1 Introduction

Polymer nanocomposites have become an up-and-coming category of materials, benefiting from the distinctive characteristics of nanoscale fillers to enhance the performance of polymers. These materials possess a combination of beneficial attributes from polymers and nanoparticles, resulting in enhanced mechanical, thermal, and electrical capabilities compared to conventional polymer matrices. A strategic approach to further enhance the properties and diversity of polymer nanocomposites involves the incorporation of metal oxides and metallic nanoparticles into polymer matrices (Kassem et al. 2023; Maksoud et al. 2021).

Polymers have been extensively used as electrical insulating materials for underground cables since the early 20th century due to their notable attributes, such as reliability, accessibility, simplicity of manufacture, and cost-effectiveness. Thermoplastic polymers, polyvinyl chloride (PVC), and polyethylene (PE) are the predominant synthetic polymers for cable applications. PVC is a polymer with remarkable versatility and widespread use, offering several benefits. PVC, owing to its economical nature and favorable dielectric and processing characteristics, is extensively used as an insulating material. Moreover, it exhibits consistent chemical characteristics, has exceptional fire retardancy attributed to the use of chlorine, and demonstrates a commendable level of environmental sustainability.

Furthermore, its remarkable electrical insulating properties make it a preferred choice for electrical cables and wiring applications (Abdelghany et al. 2019; Ebnalwaled and Thabet 2016; Elsad et al. 2021; Muzaffar et al. 2019). In a recent study by Abdel-Gawad et al. (Abdel-Gawad et al. 2018), PVC insulating materials’ dielectric and mechanical properties were enhanced by incorporating functionalized SiO2 into the matrix. Abdel Maksoud et al. (Abdel Maksoud et al. 2023a, b) have recently studied the effect of Cu/Cu2O rods on PVC’s optical and dielectric properties.

The metallic tungstate family is an area of interest for researchers, and one notable member is silver tungstate (Ag2WO4). This compound exhibits significant structural versatility, leading to various potential technological applications. Extensive research has been conducted on the versatile characteristics of materials based on Ag2WO4. These properties include a notable capacity for adsorbing dyes and exhibiting antibacterial, photoluminescent, electrochemical sensing, photocatalytic, lubricating, light-emitting diode, gate dielectric, and electro-catalytic capabilities (Lima Patrocinio et al. 2023; Tahir et al. 2023; Akram et al. 2023; Nobre et al. 2019; Gouveia et al. 2022).

A high-energy electron beam (E-beam) irradiation strategy has gained extensive application in modifying polymeric materials. This technique enables the induction of cross-linking, branching, grafting, and chain scission within these materials and may be carried out in various active or inert conditions (Dadbin et al. 2005; Wang et al. 2020). The study by Kim et al. (Kim et al. 2023) examines the impact of E-beam irradiation on a range of characteristics shown by polyethylene composite materials that have been coated with polyurethane-treated short fibers of carbon, including thermal, dynamic mechanical, electrical, and electromagnetic interference shielding. Furthermore, E-beam irradiation is environmentally friendly and functions without using solvents and reagents commonly employed in moist chemical processes. During production, it offers benefits, including rapid processing, a high flow rate, uniformity, and environmental and labor protection (Abou Elmaaty et al. 2022). E-beam irradiation has extensive applicability in a variety of fields, such as fiber surface alteration (Thite et al. 2018), water treatment (Deogaonkar et al. 2019), characteristic enhancement (Chen et al. 2020), sterilization of medical instruments and food products (Abou Elmaaty et al. 2022), and polymer and composite curing (Pramanik et al. 2014; Kim et al. 2005).

This work aimed to synthesize Ag2WO4 with a rod-like shape, utilizing the co-precipitation technique. TheAg2WO4 rods were incorporated into PVC using the solution casting technique, resulting in a PVC/Ag2WO4 nanocomposite film. The effects of exposing the PVC/Ag2WO4 nanocomposite film to different doses of electron beam (E-beam) irradiation (0, 25, 50, and 100) kGy were investigated. The study focused on analyzing the changes in the film’s structure, optical properties, thermal behavior, electrical modulus, impedance modulus, and dielectric properties.

2 Experimental

2.1 Materials

Sigma Aldrich provided the polyvinyl chloride (PVC) with a molecular weight of 48000. Tetrahydrofuran (THF) and di-octyl phthalate (DOP) (Molecular weight: 390.6 g/mol and specific gravity: 0.978 at 20 °C) were purchased from (New Delhi, INDIA). The sodium tungstate dihydrate (Na2WO4.2H2O) and silver nitrate (AgNO3) were obtained from Alfa-Aesar (USA) and double-distilled water.

