Effect of BaWO 4 nanoparticles on the structural and optical characteristics of the PS/BaWO 4 nanocomposites for optical applications

Abstract

This work explores the effect of BaWO₄ nanoparticles (NPs) with varying concentrations (0, 1, 2, and 3 wt%) on the structural, surface/volume energy loss functions, and linear/non-linear optical properties of polystyrene/BaWO₄ nanocomposites. The XRD pattern indicates the formation of pure BaWO₄ NPs with a tetragonal structure. SEM image revealed the uniform scroll-like shape of the synthesized BaWO₄. The direct bandgap energy reduced from 3.88 eV in the PS film to 3.85 eV, 3.73 eV, and 3.71 eV with increasing BaWO₄ loading. Meanwhile, the Urbach energy for PS film was 1.25 eV, which rose to 1.38, 1.43, and 1.54 eV with enhanced BaWO₄ contents. In addition, the refractive index of the PS film boosted after the incorporation of BaWO₄ with a ratio of 1% and 2%wt. However, it dropped after the addition of 3% of the BaWO₄. The optical conductivity and electrical conductivity of pristine PS improves after incorporating BaWO₄ into the PS matrix, attributable to an increase in charge transfer and a corresponding rise in the absorption coefficient. Moreover, optical parameter such as, the oscillator energy (E₀) and the dispersion energy (E_d), relaxation time (τ), N/m* were concluded. The oscillation frequency (ω_P) value was also found to be 0.13× 10¹³ sec⁻¹ for PS polymer, which increased to 0.23× 10¹³ sec⁻¹ and 0.34 × 10¹³ sec⁻¹ for PS/1%BaWO₄ and PS/2%BaWO₄ films, respectively, and then declined to 0.08× 10¹³ sec⁻¹ for PS/3%BaWO₄ film. The non-linear refractive index (n ₂ ), linear optical susceptibility (χ⁽¹⁾), and third-order non-linear optical susceptibility (χ⁽³⁾) for the pristine PS and all PS/BaWO₄ nanocomposite films were derived. These results confirm that the PS/1% BaWO₄ and PS/2% BaWO₄ samples are suitable for utilization in photonic devices, anti-reflective coatings, and waveguide technology, while, the PS/3% BaWO₄ sample is employed in applications that depend on the rapid transmission of optical signals, such as optical communications.

Introduction

Polymer composite materials have attracted substantial attention due to their capacity to integrate the beneficial characteristics of nanofillers and polymers, resulting in improved functionalities.^1–5 Polystyrene (PS) is a widely used optical polymer due to its long-lasting, excellent chemical properties, and low cost. It is particularly sought for use in optical/electrical device components and food packaging. Nevertheless, their weak refractive index and restricted absorption range have restricted the potential applications of polystyrene in optical devices. Consequently, an investigation is necessary to customize the optical characteristics of polystyrene to satisfy the current application requirements of these polymers.^6,7 It has been predicted that the properties of the nanocomposite will be affected by the nanoparticles (NPs), which are highly effective as nanofillers. ¹ For instance, Ibrahim et al. ⁸ recently demonstrated that the thermal and antibacterial properties of PS-nanocomposite affect the ZnO and TiO₂ NPs. The encapsulation or coating of the NPs exhibited exceptional thermal stability and antibacterial efficacy. Alrefaee et al. ⁹ have reported the synthesis of recycled PS/PVP/reduced graphene oxide nanocomposites for optoelectronic devices. Azhen and Shujahadeen ¹⁰ have also reported the optical behaviour of PS/natural bitumen composite.

Barium tungstate (BaWO₄) is the most substantial member of the alkaline earth tungstate family. Like numerous ABX4-type compounds, BaWO₄ crystallizes in the tetragonal scheelite-type structure at ambient temperature. BaWO₄ has garnered significant attention due to its exceptional luminescence, magnetic properties, and electrical conductivity. ¹¹ BaWO₄-based materials are essential in a wide variety of technological uses, such as light-emitting diodes, ¹² humidity sensors, ¹³ optical filters, ¹⁴ optoelectronic, ¹⁵ dielectric materials, ¹⁶ and luminescence. ¹⁷ The BaWO₄/chitosan nanocomposite was effectively prepared as a flexible photodetector, as reported by Hemmati et al.. ¹⁸ Additionally, Sridhar et al. ¹⁹ have studied the photocatalytic and photoluminescence characteristics of rGO/BaWO₄ nanocomposite. Alamdari et al. ²⁰ have reported the synthesis of a flexible nanocomposite of erbium-doped barium tungstate (BaWO₄:Er-1at.%) thin film.

