Abstract
In the current work, a novel methodology based on the green approach has been carried out to prepare polymer composites with declined optical band gap. The extracted dye of black tea was used to create Mn2+ metal complexes. The XRD outcomes establish that Mn2+ complexes disrupt the hydrogen bonding between polyvinyl alcohol (PVA) chains. The FTIR results confirm the occurrence of interactions among the components of PVA composites. The UV–visible spectroscopy study was carried out to measure the fundamental optical and optoelectronic parameters, including absorption edge, refractive index (n), dielectric loss (), band gap energy (), phase velocity, grouped velocity, sheet resistance (), and thermal emissivity () of the pure PVA and composite films. The results showed that the doped PVA exhibits a band gap of 1.62 eV. Furthermore, Tauc’s method was implemented to determine the possible types of electronic transitions. The ASF method was examined as an alternative to Tauc’s approach to determine the values. Increasing in band tail from 0.269 to 0.362 eV indicates a remarkable presence of disorder phases in composite films. The W-D model was used to evaluate the oscillator energy . From Taucs model it was found that the optical band gap declines from 5.893 eV for pure PVA to 1.849 eV for PVA composites. The refractive index of PVA polymer was found to improve for PVA inserted with Mn-metal complexes. The results establish that polymer metal complexes are more efficient in increasing light-matter interactions.
Introduction
Polymer materials have gained significant attention in modern technology due to their cost-effectiveness, lightweight nature, flexibility, and natural abundance. These properties make them highly suitable for various optoelectronic applications, including polymer optical fibers, waveguides, and optical storage systems [1]. Nevertheless, enhancing their electrical, mechanical, and optical properties is essential for expanding their functional capabilities. A widely explored approach involves doping polymers with suitable additives to achieve desired material characteristics [2, 3]. Under this theme, Polymer composites, which are materials made from various chemical or physical components integrated within polymer matrices, demonstrate enhanced properties compared to pure polymers. These advanced materials play a crucial role in optical systems and are extensively used as shielding materials against electromagnetic and radio frequency interference in electronic devices, optical sensors, polarizers, data storage units, solar panels, and even in various biomedical applications [4–8]. A particularly effective method for enhancing the optical and electrical properties of polymer composites is the incorporation of transition metal complexes, which form coordination bonds with ligands and significantly influence material properties [9, 10].
One type of polymer composite material is created by incorporating transition metals into the host polymer. Transition metals, typically considered heavy metals because of their atomic density exceeding 4,000 kg/m³, this range normally present environmental and health hazards as they are non-biodegradable [11–13]. However, their hazardous effects can be mitigated when they are captured by ligands in coordination complexes, making them a viable component in green chemistry approaches. One major challenge in material science is developing biocompatible materials that reduce environmental pollution. In this context, green synthesis techniques, particularly those utilizing plant extracts, offer a sustainable and effective approach for producing metal-polymer composites [14]. Among various plant-based methods, polyphenol-rich extracts from tea plants (Camellia sinensis) have demonstrated a remarkable ability to form metal-polyphenol complexes. Although polyphenols can react with metal ions to form complexes, they do not necessarily reduce metal ions to nanoparticles [15]. Previous studies have shown that black and green tea extracts can effectively reduce the optical band gap of polar polymers such as poly(methyl methacrylate) (PMMA) [16] and polyvinyl alcohol (PVA) [17]. The coordination compounds formed between transition metals and polyphenols enhance the electronic interactions within the polymer matrix, improving its optical properties [18, 19]. Polyvinyl alcohol is a particularly promising host polymer for composite fabrication due to its hydroxyl functional groups, which facilitate hydrogen bonding and allow for the growth of inorganic nanoparticles within its structure. Moreover, the PVA polymer consists of a carbon chain backbone with hydroxyl groups attached to methane carbon atoms. These hydroxyl groups promote the formation of hydrogen bonds, thereby influencing the structural configuration of the polymer composite by facilitating the growth of inorganic nanoparticles within the polymer matrix [20, 21]. Several studies have reported significant reductions in the optical band gap of PVA-based composites upon the addition of metal complexes. For instance, Aziz et al. [22] incorporated aluminum-complexes into the PVA matrix, reducing the energy gap from 6.39 eV to 1.68 eV. Similarly, Nofal et al. [23] demonstrated a decrease in energy gap from 5.8 to 1.82 eV when mixing PVA with a cobalt-polyphenol complex extracted from black tea. Additional studies by Brza et al. [15, 24] reported that the inclusion of cadmium and cerium metal complexes in polymers significantly reduced their optical band gaps. In this study, a green approach was employed to synthesize Mn (II)-polyphenol complexes by combining manganese acetate with black tea extract. Green chemistry approaches for synthesizing coordination compounds have been recognized as innovative methods for reducing the energy gap of polymers, particularly in comparison to the incorporation of metal salts. Additionally, extracted dyes from black tea, which are rich in polyphenols, are utilized for the synthesis of Mn-metal complexes due to their high abundance of hydroxyl (OH), carbonyl (C=O), and amine (NH) functional groups. The resulting complex was then incorporated into a PVA polymer matrix in varying proportions to fabricate polymer composite films. The optical and structural properties of these films were systematically analyzed. The results demonstrate a substantial reduction in the optical band gap, decreasing from 6.1 eV in pure PVA to 1.62 eV in the optimized composite film. This decrease indicates an increase in the amorphous phase within the polymer composite, leading to the formation of additional localized energy states. These findings establish that metal complexes synthesized through green chemistry approaches are effective alternatives to traditional ceramic fillers or metallic powders for tuning the optical properties of polymer composites. The present study contributes to advancing sustainable material development and highlights the potential of Mn (II)-metal complexes for future optoelectronic applications.
Methodology
Metal complex preparation
Sample preparation commenced with warming 800 ml of distilled water up to 90C, then a powder of 23.68 g of black tea leaves was added to the hot water. The mixture was left to cool down to about 50. The solution was then filtered by (W. man paper 41, cat. no. 1441) with a pore radius of 20 μm to discard all residue within the solution. Besides, 20 g of manganese acetate (Mn (CH3CO2)2.2H2O) salt [MW = 245.09g/mol] was dissolved in 300 ml of distilled water. The mixtures of dissolved salt and filtered dyes of black tea were mixed and stirred on a hot plate at 70°C for 60 min. Upon steady stirring, the solution begins to change its color from dark to brown and many particles were formed in the shape of clouds and starts to precipitate at the bottom of the beaker. The Mn- metal complex was washed several times to remove anions. To prepare polymer composites based on PVA, 5.5 g of pure PVA powder (with an average molecular weight of 18000 g/mol) was added to 240 ml of distilled water and stirred for an hour at 90°C. Finally, the PVA solution which almost transparent was left to cool down to room temperature.
Sample preparation
Scheme 1 exhibits comprehensive steps of the preparation of polymer composite films (PVA/Mn-PPHNL) using the well-known solution casting method. The polymer film fabrication begins by incorporating different amounts of metal complex (Mn-polyphenol) into Pure PVA polymer solution, ranging from 0 to 21 ml in steps of 7 ml. In order to achieve a homogeneous solution, the mixtures were consistently stirred for 30 min. The samples were then labeled as PVMnMC0, PVMnMC1, PVMnMC2, PVMnMC3. The first one refers to pure PVA film and, the next three films were incorporated with 7, 14, and 21 ml of Mn-polyphenol. We stopped from the 21 ml concentration because when 28 ml of Mn-polyphenol was added to the PVA polymer, the film was brittle, and the absorption spectra for 21 and 28 almost overlapped. This indicates that PVA was able to accept the metal complex to its maximum limit, and increased concentration above 21 ml (metal complex) doesn’t change the absorption pattern. The polymer composite films, which had an average thickness of 0.075, 0.13, and 0.13 mm, were then made by placing the solutions onto several plastic dry Petri plates and allowing them to dry for a week at ambient temperature.
Spectroscopic studies
Well-known techniques like Fourier-transform infrared (FTIR) analysis, X-ray diffraction (XRD), and UV-visible absorption spectroscopy were used to examine the structural and optical characteristics of the polymer composite. An X-ray diffractometer (ADX 2700) with an electromagnetic radiation source of Cu kα and wavelength (0.154 nm) was employed to record the XRD patterns of polymer films at room temperature, with Bragg’s angle (2θ) in the range of 10° to 90° and a scan rate of 2 min−1. Next, an FTIR spectrophotometer (Perkin Elmer, the Nicolet iS10) was used to conduct (FTIR) study. Utilizing a spectral resolution of 2 cm−1, the analysis was carried out over a spectral range of 500–4000 cm−1. Ultimately, the synthetic series of samples’ UV-visible spectra, which include PVMnMC0, PVMnMC1, PVMnMC2, and PVMnMC3 films, were obtained using the UV–Visible spectrophotometer (Perkin Elmer double-beam UV–Vis–NIR spectrometer Lambda 25 absorption). The aforementioned techniques facilitate thorough structural and optical investigation of the polymer films. In particular, absorption spectroscopy, making use of the absorbance and transmittance information, lays the groundwork for understanding and measuring substantial optical properties, for instance, band gap, dielectric constant, refractive index, absorption coefficient, and localized density, as shown in Scheme 2.
Declaration of generative AI and AI-assisted technologies in the writing process
During the preparation of this work, we used [QuillBot] in order to reduce the similarity, that is, for paraphrasing. After using this service, we reviewed and edited the content as needed and we take full responsibility for the content of the publication.
Results and discussion
X-ray diffraction analysis
X-ray diffraction (XRD) is the most effective method for analyzing the structural characteristics of the materials. The study reveals the existence of both crystalline and amorphous phases within the substance. Figure 1a shows the XRD spectrum of Mn-polyphenol, which indicates that the synthetic material is mainly amorphous since no obvious crystalline peaks over the entire spectrum. However, there is a hump manifestation between and [23, 24]. Afterward, the addition of Mn-polyphenol to PVA is thought to significantly affect the Reinforced polymer’s physical characteristics through several interactions that partially change the polymer phases from crystalline to amorphous. The XRD patterns of pure PVA film and its incorporated composites exhibit two distinct peaks, as illustrated in Fig. 1b. Early research also reveals that there is a typical sharp peak, , in addition to a broad diffraction peak at , highlighting the PVA structure’s partially crystalline nature [25]. The diffraction peak at has a remarkably high intensity due to the robust hydrogen bonds provided by the hydroxyl groups in side chains [26]. However, upon adding the metal complex to PVA, the peak at almost vanishes, whereas the peak at is broadened. This peak widens together with the intensity declining at . This shows that the disordered phase within the material structure is expanding. It has also been reported elsewhere that when metal complex adds to PVA, the intensity of these peaks decrease [17, 27].Based on [28] these findings it is possible to suggest that metal complexes provide more amorphous phases and crystalline phases declines within the polymer and thus the disorder fraction rises with the addition of the dopant [29]. The remarkable miscibility and compatibility of the polymer and metal complex components are demonstrated by the strong interactions between the metal complex’s OH and NH groups and the polar functional group, or OH, of PVA. The composite’s degree of crystallinity is decreased by this complex formation [30]. Therefore, the Urbach energy () can be supported by the XRD results seen in this work. It is known that Urbach energy can be used to look into how materials behave in terms of order and disorder.

