Figs. 2(a-d) Figs. 2(a-d) . Figure 2(a) Figure 2(a) reveals an agglomeration of fibers, an irregular fracture surface, and micro-cracks that exist in the uncured particleboard composites despite the compression forced onto the cell walls and parenchyma tissue during the hot pressing. The observed void spaces and gaps by the lumen can be attributed to the non-homogeneous distribution of particle sizes, which could decrease the compactness and weaken the bonding between the fiber and the matrix, thus affecting the ability of samples DSF0, SPC0, and SPI0 to serve as X-ray radiation shielding materials. However, Figs. 2(b-d) Figs. 2(b-d) , with more uniform distribution of particles owing to their weaker agglomeration and better particle dispersion, shows a well-formed crystal of the cured particleboard composites. As a result, no isolate nanoparticles are observed, implying that with increasing attenuation of incident photons, DSF15ʹ, SPC15ʹ, and SPI15ʹ exhibit better X-ray attenuation ability. The oxidized IA-PAE and ring-opened azetidinium cross-linking can explain relatively smooth and compact fracture surfaces [ 8 8 ]. Thus, the morphologies of the DSF-, SPC-, and SPI-based particleboard composites are markedly affected by the concentration of NaOH/IA-PAE, thereby improving water resistance and advanced compact cross-section formation. Thus, DSF15ʹ, SPC15ʹ, and SPI15ʹ particleboard composites exhibit uniform densities throughout the samples. Therefore, these composites are likely to exhibit better radiation shielding characteristics. 3.2 XRD analysis 2 All of the XRD patterns in Fig. 3 Fig. 3 indicate preferential (101), (002), and (004) orientations, which are assigned predominant peaks at 2 <math id="M115"><mi>θ</mi></math> in the 13.29 <math id="M116"><mo>°</mo></math> – 14.67 <math id="M117"><mo>°</mo></math> , 22.20 <math id="M118"><mo>°</mo></math> – 22.37 <math id="M119"><mo>°</mo></math> , and 34.52 <math id="M120"><mo>°</mo></math> – 34.61 <math id="M121"><mo>°</mo></math> ranges for DSF-based particleboards, whereas for SPC-based particleboards, the predominant peaks appear in the 13.09 <math id="M122"><mo>°</mo></math> – 14.70 <math id="M123"><mo>°</mo></math> , 22.12 <math id="M124"><mo>°</mo></math> – 22.41 <math id="M125"><mo>°</mo></math> , and 34.48 <math id="M126"><mo>°</mo></math> – 34.75 <math id="M127"><mo>°</mo></math> ranges, respectively. On the other hand, SPI-based samples exhibit predominant peaks approximately in the 13.68 <math id="M128"><mo>°</mo></math> – 14.67 <math id="M129"><mo>°</mo></math> , 22.27 <math id="M130"><mo>°</mo></math> – 22.39 <math id="M131"><mo>°</mo></math> , and 34.40 <math id="M132"><mo>°</mo></math> – 34.72 <math id="M133"><mo>°</mo></math> ranges, respectively. All of the peaks exhibited by the particleboard samples are in excellent agreement with the reported data by the Joint Committee on Powder Diffraction Standards (JCPDS), card no. 36–1451 [ 24 24 ]. Figure 3 Figure 3 clearly shows that in all of the considered cases, the intensities of the (101) and (004) peaks are low, compared with the (002) reflection peak. This indicates that the preferential orientation of the crystallites in the (002) orientation is in the direction perpendicular to the substrate. Moreover, the observed crystallinity index values for the DSF-, SPC-, and SPI-based samples varied in the 36.67 – 41.58%, 27.98 – 42.90%, and 29.99 – 43.12% ranges, respectively, suggesting the predominance of an amorphous phase. Obviously, all of the studied samples had a typical FWHM in the 0.04 <math id="M134"><mo>°</mo></math> – 2.23 <math id="M135"><mo>°</mo></math> range. The proportionate observed values of the crystallinity index indicate that denser structures were formed in the DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . samples, improving the water resistance, consistent with the SEM analysis. This can be ascribed to the cross-linked and interpenetrating structure created by NaOH/IA-PAE with Rh. spp. These results support the suitability of DSF-, SPC-, and SPI/NaOH/IA-PAE-based Rh. spp. particleboards as convenient radiological safety materials for medical applications. 