The primary research focus is the optical characteristics of polystyrene/metal nanoparticles. However, polystyrene-filled BaWO₄ has yet to be examined. This investigation aimed to examine the effect of the BaWO₄ scrolls with different weight percentages (0, 1, 2, and 3 wt%) on the optical behavior and structure of the polystyrene/BaWO₄ nanocomposites. The optical properties of the prepared films were assessed using absorption, transmission, and the optical energy band. The polystyrene/BaWO₄ nanocomposites were synthesized using the casting method.

Experimental

Barium chloride dihydrate (BaCl₂. 2H₂O, 99%) and sodium tungstate dihydrate (Na₂WO₄·2H₂O, 99%) were used to synthesize the BaWO₄. Sodium tungstate dihydrate and barium chloride dihydrate salts (1:1) were individually dissolved in 20 mL of distilled water in two distinct beakers and stirred for 15 min. Then, the two solutions have been mixed. Furthermore, a white precipitate was formed. The BaWO₄ was collected and washed with ethanol and deionized water many times. Subsequently, the product BaWO₄ was subjected to drying in a furnace for 2 hours at 250°C. The BaWO₄ was ultimately crushed to achieve a fine powder. Polystyrene (PS) solution was prepared by dissolving PS in 15 mL of toluene and then placed on a stirrer for 30 min. BaWO₄ NPs were added to the PS solution with different concentration ratios (0, 1, 2, and 3 wt%) and stirred via a magnetic stirrer for 30 min. The PS, PS/1%BaWO₄, PS/2%BaWO₄, and PS/3%BaWO₄ nanocomposites were dried in the air.

Results

Structure Analyses

Figure 1 shows the XRD pattern of BaWO₄ NPs. The diffraction peaks belong to the (101), (112), (004), (200), (204), (220), (116), (312), (224), (400), (208), and (316) planes of BaWO₄ NPs, consistent with JCPDS card number 72–0746. The XRD pattern indicates the formation of pure single-phase BaWO₄ NPs with a tetragonal structure consistent with published findings.^21–23 The Scherer formula can be employed to establish the crystallite size (D) of BaWO₄ NPs ²⁴ :

$\mathit{D}=\frac{\mathbf{0.9}\hspace{0.17em}\mathbf{x}\hspace{0.17em}\mathit{\lambda }\hspace{0.17em}}{\mathit{\beta }\hspace{0.17em}\mathbf{cos}\hspace{0.17em}\left(\mathit{\theta }\right)}$

(1)

Figure 1.

(a) XRD pattern, (b) SEM image, and (c) EDX spectra of BaWO₄ NPs.

It has been established that the BaWO₄ NPs have a crystallite size of 39 nm.

The characteristic scanning electron microscopy (SEM) image of BaWO₄ is depicted in Figure 1(b). The uniform scroll-like shape of the synthesized BaWO₄ is shown in the SEM image. Figure 1(c) illustrates the EDX spectra of BaWO₄ NPs. The BaWO₄ NPs’ purity was indicated by the presence of Ba, W, and O, which were free of any additional elements. Additionally, the mapping images demonstrated that the BaWO₄ NPs demonstrate the uniform distribution of all elements, as illustrated in Figure 2.

Figure 2.

Mapping images of BaWO₄ NPs.

The XRD pattern of the pristine sample (pure PS) and PS/BaWO₄ nanocomposites with varying concentrations of BaWO₄ NPs is illustrated in Figure 3. The pure PS sample, which had no additives, exhibited a broad hump around 2θ∼20° in the XRD pattern, which confirmed the amorphous character of the PS film.^25,26 The insertion of BaWO₄ NPs into the PS matrix results in a decrease in the intensity of the same hump and a broadening of its shape. Additionally, new peaks are observed, as illustrated in Figure 3. This suggests that the BaWO₄ NPs in the PS matrix are growing. The agglomeration of BaWO₄ NPs in the PS matrix is the cause of this growth as the concentration of the BaWO₄ NPs increases. Additionally, this may be associated with the intermolecular interaction and the bonds established between the PS and BaWO₄ NPs. Similar behavior was observed for PS/TiO₂ nanocomposites by Rahimli. ²⁵

Figure 3.

