1 Introduction

Many scientists around the world are focusing their attention on enhancing and characterizing the properties of polymer composites because of the benefits they offer in a variety of optoelectronic applications (El-naggar et al. 2023a, a, b, b, c). Lightweight, low-cost, easily dispersed in water, and quick to prepare are just some of the many impressive properties’ polymers possess (El-Naggar et al. 2023a, a, b, b, c). Recently, there has been a need for research into nanofiller-based polymer nanocomposites with high dielectric properties for applications involving energy storage (Bera et al. 2023).

Poly (vinyl chloride) (PVC) has attracted a lot of interest because of its versatile applications and high-quality physicochemical properties. Hydrophobicity, inflammability, formulation flexibility, and low cost are just a few of these advantages (Suvaran et al. 2022).

To create advanced flexible optoelectronic technologies, oxides, sulfides, metal salts and/or iodides materials can be used as filler materials. For example, Ragab et al. incorporated nano ZnO/TiO2 in polyethylene oxide/carboxymethyl cellulose blend (Ragab 2023). By incorporating toluidine blue dye as an efficient laser optical limiter into polyvinyl alcohol (PVA) composite films, Mohamed et al. developed a smart optical sensor with enhanced conductivity and dielectric properties (Mohammed et al. 2022). Rechargeable batteries, such as lithium and nickel-cadmium (Ni–Cd) polymer batteries, have seen a rise in demand and widespread use due to the growing portable power needs of electronic and medical devices over the past decade. Yassin et al. found that (PVA–PVP)/(Ni–Cd) composite can be used in manufacturing (Ni–Cd) batteries and energy storage devices (Yassin 2020).

Dielectric data for PVC/PVP/ZnFe2O4 polymers showed that increasing amounts of ZnFe2O4 decreased the dielectric constant values of the composite. Additionally, the DC conductivity values dropped as ZnFe2O4-polymer resistance increased with increasing zinc ferrite contents up to 15.0 wt% (Alhulw et al. 2021). The optical dielectric constants and optical conductivity of the polymer both increase with increasing amounts of Cd0.5Zn0.5Fe2O4 in the PVA matrix (Soliman and Abouhaswa 2020). Depending on the amount of manganese doped into Cd-ferrite, the direct energy gap and other optical parameters change in nanocomposite samples of Cd1 − xMnxFe2O4/poly (methyl methacrylate) (PMMA) (Heiba et al. 2020).

To protect against electromagnetic interference (EMI), near-infrared (NIR), and thermal imaging cameras, Anum et al. (2021). Doping a PVA/PEG blend with methyl blue dye improved its luminescence, structural, and dielectric features. The PVC/Cu/Cu2O nanocomposite films’ improved dielectric and optical properties make them a good option for use in energy storage devices (Abdel Maksoud et al. 2023). Doping virgin PVC/PMMA with nano Li4Ti5O12 improved their electrical characteristics. Li4Ti5O12/PVC/PMMA blends can be employed in different electrochemical and industrial fields such as Li-ion batteries (Al-Muntaser et al. 2020). Al2O3/PVC or NiO/PVC composite is found to have an increase in nonlinear refractive index and third-order nonlinear optical susceptibility with increasing Al2O3 or NiO amounts, which makes these films suitable for optical device technology (Taha 2019; Taha et al. 2019). By incorporating suitable amounts of I2 nanofiller into the PVC polymeric matrix, the optical, chemical, and thermal features of PVC-I2 thin films can be dramatically altered (Telfah et al. 2022a, b). As the percentage of I2 in polyethylene oxide polymer rises, the optical band gap energy decreases and the refractive index rises (Telfah et al. 2022a, b).

Oxides with a spinel structure are commonly used as practical and low-cost sensors for detecting toxic and hazardous materials. FeCr2O4 is one of the most significant spinel compounds because of its potential uses. FeCr2O4 exhibited multiferroic properties (Singh et al. 2011). Furthermore, high theoretical capacity, environmental friendliness, a high abundance, a wide volume variation, and low electronic conductivity are all characteristics of Cr-based ferrite (CrFe2O4) nanoparticles (Mubasher et al. 2020).