3.3 Elemental atomic compositions, mass attenuation coefficients, and molar extinction coefficients of DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards 2 The elemental compositions of the presently studied uncured and cured DSF-, SPC-, and SPI/NaOH/IA-PAE-based Rh. spp . particleboard samples are listed in Table 1 Table 1 . Both the atomic numbers and atomic weights of the elements found in the particleboard samples were taken from a recent IUPAC technical report [ 25 25 ]. The shielding properties of the DSF-, SPC-, and SPI-based samples increased proportionally with increasing the Fe content from the IA-PAE, which is likely to be advantageous for using these materials in shielding. The <math id="M136"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> values were computed at the specific energies for the three soy protein-based Rh. spp. particleboard samples, as shown in Table 2 Table 2 , and the results are shown in Figs. 4(a-c) Figs. 4(a-c) . These findings are consistent with the results obtained for different composite materials, such as silicate, borate heavy metal oxide glasses, geological materials, and biological matters [ 1 1 , 3 3 , 5 5 , 26 26 ]. It is evident from Table 1 Table 1 that all of the presently considered samples have appropriate densities ranging from 1.01 g/cm 3 to 1.12 g/cm 3 , with optimal values for DSF15ʹ, SPC15ʹ, SPI15ʹ, and SPC0 particleboards. In contrast to lower-density absorbing materials, several primary X-ray beams were attenuated by DSF15ʹ, SPC15ʹ, SPI15ʹ, and SPC0. Owing to closely packed particles, the possibility of X-ray interaction with the atoms of the absorbing material is relatively high [ 3 3 ]. It can be seen that the <math id="M137"><mrow><msub><mi>μ</mi><mi>m</mi></msub></mrow></math> values of the particleboard samples are affected by the IA-PAE concentration, and for all of the IA-PAE addition levels, the <math id="M138"><mrow><msub><mi>μ</mi><mi>m</mi></msub></mrow></math> values decrease exponentially with increasing photon energy [ 3 3 , 8 8 , 17 17 ]. However, this decrease is more apparent for high energies. In addition, photoelectric absorption is the dominant attenuation mechanism in the present study, which is more likely to interfere with photons as its cross-section varies with the atomic number as <math id="M139"><mrow><msup><mi>Z</mi><mn>4</mn></msup></mrow></math> and <math id="M140"><mrow><msup><mi>Z</mi><mn>5</mn></msup></mrow></math> in low- and high-energy regions, respectively, and scales with energy as <math id="M141"><mrow><msup><mi>E</mi><mrow><mn>3.5</mn></mrow></msup></mrow></math> [ 3 3 , 27 27 ]. It is apparent from Table 2 Table 2 and Figs. 4(a-c) Figs. 4(a-c) that the <math id="M142"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> values for each of the DSF-, SPC-, and SPI-based particleboard samples decreased very sharply for the 1.105 ± 0.030 – 0.429 ± 0.011 (cm 2 /g), 1.095 ± 0.012 – 0.414 ± 0.041 (cm 2 /g), and 1.102 ± 0.012 – 0.429 ± 0.010 (cm 2 /g) ranges, as the photon energy changed from 16.59 – 25.26 keV. Based on Figs. 4(a-c) Figs. 4(a-c) , it is obvious that among the selected samples, the DSF15ʹ, SPC15ʹ, and SPI15ʹ samples had the highest values of <math id="M143"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> , since they were the most dense. This is because the highest amounts of carbon, oxygen, and other elements were contained in these particleboard samples ( Table 1 Table 1 ). It is also possible