XRD patterns of PS/BaWO₄ nanocomposites.

Optical Characteristics

One of the most critical strategies for identifying a new material for optical devices is to investigate its optical characteristics. The optical absorption spectra of the PS and PS/BaWO₄ nanocomposite films with variable weight percentages of BaWO₄ NPs are depicted in Figure 4(a). Spectra of the PS and PS/BaWO₄ nanocomposites exhibit a shoulder-shaped peak at approximately 260 nm. This peak may result from the electrical transitions within the polystyrene backbone structure and the correlative interactions among phenyl groups in the PS matrix.^27,28 Furthermore, a gradual rise in optical absorbance has been noticed with the rising concentration ratio of BaWO₄ NPs. This rise may be attributed to establishing multiple absorption sites after including nanoparticles, which restricts the transformation of light within the medium, resulting in an overall enhancement of the absorbance spectra. ²⁹ The nanocomposite films’ substantial absorbance makes them ideal for applications necessitating shielding from ultraviolet radiation. ³⁰ The optical absorption coefficients (α) of the pristine and doped films were assessed based on the absorbance measurements by employing the relation ³¹ :

$\mathbf{\alpha }=\frac{\mathbf{2.303}\times \mathbf{A}}{\mathbf{d}}$

(2)where A represents absorbance and d denotes the thickness of the samples.

Figure 4.

(a) The absorbance (A) versus wavelength (λ) and (b) the absorption coefficient (α) versus the incident photon energy (h $\nu$ ) of PS/BaWO₄ nanocomposites.

Figure 4(b) illustrates the optical absorption coefficient as a function of photon energy for PS and BaWO₄ NPs-doped PS films. The absorption coefficient of PS/BaWO₄ nanocomposites rises after the doping of BaWO₄ NPs. This rise may result from the interaction between the PS and BaWO₄ NPs, which results in the development of structural defects. The absorption edge refers to a domain where electrons transition from a low-energy state to a higher-energy one due to photon absorption. The absorption edge (Ee) of PS/BaWO₄ nanocomposites may be estimated by extending the linear segments of the α versus hυ curves to the point of zero absorption. The absorption edge of the PS film is seen at 3.09 eV, which declines to 3.01 eV, 2.68 eV, and 2.64 eV for the PS/1% BaWO₄, PS/2% BaWO₄, and PS/3% BaWO₄ nanocomposites, respectively (refer to Table 1). Table 2 compares the optical band gap values of Ps/BaWO₄ nanocomposites with those of different nanocomposites.

Table 1.

Values of the E_e, ${\mathrm{E}}_{\mathrm{g}}^{\text{dir}}$ , ${\mathrm{E}}_{\mathrm{g}}^{\text{ind}}$ , and E_U for the PS, PS/1% BaWO₄, PS/2% BaWO₄, and PS/3% BaWO₄ nanocomposite films.

	Absorption edge (Ee) (eV)	Direct bandgap	Indirect bandgap	Urbach tail (EU) (eV)
		$\left({\mathit{E}}_{\mathit{g}}^{\mathit{d}\mathit{i}\mathit{r}}\right)$ (eV)	$\left({\mathit{E}}_{\mathit{g}}^{\mathit{i}\mathit{n}\mathit{d}}\right)$ (eV)
PS	3.09	3.88	3.45	1.25
PS/1% BaWO4	3.01	3.85	3.42	1.38
PS/2% BaWO4	2.68	3.73	3.21	1.43
PS/3% BaWO4	2.64	3.71	3.16	1.54

Table 2.

Comparison between optical band gap values of Ps/BaWO₄ nanocomposites with different nanocomposites.