Figure 1.
The XRD pattern displays (a) the Mn-polyphenol complex and (b) the pure PVA and modified samples.
Fourier transform infrared (FTIR) analysis
When infrared (IR) radiation is absorbed by optical medium, electromagnetic waves cause the molecules to be excited from lesser to greater vibrational energy levels. A molecular absorption spectroscopic method, FT-IR spectroscopy, provides molecule-scale information on polymer composites using the Beer-Lambert Law. Furthermore, correlating the chemical compounds in the sample with the absorption bands, also known as vibrational bands, is an essential step in interpreting the infrared spectra. Figure 2 shows the FTIR spectrum of the black tea (BT) extract solution and Mn-polyphenol compound. A broadband was observed at 3416 cm−1, and it has been suggested that this is related to polyphenols’ O-H and N-H stretching modes [31, 32]. An earlier study confirmed that the N-H stretching of amines I, II, and amides and the O-H stretching of hydroxyl groups (alcohols, phenols, and carboxylic acids) were responsible for the broadband in the 3490–3000 cm−1 region [33]. According to Saif et al. [34], the broad absorption band at 3310.7 cm−1 was attributed to the existence of several hydroxyls (OH) functional groups within alcohols and phenolic compounds. The C=O stretch of flavonoids and catechins at 1702 cm−1 and the C=C stretch in aromatic rings at 1645 cm−1 can be connected by a noticeable band. The bonded conjugated ketones, aldehydes, quinines, and ester vibrations are linked to the spectral range 1750 and 1620 cm−1 [32, 33]. A prominent peak centers at nearly 2938 cm−1, which is connected to the CH stretching mode [35]. Furthermore, it has been determined that amino acid C-O stretching results in a band at 1045 cm−1 [32, 33]. The FTIR spectrum of black tea powder has been investigated by Borregales et al. [36]. The study emphasizes that. The OH and C-O groups’ stretching and the C-OH bonds’ bending are responsible for the relatively broad bands at about 3282, 1142, and 1032 cm−1, respectively. The same study also confirms the existence of substantial phenol groups within the powder. Both symmetric and asymmetric stretching aliphatic groups of C-H bonds are responsible for the bands seen at 2922 and 2848 cm−1 carboxylic acid (R-COOH) [32, 33, 36]. The wake band was reported to be caused by C-H out-of-plane bending, ranging from 819 cm−1 to 834 cm−1 [32, 36]. The principal ingredients in black tea are Alkaloids and amino acids. L-theanine, which is found in both black and green tea, is the primary amino acid in tea. Theophylline, theobromine, protein, caffeine, theaflavins, and catechins [37–39]. Polyphenols and free amino acids are crucial constituents in terms of quality. Particularly, the primary polyphenol component, catechins, are well known for their antioxidant qualities, which have led to their evaluation in numerous diseases linked to free radicals, such as cancer, cardiovascular, and neurological disorders [40, 41]. The FTIR bands peaks corresponding to the OH stretch at approximately 3372 cm−1, CH antisymmetric and symmetric stretch at 2926 cm−1, C=O stretch at 1697 cm−1, ring stretch (benzene ring in aromatic compounds) at 1618 cm−1 at CH3 antisymmetric deformation at 1451 cm−1, O-H deformation and C-O stretch in phenol at 1372 cm−1, C-O-C stretch in cyclic ethers at 1234 cm−1 were observed in prior research, indicating the catechin component in black tea [24, 42–44].

Figure 2.
FTIR spectra of (a) extracted black tea and, (b) Mn-polyphenol.
Research shows that when polyphenol combines with metal cations, it forms cation–polyphenol complexes. This exciting process can be observed through the appearance of a colloidal suspension and a vibrant green solution at both the bottom and top of the container [15]. Prior study utilizing the FTIR approach demonstrates the capability to efficiently ascribe metal ions interacting with polyphenols to generate a coordination compound(Ce(III)-complexes, Cd(II)- polyphenol complex, Sn(II)-polyphenol complex, Co(II)-polyphenol complex, Zn(II)-polyphenol complex) [15, 23, 24, 45, 46]. The primary goal of the current research is to showcase the potential of attributing Mn+2 ions to metal complexes of manganese using the FTIR approach. Observed bands across the FTIR spectrum of black tea were also spotted over the spectrum of Mn (II)-polyphenol complexes, Although the latter exhibits slight shifting and reducing intensities, as shown in Fig. 2b. Nonetheless, the bands which were appeared at 2938 cm−1. The results shown in Fig. 2b showed a significant reduction in the FTIR spectrum of the Mn (II)-polyphenol complex, with peaks shifting to 2922 and 2857 cm−1, respectively, this can be interpreted as forming coordination bonds between Mn ions and polyphenols, resulting in vibrational attenuation and a significant enhancement in reducing mass. Moreover, several complexes influenced the chemistry of the interaction between Mn ions and the extracted tea solution. The Mn-polyphenol and Mn-caffeine complexes exhibit significant potential. Overall, the Mn (II) complex is prepared from manganese salt and Schiff base or by reaction of manganese salt with aldehyde or ketone and amino acid in an alcoholic or aqueous-alcoholic solution of an inert atmosphere. The IR spectra demonstrate the coordination of hydroxy oxygen to Mn, evidenced by the removal of (OH) and a change from 3416 to 3414 cm−1 [47]. Figure 3 illustrates the suggested formation of complex compounds between Mn cations and the polyphenols and caffeine present in the tea extract solution. The hypothesized structure for Mn-complex formation indicates that Mn (II) ion has the capability to form complexes with polyphenols.