2.2 Synthesis of Ag2WO4 NPs

Stoichiometric weights of Na2WO4.2H2O and AgNO3 were dissolved separately in 50 mL of double-distilled water. The sodium tungstate dihydrate solution was introduced dropwise into the silver nitrate solution while stirring with a magnetic agitator. One hour was spent stirring this suspension at room temperature. Following separation, the precipitate Ag2WO4 was carefully washed with double-distilled water and desiccated at 250°C for three hours (Rajamohan et al. 2017; Shi et al. 2016; Zhu et al. 2017).

2.3 Synthesis of PVC/Ag2WO4 nanocomposite films

For pure PVC, 3.5 g of PVC dissolved in 100 mL of THF solution with a magnetic stirrer for an hour. After that, 3 ml of di-octyl phthalate (DOP) was introduced to the mixture as a plasticizer (Alshahrani et al. 2021a, b). For PVC/Ag2WO4 nanocomposite films, Ag2WO4 (6%wt.) was added to the above mixture. A total of 24 h of stirring were required to ensure that the Ag2WO4 rods were distributed uniformly throughout the PVC. The pure PVC and PVC/Ag2WO4 nanocomposite films were created by casting the solutions onto Petri plates (Kassem et al. 2023). After a day, the nanocomposite films could be removed from the Petri plates since the THF solvent had evaporated. Then, the PVC/Ag2WO4 nanocomposite film was exposed to E-beam irradiation with different doses (0, 25, 50, and 100 kGy) using a 3 MeV linear electron beam accelerator facility at the (National Center for Radiation Research and Technology, Egyptian Atomic Energy Authority (EAEA), Nasr City, Cairo, Egypt. The voltages were adjusted to 3 MeV, the beam current to 10 mA, and the velocity to 3.39 m/min.

2.4 Characterization

The Ag2WO4 pure polyvinyl chloride (PVC) and E-beam irradiated PVC/Ag2WO4 nanocomposite were subjected to characterization. The crystal structure and phase investigations were conducted using X-ray diffraction (XRD) using a Shimadzu 6000 XRD instrument, employing an 8°/min scanning rate. FTIR spectra of PVC/Ag2WO4 nanocomposite films were acquired using (Nicolet iS10) in the United States. Scanning electron microscopy (SEM) and energy dispersive x-ray spectroscopy (EDX) techniques were used to assess a nanocomposite film’s surface morphology and elemental composition with an accelerating voltage of 220 kV, namely the JEOL JTEM-1230 model. The optical characterization was conducted using a (Jasco, V-570) UV-vis-NIR spectrophotometer. The optical properties of Ag2WO4 were studied via diffuse reflectance spectroscopy DRS. Thermal properties were conducted using TGA Q500, and the data were analyzed by TA Universal analysis. Electrical and dielectric tests were carried out using a powerful broadband dielectric spectrometer, BDS, in conjunction with a high-resolution Alpha analyzer equipped with an active sample head (Novocontrol GmbH idea 40). In a parallel plate configuration, the samples were sandwiched between two brass electrodes with a 10–20 mm diameter coated in gold. WINDETA software managed the data collecting and control operations. The tests were made across a frequency range of 0.1 Hz to 20 MHz.

3 Results and discussion

3.1 Structural studies

Figure 1(a) displays the X-ray diffraction (XRD) pattern of the co-precipitated Ag2WO4. The synthesized Ag2WO4 crystals display polymorphism, existing in two different forms: the α-polymorph, which is thermodynamically stable and has an orthorhombic structure with the space group (Pn2n), and the β-polymorph, which is metastable and has a hexagonal structure with the space group (P63/m) (Gouveia et al. 2022). XRD Ag2WO4 matched well with the orthorhombic (JCPDS # 34–0061) and hexagonal (JCPDS # 33-1195) crystallite phases (Rajamohan et al. 2017). Similar behavior has been documented in numerous investigations (Shi et al. 2016; Zhu et al. 2017). The Williamson-Hall analysis is a straightforward method that uses integral breadth to determine the broadening caused by size and strain. This method is achieved by studying the peak width as a function of 2θ. The crystallite size D of Ag2WO4 powder was determined using the Williamson-Hall equation (Mote et al. 2012):

$$\varvec{\beta }\mathbf{cos} \left(\varvec{\theta }\right)= \frac{0.9 \mathbf{x} \varvec{\lambda } \left(\varvec{n}\varvec{m}\right)}{\varvec{D}}+4\varvec{\epsilon }\mathbf{sin}\varvec{\theta }$$
(1)