Composites	Optical bandgap (eV)	Ref.
PS/Bitumen	4.34–1.13	10
PS/SnTiO3	4.4-–3.4	32
PS/Dy2O3	4.6–4.35	33
PS/SnO2	3.397–3.095	34
PMMA/PS/ZnO	4.45–3.12	35
PS/TiO2	3.77–2.34	36
rGO/BaWO4	4.43–3.13	37
PS/BaWO4	3.88–3.71	This work

The correlation between absorption coefficients (α) and photon energy (hυ) for both direct and indirect permitted transitions is as follows ³⁸ :

$\mathbf{\alpha }\mathbf{h}\mathbf{\nu }=\mathbf{A}\hspace{0.17em}{\left(\mathbf{h}\mathbf{\nu }-{\mathbf{E}}_{\mathbf{g}}\right)}^{\mathbf{m}}$

(3)where Eg signifies the optical band gap energy, A is a constant, and m = 1/2 or 2 for direct and indirect permitted transitions, respectively.

Figure 5(a) illustrates the plot of (αhυ)² against hυfor the pristine PS film and three BaWO₄-doped PS nanocomposite films, which was used to determine $E_g^{dir}$ . The direct energy gap values ( $E_g^{dir}$ ) were determined to be 3.88, 3.85, 3.73, and 3.71 eV for PS, PS/1%BaWO₄, PS/2%BaWO₄, and PS/3%BaWO₄ nanocomposite films, respectively (refer to Table 1). Simultaneously, the $E_g^{indir}$ was determined from the graph of (αhυ)^1/2 versus hυ, as seen in Figure 5(b). The indirect bandgap energy ( $E_g^{indir}$ ) reduced from 3.45 eV in the PS film to 3.42 eV, 3.21 eV, and 3.16 eV in the PS/1% BaWO₄, PS/2%BaWO₄, and PS/3%BaWO₄ nanocomposite films, respectively (Table 1). Elevating the concentration of BaWO₄ NPs reduced both the direct and indirect band gaps in the PS/BaWO₄ films. Introducing BaWO₄ NPs reduced the optical band gap, likely attributable to the development of intermediate levels within the energy gap. ³⁹ Creating new energy levels may transport electrons from the valence bands into newly formed local states. ⁴⁰

Figure 5.

(a) (αh $\mathrm{\nu }$ )² versus (h $\mathrm{\nu }$ ) and (b) (αh $\mathrm{\nu }$ )^1/2 versus (h $\mathrm{\nu }$ ) for the PS/BaWO₄ nanocomposite films.

The Urbach energy is an exponential component that may be found close to the band gap edge and along the absorbance coefficient curve. This implies that the material’s crystallinity is low, and the material’s structure is amorphous and disordered. ⁴¹ When calculating the Urbach energy (EU) of samples, it is necessary to take into account both the absorbance coefficient (α) and the photon energy (hυ), which may be discovered by the equation that follows ⁴² :

$\mathbf{\alpha }\left(\mathbf{\nu }\right)={\mathbf{\alpha }}_{\mathbf{o}}\hspace{0.17em}\mathbf{exp}\left(\frac{\mathbf{h}\mathbf{\nu }}{{\mathbf{E}}_{\mathbf{U}}}\right)$

(4)

By graphing the inverse slope of the straight line against the photon energy (hυ), as shown in Figure 6, it is possible to derive the E_U for the PS/BaWO₄ nanocomposite films. This may be achieved by assuming that α_o remains constant. Table 1 contains a listing of the Urbach energy values. As shown, the values of Urbach energy were enhanced by promoting the BaWO₄ NPs concentrations in the PS/BaWO₄ nanocomposite films. The computed value of the Urbach energy for PS film was found to be 1.25 eV, and it rose to 1.38, 1.43, and 1.54 eV for the PS/1%BaWO₄, PS/2% BaWO₄, and PS/3% BaWO₄ nanocomposite films, respectively. This is evidence that the degree of disordering in the PS film structure has risen, as well as the number of localized states present in the forbidden band gaps, which has led to a reduction in the values of the optical energy gap.

Figure 6.

The relation between lnα and h $\mathrm{\nu }$ for the PS/BaWO₄ nanocomposite films.

As shown in Figure 7(a), the optical reflectance spectra of the pure PS and three nanocomposite films of the PS, including varying amounts of BaWO_4, are exhibited. The figure demonstrated that the reflectance spectra of all films significantly decline as the wavelength increases up to 400 nm, after which they experience a slight decline in the range spanning from 400 to 2000 nm. In addition, it is possible to see that the reflectance spectrum is boosted after the incorporation of BaWO₄ with a ratio of 1% and 2%wt. However, it dropped after the addition of 3% of the BaWO₄. The rise in scattering, disorder degree, number of vacancies, and agglomerations of atoms may be the causes of this change in the refractive spectra of the PS/BaWO₄ nanocomposite films compared to the pristine PS.^43,44

Figure 7.