Figure 3.
Formation of complex compounds between and the polyphenols complex.
Figure 4a–d demonstrates the FTIR spectra corresponding to the pure PVA and the polymer composite films with various Mn-PPNL additives (7, 14, and 21 ml), respectively.

Figure 4.
(a–d) FTIR measurements of pure and modified PVA films containing varying quantities of coordination compounds.
The spectral region between (1400–600 cm−1) considers the fingerprint of PVA, which includes CH2 in-plane rocking (long chain band) at 845 cm−1 [48]. This peak shift and its intensity decrease for the modified PVA samples while it is about to perish after adding 21 ml of the dopant material. A featured peak corresponding to –C–O– stretching vibration in pure PVA presents itself at 1101 cm−1. It is considerably altered and diminishes in strength throughout the combined films [22]. The C-C stretching at 1254 cm−1 for pure PVA shifts and exhibits a drop in intensity for the modified samples [49]. Furthermore, the vibrational bending of CH2 wagging (out of plane) at 1411 cm−1 indicates pure PVA. These features of CH2 wagging drops clearly in the spectra associated with doped PVA, and their intensity declines with increasing the proportion of Mn (II)-complexes such that the peak nearly diminishes for 21 ml of Coordination compound [50, 51]. The vibrational frequencies at 1728 cm−1 of pure PVA are attributed to C = O stretching of the acetate group, which is the residual part of PVA shift to 1720 cm−1. This demonstrates that the connection between the metal complex and PVA originates from the O–H group and the C–O group of pure PVA [48, 52]. In the case of the modified samples, the displacement occurs towards lower wave numbers. The C-H asymmetric stretching vibration corresponds to a band at 2938 cm−1, which exhibits notable shifts and reductions in intensity for PVA hybrid samples, which also deviates and loses some of its intensity upon incorporating polymer material [53]. Furthermore, the O–H stretching absorption of hydroxyl groups could be identified via a wide and strong absorption peak at 3340 cm−1 for pure PVA. The presence of robust intra- and inter-hydrogen bonding contributes to the high intensity of this band. The modified samples exhibit an apparent band displacement, accompanied by a significant reduction in intensity [24].
One identified cause of the decline and diminished strength of band interaction with the Mn-polyphenol complex colloid and PVA functional groups is established. The entire change that occurred in the PVA spectrum results from the fact that the molecular weight has been increased; therefore, the material’s capability to absorb electromagnetic light has also been enhanced, which has also led to the weakening of vibrational intensity of functional groups [27]. Consequently, incorporating PVA polymer with (Mn-polyphenol) fulfills the purpose of the study to harvest more light energy and promote the optical properties of the polymer materials.
Optical properties
Absorption study of the extracted dye and metal complex
The electronic transition that characterizes an electron’s excitation from its ground state to its excited state is known as ultraviolet-visible spectroscopy. UV-visible spectroscopy is a non-destructive and efficient technique that allows qualitative and quantitative estimation of the gap energy (), which is an essential optical parameter that determines the optical usage of a given material. The molecular orbital theory describes how electrons in σ, π, and n-orbitals are promoted from the Lowest energy state to excited states when a light photon is absorbed by polymeric materials in the ultraviolet and visible regions [54]. Accordingly, molecular structure determines both the intensity of absorption and the wavelength of maximum absorption. If the molecular structure of a given molecule is altered, transitions to the anti-bonding orbital that occur in the ultraviolet range could also take place in the visible range [55, 56]. The extracted black tea dye sample (B.T)’s absorption spectra are shown in Fig. 5a, which displays how the absorption varies with wavelength. Tea leaves have been chemically analyzed to consist of intricate, such as Alkaloids, proteins, glucides, amino acids, polyphenols, volatile compounds, minerals, and trace elements (18) [16]. The main absorption window of the material is located in the UV band (180–420 nm), where the electronic transition from n to σ* is caused by electronic transitions, while the transitions from π to π* and n to π* of CTH, methylxanthines, and caffeine occur at higher wavelengths since they require less energy [45].

Figure 5.
(a, b) Optical absorption spectra of extracted black tea and Mn (II)-polyphenol.
According to previous studies, the n-π* electronic transitions of catechins and methylxanthines, which include caffeine (CF), theobromine (TB), and theophylline (TP), are linked to the absorbance of incident light with wavelength range between 200 and 350 nm. The absorption near (275 nm) is associated with the absorption of caffeine’s C=O chromophore, depending on the substituents on the benzene ring, the π-π* absorption of aromatic compounds at 230–330 nm [57, 58]. Figure 5a and b corresponds to the absorbance spectrum of Mn-PPHNL, which exhibits a relatively high absorption window, including two peaks at longer wavelengths (450–700 nm). The absorbance enhancement is ascribed to the formation of charge transfer molecular systems and the presence of π electrons [45].The UV-visible spectrum is where metal nanoparticles must show a surface Plasmon resonance (SPR) peak. Due to the capping of polyphenols, the synthesized Mn (II)-complex has no metal properties on the particle surfaces. The lack of an SPR peak in the Fig. 5a and b evidences this. spectrum. Hypothetically, the absorption spectrum shown in Fig. 5b could potentially improve the absorbance of polymer materials when the metal complex is added to a convenient polymer with a proper amount. Several studies also emphasize that metal complex additives boost absorption efficiency of the polymer materials at visible spectral range [24, 30, 59]. On the other hand, although it shows a lesser intensity, the Mn-metal complex’s absorption spectrum shows the same peak. This finding implies that Mn acetate and black tea have a beneficial interaction [30]. Following the results in Fig. 5, the next step is to show how adding varying amounts of coordination chemicals to PVA polymer altered the absorption bands.
Absorbance and transmittance study of polymer composites
Electromagnetic light incident on a given optical medium, for instance, from air into a solid material. At the interface between the two media, and through the optical medium, some light will be reflected, then some will be absorbed by the medium, and the rest will be transmitted. The summation of all optical phenomena equals unity [
53].
Where T, A, and R represent, respectively, the transmissivity (), absorptivity (), and reflectivity (). In other words, what proportion of the incident light is passed on, received, and reflected by a material [60]. Ultraviolet-visible (UV–Vis) spectrophotometer has grown in importance as a tool for understanding the optical characteristics of various materials throughout light-matter interaction and electron transition within the material due to light absorption. Figure 6a shows pure and modified PVA polymer film transmission of light patterns. The figure highlights a clear difference between the spectrum corresponding to the pure PVA with the other composite films, such that the pure film exhibits a significant absorption in the UV region, whereas it maintains its highly transparent characteristics at the broadband range between 1070 and 250 nm. On the other hand, regarding polymer composites, transmittance declines considerably with increasing additive concentration in the polymer material. Although scattering causes optical loss within the material, transmission decline is mainly attributed to absorption via electronic transition. It is more convenient to show absorption spectra instead of a spectrum to gain a clearer insight into the phenomenon, as illustrated in Fig. 6b. The spectra associated with polymer composites reveal that absorption has been improved as Mn-polyphenol concentration increases. The black line, which represents pure PVA film, implies that light absorbed does not take place, and the material stays transparent in the visible spectrum, emphasizing that the incident photon energy within this region is lower than the energy difference between the two states of the material. When the energy of the photons is higher below 250 nm, then absorption has taken place, and the valence electrons undergo a transition between two electronic energy states. Thereby, extensive absorption of modified polymer films is thought to be highly linked to the extending and enhancing absorption of the composite structures; the argument is also stated in [24]. From Fig. 6b and the spectrum of pure PVA film, the electronic transitions mostly occur in UV region. This is also common in polymers since the majority of polymers have bond energy located at the UV range [61]. The absorbing spectrum at 250 nm, resulting from unsaturated bonds, notably C=O and C=C, located in the polymer’s tail head, is ascribed to the π → π* electronic transition type [62]. Moreover, the sharp absorption edge in pure PVA indicates that the PVA film is mainly a semi-crystalline structure [63]. Afterwards, following the addition of manganese –polyphenol mixture to PVA, the absorption window of the composite films is extended toward the visible region. It is well known that the majority of organometallic materials have distinguished optical absorption and emission over spectral range from 400 to 800 nm [27]. This could be explained by the way that ligands (functional groups) facilitate the formation of orbital overlapping. Subsequently, electrons can convey energy across the molecules, resulting in the absorption spectra [27]. Hence, the energy gap of materials can be from the absorption study, which is significant from the perspective of technological application. Therefore, the energy gap of materials can be adequately estimated from the absorption study, which is significant from the perspective of technological application. Since the Light-interaction property of polymer materials is directly related to their structural and electronic properties, these properties could be amended. Hence, the polymers have recently shown great potential to be utilized as key entities in various applications [5].