Where \(\beta\) denotes full-width at half maximum intensities, ε denotes strain, and the wavelength (λ) of radiation = 0.15406 nm of the Cu Kα radiation used in the analysis. By plotting β Cos(θ) Vs. 4Sin(θ), the crystallite size of Ag2WO4 can estimated from the y intercept. Figure 1(b) depicts the Williamson–Hall (W–H) plot of Ag2WO4. The determined value of D for Ag2WO4 powder was 61.9 nm. In the same context, the crystallite size for the orthorhombic and hexagonal crystallite phases was calculated using the Scherrer Equation and found to be 37.61 and 40.8 nm, respectively (Holzwarth and Gibson 2011). In order to provide more elucidation on the surface morphology of pure Ag2WO4, a scanning electron microscope (SEM) picture was obtained and is shown in Fig. 1(c). The produced Ag2WO4 yielded microcrystals that exhibited rod-like shape, consistent with the findings reported in the examined literature (Nobre et al. 2019; Gouveia et al. 2022).

Fig. 1
figure 1

(a) XRD pattern, (b) W–H plot, and (c) SEM image of Ag2WO4 powder

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Fourier transform infrared spectroscopy (FTIR) is a very effective and intriguing technique used to elucidate the vibrational modes of functional groups inside a material and investigate the interaction and complexation of chains with included nanofillers. The Fourier-transform infrared (FTIR) spectra of silver tungstate Ag2WO4 are shown in Fig. S1(a). The Ag2WO4 displays an absorption peak at around 545 cm− 1, suggesting the presence of octahedral WO6 units (Pontes et al. 2003). The prominent absorption peak seen at 750 cm− 1 was assigned to the asymmetric stretching vibrations of the O-W-O bonds. Additionally, the minor peak observed at 1360 cm− 1 was ascribed to the stretching mode of the WO42− anion (Li et al. 2017). The elemental analysis of the Ag2WO4 sample was conducted using energy-dispersive X-ray Analysis (EDX); the results are shown in Fig. S1 (b). The EDX examination revealed the existence of silver (Ag), tungsten (W), and oxygen (O). The XRD, FTIR spectra, and EDX analysis confirmed the synthesis of a pure Ag2WO4.

Furthermore, EDX map** images of PVC/Ag2WO4 nanocomposite film are shown in Fig. 2. The images illustrated the uniform distribution of the C, Cl, O, W, and Ag elements overall PVC/Ag2WO4 nanocomposite film. Additionally, the images showed that the PVC/Ag2WO4 nanocomposite film had been successfully prepared and was of high purity.

Fig. 2
figure 2

EDX map** images of PVC/Ag2WO4 nanocomposite film

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The XRD patterns of pure PVC, unirradiated, and E-beam irradiated PVC/Ag2WO4 nanocomposite films are illustrated in Fig. 3. The observed pattern of pure PVC confirms the amorphous nature of the polymer sample (Kassem et al. 2023). The XRD pattern of PVC/Ag2WO4 nanocomposite films exposed to electron beam irradiation reveals the presence of the distinctive peak associated with the PVC/Ag2WO4 nanocomposite films. This peak is seen at the same angle as in the XRD pattern of non-irradiated PVC nanocomposite films. A correlation between the dose of electron beam irradiation and the intensity of XRD peaks is illustrated. However, after applying electron beam irradiation, the intensity of this peak reduces at a 2θ of 31.58° due to a decrease in crystallinity. This reduction in crystallinity might be attributed to the hindrance of crystal development in the PVC matrix caused by cross-linking generated by E-beam irradiation. Kumar Ghosh et al. (Ghosh et al. 2024) have reported a similar behavior of the effect of E-beam irradiation on XRD patterns of graphene nanoplatelets integrated into linear low-density polyethylene.

Furthermore, the PVC matrix may generate highly hot free radicals in response to the ionizing radiation. These radicals subsequently become chemically active and initiate the PVC-crosslinking process. This behavior was documented in numerous studies (Alshahrani et al. 2021a, b; Nouh and Benthami 2019).