to attribute the presence of higher carbon and oxygen concentrations to the high percentage of their flow at high temperatures in the composite samples. This can also be owing to the chemical composition of DSF, SPC, SPI, NaOH/IA-PAE, and Rh. spp . particles, and significantly affects DSF15ʹ, SPC15ʹ, and SPI15ʹ particleboards, which can help to improve their performance in radiation shielding applications. These findings suggest that, relative to the other sample composite formulations, 15 wt% IA-PAE better attenuates 16.59 – 25.26 keV photons, because these photons interact primarily through the photoelectric effect with the absorbing material. These results confirm the validity of DSF-, SPC-, and SPI/NaOH/ Rh. spp . with 15 wt% IA-PAE as appropriate radiation shielding materials. 1 2 Sample code 2 1 16.59 keV 2 1 17.46 keV 2 1 21.21 keV 2 1 25.26 keV 1 1 <math id="M145"><mrow><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> (cm 2 /g) 1 1 <math id="M146"><mrow><mi>Δ</mi><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> ±(%) 1 1 <math id="M147"><mrow><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> (cm 2 /g) 1 1 <math id="M148"><mrow><mi>Δ</mi><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> ± (%) 1 1 <math id="M149"><mrow><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> (cm 2 /g) 1 1 <math id="M150"><mrow><mi>Δ</mi><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> ± (%) 1 1 <math id="M151"><mrow><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> (cm 2 /g) 1 1 <math id="M152"><mrow><mi>Δ</mi><msub><mi>μ</mi><mstyle mathvariant="bold" mathsize="normal"><mi>m</mi></mstyle></msub></mrow></math> ± (%) 1 1 DSF0 1 1 1.096 1 1 0.018 1 1 0.914 1 1 0.015 1 1 0.620 1 1 0.031 1 1 0.435 1 1 0.023 1 1 SPC0 1 1 1.088 1 1 0.015 1 1 0.921 1 1 0.047 1 1 0.611 1 1 0.035 1 1 0.438 1 1 0.029 1 1 SPI0 1 1 1.102 1 1 0.026 1 1 0.919 1 1 0.016 1 1 0.622 1 1 0.024 1 1 0.440 1 1 0.017 1 1 DSF1 1 1 1.049 1 1 0.037 1 1 0.925 1 1 0.030 1 1 0.638 1 1 0.025 1 1 0.429 1 1 0.011 1 1 SPC1 1 1 1.033 1 1 0.019 1 1 0.916 1 1 0.011 1 1 0.559 1 1 0.030 1 1 0.414 1 1 0.041 1 1 SPI1 1 1 1.057 1 1 0.023 1 1 0.949 1 1 0.015 1 1 0.633 1 1 0.018 1 1 0.428 1 1 0.010 1 1 DSF5 1 1 1.095 1 1 0.016 1 1 0.988 1 1 0.047 1 1 0.652 1 1 0.019 1 1 0.451 1 1 0.023 1 1 SPC5 1 1 1.087 1 1 0.035 1 1 0.965 1 1 0.013 1 1 0.611 1 1 0.022 1 1 0.426 1 1 0.037 1 1 SPI5 1 1 1.098 1 1 0.011 1 1 0.979 1 1 0.031 1 1 0.583 1 1 0.024 1 1 0.449 1 1 0.015 1 1 DSF10 1 1 1.069 1 1 0.035 1 1 0.998 1 1 0.012 1 1 0.670 1 1 0.022 1 1 0.465 1 1 0.016 1 1 SPC10 1 1 1.071 1 1 0.026 1 1 0.985 1 1 0.033 1 1 0.654 1 1 0.035 1 1 0.418 1 1 0.041 1 1 SPI10 1 1 1.091 1 1 0.018 1 1 0.992 1 1 0.022 1 1 0.655 1 1 0.017 1 1 0.437 1 1 0.015 1 1 DSF15 1 1 1.084 1 1 0.021 1 1 0.997 1 1 0.043 1 1 0.660 1 1 0.014 1 1 0.460 1 1 0.016 1 1 SPC15 1 1 1.076 1 1 0.016 1 1 0.969 1 1 0.012 1 1 0.651 1 1 0.027 1 1 0.452 1 1 0.018 1 1 SPI15 1 1 1.089 1 1 0.031 1 1 0.944 1 1 0.014 1 1 0.593 1 1 0.025 1 1 0.458 1 1 0.011 1 1 DSF5ʹ 1 1 1.044 1 1 0.025 1 1 0.957 1 1 0.037 1 1 0.645 1 1 0.023 1 1 0.442 1 1 0.018 1 1 SPC5ʹ 1 1 1.027 1 1 0.012 1 1 0.965 1 1 0.016 1 1 0.599 1 1 0.017 1 1 0.434 1 1 0.013 1 1 SPI5ʹ 1 1 1.081 1 1 0.022 1 1 0.943 1 1 0.035 1 1 0.603 1 1 0.026 1 1 0.446 1 1 0.020 1 1 DSF10ʹ 1 1 1.060 1 1 0.031 1 1 0.961 1 1 0.050 1 1 0.653 1 1 0.012 1 1 0.465 1 1 0.016 1 1 SPC10ʹ 1 1 1.066 1 1 0.012 1 1 0.972 1 1 0.023 1 1 0.629 1 1 0.022 1 1 0.454 1 1 0.014 1 1 SPI10ʹ 1 1 1.097 1 1 0.028 1 1 0.964 1 1 0.023 1 1 0.616 1 1 0.018 1 1 0.461 1 1 0.020 1 1 DSF15ʹ 1 1 1.105 1 1 0.030 1 1 1.010 1 1 0.016 1 1 0.747 1 1 0.022 1 1 0.499 1 1 0.017 1 1 SPC15ʹ 1 1 1.095 1 1 0.012 1 1 1.023 1 1 0.019 1 1 0.686 1 1 0.022 1 1 0.485 1 1 0.011 1 1 SPI15ʹ 1 1 1.102 1 1 0.012 1 1 1.031 1 1 0.012 1 1 0.740 1 1 0.017 1 1 0.494 1 1 0.014 Figures 