Figure 6.
(a) Transmittance, (b) absorbance spectra for pure and modified PVA sample.
Absorption edge study
Band strength or band-gap energy can be rigorously estimated from the absorption edge in order and non-crystalline substances using the informative UV-vis technique for studying the electronic transitions [
64]. A material’s ability to absorb light is determined by a substantial parameter called optical absorption coefficient
[
65]. The edge of absorption fractional attenuation in intensity per unit distance is represented by
, which is defined as a zone where electrons acquire photon energy to excite from a low-energy state to a high-energy state. The typical absorption boundary area can be utilized to determine the minimum photon energy necessary for electron transition from the valence band (V.B.) to the conduction band (C.B.). The band gap energy may be calculated via several approaches, and the resultant value should approximate that of the absorption edge [
66]. In particular, from the absorbance, one can determine the relative decrease rate in the incident light intensity or the absorption coefficient as a function of frequency,
α(v). applying Beer Lambert’s law.
Where () is thickness of the sample [49, 64]. Figure 7 exhibits the optical absorption coefficient function to photon energy () for both pure and modified PVA solid composites. The absorption edge of PVA has significantly changed to lower photon energy with the incorporation of metal complexes. According to Fig. 7, moving the absorption edge toward the lower energy confirms that the doped samples’ optical band gap has significantly reduced. Quantitatively Table 1 highlights the magnitude of the absorption coefficient for PVMnMC0 is 6.1 eV. Then it decreases to 2.10, 1.80 and 1.6 eV for PVMnMC1, PVMnMC2 and PVMnMC3 respectively.

Figure 7.
Variation of absorption coefficients corresponding to incident photon energy for all the composite samples.
Table 1.The pure and doped PVA samples have different values for the absorption edge and Urbach energy.
Sample composition
. | Absorption edge (eV)
. | Urbach energy (eV)
. |
---|
PVMnMC0 | 6.1 | 0.269 |
PVMnMC1 | 2.10 | 0.3244 |
PVMnMC2 | 1.80 | 0.3458 |
PVMnMC3 | 1.61 | 0.3621 |
Sample composition
. | Absorption edge (eV)
. | Urbach energy (eV)
. |
---|
PVMnMC0 | 6.1 | 0.269 |
PVMnMC1 | 2.10 | 0.3244 |
PVMnMC2 | 1.80 | 0.3458 |
PVMnMC3 | 1.61 | 0.3621 |
Table 1.The pure and doped PVA samples have different values for the absorption edge and Urbach energy.
Sample composition
. | Absorption edge (eV)
. | Urbach energy (eV)
. |
---|
PVMnMC0 | 6.1 | 0.269 |
PVMnMC1 | 2.10 | 0.3244 |
PVMnMC2 | 1.80 | 0.3458 |
PVMnMC3 | 1.61 | 0.3621 |
Sample composition
. | Absorption edge (eV)
. | Urbach energy (eV)
. |
---|
PVMnMC0 | 6.1 | 0.269 |
PVMnMC1 | 2.10 | 0.3244 |
PVMnMC2 | 1.80 | 0.3458 |
PVMnMC3 | 1.61 | 0.3621 |
Refractive index, phase velocity and group velocity analysis
The refractive index of dielectric optical media is typically regarded as an intrinsic property that is intimately related to the dipole moments of the molecules and atoms that compose the optical system. It is also considered a substantial optical parameter that substantially defines how a propagation light beam could interact with a given optical medium. Taking into consideration an optical medium with adequate absorbance, the refractive index equation can be expressed as [
67].
Where refers to the complex refractive index, is an actual index of refractive, and represents the extinction coefficient, which relates to the capability of absorbing light by the medium. Nevertheless, the refractive index of an optical medium is not a straightforward parameter and it is simultaneously related to several parameters and microscopic structure of the guiding medium. In particular, how the electric field component of propagation electromagnetic wave exerts time-varying forces on a material’s internal charge structure. Regarding polymer composite materials, The refractive index rises with the amount of a metal complex due to the inertia of polar molecules at elevated wavelengths, which prevents them from synchronizing with the alternating field [62]. Another optical parameter that determines the refractive index is polarizability, which is associated with the molecular identity and number of atoms per unit volume in polymer materials. Stated differently, the polarizability of a molecule is determined by the number and mobility of its electric charge system [9]. Therefore, adding more additives to the host polymer entails increasing the concentration of charge carriers. As a result, and according to the Lorentz–Lorenz formula, there will be more polarizable and higher-density molecules, which will elevate the index of refraction [68].
Nonetheless, the Kramers–Kronig relation is recognized as an efficient formula that relates the actual and imaginary components of the complex refractive index. The relationship is articulated in several forms. One of its formats includes the reflectance (
) and extinction coefficient (
), as indicated:
Where , It is directly correlated to both the absorption coefficient () and the wavelength () while being inversely related to the specimen’s width (). Using Beer-Lambert law, one can compute the reflectance () from the absorbance () and transmittance (). The transmittance can be deduced from () [62, 69]. There is a growing demand for sizeable refractive index optical materials in the fields of advanced optoelectronics fabrication, filters, optical adhesives, highly reflective and antireflection coatings, and ophthalmic lenses. Any technique that boosts a material’s electron density generally grows its refractive index as well [70]. It has been reported that the linear evolution of with the amount of additive indicates adequate and uniform distribution of the filler throughout the host polymer [71]. Moreover, refractive index and optical band gap are identified as the fundamental factors in determining a material’s optical behavior [72]. In this domain, several published research has demonstrated that increased () of modified polymer materials invariably causes the optical band gap to decrease [63, 73–77]. Particularly, the incorporation of complex metals into pure PVA enhances the density of the polymer composite film, thereby boosting the refractive index. This increase in density leads to a desired interaction between Mn-polyphenol and PVA polymer [78]. Accordingly, here in this study, we aimed to improve the optical properties of PVA by enhancing the refractive index. Figure 8 displays the refractive index against wavelength for pure and modified PVA. It becomes evident that when the concentration of the metal complex rises, so does the refractive index, such that it increases from 1.14 to 1.33, which is sufficient to significantly reduce the energy band gap of the polymer material. The primary beneficial uses of high-refractive-index polymers may be advantageous for optical storage devices [15], light-emitting diodes(OLEDs) [26], various semiconductors [79], ophthalmic applications [80], and immersion lithography [9].

Figure 8.
Pure and doped PVA film Refractive index () against of wavelength.
From optics, phase velocity is the speed at which a specific section of an electromagnetic wave, such as the wave’s peak or trough, travels through a medium. The materials
and the light’s wavelength (
) passing through it are taken into consideration to determine the value of phase velocity [
81]. In contrast, in a frequency-dependent medium, it is usually smaller by a factor of
. Thus, with a greater index of refraction of the pure PVA: PVA composite, slower light propagates. This is because film that has been mixed with metal complexes becomes denser and, as a result, the refractive increases, as illustrated in
Fig. 9a. It is additionally noteworthy that the bonding nature of the material is directly linked with the refractive index. Ionic compounds often exhibit lesser refractive index values compared to covalent compounds. When ions form covalent bonds, they share more electrons than when they form ionic bonds. Consequently, extra electrons are dispersed throughout the structure and interact with incident electron to reduced its velocity [
82]. On the other hand, the group velocity of a propagating wave is the rate at which the overall envelope generates the wave’s amplitude and frequency. The values of the parameters are calculated using the following formula, which is illustrated in
Fig. 9b.