Fig. 3
figure 3

XRD patterns of pure PVC and E-beam irradiated PVC/Ag2WO4 nanocomposite films (0, 25, 50, and 100 kGy)

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FTIR spectroscopy investigated the chemical changes during the PVC/Ag2WO4 nanocomposite film and the impact of E-beam irradiation. The FTIR spectrum of pure PVC and E-beam irradiated PVC/Ag2WO4 nanocomposite films is illustrated in Fig. 4. In the case of polyvinyl chloride (PVC), the CH stretching vibrations is detected in the region from 2800 to 2925 cm− 1 and the carbonyl (C = O) stretching vibration at around 1700 cm− 1. These bands may be attributed to the characteristic peaks of DOP used in PVC films’ preparation (Ul-Hamid et al. 2015; Pandey et al. 2016; Yaseen et al. 2021). Fig. S2 shows FTIR measurements for DOP, pure PVC film without DOP, and the as-obtained pure PVC powder. The deformation mode of the CH2 group is found at 1380 cm− 1, while the rocking mode of the CH group is discovered at 1268 cm− 1. The wagging mode of the trans-CH bonds is detected at 958 cm− 1, while the stretching mode of the C-Cl bond is noticed at 834 cm− 1. Finally, the wagging mode of the cis CH bonds is detected at 618 cm− 1 (Ul-Hamid et al. 2015; Rajendran and Uma 2000). Moreover, the intensity and width of the bands in the PVC/Ag2WO4 nanocomposite films are slightly influenced by E-beam irradiation.

Fig. 4
figure 4

FTIR spectra of PVC + DOP and E-beam irradiated PVC/Ag2WO4 nanocomposite films (0, 25, 50, and 100 kGy)

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3.2 Optical properties

Optical investigations were conducted to enhance comprehension of the impact of electron beam irradiation on nanocomposite films composed of PVC and Ag2WO4 nanorods.

As reported, the band gap of Ag2WO4 is between 1 and 3 eV. According to the current body of literature, the band gap energy of Ag2WO4 varies in response to various influences, such as temperature, particle dimensions, and crystalline phase (Gouveia et al. 2022; Cavalcante et al. 2012; Ayappan et al. 2020). However, the optical properties of Ag2WO4 were studied via diffuse reflectance spectroscopy DRS. Figs. S3 (a) and S3(b) showed the absorbance and transmittance spectra of Ag2WO4 powder. It is noted that the Ag2WO4 has two distinctive peaks. This behavior may be attributed to Ag2WO4 having two structural phases. Concerning the crystalline phase of Ag2WO4, it is noteworthy that the material can exist in distinct phases, such as α-Ag2WO4 and β-Ag2WO4, each characterized by unique crystal structures and properties. In the same context, the optical band gap of Ag2WO4 can be estimated via i.a. the Kubelka–Munk method (Dolgonos et al. 2016). It is illustrated that the Ag2WO4 possesses two optical band gaps (see Fig. S3 (c)) of 2.45 eV and 4.3 eV.

Figure 5(a) displays the optical absorbance spectra obtained for the polymer nanocomposites within the 200 to 1100 nm wavelength range. Furthermore, an observable phenomenon known as redshift occurs for the absorbance spectra (Fig. 5(a)), whereby the absorbance curves shift towards longer wavelength values when the dose of E-beam irradiation increases from 0 to 100 kGy. Fig. S4 demonstrates the transmittance (T) of PVC/Ag2WO4 nanocomposite films. It is revealed that at λ ≥ 400 nm, the PVC exhibits a transmittance (T) between 80% and 90%, and then the transmittance declined for the unirradiated and E-beam irradiated PVC/Ag2WO4 nanocomposite films. Incorporating Ag2WO4 into PVC is responsible for lessening the transmittance of the PVC/Ag2WO4 nanocomposite films. The observed alteration can be ascribed to the optical characteristics of Ag2WO4, which potentially impact the light propagation across the PVC/Ag2WO4 nanocomposite film. Light absorption and scattering are two variables that might lead to reduced transparency of PVC/Ag2WO4 nanocomposite films. The introduction of Ag2WO4 nanorods, for instance, may induce light absorption and scattering. Additionally, agglomeration development may contribute to the overall reduction in transmittance of PVC/Ag2WO4 nanocomposite films. The reduction in transmittance of PVC/Ag2WO4 nanocomposite films makes them suitable as UV-blocking materials, items that protect sensitive components, and, in particular, electronic devices; lowering transmittance boosts contrast or lessens glare (Rawat et al. 2018; Han and Yu 2006). Furthermore, PVC/Ag2WO4 nanocomposite films possess substantial atomic numbers of the heavy elements Ag and W, rendering them appropriate candidates for implementation as flexible ionizing radiation shielding materials (Kassem et al. 2023; Maksoud et al. 2021).

The shift to longer wavelength values in absorbance observed suggests an associated reduction in the optical bandgap of the PVC/Ag2WO4 nanocomposite films, which may be ascribed to the treatment with E-beam irradiation. The phenomenon described may be attributed to attractive polarization interactions between the absorber and radiation, resulting in a decline in the energy levels between the excited and unexcited states.