Furthermore, large cations (for example, TEA+, TBA+, TPA+) in tetraethylammonium iodide (TEAI, C8H20IN), tetrabutylammonium iodide (TBAI, C16H36IN) and tetrapropylammonium iodide (TPAI, C12H28IN) salts are accountable for separating the polymer matrix, creating more space for the movement of smaller cations (Na+, Li+, K+, Ca2+) and iodide ions (Khan et al. 2017). Dye-sensitized solar cells (DSSCs) will operate more effectively with iodide anions that have a higher energy (Yee et al. 2020).

Due to its simplicity, low cost, and concession of control of structure and properties, the sol-gel route is a convenient method for producing nano ferrite (Dippong et al. 2021). In addition, solution casting procedure is the most prominent, effective and cheap technique to manufacture films at laboratory-scale.

For potential use in optoelectronics and in energy storge systems, this work investigates how nano FeCr2O4 doping and the changing of the TPAI dopant level affects the PVC’s optical and electrical characteristics.

2 Methods and materials

FeCr2O4 was prepared by dissolving stoichiometric amounts from iron(III) nitrate nonahydrate (Fe(NO3)3·9H2O, Sigma-Aldrich, 99%) and chromium (III) chloride (CrCl3·6H2O, Sigma-Aldrich, 96%) and citric acid (1:1) in distilled water (10 ml) and ethylene glycol (20 ml) while stirring and heating at 75 °C (1 h). A solution was dried in furnace at 80 °C for 12 h. A powder was made by heating the precursor to 700 °C for 1 h, Fig. 1a.

Fig. 1
figure 1

Preparation schema for a FeCr2O4 filler and b PVC/FeCr2O4/10 wt% TPAI polymers

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To produce PVC film, 2 g of polyvinyl chloride powder (PVC, Sigma-Aldrich) was dissolved in 100 ml tetrahydrofuran (THF) using a magnetic stirrer for 2 h at room temperature (RT). To make PVC/FeCr2O4/x wt% TPAI (x = 0, 2.5, 5, 10, 20), we repeated the prior step with varying concentrations of tetrapropylammonium iodide (TPAI, Sigma Aldrich, 98%) and/or 5 wt% FeCr2O4. After the solutions had formed, they were dried for two days in Petri dishes to create films, Fig. 1b. The resulting polymers have a thickness in the range 0.32–0.38 mm (as measured with a digital micrometer).

X-ray diffraction (X’Pert MPD, Philips, Cu-source) was utilized for analysis of the synthesized nanofiller (FeCr2O4), TPAI, and all polymers. MAUD software, which is based on the Rietveld method, was used to investigate the structure of FeCr2O4 (Lutterotti 2010; Rodríguez-Carvajal 1993).

All polymers were analyzed using Fourier transform infrared spectroscopy (Bruker Tensor 27 FTIR Spectrometer). Images of polymers’ surfaces were captured by a JEOL (Akishima, Tokyo, Japan JED-2200 Series) scanning electron microscope. The UV diffuse reflectance (R), absorbance (A), and transmittance (T) of all polymers were measured using a JASCO-V-670 spectrophotometer with an integrating sphere assembly. The luminescence spectrophotometer (RF-1501 SHIMADZU, Ltd) was used to determine the fluorescence (FL) of each polymer. The optical band gap energies ( \({E}_{g})\) were determined using (El-naggar et al. 2023a, b, c):

$$h\nu=H{\left(h\nu-{E}_{g}\right)}^{m} \left(1\right)$$
(1)

where h, \(upsilon\) f, H, α = 2.303 A/t, A and t are Planck’s constant, frequency of incident light, constant known as the disorder parameter, absorption coefficient, absorbance and thickness of each sample, respectively. m = 0.5 or 2 for direct and indirect transition, respectively.

The formula presented in Ref. (El-naggar et al. 2023a, b, c, d) was used to determine the linear optical parameters of all polymers.