Figure 9.
(a, b) Phase and group velocity function of wavelength.
In Fig 9a and b, the relationship between phase and group velocities and wavelength for the examined compositions is readily discernible. In these illustrations, the phase velocity exhibits more clear dependence and significant variation against wavelength compared with group velocity, as the latter shows only some bumpy features at about (600 nm) and the peak develops as the metal complex increased [83].
Wemple and DiDomenico (W–D) method and optoelectronic parameters
Derived from the optical dielectric response of a material via refractive index dispersion in a low-frequency regime, Wemple–DiDomenico (W-D) introduced a single oscillator model [84]. A method has been presented to compute the fundamental optical variables, including static refractive index (), dispersion energy (), and oscillator energy (). These are essential parameters regarding optoelectronic applications.
The dispersion energy parameter (
) articulates the arrangement of electrons and the allocation of electric charges within each lattice cell of the optical medium. Therefore, it defines the strength of the electronic transition on the molecular scale, and it is strongly tied to the bonding nature between molecules. Correspondingly, The average energy gap of a specific oscillator is posited to be linked to a singular oscillator parameter (
), latter determines the band structure of the material [
5]. The W-D approach establishes a link between the energy (
) of incident light right below the absorption edge and the refractive index (
):
In this context, ‘ represents the single effective oscillator energy, offering quantitative and thorough insights into the material’s overall band structure, whereas measures the average intensity of inter-band optical transitions closely associated with the material’s structural order. Consequently, the parameter is intrinsically associated with ionicity, anion valency, and the coordination number of the material [85]. The parameters ( and ) can be deduced from graphical plot between and as shown in Fig. 10, and values can be calculated from slope and intercept on vertical axis [86].

Figure 10.
Variant as a function for (a) PVMnMC0, (b) PVMnMC1, PVMnMC2 and PVMnMC3 films.
The numerical values of dispersion energy and oscillator energy are presented in Table 2. At long wavelengths, where the mean photon energy () approaches zero, the refractive index becomes invariant, referred to as the static refractive index () is measured from the linear part extrapolation. This is derived from Equation (7) and simplified to Equation (9), attributed to the resonance effect resulting from the specimen’s polarization by incident light photons. Considering the metal complex effect, as it is shown in Table 2. An () increases with increasing additive concentration, whereas () decreases more drastically. Furthermore, it is well established that oscillator energy is correlated with the lowest direct band gap. Hence this parameter is typically thought of as an average energy gap. Thus, these findings suggest the metal complex incorporated into pure PVA modifies the optical properties of the host polymer. Quantitative measurements of optical parameters could aid in customizing and modeling these films’ characteristics for application in optical and optoelectronic devices and components [22, 46, 62, 85].
Table 2.Dispersion and oscillator energy calculate from theoretical Wemple-DiDomenico (WD), moments of the optical spectrum, single oscillator model and static refractive index.
Concentration
. | Dispersion Energy ()
. | Oscillator Energy ()
. |
. |
. |
. |
---|
PVMnMC0 | 1.533 | 5.893 | 0.2732 | 0.0078 | 1.128 |
PVMnMC1 | 0.7149 | 2.133 | 0.3351 | 0.0736 | 1.155 |
PVMnMC2 | 0.7545 | 1.963 | 0.3843 | 0.0997 | 1.176 |
PVMnMC3 | 0.7849 | 1.849 | 0.4244 | 0.1241 | 1.193 |
Concentration
. | Dispersion Energy ()
. | Oscillator Energy ()
. |
. |
. |
. |
---|
PVMnMC0 | 1.533 | 5.893 | 0.2732 | 0.0078 | 1.128 |
PVMnMC1 | 0.7149 | 2.133 | 0.3351 | 0.0736 | 1.155 |
PVMnMC2 | 0.7545 | 1.963 | 0.3843 | 0.0997 | 1.176 |
PVMnMC3 | 0.7849 | 1.849 | 0.4244 | 0.1241 | 1.193 |
Table 2.Dispersion and oscillator energy calculate from theoretical Wemple-DiDomenico (WD), moments of the optical spectrum, single oscillator model and static refractive index.
Concentration
. | Dispersion Energy ()
. | Oscillator Energy ()
. |
. |
. |
. |
---|
PVMnMC0 | 1.533 | 5.893 | 0.2732 | 0.0078 | 1.128 |
PVMnMC1 | 0.7149 | 2.133 | 0.3351 | 0.0736 | 1.155 |
PVMnMC2 | 0.7545 | 1.963 | 0.3843 | 0.0997 | 1.176 |
PVMnMC3 | 0.7849 | 1.849 | 0.4244 | 0.1241 | 1.193 |
Concentration
. | Dispersion Energy ()
. | Oscillator Energy ()
. |
. |
. |
. |
---|
PVMnMC0 | 1.533 | 5.893 | 0.2732 | 0.0078 | 1.128 |
PVMnMC1 | 0.7149 | 2.133 | 0.3351 | 0.0736 | 1.155 |
PVMnMC2 | 0.7545 | 1.963 | 0.3843 | 0.0997 | 1.176 |
PVMnMC3 | 0.7849 | 1.849 | 0.4244 | 0.1241 | 1.193 |
Employing dispersion energy and oscillator energy, the moments of the optical spectrum (
and
) can provide a quantification of inter-band transition strengths, as delineated by the following equations.
The second table presents the values of and for all composites, indicating a rise with the addition of the metal complex. The optical moments are directly associated with macro parameters such as dielectric constants and the adequate number of valence electrons in polymer composite films [5, 87].
Optical bandgap study
Optical Dielectric method and Taucs model
An energy range in solid materials without any electron states is known as the band gap energy. These states are forbidden from energy due to their position between the bands of valence and conduction, which normally forbid any transition. You need to have enough energy to match the forbidden energy in order to move from these two bands. According to Kumar and Rao’s review paper, materials with band gap energies between 1.0 and 1.7 eV are suitable for use in real-world optoelectronic applications [
88]. Several studies have been conducted aiming to acquire compounds with narrower band gaps, which allow to match the excitation of electrons with the photon energy of visible light and near IR [
89]. The characteristics of electron transitions in charge transfer complexes and semiconducting polymers remain inadequately comprehended. Let electrons move from valence to conduction bands, the phonons must supply the necessary momentum, and the incident photons must have enough energy to surpass the forbidden energy [
90]. Therefore, the present work employs two methods for investigating the Energy gap, grounded in experimental and theoretical frameworks. Tauc’s technique was applied using the optical absorption theory. It is a well-known technique for investigating band-gap configuration, which links photon energy and absorption coefficient. However, for the sake of rigorous study band gaps, theoretical physicists have created a number of models based on quantum methods. The optical dielectric function theoretically contains all intrinsic effects corresponding to processes of light-matter interaction. Previous studies have shown that the main peak of optical dielectric loss (
) is mainly determined via electron migration from the valence to the conduction band. Thus, for energy gap analysis,
parameter versus
ability is taken into account [
21,
52,
59,
91–94]. The electronic band structure and optical properties are intricately linked. Knowledge of the actual and fictitious parts of the dielectric function enables the determination of essential optical functions. More precisely, Optical polarizability and attenuation of the material are associated with the real and imaginary components of the dielectric, respectively. Therefore, photonic dielectric loss is essential for precisely ascertaining the energy gap [
95]. The basis for characterizing the photon-electron interaction within a system is the time-dependent perturbations of the unexcited state, which is based on quantum mechanics. The transition from full to vacant states is brought about by both photon emission and absorption. The virtual part
of the dielectric function has the following form [
46,
96].
Where
are the angular frequency of the incident photon, crystal volume, electron charge, permittivity of free space, position vector, and a given vector determined by the incident electromagnetic wave polarization, respectively. The superscripts
C and
V signify the conduction and the valence bands, respectively. Hence, from
Equation (14), it is evident that optical dielectric loss, namely the imaginary component of the optical dielectric function, is associated with both the real and imaginary components of dielectric loss in the band structure (
) [
46]. According to Bouzidi
et al. [
97], it is highly possible that an interband transition occurs within the material; a photon pushes an electron from an occupied state in the valence band to an unoccupied state in the conduction band. During this process, the light is absorbed, resulting in increased atomic vibration and the formation of excitons, leaving a hole behind. This is fundamentally a quantum mechanical process [
98]. In the context of polymer materials incorporated with metal complexes, the dielectric loss peaks shift towards lower photon energy. The valence and conduction band in a solid are strongly correlated with the optical dielectric loss when viewed from a quantum-mechanics (i.e. microscopy) perspective. Additionally, the primary crest in the imaginary portion of the dielectric function has been confirmed microscopically to strongly correspond with the inter band transitions [
99]. Experimentally, imaginary portion of optical dielectric function
is measured by
[
22]. Prior research has shown a clear association between inter-band transitions and the peaks in the
spectra [
20,
100]. The actual energy gap may be calculated using the optical dielectric loss, measured empirically by intersecting linear sections of
spectra on the horizontal axis of photon energy (see
Fig. 11). Move electron from ground state to excited state essentially indicated by the
parameter [
22,
24]. Within the domain of semiconductor components, nanomaterials, and solar industries, the estimation of the materials energy gap is regarded as a crucial step toward materials feasibility for a desired application. It is important to note that the energy gap and kind of electronic transitions controlling a material’s optoelectronic behavior can be found using the optical absorption spectrum. The quantum mechanics perspective is regarded as a profound insight into understanding the principles of light-matter interaction and, hence, the mechanism of electronics. Nevertheless, quantitatively, Tauc’s equation is recognized as the most reliable method for estimating the energy gap of composite materials. Accurate measurement of the band gap from optical absorption demands other approaches, particularly due to the tail states near the VB and the CB. Tauc’s model could be considered the most convenient method for deducing the band gap [
76,
89]. Generally speaking, there are two categories of materials for insulators and semiconductors; depending on the material’s band structure, there are various types of transitions, direct and indirect band gaps. Electronic momentum cannot be preserved during the transition between the (V.B.M) maximum and (C.B.M) minimum in amorphous semiconductors with indirect band topologies, where the (V.B.M) and the (C.B.M) do not lie at the similar wave vector, an indirect electron transition takes place. In contrast, the point of transition from the valence to the conduction band is where the momentum of materials in a direct band structure is preserved. In direct band gap materials, the zero-crystal momentum point is where the two worlds (V.B.M and C.B.M) intersect [
16,
27,
95]. Considering the previous explanation regarding the fundamental physics of the field, the photonic band gap was computed from the corresponding variation of absorption coefficient as a function wavelength using Tauc’s relation.