The optical band gap (Eg) of the PVC/Ag2WO4 nanocomposite films has been established using the equation and Tauc plot relation (Krumhansl and State 1957).

$$\varvec{\alpha }\varvec{h}\varvec{\nu }={\varvec{A}(\varvec{h}\varvec{\nu }-{\varvec{E}}_{\varvec{g}})}^{\varvec{s}}$$
(2)

The formula incorporates a constant represented by the symbol A. The absorption coefficient, denoted as 𝛼, is a parameter that characterizes the ability of a material to absorb electromagnetic radiation. It is influenced by the photon energy, represented as h𝜈, and the specific transition, denoted by the variable s. The value of s may take on four possible values: 1/2, 2, 3/2, and 3. These values correspond to different types of transitions in the system: allowed indirect, allowed direct, forbidden direct, and forbidden indirect transitions, respectively (Abdel Maksoud et al. 2023a, b).

Figure 5(b) depicts the relationship between the (𝛼h𝜈)1/2 Vs. and the h𝜈 axis, illustrating the fluctuation of this relationship. The determination of the energy gap involves the fitting of the linear part of the curve and then identifying the point of intersection between the straight line and the h𝜈 axis. The study included determining the range of optical band gap values seen in PVC/Ag2WO4 nanocomposite films exposed to various doses of E-beam irradiation. The indirect optical band gap values of 4.12 eV and 4.01 eV were determined for the pure PVC and unirradiated PVC/Ag2WO4 nanocomposite film, respectively. Nevertheless, after applying higher doses of E-beam irradiation, the indirect optical bandgap value decreased, reaching 3.90, 3.84, and 3.81 eV for E-beam radiation doses of 25, 50, and 100 kGy, respectively. The observed reduction in the optical band gap signifies a modification in the energy levels between the valence and conduction bands of PVC nanocomposite films, indicating a significant alteration in the electronic structure of the PVC matrix. The observed alteration in the optical band gap may be attributed to the ability of the E-beam to generate localized electronic states inside the optical band gap of PVC nanocomposite films. These states function as centers for trap** and recombination, resulting in the previously stated change in the optical band gap. The observed reduction in the optical band gap may be attributed to the simultaneous increase in sample disorder, which is a consequence of the change in polymer structure (Abdullah et al. 2015; Aziz et al. 2015).

The estimation of the Urbach energy, Eu, may be conducted for pure PVC and PVC/Ag2WO4 films both before and after exposure to E-beam irradiation at various. This estimation is achieved by examining the relationship between the natural logarithm of the absorption coefficient (ln α) and the photon energy (hυ), as seen in Fig. 5(c) (Urbach 1953):

$$\varvec{\alpha }={\varvec{\alpha }}_{0}{\varvec{e}}^{\raisebox{1ex}{$\varvec{h}\varvec{\nu }$}\!\left/ \!\raisebox{-1ex}{${\varvec{E}}_{\varvec{u}}$}\right.}$$
(3)

Structural disorder, stoichiometric imperfections, and surface passivation influence the Urbach energy. The Urbach energy parameter also indicates the level of disorder in the phonon states inside the film. The results presented in the study indicate that the Urbach energy (Eu) exhibits a rise from 5.88 eV in pure PVC film to 8.26 eV in unirradiated PVC/Ag2WO4 nanocomposite film, which may be attributed to the introduction of Ag2WO4 into PVC that was disrupting the orderly arrangement of polymer chains. On the other hand, the Urbach energy of the E-beam irradiated PVC/Ag2WO4 nanocomposite films reduced significantly to 7.40, 6.21, and 5.25 eV when exposed to electron beam irradiation at a dosage of 25, 50, and 100 kGy, respectively, which may be attributed to that E-beam irradiation-induced cross-linking process and rearrangement in PVC chain (Abdel Maksoud et al. 2023a, b; Alshahrani et al. 2021a, b).

Fig. 5
figure 5

(a) absorbance, (b) (𝛼h𝜈)1/2 Vs. h𝜈, and (c) ln (𝛼) Vs. h𝜈 for pure PVC and E-beam irradiated PVC/Ag2WO4 nanocomposite films (0, 25, 50, and 100 kGy)

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3.3 Thermal analyses

Thermo-gravimetric studies were conducted to assess the differences in thermal stability between the samples before and after irradiation. The weight loss curves and their respective first derivatives enable the observation of many processes and stages occurring in the materials during decomposition. Investigations of changes in polymer structure and the influence of various formulation components may provide valuable insights into the thermal characteristics of the material.