The dielectric constant as a function of frequency (f = 100 Hz-1 MHz) at RT can be determined by applying an ac voltage of 2 V and measuring the resulting change in capacitance (C) and dissipation factor (tan δ). The following equations (El-Naggar et al. 2023a, b, c) were used to calculate the complex electric modulus (M*= M/+iM//), ac conductivity (σac), and dielectric constant (ε′, ε″) of all polymers:

$${\epsilon }^{\prime}=\text{d}\text{C}/{\epsilon }_{0}\text{A} \left(2\right)$$
$${\sigma }_{ac}=2\pi f{\epsilon }_{0}{\epsilon }^{\prime}\text{tan}\delta$$
(3)
$$\text{tan}\delta ={\epsilon }^{.}/{\epsilon }^{\prime}$$
(4)
$${M}^{\prime}=\frac{{\epsilon }^{\prime}}{{\epsilon }^{,2}+{\epsilon }^{\prime\prime2}}$$
(5)
$${M}^{\prime\prime}=\frac{{\epsilon }^{\prime\prime}}{{\epsilon }^{,2}+{\epsilon }^{\prime\prime2}}$$
(6)

where εo, and A are the permittivity of free space and area of the disk, respectively.

3 Results and discussion

3.1 Structural investigation

The matching between the measured and calculated, from Rietveld refinement method, x ray diffraction patterns of FeCr2O4 powder is depicted in Fig. 2a. A single phase with cubic structure \(F d\stackrel{-}{3}m\) was obtained with a cell parameter a = 8.275(4) Å. The average crystallite size is in the nano range 9.4 nm with a little bit of a large lattice microstrain 0.0049. The x ray diffraction patterns obtained for the blend PVC/FeCr2O4/x% TPAI are given in Fig. 2b. The dominant amorphous phase of PVC was reflected in the high background of all XRD patterns, with weak diffraction peaks at 36.7 and 41.6° and two halos at approximately 15 and 17°, providing evidence of a little degree of crystallization. PVC has an orthorhombic unit cell and space group Pacm (Gilbert 1994). The crystalline syndiotactic isomer in the polymer is small compared to the amorphous atactic and isotactic isomers, so the diffracted intensity is low (Gilbert 1994; Brunner 1972). The diffraction data shows no significant differences between undoped and doped PVC with FeCr2O4, which may be due to its low contents or its uniform distribution. Lading TPAI up to 5% results in diffraction patterns similar to that of PVC doped with FeCr2O4 without any characteristic peaks from TPAI salt, indicating complete dissociation of the salt in the blend matrix. The undissociated salt, represented by the diffraction peaks of the TPAI salt, became more visible as the PVC was doped with a higher concentration of TPAI.

Figure 2c, d shows the SEM micrographs of undoped and doped PVC with FeCr2O4 and 10 wt% TPAI (as an example). As revealed from the graph the SEM image for PVC has a pore less and smooth surface. As FeCr2O4 and TPAI were added to PVC polymer, the film became rough, demonstrating the nanofiller’s physical interaction with the host polymer (Yassin 2023).

A spectroscopic study relied on FT-IR data was applied at room temperature for PVC/FeCr2O4/TPAI samples. Figure 3 displays the FTIR transmittance data for unloaded and FeCr2O4 and/or TPAI-loaded PVC polymers. All polymers exhibit stretching of the C–Cl bond and vibrations of the carbonyl group at 792 and 1724 cm−1 (Mallakpour and Shamsaddinimotlagh 2018; Jia and Hu 2017; Chen et al. 2017). CH stretching, CH bending, and CH rocking vibrations are detected at 2922, 1401, and 1152 cm−1 in pure and doped PVC polymers, respectively (Soman and Kelkar 2009; Rajendran et al. 2007). The peak positions and intensities of the vibration bands of PVC host polymer were slightly modified by doping. These shifts indicated that the host polymer and the filler were coupled. Yassin et al. argued these variation to the physicochemical interactions, of the host matrices which acting as electron donors and the filler which acting as electron acceptors (Yassin 2023).