Variation of (a) R versus λ, (b) K _o versus λ, and (c) n versus λ for the PS/BaWO₄ nanocomposite films.

In order to determine the refractive index (n) and extinction coefficient (k_o) of PS/BaWO₄ nanocomposite films, the following equations were used^45,46:

${\mathit{k}}_{\mathit{o}}=\frac{\mathbf{\alpha }\mathbf{\lambda }}{\mathbf{4}\mathbf{\pi }}$

(5)

$\mathit{n}=\frac{\left(\mathbf{1}+\mathit{R}\right)}{\left(\mathbf{1}-\mathit{R}\right)}+\sqrt{\left(\frac{\mathbf{4}\mathit{R}}{{\left(\mathbf{1}-\mathit{R}\right)}^{\mathbf{2}}}-{\mathit{k}}^{\mathbf{2}}\right)}$

(6)

The electronic transition that occurs within the materials is also indicated by the extinction coefficient (k_o), which measures the electromagnetic energy lost due to scattering and absorption. The variation of (k_o) as a function of the wavelength (λ) is depicted in Figure 7(b)7 (b) for the pristine PS and BaWO₄-doped PS nanocomposite films. It is remarkable to observe that the pure and nanocomposite films exhibit comparable behaviors. As illustrated in Figure 7(b), the values of k_o for all BaWO₄-doped PS nanocomposite films reduce as the wavelength rises. This demonstrates that the electromagnetic waves traveling through the material travel faster in a longer wavelength.

Furthermore, the extinction coefficient values exhibit an increasing trend following the addition of the BaWO₄ with varying ratios. The enhancement results from an enhancement in absorption behavior following doping, which alters the interaction between free carriers and incident light in the BaWO₄-doped PS nanocomposite films. ⁴⁷ The refractive index (n) corresponding to wavelength (λ) for the BaWO₄-doped PS nanocomposite films is illustrated in Figure 7(c). The refractive index measurements of the BaWO₄-doped PS nanocomposite films exhibited a normal dispersion that declined as the wavelength rose. Additionally, it is evident that the refractive index of the PS/1% BaWO₄ and PS/2% BaWO₄ films are higher in comparison to the pure PS, while the PS/3% BaWO₄ film experiences a reduction. The alteration in refractive index following doping is a consequence of the alteration in the intra-intermolecular bonding between the BaWO₄ and the host PS, which leads to an alteration in the density of chain packing. ⁴⁸ Consequently, the refractive index rises of the PS/1% BaWO₄ and PS/2% BaWO₄ samples indicate that they are suitable for utilization in photonic devices, anti-reflective coatings, and waveguide technology. Conversely, the sample with a low refractive index is employed in applications that depend on the rapid transmission of optical signals, such as optical communications. ⁴⁹

The formulas were employed for determining the dielectric constant of the matter, both real and imaginary^50,51:

${\mathbf{\epsilon }}_{\mathit{r}}={\mathit{n}}^{\mathbf{2}}-{\mathbf{K}}^{\mathbf{2}}$

(7)

${\mathbf{\epsilon }}_{\mathit{i}}=\mathbf{2}\hspace{0.17em}\mathit{n}\hspace{0.17em}\mathit{k}$

(8)where ɛ_r is associated with the real portion of the dielectric, and ɛ_i denotes the imaginary portion. In this case, the ɛ_r represents the dispersion of light within the samples, while the ɛ_i denotes the energy that is absorbed as a result of the dipole moment motion. Figure 8(a) and (b) illustrates the variations in the ɛ_r and ɛ_i parts of the dielectric constant for the PS and PS/BaWO₄ nanocomposite films, respectively, with varying BaWO₄ content loadings. The ɛ_r diminishes with increasing wavelength for all PS/BaWO₄ nanocomposite films, matching the behavior of the refractive index. Furthermore, the values of ɛ_r rose after incorporating the BaWO₄ in PS/1% BaWO₄ and PS/2% BaWO₄ films however a reduction was seen in the PS/3% BaWO₄ film. Simultaneously, the ɛ_i of the untreated PS film enhanced by adding the BaWO₄ at varying concentrations. This rise may result from defects generated by the interaction between BaWO₄ and the PS matrix. This enhancement in the dielectric constant of the PS/BaWO₄ films confirms the elevation of charges inside the PS. ⁵²

Figure 8.