Figure 11.
against to the PVMnMC0, PVMnMC1 and PVMnMC2, PVMnMC3 samples.
Where, symbolize the absorption coefficient, the , a constant related to band, configuration, and the optical bandgap of the material, respectively, and p is a fixed, establishes the kind of transition and the density of state distribution. When takes rational number values, for instance; 1/2 and 3/2, the transition is then indicated by direct allowed and forbidden transitions, respectively, whereas if it takes integer values such as 2 and 3, the transitions are indicated by indirect allowed and forbidden transitions, respectively [8, 9, 69]. Figure 12 depicts Tauc’s model representation of various electronic transitions that highly likely occur between CB and VB. Earlier studies have established that the energy gap may be identified regarding the basis of dielectric loss and the type of electronic transition deduced from Tauc’s model [16, 27, 59, 62, 99, 101, 102].

Figure 12.
Schematic demonstration of electron migration based on Tauc’s method: (a) direct allowed, (b) direct forbidden, (c) indirect allowed, and (d) indirect forbidden.
By extrapolating the intersection of the linear component of the against the hv axis, one may get the value of in Fig. 13a–d. From the Fig. 13a–d, it is clear that the energy bandgap corresponding to pure PVA film is 6.1 eV, then it drops remarkably to 2.2, 1.78 and 1.62 eV for PVMnMC1, PVMnMC2 and PVMnMC3 respectively. The relatively large bandgap emphasizes the fact that PVA in its pure form is an insulator, meaning that interband transitions could only occur at relatively high photon energies (UV region), which also indicates that there is no free carrier absorption [17]. Nevertheless, a considerable decrease in results from introducing an excessive number of state localization (trap levels) into the forbidden bandgap by the incorporation of the additive metal complex into the polymer [8, 59, 103].

Figure 13.
The plot of against the of the PVA sample for (a) , (b) , (c) and (d)
Scheme 3 demonstrates how adding metal complexes to pure PVA polymer creates a localized state between VB and CD, which results in reducing the band gap. Polymer composites with a smaller photonic energy gap were found to be essential for photovoltaic and other optoelectronic applications, particularly for organic light-emitting diode (OLED), and optoelectronics applications, restructured materials for instance, organic polymers, functional materials, and composites with appropriate optical bandgaps are essential [69, 104–106].
Comparing Tauc’s equation plots to optical dielectric loss charts reveals the electronic transition and optical energy gap [62, 99], as shown by a comparison of value obtained in both Figs 11 and 13 (see Table 3). Thereby, the types of transitions can be determined such that for PVMnMC0, it is direct allowed (); for PVMnMC1, PVMnMC2 and PVMnMC3, it is directly forbidden (). Moreover, the decline of the energy gap may be correlated to the increase in the amorphous matter in the composite sample, which arises due to structural modification of the polymer material [7].
Table 3.The energy gap from Tauc’s method versus and .
Sample code
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 6.2 | 5.9 | 5.75 | 5.7 | 6.1 |
PVMnMC1 | 2.7 | 2.1 | 1.9 | 1.7 | 2.2 |
PVMnMC2 | 2.3 | 1.7 | 1.55 | 1.45 | 1.78 |
PVMnMC3 | 1.9 | 1.6 | 1.35 | 1.3 | 1.62 |
Sample code
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 6.2 | 5.9 | 5.75 | 5.7 | 6.1 |
PVMnMC1 | 2.7 | 2.1 | 1.9 | 1.7 | 2.2 |
PVMnMC2 | 2.3 | 1.7 | 1.55 | 1.45 | 1.78 |
PVMnMC3 | 1.9 | 1.6 | 1.35 | 1.3 | 1.62 |
Table 3.The energy gap from Tauc’s method versus and .
Sample code
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 6.2 | 5.9 | 5.75 | 5.7 | 6.1 |
PVMnMC1 | 2.7 | 2.1 | 1.9 | 1.7 | 2.2 |
PVMnMC2 | 2.3 | 1.7 | 1.55 | 1.45 | 1.78 |
PVMnMC3 | 1.9 | 1.6 | 1.35 | 1.3 | 1.62 |
Sample code
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 6.2 | 5.9 | 5.75 | 5.7 | 6.1 |
PVMnMC1 | 2.7 | 2.1 | 1.9 | 1.7 | 2.2 |
PVMnMC2 | 2.3 | 1.7 | 1.55 | 1.45 | 1.78 |
PVMnMC3 | 1.9 | 1.6 | 1.35 | 1.3 | 1.62 |
It is worth mentioning here that adding Mn salt apart from BT to PVA polymer is referred to as a polymer electrolyte, and it is another technique for reducing the band gap of polymers. Although, considering polymer electrolytes, the findings of this investigation indicate that the bandgap diminishes to 4.95 eV (see Fig. 14). The present study’s uniqueness may be asserted as the technique of converting metal salts into metal complexes utilizing green approaches and then combined with polar polymers to create polymer composites with the desired optical band gap. Thus the novelty of this work can be found from the idea that transferring of transition metal salts to metal complexes using green approaches is exceptional to fabricate polymer composites with controlled optical band gaps and enhanced absorption properties. Based on the achievements of this work is is possible to say metal complexes will replace all conventional methods to deliver polymer composites with desired optical properties for various applications.