5(a-c) Figures 5(a-c) clearly show the dependence of molar extinction coefficients for DSF/NaOH/IA-PAE/ Rh. spp ., SPC/NaOH/IA-PAE/ Rh. spp ., and SPI/NaOH/IA-PAE/ Rh. spp . particleboards on the incident photon energy. Clearly, <math id="M153"><mi>ε</mi></math> for all of the studied particleboard samples depends inversely on the photon energy, and the trend is identical to that of <math id="M154"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> . From these figures, <math id="M155"><mi>ε</mi></math> values reached their maxima in the 88.976 – 186.164 (cm 2 /mol) range for DSF-based particleboards, 94.250 – 172.861 (cm 2 /mol) range for SPC-based particleboards, and 60.292 – 205.235 (cm 2 /mol) range for SPI-based particleboards, at the selected photon energies; the photoelectric effect plays a dominant role. In addition, from Figs. 5(a-c) Figs. 5(a-c) , <math id="M156"><mi>ε</mi></math> increases with IA-PAE for all selected particleboard samples, but tends to decrease sharply with increasing photon energy, which could be attributed to the high molecular weight of IA-PAE. The DSF15ʹ, SPC15ʹ, and SPI15ʹ samples exhibit the highest <math id="M157"><mi>ε</mi></math> among the DSF-, SPC-, and SPI-based particleboard samples because of their higher number of atoms compared with the other samples, which means their molecular weight is higher, compared with the other samples. The higher values of <math id="M158"><mi>ε</mi></math> for the DSF15ʹ, SPC15ʹ, and SPI15ʹ particleboards suggest better shielding properties, compared with the other particleboard samples. 3.4 Effective atomic numbers and effective electron densities of the DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards 2 The evaluated values of <math id="M159"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> and experimental uncertainties for the current samples are listed in Table 3 Table 3 . Some typical plots of <math id="M160"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> versus the photon energy are shown in Figs. 6(a-c) Figs. 6(a-c) . The behavior of <math id="M161"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> for all of the particleboards was almost identical. Similar trend were observed for different materials, such as biological compounds, concretes, alloys, and glass systems [ 28 28 – 31 31 28–31 ]. The value of <math id="M162"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> for the DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards increased with increasing the IA-PAE modifier content, and appeared to decrease with increasing incident photon energy, as in the case of <math id="M163"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> and <math id="M164"><mi>ε</mi></math> . This suggests that, at low energies, photons are more likely to interact with particleboards. As shown in Table 3 Table 3 , the <math id="M165"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> values for all of the studied particleboard samples are in the 9.010 ± 0.120 – 16.033 ± 0.104 range. In addition, the <math id="M166"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> values for all of the studied samples varied significantly with the atomic number of the constituent elements in the studied composite samples [ 31 31 ]. The atoms of higher–atomic–number absorbing material are more likely to encounter photon targets; thus, the interaction probability is relatively high owing to the photoelectric interaction. Therefore, the likelihood of X-ray attenuation occurring in the sample is high. Thus, the higher values of <math id="M167"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> observed at low photon energies are owing to the contribution of the photoelectric absorption, which is more likely, compared with the Compton scattering and pair production