Fig. 2
figure 2

a Rietveld refinement of FeCr2O4, b XRD diffraction data for undoped and doped PVC with FeCr2O4 and TPAI and c, d SEM patterns for PVC and PVC/FeCr2O4/10 wt % TPAI

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Fig. 3
figure 3

FTIR data for undoped and doped PVC with FeCr2O4 and TPAI

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3.2 Optical features

Measurements of PVC and PVC/FeCr2O4/x wt% TPAI polymers’ diffused absorbance (A), transmittance (T), and reflectance (R) spectra are shown in Fig. 4. Figure 4a shows that all samples have two absorption peaks, at 232 and 283 nm, which are associated with electron transfer from π→π* and n → π∗ transitions owing to (C=C) unsaturated bonds and the C–Cl bond, respectively (Heiba et al. 2023). The graph shows that the absorbance spectrum of PVC polymer increased with the amount of FeCr2O4 loaded into the matrix and increased even more with the addition of TPAI. A similar result was detected in polyethylene oxide (PEO) and carboxymethyl cellulose (CMC) doped with ZnO/TiO2 NPs (Taha 2019) or PVA doped with toluidine blue dye (Mohammed et al. 2022). After TPAI loading, the absorbance peaks shifted to longer wavelengths “red shifted,“ because of the TPAI’s interaction with the polymer chains, which narrowed the optical band gap (Aziz et al. 2017; Zhao et al. 2021). Doped polymers have good absorbance in the wavelength up to 500 nm (UV and visible ranges) as demonstrated by the graph. These findings confirmed the potential for boosting industrial deployment of doped PVC in fields like coatings, adhesives, medicine, and solar cells. The difference in transmittance (T) between the doped and undoped PVC film is shown in Fig. 4b. In the range of 300–800 nm, 92% of light is transmitted through a PVC film. The transmittance becomes lower with the addition of different contents from TPAI and reached the lower value 42% as the amount of TPAI becomes 5 wt %. This correlates with the TPAI’s high absorbency. Reflectance (R) spectra of the investigated samples are displayed in Fig. 4c, where the R% values demonstrate a significant increase following doping with FeCr2O4 and/or TPAI. At 500 nm, R increased from 9 to 19% as PVC doped with FeCr2O4 then it reduced to its lowest value (13%) as the amounts of TPAI became 5% in the polymer matrix. A similar result was observed when polyethylene oxide (PEO) doped with different I2 concentrations (Telfah et al. 2022a, b).

Fig. 4
figure 4

a Absorbance, b transmittance and c reflectance spectra for undoped and doped PVC with FeCr2O4 and TPAI

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All polymers’ direct and indirect optical band gaps (Eg) were calculated using plots of (αhν)2 or (αhν)0.5 versus hν, respectively (Fig. 5). Extrapolating the linear portions of these plots until they intersected hν = 0 yielded the Eg values, Table 1. The obtained direct and indirect Eg values are (5.15, 4.26) and (4.95, 4.1) eV for PVC, respectively. Upon loading the PVC with FeCr2O4 the direct and indirect Eg values were reduced to (5, 4.23) and (4.95, 4.1) eV, respectively. After that they reduced further but irregularly as the amount of TPAI doing increased reached their lowest values (3.73, 2.98) and (3.11, 2.42) eV for direct and indirect transition as the amounts of TPAI became 2.5 wt%. A similar result was observed for PVC doped with iodine (Telfah et al. 2022a, b). The optical band gap of the host material is narrowed when it is loaded with nanofillers because new localized energy states are formed between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) levels (El-naggar et al. 2022a, b, c).

Fig. 5
figure 5

Tauc relation for a direct and b indirect optical band gaps for undoped and doped PVC with FeCr2O4 and TPAI

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Table 1 Direct and indirect optical band gap energies for undoped and doped PVC with FeCr2O4/TPAI
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Figure 6 displays the results of an investigation into how FeCr2O4 and/or TPAI affect the extinction coefficient (k) and refractive index (n) of PVC. As can be seen, the k value increased with doped PVC with FeCr2O4 and increased further as the amount of TPAI increased in the host polymer, reaching its highest value as the amount of TPAI became 2.5 wt%, Fig. 6a. The reaction between light and medium molecules causes energy loss, which leads to a higher k value and a higher absorption coefficient in the material (Abdel-Kader et al. 2023). Furthermore, the value of n of PVC increased as it loaded with FeCr2O4 and it increased further as it loaded with TPAI in the whole wavelength except at λ = 300–450 nm, the situation is reversed. When different fillers are added to PVC, the host polymer’s polarizability changes, as indicated by a change in the packing density, or n value (El-naggar et al. 2022a, b, c). Increases or decreases in the value of n in the doped polymer may be linked to modifications to the polymer’s structure, which in turn may have a significant impact on the films’ varying physical properties. The investigated polymers have potential for use in polymer-optoelectronics, highly reflective fields, and strong optical confinement (Aziz et al. 2015).