Figure 14.
Attenuation coefficient against for PVA/Mn(CH3COO)2 polymer electrolyte (PE) sample.
This is attributed to the fact that the Mn-polyphenol complex contains many functional groups such as (OH, NH, and C=O, C=C) around the Mn metal, which facilitates frequent interaction of these functional groups with the OH groups of the PVA through hydrogen bonding. The new bonding leads to a well-integrated structure of the polymer complex and hence reduces the band gap from 6.1 to 1.62 eV. This means using the green method can modify the insulator PVA polymer close to the semiconductor polymer material. This enhances the packing density of the polymer film and lowers the optical bandgap. The energy gap value (typically > 2) for PVA/Mn-polyphenol metal complex composite films makes them suitable basic structures for solar cell applications [107], photo-detectors [16], and light-emitting diodes (OLED) [9].
It has been reported that the fundamental electronic properties of optical materials are strongly linked to the index of refraction and photonic energy gap [108]. Figure 15 illustrates a significant correlation between the refractive index and the energy gap; specifically, a reduction of the energy gap is directly linked to an increase in the refractive index. The augmentation of n after the incorporation of a metal complex signifies a substantial rise in charge carrier concentration inside the polymer composite, resulting in a reduction of , attributable to the emergence of additional energy states between the conduction and valence bands. Moreover, it is well-recognized that the refractive index is contingent upon both density and polarizability. Table 4 presents the energy gap and refractive index of various polymer composites. It is evident from the data that the metal complex has a more significant impact, reducing the band gap considerably to approximately 1.6 eV. In contrast, other additives, such as ceramic fillers and nanoparticles, only decrease the energy gap by 2–3 eV. It can be notice that the refractive index of polymer composites inserted with ceramic fillers are higher which attributable to the fact that ceramic filler makes the polymer composites more opaque while in metal complexes interact with the host polymer very well and keeps the transparency of the composite films.

Figure 15.
Energy bandgap and optical refractive index versus concentration of metal-complex.
Table 4.Energy gap and refractive index of PVA reinforced with various ceramic fillers and nanoparticle.
Polymer composite
. | Energy gap (eV)
. | Refractive index ()
. | Reference
. |
---|
PVA: CeO2 nanocomposite | 6.34–6.09 | 1.93 | [26] |
PVA: PbS nanoparticle | 6.3–5.25 | 1.27–2.16 | [20] |
PVA: PbO2 | 6.32–4.33 | 1.15–1.42 | [76] |
PVA: NaNO2 | 5.71–5.05 | 1.14–2.25 | [123] |
PVA: Al powder | 6.2–5.2 | 1.1–2.14 | [7] |
PVA: Sn nanoparticles | 3.05–2.85 | – | [124] |
PVA: GO | 4.09–4.039 | – | [125] |
PVA: Zn-metal complex | 6.05–1.74 | 1.1553–1.3569 | [30] |
PVA: Mn-metal complex | 6.1–1.62 | 1.14–1.33 | Present work |
Polymer composite
. | Energy gap (eV)
. | Refractive index ()
. | Reference
. |
---|
PVA: CeO2 nanocomposite | 6.34–6.09 | 1.93 | [26] |
PVA: PbS nanoparticle | 6.3–5.25 | 1.27–2.16 | [20] |
PVA: PbO2 | 6.32–4.33 | 1.15–1.42 | [76] |
PVA: NaNO2 | 5.71–5.05 | 1.14–2.25 | [123] |
PVA: Al powder | 6.2–5.2 | 1.1–2.14 | [7] |
PVA: Sn nanoparticles | 3.05–2.85 | – | [124] |
PVA: GO | 4.09–4.039 | – | [125] |
PVA: Zn-metal complex | 6.05–1.74 | 1.1553–1.3569 | [30] |
PVA: Mn-metal complex | 6.1–1.62 | 1.14–1.33 | Present work |
Table 4.Energy gap and refractive index of PVA reinforced with various ceramic fillers and nanoparticle.
Polymer composite
. | Energy gap (eV)
. | Refractive index ()
. | Reference
. |
---|
PVA: CeO2 nanocomposite | 6.34–6.09 | 1.93 | [26] |
PVA: PbS nanoparticle | 6.3–5.25 | 1.27–2.16 | [20] |
PVA: PbO2 | 6.32–4.33 | 1.15–1.42 | [76] |
PVA: NaNO2 | 5.71–5.05 | 1.14–2.25 | [123] |
PVA: Al powder | 6.2–5.2 | 1.1–2.14 | [7] |
PVA: Sn nanoparticles | 3.05–2.85 | – | [124] |
PVA: GO | 4.09–4.039 | – | [125] |
PVA: Zn-metal complex | 6.05–1.74 | 1.1553–1.3569 | [30] |
PVA: Mn-metal complex | 6.1–1.62 | 1.14–1.33 | Present work |
Polymer composite
. | Energy gap (eV)
. | Refractive index ()
. | Reference
. |
---|
PVA: CeO2 nanocomposite | 6.34–6.09 | 1.93 | [26] |
PVA: PbS nanoparticle | 6.3–5.25 | 1.27–2.16 | [20] |
PVA: PbO2 | 6.32–4.33 | 1.15–1.42 | [76] |
PVA: NaNO2 | 5.71–5.05 | 1.14–2.25 | [123] |
PVA: Al powder | 6.2–5.2 | 1.1–2.14 | [7] |
PVA: Sn nanoparticles | 3.05–2.85 | – | [124] |
PVA: GO | 4.09–4.039 | – | [125] |
PVA: Zn-metal complex | 6.05–1.74 | 1.1553–1.3569 | [30] |
PVA: Mn-metal complex | 6.1–1.62 | 1.14–1.33 | Present work |
ASF method
Absorption spectra fitting (ASF) is regarded as a model for analyzing the energy gap of a given material. Its mathematical form is a modified version of Tauc’s formula as presented in equ.15, which describes the absorption coefficient as a function of wavelength [
109,
110].
, which relates to the optical gap wavelength, Planck’s constant (
), and the speed of light (
), correspondingly. Moreover, another way to rephrase
Equation (16) is by employing Beer-Lambert’s law:
To the power of together with the reflection-affected constant D2. The gap in the optical band may be estimated by an absorption spectrum fitting method in conjunction with equation (17). The forbidden optical gap (eV) was estimated by extrapolating the linear segment of from the versus. curve. Figure 16a–d shows the plot of the polymer films for , , , versus . The least squares method revealed that . One may find the values in Table 5. The band gap values deduced from ASF for MnMC is perfectly match the results achieved earlier. Mathematically, it is calculated by using the relationship: the. Lastly, each film’s value was noted in Table 4. It is also important to note that the bandgap determined using the ASF technique is almost the same as the one derived using Tauc’s equation, which supports the argument that the archived band gap values are trustworthy and reproducible results. Some reports have also shown the ASF model credibility in determining bandgap energy [111–113]. The useful of ASF method over Taucs model is that no needs to measure the film thickness and less calculation is required to draw the figures. Thus ASF method is well applicable for thin film materials or solutions because the absorbance parameters are measurable.