processes. Therefore, <math id="M168"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> for the total photon interaction is high at low photon energies and low at high photon energies, with a peak owing to the photoelectric effect in the studied particleboard samples, which occurs around the K-absorption edge of the medium- Z element. It can be seen from Figs. 6(a-c) Figs. 6(a-c) that the maximal values of <math id="M169"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> were observed for DSF15ʹ, SPC15ʹ, and SPI15ʹ, respectively, which can be explained by the chemical composition and relatively high values of <math id="M170"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> in these samples, compared with the other samples. This improvement in the <math id="M171"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> values of DSF15ʹ, SPC15ʹ, and SPI15ʹ with an enhancement in the IA-PAE concentration suggests that the shielding ability of the particleboards can be improved by incorporating NaOH/IA-PAE. The minimal <math id="M172"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> values were found to effectively correspond to DSF0, SPC0, and SPI0, respectively, at 25.26 keV. This can be explained by noting that as the photon energy increased, the <math id="M173"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> value could decrease owing to the increased transmission of incident photons through the particleboard material, reducing photon attenuation in the particleboard samples. Therefore, the DSF15ʹ, SPC15ʹ, and SPI15ʹ particleboard exhibited the highest photon shielding efficiency. 1 1 Sample code 1 1 16.59 keV 1 1 17.46 keV 1 1 21.21 keV 1 1 25.26 keV 1 1 DSF0 1 1 12.538 ± 0.100 1 1 10.945 ± 0.118 1 1 10.131 ± 0.064 1 1 9.010 ± 0.120 1 1 SPC0 1 1 12.655 ± 0.168 1 1 11.048 ± 0.122 1 1 10.177 ± 0.126 1 1 9.038 ± 0.133 1 1 SPI0 1 1 11.906 ± 0.121 1 1 11.261 ± 0.130 1 1 10.153 ± 0.111 1 1 9.026 ± 0.091 1 1 DSF1 1 1 10.830 ± 0.167 1 1 10.339 ± 0.127 1 1 10.448 ± 0.152 1 1 9.404 ± 0.126 1 1 SPC1 1 1 10.615 ± 0.104 1 1 10.316 ± 0.158 1 1 10.363 ± 0.144 1 1 9.311 ± 0.077 1 1 SPI1 1 1 10.811 ± 0.130 1 1 11.001 ± 0.109 1 1 10.401 ± 0.132 1 1 9.518 ± 0.105 1 1 DSF5 1 1 11.705 ± 0.095 1 1 10.782 ± 0.115 1 1 10.777 ± 0.146 1 1 9.784 ± 0.169 1 1 SPC5 1 1 11.958 ± 0.173 1 1 10.526 ± 0.121 1 1 10.635 ± 0.141 1 1 9.752 ± 0.132 1 1 SPI5 1 1 11.853 ± 0.111 1 1 10.631 ± 0.146 1 1 10.668 ± 0.172 1 1 9.687 ± 0.145 1 1 DSF10 1 1 12.461 ± 0.150 1 1 11.834 ± 0.129 1 1 10.809 ± 0.119 1 1 9.944 ± 0.101 1 1 SPC10 1 1 12.204 ± 0.108 1 1 11.757 ± 0.131 1 1 10.957 ± 0.103 1 1 9.983 ± 0.141 1 1 SPI10 1 1 12.533 ± 0.161 1 1 11.614 ± 0.150 1 1 10.981 ± 0.180 1 1 9.907 ± 0.111 1 1 DSF15 1 1 13.469 ± 0.185 1 1 12.015 ± 0.136 1 1 11.101 ± 0.117 1 1 10.216 ± 0.127 1 1 SPC15 1 1 14.072 ± 0.143 1 1 11.978 ± 0.105 1 1 11.079 ± 0.136 1 1 10.308 ± 0.123 1 1 SPI15 1 1 13.476 ± 0.102 1 1 11.947 ± 0.185 1 1 11.062 ± 0.140 1 1 10.279 ± 0.057 1 1 DSF5ʹ 1 1 14.704 ± 0.136 1 1 12.348 ± 0.107 1 1 11.388 ± 0.151 1 1 10.493 ± 0.160 1 1 SPC5ʹ 1 1 14.669 ± 0.128 1 1 12.242 ± 0.161 1 1 11.294 ± 0.129 1 1 10.450 ± 0.144 1 1 SPI5ʹ 1 1 14.594 ± 0.140 1 1 12.336 ± 0.172 1 1 11.356 ± 0.135 1 1 10.515 ± 0.101 1 1 DSF10ʹ 1 1 15.163 ± 0.116 1 1 12.690 ± 0.133 1 1 11.616 ± 0.064 1 1 10.688 ± 0.173 1 1 SPC10ʹ 1 1 15.195 ± 0.102 1 1 12.840 ± 0.175 1 1 11.745 ± 0.103 1 1 10.723 ± 0.159 1 1 SPI10ʹ 1 1 14.964 ± 0.162 1 1 12.731 ± 0.181 1 1 11.628 ± 0.155 1 1 10.620 ± 0.142 1 1 DSF15ʹ 1 1 15.942 ± 0.185 1 1 13.115 ± 0.120 1 1 11.979 ± 0.161 1 1 10.974 ± 0.138 1 1 SPC15ʹ 1 1 16.033 ± 0.104 1 1 13.106 ± 0.154 1 1 12.128 ± 0.159 1 1 10.928 ± 0.145 1 1 SPI15ʹ 1 1 15.839 ± 0.127 1 1 13.110 ± 0.097 1 1 11.977 ± 0.133 1 1 10.961 ± 0.111 The estimated <math id="M175"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> values