Fig. 6
figure 6

a Refractive index and b extinction coefficient as function of the wavelength for undoped and doped PVC with FeCr2O4 and TPAI

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Figure 7 depicts the change in the dielectric constant (real εr and imaginary εi) parts and the (surface, volume) energy loss functions (SELF, VELF) of PVC polymer caused by the addition of FeCr2O4 and/or TPAI filler. Similar behaviors are seen between the real part (εr) and imaginary part (εi) of the dielectric constant and the refractive index and extinction coefficient. The sample’s reflectance had an effect on the n values, while the sample’s absorbance determined the k values. It is claimed that the nature of the nanofillers is what causes some peaks to appear in measurements of dielectric. Additionally, in each sample, the VELF values are higher than the corresponding SELF values. Furthermore, in the visible range, PVC polymer with FeCr2O4 has the highest εr value while PVC doped polymers with FeCr2O4 and TPAI have the highest (εi, SELF, VELF) values. The following changes may be response for changes in the dielectric constant upon loading with various fillers:

Fig. 7
figure 7

The altering of a real and b imaginary dielectric constant, c SELF and d VELF with the wavelength for undoped and doped PVC with FeCr2O4 and TPAI

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(i) The alteration in the interaction between the incident photon and the electron in the nanofillers and (ii) the variations in the dipole motion of the doped polymer as compared with undoped one, respectively (Suma et al. 2017).

The optical conductivity (σopt) of undoped and doped PVC polymers was calculated using the absorption coefficient and refractive index n (Fig. 8). σopt rose as PVC doped with FeCr2O4 and rose further as it loaded with TPAI. σopt values are thought to have risen as a result of a higher rate of photon absorption, which increased the number of electrons that were produced (Ismail et al. 2022).

Fig. 8
figure 8

Optical conductivity for undoped and doped PVC with FeCr2O4 and TPAI

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The effect of FeCr2O4 and/or TPAI filler on the first- order linear optical susceptibility (χ(1)), third-order nonlinear susceptibility (χ(3)) and nonlinear refractive index (n2) of PVC polymer has been studied. When an electric field is applied, a polarization process takes place that results in nonlinear optical parameters (Erken 2022). Figure 9 depicts the three parameters under consideration. All three parameters for all polymers followed the same general pattern. In addition, all three values are greater than what is seen in a polymer made entirely of PVC. PVC filled with FeCr2O4 only has the highest non-linear optical (NLO) parameters. A similar result was detected as PVA/PVP polymeric blends doped with potassium dichromate (AlAbdulaal et al. 2023). As PVC/FeCr2O4 doped with TPAI, the NLO parameters decreased irregularly. Variations in the polymer absorption process due to filler type are largely responsible for these findings. Doped polymers have been recommended for use in photonic and optical applications due to their achieved nonlinear optical features.

Fig. 9
figure 9

a–c Wavelength dependent of the nonlinear optical parameters for undoped and doped PVC with FeCr2O4 and TPAI

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3.3 Fluorescence analysis

The FL emission spectra measured under different excitation wavelengths, λexc=317, 380, and 434 nm, are shown in Fig. 10 for pure PVC and loaded with FeCr2O4/x w% TPAI. The emission band appeared at 397 nm is characteristic of PVC excimer fluorescence through the π*–π electronic transition (El–Hachemi et al. 2021). This characteristic band is shifted to 405 and 468 nm under λexc=380 and 434 nm excitation wavelengths. The shoulder peaks appeared at 428 and 382 nm may be assigned to trapped energy levels arising from defect impurities, or π*– n transition (El–Hachemi et al. 2021).