Figure 16.
(a–d) ASF plots for versus Satisfied Tauc’s models.
Table 5.Optical gap wavelength () value for pure and modified PVA samples for different type transition.
|
. |
. |
. |
. |
---|
Samples
. |
. |
. |
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 204.0816 | 6.075167 | 204.0816 | 6.075167 | 196.0784 | 6.323133 | 202.0202 | 6.1371585 |
PVMnMC1 | 500 | 2.47966 | 512.8205 | 2.417669 | 434.7826 | 2.851609 | 512.8205 | 2.4176685 |
PVMnMC2 | 645.1613 | 1.9217365 | 571.4286 | 2.169703 | 526.3158 | 2.355677 | 606.0606 | 2.0457195 |
PVMnMC3 | 714.2857 | 1.735762 | 625 | 1.983728 | 625 | 1.983728 | 666.6667 | 1.859745 |
|
. |
. |
. |
. |
---|
Samples
. |
. |
. |
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 204.0816 | 6.075167 | 204.0816 | 6.075167 | 196.0784 | 6.323133 | 202.0202 | 6.1371585 |
PVMnMC1 | 500 | 2.47966 | 512.8205 | 2.417669 | 434.7826 | 2.851609 | 512.8205 | 2.4176685 |
PVMnMC2 | 645.1613 | 1.9217365 | 571.4286 | 2.169703 | 526.3158 | 2.355677 | 606.0606 | 2.0457195 |
PVMnMC3 | 714.2857 | 1.735762 | 625 | 1.983728 | 625 | 1.983728 | 666.6667 | 1.859745 |
Table 5.Optical gap wavelength () value for pure and modified PVA samples for different type transition.
|
. |
. |
. |
. |
---|
Samples
. |
. |
. |
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 204.0816 | 6.075167 | 204.0816 | 6.075167 | 196.0784 | 6.323133 | 202.0202 | 6.1371585 |
PVMnMC1 | 500 | 2.47966 | 512.8205 | 2.417669 | 434.7826 | 2.851609 | 512.8205 | 2.4176685 |
PVMnMC2 | 645.1613 | 1.9217365 | 571.4286 | 2.169703 | 526.3158 | 2.355677 | 606.0606 | 2.0457195 |
PVMnMC3 | 714.2857 | 1.735762 | 625 | 1.983728 | 625 | 1.983728 | 666.6667 | 1.859745 |
|
. |
. |
. |
. |
---|
Samples
. |
. |
. |
. |
. |
. |
. |
. |
. |
---|
PVMnMC0 | 204.0816 | 6.075167 | 204.0816 | 6.075167 | 196.0784 | 6.323133 | 202.0202 | 6.1371585 |
PVMnMC1 | 500 | 2.47966 | 512.8205 | 2.417669 | 434.7826 | 2.851609 | 512.8205 | 2.4176685 |
PVMnMC2 | 645.1613 | 1.9217365 | 571.4286 | 2.169703 | 526.3158 | 2.355677 | 606.0606 | 2.0457195 |
PVMnMC3 | 714.2857 | 1.735762 | 625 | 1.983728 | 625 | 1.983728 | 666.6667 | 1.859745 |
Urbach energy study
The width of localized states within the optical bandgap is represented by the Urbach tails
, and it can be expressed by the following mathematical relationship [
114,
115].
is typically considered to indicate the breadth of the tail of localized states in the band gap and denotes energy that is either constant or slightly correlated with temperature, and
is a fixed that refers to absorption at the interface of the incident light and surface of an optical medium. The band tail energy, also known as the Urbach energy (
), may be determined from the slope of the linear graph plotting
versus
. Exponential tail is a result of localized states produced by disordered and amorphous phases that are extended over the band gag [
116].
Figure 17 exhibits the
. The band tail results for pure and modified PVA films were derived from the inverse of the slopes of the linear segments of the plots and are shown in
Table 1 [
117].

Figure 17.
Urbach plot for pure and modified PVA solid composites.
It is apparent that when the concentration of metal complex in PVA grows, Urbach energy correspondingly elevates. This suggests, albeit subtly, that the degree of disorder in polymer composite films is increasing. The rising energy tails indicate that the composites’ band structure is becoming more disordered and imperfect. The narrower tail width of pure PVA in comparison to composite samples can be attributed to its orderly structure and, consequently wider energy band gap [118, 119]. Adding a metal complex to pure PVA causes the band tail expansion and crystallinity reduction in PVA composites. When comparing Tables 1 and 3, one could notice that a bandgap decrease is well associated with increasing Urbach energy.
Kirchhoff’s functions
Pure polymer materials possess relatively high thermal emissivity, with values of 0.7–0.9 in the infrared (IR) spectrum. The desired thermal emissivity is below 0.6, which is also essential in areas such as spacecraft thermal control, solar regulation, and optical coatings [
120]. Therefore, most optical applications demand materials with minimal thermal emission. The capability of a given material to emit energy at a particular wavelength range is measured by its emissivity[
117]. The two most relevant optic parameters associated with emissivity for the thin films are sheet resistance (
) and thermal emissivity (
). In the context of light-matter interaction, the two parameters are a function of wavelength. The term “surface functions,” also known as Kirchhoff’s functions, refers to the thin film’s sheet resistance and the thermal emissivity that results from photons falling on its surface to excite electrons. These functions are mathematically represented by [
83,
121].
The quantity of heat energy that is released from the outermost layer of the exposed thin films is directly related to the incident photon beams on the thin film’s exposed surface. The rate at which heat is emitted from the surface of thin films determines how many photon beams arrive at its surface. Thus, it is possible to consider the thermal emission as a variable. Kirchhoff’s functions and sheet resistance grow with wavelength and shrink with increasing metal complexes. This is because of the way these functions behave in relation to the linear refraction shown in Fig. 18. Furthermore, the Fig. 18 demonstrates that the spectra of for the doped PVA were contingent upon λ, and the measured values of are significantly low (∼) in comparison to the blackbody (∼1). The behavior of in relation to for the examined doped PVA closely resembles the variation in with [122]. This link suggests that materials exhibiting lower sheet resistance generally possess enhanced thermal emissivity, hence enhancing their ability to release heat radiation. This is essential for usage and necessitates effective thermal management or radiative cooling [93].

Figure 18.
Kirchhoff’s functions pathway for the pure and modified PVA thin samples.

Scheme 1.
Schematic demonstration of polymer composite films fabrication.

Scheme 2.
The flowchart demonstrates comprehensive investigation of the optical characteristics of the Reinforced polymer.

Scheme 3.
Effect metal complex on the band gap reduction.
Conclusion
This study utilized the solution casting method to fabricate PVA composite films with varying concentrations of a metal complex. The polyphenol complex was synthesized using a black tea leaf extract solution. The findings demonstrate that metal complexes are a promising alternative to other additives—such as ceramic fillers, salts, or metallic nanoparticles—for reducing the optical band gap, lowering the PVA polymer energy gap, and enhancing optoelectronic properties. XRD and FTIR analyses reveal strong interactions between the polymer’s functional groups and Mn-metal complex particles. Both the Urbach energy parameter and X-ray diffraction results indicate that incorporating the metal complex transforms the PVA structure from semi-crystalline to amorphous. As the metal complex concentration increases, the Urbach energy rises from 0.269 to 0.3621 eV. UV-visible spectroscopy was used to determine key optical parameters. The absorption edge shifts toward lower frequencies and higher wavelengths as the metal complex content increases, suggesting strong reactivity between the PVA polymer and the metal complex. Quantitatively, the energy gap decreases from 6.2 eV for pure PVA to 1.62 eV for the optimized composite film, and refractive index increases from 1.14 to 1.33. These enhanced optical properties make the films suitable for applications such as photovoltaic cells, photodetectors, optical sensors, and solar cells. Additionally, the incorporation of metal complexes improves the refractive index and the imaginary part of the dielectric constant in polar polymers. Using Tauc’s model, the optical dielectric loss was analyzed to determine the electron transition type. Both Tauc’s model and the optical dielectric loss parameter confirm that the band gap decreases as the metal complex concentration increases, indicating the formation of localized states between the valence band (VB) and conduction band (CB). Finally, Kirchhoff’s function was used to examine the surface resistance and thermal emissivity of all fabricated films.
Acknowledgements
The authors gratefully acknowledge the financial support for this study from University of Sulaimani and Charmo University.
Author contributions
Hawkar A. Mohammed (Formal analysis [equal], Investigation [equal], Methodology [equal], Validation [equal], Writing—original draft [equal]), Pshko A. Mohammed (Conceptualization [equal], Project administration [equal], Validation [equal], Writing—review & editing [equal]), and Shujahadeen B. Aziz (Conceptualization [equal], Project administration [equal], Resources [equal], Supervision [equal], Validation [equal], Writing—review & editing [equal])
Supplementary data
Supplementary data is available at OXFMAT Journal online.
Conflict of interest: None declared.
Funding
None declared.
Data availability
The data underlying this article will be shared on reasonable request to the corresponding author.
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