This study used Kissinger’s model to determine the activation energy (Ea) of developed PVC/Ag2WO4 nanocomposite film. The Kissinger model/method is commonly used to estimate the activation energy of a chemical reaction based on non-isothermal data analogy and assuming that the reaction follows first-order kinetics (Vyazovkin 2020; Budrugeac 2007). The Kissinger method is a relatively simple method to determine Ea. The analysis of non-isothermal data, typically DGA, can be repeatedly obtained through thermal experimental techniques (Gao et al. 2023). A controlled heating rate condition is applied to the reactants during these experiments. This method requires only a few data points, including the temperature and corresponding conversion values at different heating rates (Liu et al. 2022; Ranjan and Goswami 2022). Although the Kissinger method is simple, it provides reasonably accurate results. Generally, it balances simplicity and accuracy, making it a valuable tool in many research and industrial applications.

In this method, determining the highest decomposition peak temperature (T) was the basis for the analysis obtained from the DTG thermogram. Equation (4) was used to calculate the activation energy, Where Ea is the activation energy, β is the heating rate, Tp is the decomposition temperature, and R is the universal gas constant. To get the slope – Ea/R from ln(β/T2p) against (1/Tp) (Vyazovkin et al. 2011; Trache et al. 2016)

$$-\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}=\frac{\mathbf{d} \mathbf{l}\mathbf{n}(\varvec{\beta }/{\mathbf{T}}_{\mathbf{p}}^{2})}{\mathbf{d}(1/{\mathbf{T}}_{\mathbf{p}})}$$
(4)

Figure 6(a,b, and c) shows the thermogravimetric analysis (TGA) and derivative thermogravimetry (DTG) curves for the pure polyvinyl chloride (PVC), unirradiated PVC/Ag2WO4 nanocomposite films, and E-beam irradiated PVC/Ag2WO4 nanocomposite films. The curves were obtained using three different heating rates: 6, 8, and 10 °C/min. The thermogravimetric (TG) graphs illustrate several decomposition stages corresponding to the various regions of mass loss.

Thermal decomposition occurs across a broad temperature range in the TGA and DTG curves, demonstrating a significant sensitivity to the heating rate. Additionally, the thermal stability of PVC/Ag2WO4 nanocomposite films improves with increasing E-beam radiation doses for all heating rates. The derivative curves reveal that the maximal decomposition temperature (peak) arises at higher temperatures as the heating rate increases.

The activation energy of the E-beam irradiated PVC/Ag2WO4 nanocomposite films was conducted for different radiation doses (0, 25, 50, and 100 kGy). For comparison, the activation energy of the pure PVC (14.4 kJ/mol) was also conducted, as shown in Fig. 6(d). For unirradiated PVC/Ag2WO4 nanocomposite film, Ea’s activation energy decreased to 12.89 kJ/mol. The Ea of the PVC/Ag2WO4 nanocomposite films increases with the e-beam irradiation dose. The increase in activation energy for PVC polymers when nano Ag2WO4 are added under radiation dose can be elucidated to the following: first, the nanoparticles serve as nucleation sites for linking reactions within the PVC polymer matrix. When exposed to E-beam radiation, these sites facilitate cross-linking between polymer chains, leading to a higher density of cross-links. This results in more energy required for chain mobility and enhances the thermal degradation resistance (Marković et al. 2011; Bijanu et al. 2021). Second, energy transfer and dissipation are other mechanisms that comprise the absorption of radiation energy by the nanoparticles within the polymer matrix. Where the nanoparticles absorb and dissipate a portion of the energy, this would reduce the direct interaction of radiation with the PVC polymer. Consequently, this leads to a decrease in the formation of active radicals, increasing the activation energy required for degradation (Sengupta et al. 2017; Barakat 2023).

Fig. 6
figure 6

TGA and DTA at heating rates of (a) 6°/min, (b) 8°/min, (c) 10°/min, and (d) activation energy of pure PVC and E-beam irradiated PVC/Ag2WO4 nanocomposite films (0, 25, 50, and 100 kGy)

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3.4 Dielectric properties

Figure 7(a) and 7(b) illustrate the complex permittivity spectrum of the PVC/Ag2WO4 nanocomposite films, including the real part 𝜀′ and dielectric loss 𝜀′′, at different E-beam doses. The spectra described dielectric-related characteristics, including dielectric polarization phenomena and the dynamics of the polymer. In order to determine the dielectric constant, 𝜀′, the vacuum permittivity, capacitance, thickness, and area of the sample were utilized. The dielectric loss, 𝜀′′, is proportional to the amount of energy lost and includes the product of both ionic transportation and the polarization of a charge or dipole. At lower frequencies, the presence of accumulated charge carriers leads to a higher permittivity value (represented by ɛ′) and results in the formation of a space-charge layer at the interface between the pure PVC and PVC/Ag2WO4 nanocomposite films and the electrode.