for the different particleboard samples are summarized in Table 4 Table 4 . In addition, the dependence of <math id="M176"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> on the incident photon energy is shown in Figs. 7(a-c) Figs. 7(a-c) . Evidently, both the <math id="M177"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> and <math id="M178"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> values are closely related, and a similar trend was noticed for the dependence of <math id="M179"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> on the incident photon energy, since <math id="M180"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> is directly proportional to <math id="M181"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> , as is evident from Figs. 7(a-c) Figs. 7(a-c) . The <math id="M182"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> values for the different photon energy ranges were 1.921 ± 0.091 <math id="M183"><mo>×</mo></math> 10 23 – 3.644 ± 0.071 <math id="M184"><mo>×</mo></math> 10 23 (electrons/g), 1.777 ± 0.046 <math id="M185"><mo>×</mo></math> 10 23 – 3.664 ± 0.029 <math id="M186"><mo>×</mo></math> 10 23 (electron/g), and 2.007 ± 0.013 <math id="M187"><mo>×</mo></math> 10 23 – 3.620 ± 0.051 <math id="M188"><mo>×</mo></math> 10 23 (electrons/g) for the DSF-, SPC-, and SPI-based Rh. spp . particleboards. Since the DSF15ʹ, SPC15ʹ, and SPI15ʹ samples exhibited a wide range of atomic numbers, from carbon to zinc, compared with the other particleboard samples, they had higher <math id="M189"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> . The maximal values of <math id="M190"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> registered for the DSF15ʹ, SPC15ʹ, and SPI15ʹ samples suggest their preferable radiation shielding effectiveness compared with the other studied particleboards. Therefore, the presence and symmetrical distribution of DSF15ʹ, SPC15ʹ, and SPI15ʹ with high effective electron densities increased the interaction probability between photons and the particleboard composites. 1 1 Sample code 1 1 16.59 keV 1 1 17.46 keV 1 1 21.21 keV 1 1 25.26 keV 1 1 DSF0 1 1 2.674 ± 0.042 1 1 2.334 ± 0.068 1 1 2.160 ± 0.043 1 1 1.921 ± 0.091 1 1 SPC0 1 1 2.488 ± 0.079 1 1 2.172 ± 0.020 1 1 2.001 ± 0.050 1 1 1.777 ± 0.046 1 1 SPI0 1 1 3.247 ± 0.006 1 1 2.504 ± 0.015 1 1 2.257 ± 0.009 1 1 2.007 ± 0.013 1 1 DSF1 1 1 2.559 ± 0.017 1 1 2.443 ± 0.049 1 1 2.468 ± 0.026 1 1 2.222 ± 0.058 1 1 SPC1 1 1 2.491 ± 0.013 1 1 2.421 ± 0.040 1 1 2.432 ± 0.035 1 1 2.185 ± 0.074 1 1 SPI1 1 1 2.754 ± 0.080 1 1 2.802 ± 0.055 1 1 2.649 ± 0.041 1 1 2.425 ± 0.016 1 1 DSF5 1 1 2.415 ± 0.056 1 1 2.205 ± 0.071 1 1 2.224 ± 0.015 1 1 2.010 ± 0.039 1 1 SPC5 1 1 2.671 ± 0.081 1 1 2.351 ± 0.060 1 1 2.375 ± 0.073 1 1 2.178 ± 0.021 1 1 SPI5 1 1 2.817 ± 0.022 1 1 2.530 ± 0.038 1 1 2.539 ± 0.054 1 1 2.305 ± 0.030 1 1 DSF10 1 1 2.944 ± 0.075 1 1 2.796 ± 0.040 1 1 2.554 ± 0.081 1 1 2.349 ± 0.010 1 1 SPC10 1 1 2.864 ± 0.038 1 1 2.759 ± 0.066 1 1 2.571 ± 0.080 1 1 2.343 ± 0.017 1 1 SPI10 1 1 2.941 ± 0.053 1 1 2.726 ± 0.017 1 1 2.577 ± 0.036 1 1 2.325 ± 0.049 1 1 DSF15 1 1 2.755 ± 0.011 1 1 2.458 ± 0.032 1 1 2.271 ± 0.024 1 1 2.091 ± 0.062 1 1 SPC15 1 1 2.879 ± 0.064 1 1 2.451 ± 0.090 1 1 2.267 ± 0.051 1 1 2.109 ± 0.016 1 1 SPI15 1 1 2.642 ± 0.097 1 1 2.342 ± 0.031 1 1 2.168 ± 0.045 1 1 2.015 ± 0.090 1 1 DSF5ʹ 1 1 3.156 ± 0.014 1 1 2.651 ± 0.086 1 1 2.445 ± 0.060 1 1 2.253 ± 0.031 1 1 SPC5ʹ 1 1 3.001 ± 0.033 1 1 2.505 ± 0.070 1 1 2.311 ± 0.039 1 1 2.138 ± 0.027 1 1 SPI5ʹ 1 1 3.012 ± 0.048 1 1 2.546 ± 0.011 1 1 2.343 ± 0.052 1 1 2.169 ± 0.043 1 1 DSF10ʹ 1 1 3.582 ± 0.069 1 1 2.998 ± 0.023 1 1 2.740 ± 0.091 1 1 2.525 ± 0.020 1 1 SPC10ʹ 1 1 3.566 ± 0.060 1 1 3.013 ± 0.025 1 1 2.756 ± 0.037 1 1 2.516 ± 0.049 1 1 SPI10ʹ 1 1 3.512 ± 0.084 1 1 2.988 ± 0.061 1 1 2.729 ± 0.080 1 1 2.492 ± 0.031 1 1 DSF15ʹ 1 1 3.644 ± 0.071 1 1 2.997 ± 0.023 1 1 2.758 ± 0.025 1 1 2.508 ± 0.080 1 1 SPC15ʹ 1 1 3.664 ± 0.029 1 1 2.995 ± 0.014 1 1 2.772 ± 0.047 1 1 2.498 ± 0.016 1 1 SPI15ʹ 1 1 3.620 ± 0.051 1 1 2.996 ± 0.033 1 1 2.737 ± 0.029 1 1 2.505 ± 0.070 3.5 HVL, TVL, and MFP values of the DSF-, SPC-, SPI/NaOH/IA-PAE/ Rh. spp . particleboards 2 Figures 8(a-c) Figures 8(a-c) show the HVL ( X 1/2 ), while Figs. 9(a-c) Figs. 9(a-c) illustrate the TVL ( X 1/10 ) of the DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboard samples. From these figures, it is clear that HVL and TVL are affected by the chemical contents of the particleboard samples as well as by the incident photon energy. Furthermore, with increasing the incident photon energy, the HVL and TVL values for all of the studied particleboard samples increase rapidly and reach maxima at 25.26 keV. This can be attributed to the dominance of the photon interaction process, which in this range of energies is the photoelectric effect [ 8 8 , 17 17 , 19 19 , 21 21 , 23 23 ]. These results indicate that as the energy increases, energetic photons are more likely to penetrate their target medium. It is worth noting that with increasing the IA-PAE concentration, the variations of the HVL and TVL become identical, and the only difference is in the magnitudes of the HVL and TVL. Moreover, it is clear that DSF15ʹ, SPC15ʹ, and SPI15ʹ have the lowest HVL and TVL values, which can be explained by a steady increase in the density ( Table 1 Table 1 ) and an increase in the mass attenuation coefficients ( Table 2 Table 2 ). This can also be ascribed to the more significant presence of high–atomic– number elements in the samples. This suggests more photon interactions with DSF15ʹ, SPC15ʹ, and SPI15ʹ, which ensures more effective radiation shielding. Figures 10(a-c) Figures 10(a-c) show the dependence of MFP ( <math id="M193"><mi>λ</mi></math> ) on the photon energy, for the DSF-, SPC-, and SPI-based Rh. spp . particleboards. Evidently, MFP is high for the samples with low <math id="M194"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> and <math id="M195"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> . On the other hand, for the samples with higher <math id="M196"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> and <math id="M197"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> , the MFP values are relatively small. Evidently, MFP varies significantly across the particleboard samples as the photon energy increases from 16.59 keV to 25.26 keV. According to this figure, DSF15ʹ, SPC15ʹ, and SPI15ʹ have the lowest MFP values, which validates our hypothesis that adding NaOH/IA-PAE improved the radiation shielding properties of the DSF-, SPC-, SPI/NaOH/IA-PAE/ Rh. spp . particleboard samples. However, it should be pointed out that DSF0, SPC0, and SPI0 have the highest MFP values among all of the studied particleboard samples, followed closely by DSF1, SPC1, and SPI1. It was revealed that DSF15ʹ, SPC15ʹ, and SPI15ʹ samples with the lowest values of HVL, TVL, and MFP appear to be better materials for reducing the radiation intensity, suggesting that these materials have good shielding characteristics. 