Fig. 10
figure 10

FL spectra for undoped and doped PVC with FeCr2O4 and TPAI under different excitation wavelengths

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The FL intensity of pure PVC polymer is obviously quenched upon loading with FeCr2O4 and further decreased a little by adding 0.05% TPAI to PVC; further increasing the TPAI content did not affect the FL intensity. Fluorescence quenching may occur by a variety of molecular interactions with quencher molecule(s) such as: excited-state reactions, molecular rearrangements, energy transfer, ground-state complex formation, and collisional quenching (Lakowicz 2006). The polymer (organic) and the CrFe2O4 (inorganic) components may interact by Förster resonant energy transfer (FRET) and/or electron transfer toward the nanocrystals (NCs) depending on the relative values of the energy gap and on the surface functionalization of the NCs, resulting in exciton quenching in the polymer (Anni 2019). For FRET to be takes place, a good overlap between the polymer photoluminescence range and the NCs absorption one should be fulfilled (Anni 2019), which is realized between PVC and FeCr2O4. The existence of the NCs in the polymer presented an additional decay channel for the photogenerated excitons in the polymer. Upon loading TPAI, interaction between PVC and TPAI molecules may occur resulting in delocalization in PVC. TPAI may connect with one or more PVC polymer repeating units forming trap sites obstructing the electron-hole recombination process. The decrease in FL emission implies inhibited recombination of photogenerated charge carriers for the present system, which nominates it for photocatalytic applications.

The emitted colors from different samples have also been described using color coordinates derived from the CIE 1931 chromaticity diagram (Fig. 11). Under excitation wavelengths of 317, 380, and 434 nm, respectively, the estimated color coordinates of normalized PVC were (0.1997, 0.0797), (0.2113, 0.0552), and (0.2202, 0.2147), all of which correspond to blue-violet emission. Except for FeCr2O4 and TPAI-doped PVC, which showed orange emission under 317 nm, the emission from doped PVC with the fillers clearly exhibited a blue-violet emission under the different excitation wavelengths. The obtained sample color coordinates are presented in Table 2. The current system may even have practical implications for LED use in industry.

Fig. 11
figure 11

CIE diagram for undoped and doped PVC with FeCr2O4 and TPAI under different excitation wavelengths

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Table 2 Chromaticity coordinates (x, y) for the FL spectra denoted in Fig. 10
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3.4 Dielectric characteristics

The frequency (Log f) dependence of the real and imaginary parts of the dielectric constant (ε′, ε′′) for undoped and doped PVC polymers is shown in Fig. 12a, b. The interfacial effect between the polymer and electrode causes ε′ values to be relatively high at low frequencies. Dipoles in polymeric films aligned with the applied field’s direction, resulting in a decrease in ε′ values as frequency was raised for all samples. The ε′′ value increased with increasing frequency for all polymers up to a maximum value, after which it decreased with increasing frequency. The peaks’ locations are altered as PVC doped with FeCr2O4 and/or TPAI. This change is suggestive of a different relaxation time (Bharati et al. 2016). The values ε′ and ε′′ were increased as PVC loaded with FeCr2O4. Similar results were observed as PVA doped with toluidine blue dye or PVA/PEG doped with the methyl blue dye (Mohammed et al. 2022, 2023). In contrast the dielectric const was decreased as PEO/CMC doped with ZnO/TiO2 (Ragab 2023). Upon loaded PVC/FeCr2O4 polymer with TPAI, both ε′ and ε′′ increased irregularly, reached their maximum values as the amount of TPAI became 10 wt %. The increasing in the ε′ value may be caused by the changes in the order distribution of FeCr2O4 and/or TPAI on the PVC polymer, which in turn alters the interfacial polarization (Mohamed et al. 2014). Therefore, the incorporating of the fillers into the PVC had a beneficial influence on enhancing in the dielectric features of the host PVC, confirming the XRD and UV–Vis results. A similar result was observed as PVP/PVA/CMC blend was loaded with AuNPs (Yassin 2023). This increasing in the dielectric values can nominated the doped polymer to utilized in applications of polymer based capacitors in the energy storage devices (Al-Muntaser et al. 2023).