Additionally, the charge in the system requires a certain amount of time to change its direction in response to changes in frequency. However, the variable frequency (f) increase is accompanied by a short cyclic duration during which the dipoles lack rapid reorientation. Consequently, dipolar polarization is reduced and may potentially disappear, resulting in a decrease in the values of ɛ′ (Fig. 7(a)). The dielectric constant of the PVC matrix is enhanced by incorporating Ag2WO4, owing to the elevated dielectric constant exhibited by Ag2WO4 nanorods. In addition to displaying both ferroelectric and antiferroelectric characteristics, the Ag2WO4 is affected by variations in its dielectric constant due to temperature, pressure, and crystal structure. It is well-known that Ag2WO4 possesses dielectric constants that are more remarkable than certain other materials (Jacomaci et al. 2019). In the same context, it is also evident that the permittivity values of the nanocomposites vary with E-beam irradiation doses and at low-frequency regions.

Furthermore, the E-beam irradiated nanocomposite with 50 kGy had the lowest ɛ′ value. This behavior may be due to cross-linking and molecular or atomic rearrangement within a material that can impact its dielectric constant. Specific configurations can potentially prevent the material’s polarization, leading to a reduced dielectric constant. This could be attributed to the strong interaction between the Ag2WO4 and the PVC polymeric chains, leading to reduced chain mobility under the influence of an electric field. Another likely factor contributing to the decrease in the permittivity of the nanocomposite is the nucleation induced by Ag2WO4, causing constraints on polymer chains (Abdel-Gawad et al. 2018). The dielectric constant values of PVC/Ag2WO4 nanocomposite films could be promising for electronics applications, including energy storage, electrical cables, and power distribution systems. Figure 7(b) shows the relationship between the dielectric loss (ε″) of pure PVC and E-beam irradiated PVC/Ag2WO4 nanocomposite films (0, 25, 50, and 100 kGy) and the frequency (f). At lower frequencies, the values of ε″ exhibit a drop as the frequency rises. The losses referred to as ohmic losses result from conductivity, which does not impact the ε′ until there is a space-charge accumulation in the material (Miles et al. 1957). At higher frequencies, the losses exhibit an increasing trend, reaching a maximum before gradually declining towards relatively low levels. The occurrence of high-frequency dielectric losses may be attributed to relaxation-induced polarization. Furthermore, However, upon comparing the loss values of all films, it is observed that E-beam irradiated PVC/Ag2WO4 nanocomposite films exhibit lower losses than those with un-irradiated PVC/Ag2WO4 nanocomposite films and pure PVC, particularly at lower frequency. As a result, E-beam irradiation reduces the values of the real ɛ′ and imaginary ε″ components of PVC/Ag2WO4 nanocomposite films, thereby eliminating polarization and minimizing losses within the insulation materials of the cable.

3.5 Electric modulus analysis

The electrical modulus, denoted as M*(ω), is a complex variable incorporating details on a material’s capacitive and resistive characteristics in the angular frequency (ω). This particular testing technique proves advantageous in characterizing dielectric features shown by various materials, such as PVC nanocomposites. The electric modulus approach has the potential to distinguish the localized behavior of defects compared to the influence of the electrode effect by offering valuable insights into the bulk response (McCrum et al. 1967). Generally, the electric modulus characterizes the degree of relaxation of the electric field inside a material when subjected to a constant electric displacement. The use of modulus representation in the analysis of relaxation characteristics becomes well-established for an extensive variety of promising materials (Belal Hossen et al. 2015). The complex modulus may be expressed using the following equation (Gajula et al. 2020).

$${\varvec{M}}^{\varvec{*}}\left(\varvec{\omega }\right)={\varvec{M}}^{\varvec{{\prime }}}\left(\varvec{\omega }\right)+\varvec{j}{\varvec{M}}^{\varvec{{\prime }}\varvec{{\prime }}}\left(\varvec{\omega }\right)$$
(5)

The real part modulus, denoted as \({\varvec{M}}^{\varvec{{\prime }}}\left(\varvec{\omega }\right)\), represents the energy storage (a capacitive) part, whereas the imaginary part modulus, denoted as \({\varvec{M}}^{\varvec{{\prime }}}\varvec{{\prime }}\left(\varvec{\omega }\right)\) represents the dissipation of the energy (resistant) part.