3.6 Total molecular, effective atomic, and electronic cross-sections of the DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards 2 The energy dependence of the computed <math id="M198"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> , <math id="M199"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> , and <math id="M200"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> is displayed in Figs. 11(a-c) Figs. 11(a-c) , 12(a-c), and 13(a-c), respectively. It is worth noting from Figs. 11(a-c) Figs. 11(a-c) and 12(a-c) 12(a-c) that there is a certain variation in the values of <math id="M201"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> and <math id="M202"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> , but as the photon energy increases, the values decrease exponentially. It can be clearly seen Figs. 13(a-c) Figs. 13(a-c) that the SPC0, DSF5, SPC5, SPI5, DSF10, DSF15, SPC15, and SPI15 samples have higher <math id="M203"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> compared with the other particleboard samples, but the values drop sharply with increasing photon energy. Moreover, the values of these parameters decrease with increasing the number of elements in the particleboard samples. DSF15ʹ, SPC15ʹ, and SPI15ʹ, which contain the 15 wt% IA-PAE (highest value), exhibit the highest <math id="M204"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> . The highest values of <math id="M205"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> are observed for DSF15, SPC15, and SPI15. In contrast, the DSF15ʹ, SPC15ʹ, and SPI15ʹ samples exhibit the lowest <math id="M206"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> values compared with the other selected samples. From these results, it can be concluded that DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards have appropriate shielding characteristics, and are likely to be beneficial in medical health applications. 4 Conclusion 1 In the present work, we determined the radiation attenuation parameters of DSF-, SPC-, and SPI/NaOH/IA-PAE/ Rh. spp . particleboards with respect to low–energy X-ray interactions in the 16.59 – 25.26 keV range. All of the studied particleboard samples were amorphous, which was validated by XRD. The micrograph images of the studied DSF15ʹ, SPC15ʹ, and SPI15ʹ particleboards revealed enhancement in terms of compactness and the number of void spaces, compared with the uncured samples. The radiation attenuation parameters depended on the particleboard composition, photon energy, and concentration of NaOH/IA-PAE modifiers. The DSF15ʹ, SPC15ʹ, and SPI15ʹ particleboards had the highest values of <math id="M207"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub></mrow></math> , <math id="M208"><mi>ε</mi></math> , <math id="M209"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow></math> , and <math id="M210"><mrow><msub><mi>N</mi><mrow><mtext>el</mtext></mrow></msub></mrow></math> , while the HVL, TVL, and MFP values of these particleboards were the lowest among the other particleboards. These particleboard samples also exhibited the highest values of <math id="M211"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>m</mtext></mrow></msub></mrow></math> and the smallest values of <math id="M212"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>a</mtext></mrow></msub></mrow></math> and <math id="M213"><mrow><msub><mi>σ</mi><mrow><mtext>t</mtext><mo>,</mo><mtext>el</mtext></mrow></msub></mrow></math> , respectively. 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Material preparation, data collection, and analysis were performed by Damilola Oluwafemi Samson, Ahmad Shukri, Mohd Zubir Mat Jafri, Rokiah Hashim, Mohd Zahri Abdul Aziz, Sylvester Jande Gemanam, and Mohd Fahmi Mohd Yusof. The first draft of the manuscript was written by Damilola Oluwafemi Samson and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. 10.1007/s41365-021-00862-6 This work was supported by the Universiti Sains Malaysia (USM), from the Research University Grant allocation (Nos. 304/PFIZIK/6316173, 1001/PFIZIK/822173, 203/PTEKIND/6711525). 2020-10-27 2021-01-05 2021-01-13 2021-03-14 2021-03-01 2021-03-31 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2021 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-021-00862-6 http://dx.doi.org/10.1007/s41365-021-00862-6 . 2021 Nuclear Science and Techniques 03 32