Due to the fact that the electric modulus formalism allows for the neglect of electrode polarization, absorption, and impurity interactions, large deviations in the components of complex dielectric permittivity can be decreased. Electric modulus (M′, M′′) real and imaginary parts as a function of frequency are shown for all polymers in Fig. 12c, d. The graph clearly shows that M′ is very small at low frequencies. PVC’s M′ reduced as it was loaded with FeCr2O4 and reduced further as it doped with TPAI. Similar result was observed as PVA doped with toluidine blue dye (Mohammed et al. 2022). Based on these results, it appeared that electrode polarization and electrode effects were relatively unimportant (Howell et al. 1974). Also, the lessening in M′ values, at low frequency range, found as a result of integrating the FeCr2O4 and TPAI into the PVC polymer proposes that triggered electrons hop from one place to another. This finding approves that hopping is the foremost conduction mechanism in the system under study The values of M′ increased along with the frequency. In the presence of more efficient interfacial polarization (Naik et al. 2016), higher-frequency unsaturation values were noticed. Furthermore, M′′ displayed a peak in all polymers. The intensity of this peak was reduced as PVC loaded with CrFe2O4 and/or TPAI and the position of this peak affected by FeCr2O4 and /or TPAI.

Figure 12e shows the frequency dependence of the AC conductivity (σac) for both undoped and doped PVC using the FeCr2O4 and/or TPAI system. All polymers followed the same pattern, with σac growing larger as frequency did. This increase in σac is caused by an increase in electron hopping at relatively high frequencies. Doping PVC with FeCr2O4 resulted in a rise in AC conductivity, which was further bolstered by the addition of TPAI. Similar result was detected as PEO/CMC doped with ZnO/TiO2 (Ragab 2023). Changes in AC conductivity as PVC may result from a change in the number of charge carriers and surface defects caused by the interaction between FeCr2O4 and TPAI within the polymer matrix (Abdelhamied et al. 2022).

Fig. 12
figure 12

Changing of the a real, b imaginary dielectric constant, c real, d imaginary parts of electric modulus and e ac conductivity for undoped and doped PVC with FeCr2O4 and TPAI

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4 Conclusion

FeCr2O4 with a single-phase cubic structure \(F d\stackrel{-}{3}m\), average crystallite size 9.4 nm was used as nanofiller for PVC polymer. PVC films, ~ 0.35 mm, loaded with FeCr2O4 and different wt% of TPAI (x = 0, 2.5, 5, 10, 20) were produced with uniform distribution of the nanofiller in PVC matrixî. Doped polymers had good absorbance in wavelengths up to 500 nm (UV and visible ranges) nominating it in several fields like coatings, adhesives, medicine, and solar cells. For wavelengths ≥ 330 nm, R and n enhanced greatly when PVC doped with FeCr2O4, both reduced with TPAI doping in the range λ = 300–450 nm and increased again for λ ≥ 460 nm. Both k and σopt were increased when doping PVC with FeCr2O4 and increased further as the amount of TPAI increased, reaching highest values for TPAI 2.5 wt%. The doped polymers have potential for use in polymer-optoelectronics, highly reflective fields, and strong optical confinement. In the visible range, PVC/FeCr2O4 has the highest εr value while PVC/FeCr2O4/TPAI have the highest (εi, SELF, VELF) values. Such improvements in nonlinear optical features recommend present composite for use in photonic and optical applications. FeCr2O4 molecules acted as fluorescence quencher and reduced the FL intensity of pure PVC polymer. Loading TPAI to PVC produced little effect on the FL intensity. Except for FeCr2O4 and TPAI-doped PVC, which showed orange emission under 317 nm, the emission from undoped and doped PVC with the fillers clearly exhibited a blue-violet emission under the different excitation wavelengths. The values ε′ and ε′′ were increased as PVC loaded with FeCr2O4. Upon loaded PVC/FeCr2O4 polymer with TPAI, both ε′ and ε′′ increased irregularly, reached their maximum values as the amount of TPAI became 10 wt %. Doping PVC with FeCr2O4 resulted in a rise in AC conductivity, which was further bolstered by the addition of TPAI. The enhanced dielectric properties of PVC/FeCr2O4/TPAI nominated them to be used in different optoelectronic applications such as sensors and as polymer based capacitors in the energy storage devices.