Figure 7(c) displays the plots of complex modulus, real part modulus Vs. the imaginary part modulus (M’’ vs M’) for different doses of E-beam irradiation. Two distinct semicircles were found, each providing valuable insights into different phenomena. The first semicircle, detected in the low-frequency range, may be attributed to the capacitive grain boundary effect. On the other hand, the second semicircle, observed at higher frequencies, signifies the manifestation of the capacitive grain influence. The prevailing attributes of Fig. 7(c), as seen across different electron beam doses, may be briefly stated as follows: Lower and higher frequency impacts of grain borders and grain effects were seen. At higher frequencies, a well-resolved semicircle may be seen; this shape is attenuated by including Ag2WO4 in the PVC matrix and then enhanced by increasing the E-beam doses.

Conversely, a smaller semicircle that may be attributable to the grain boundary effect can be seen at lower frequencies, suggesting that this effect has a reducing tendency. When the E-beam doses are increased, the magnitude of the grain capacitance shows a tendency toward increase, while the magnitude of the grain boundary capacitance shows a decline. In contrast to the grain border capacitance, which exhibits a slightly lower dependence on the E-beam irradiation doses, the grain capacitance displays an intense reliance upon the E-beam doses.

3.6 Complex impedance analysis

Under various doses of electron beam irradiation, complex impedance spectroscopy was used to investigate a sample’s electrical characteristics and the interface between the PVC/Ag2WO4 films and the electrode. The following equation can express the complex impedance (Z*) (Belal Hossen et al. 2015):

$${\varvec{Z}}^{\varvec{*}}={\varvec{Z}}^{\varvec{{\prime }}}-\varvec{j}{\varvec{Z}}^{\varvec{{\prime }}\varvec{{\prime }}}$$
(6)

The real and imaginary components of the impedance are denoted by Z’ and Z’’, respectively.

Figure 7(d) displays the relationship between the real part (Z’) and the imaginary part (Z’’) of the impedance for the PVC/Ag2WO4 nanocomposite film under varied doses of E-beam irradiation. The observed phenomenon is distinguished by the presence of two semicircles, with the first semicircle exhibiting a tendency to develop and the second semicircle forming within the measured frequency range across all doses of E-beam irradiation. In general, the complex impedance plots often exhibit two semicircular arcs. These arcs have centers below the real axis, indicating a departure from perfect Debye behavior (Lee et al. 2010). A progressive reduction in the diameter of the two semicircular arcs is observed as the doses of E-beam irradiation increase (Belal Hossen et al. 2015).

Fig. 7
figure 7

Variation of (a) dielectric constant, (b) dielectric loss, (c) electric modulus (M’’ vs. M’), (d) electric impedance (Z’’ vs. Z’) of PVC/Ag2WO4 nanocomposites

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4 Conclusions

This study presents our research findings on revealing the effect of varying doses of the electron beam (E-beam) irradiation (0, 25, 50, and 100) kGy on the structure, optical, thermal, dielectric characteristics, impedance analyses, and electrical modulus of PVC/Ag2WO4 nanocomposite film. After the treatment of increasing doses of E-beam irradiation, the value of the indirect optical bandgap showed a reduction, achieving values of 3.90, 3.84, and 3.81 eV for E-beam radiation doses of 25, 50, and 100 kGy, respectively. However, upon exposure to electron beam irradiation at 25, 50, and 100 kGy doses, the Urbach energy significantly decreases to 7.40, 6.21, and 5.25 eV, respectively. This reduction can be attributed to the cross-linking process and rearrangement in the PVC chain induced by E-beam irradiation. The optical properties of PVC/Ag2WO4 nanocomposite films make them candidates for UV-blocking materials and electronic devices where lowering transmittance enhances contrast or eliminates glare. The PVC/Ag2WO4 nanocomposite films are also suitable for flexible ionizing radiation shielding materials as they contain heavy elements (Ag and W) with large atomic numbers.

The results revealed that the Ea value rose from 12.89 to 31.17 kJ/mol when the E-beam irradiation dosage escalated from 0 kGy to 100 kGy. Besides, the use of E-beam irradiation leads to a decrease in the magnitudes of the real component (ɛ′) and imaginary component (ε″) of PVC/Ag2WO4 nanocomposite films. This reduction effectively eliminates polarization and minimizes losses within the insulation materials of the cable. On the other hand, the impact of E-beam irradiation on the modulus and complex impedance was analyzed.