The correlation between (a) ε _r and λ, and (b) ε _i and λ for PS/BaWO₄ films.

Additionally, the optical conductivity (σ_opt) and electrical conductivity (σ_elec) can be calculated utilizing the following expression^51,53–56:

${\mathit{\sigma }}_{\mathit{o}\mathit{p}\mathit{t}}=\frac{\mathit{\alpha }\mathit{n}\mathit{c}}{\mathbf{4}\mathit{\pi }}$

(9)

${\mathit{\sigma }}_{\mathit{e}\mathit{l}\mathit{e}}=\frac{{\mathit{\sigma }}_{\mathit{o}\mathit{p}\mathit{t}}\mathit{n}}{{\mathit{K}}_{\mathit{O}}}$

(10)

Figure 9(a) illustrates the variation in optical conductivity (σ_opt) versus wavelength (λ) for both pure PS and PS/BaWO₄ films. This figure indicates that the optical conductivity of pristine PS improves after incorporating BaWO₄ into the PS matrix, attributable to an increase in charge transfer and a corresponding rise in the absorption coefficient. Furthermore, Figure 9(b) illustrates the variation in electrical conductivity (σ_ele) as a function of wavelength (λ). The electrical conductivity for PS/BaWO₄ films rises with the addition of BaWO₄ at concentrations of 1% and 2%, then declines when the concentration is enhanced to 3% wt.

Figure 9.

The correlation between (a) σ _opt and λ, and (b) σ _elec and λ for PS/BaWO₄ films.

Both the surface energy loss function (SELF) and the volume energy loss function (VELF) are included in the functions that measure energy loss. In the process of electrons moving through a material, the loss of fast electron energy is denoted by the symbol VELF. On the other hand, SELF is an abbreviation that stands for the significance of the chance that fast electrons would experience a loss of energy when they travel over the material’s surface. The real and imaginary portions of the complex dielectric were employed to ascertain the values of SELF and VELF, as follows ⁵⁷ :

$\mathit{V}\mathit{E}\mathit{L}\mathit{F}=\frac{{\mathit{\epsilon }}_{\mathit{i}}}{{\mathit{\epsilon }}_{\mathit{r}}^{\mathbf{2}}+{\mathit{\epsilon }}_{\mathit{i}}^{\mathbf{2}}}$

(11)

$\mathit{S}\mathit{E}\mathit{L}\mathit{F}=\frac{{\mathit{\epsilon }}_{\mathit{i}}}{{\left({\mathit{\epsilon }}_{\mathit{r}}+\mathbf{1}\right)}^{\mathbf{2}}+{\mathit{\epsilon }}_{\mathit{i}}^{\mathbf{2}}}$

(12)

Figure 10(a) and (b) illustrates the variations in VELF and SELF as a function of the hυ for all PS/BaWO₄ nanocomposite films. The energy of the rapid electrons is lost more during their propagation within the investigated materials than during their transit on their surfaces. The higher values of VELF than SELF for the same nanocomposites under investigation can be used to explain this behavior.

Figure 10.

The variations in (a) VELF and (b) SELF for PS/BaWO₄ nanocomposite films.

The oscillator energy (E₀) and the dispersion energy (E_d) for PS/BaWO₄ nanocomposite films ⁵⁸ :

$\frac{\mathbf{1}}{{\mathit{n}}^{\mathbf{2}}-\mathbf{1}}=\frac{{\mathit{E}}_{\mathit{O}}}{{\mathit{E}}_{\mathit{d}}}-\frac{\mathbf{1}}{{\mathit{E}}_{\mathit{O}}\hspace{0.17em}{\mathit{E}}_{\mathit{d}}}{\left(\mathit{h}\mathbf{\nu }\right)}^{\mathbf{2}}$

(13)

The slopes and intercepts of the graph depicting (n² − 1)⁻¹ versus (hυ)² in Figure 11 may be used to derive the values of E_o and E_d for all PS/BaWO₄ nanocomposite films. The values are specified in Table 3. The E_o values dropped from 5.26 eV to 3.40 eV with a higher concentration of the BaWO₄ scrolls, aligning with a decline in the energy gap. ³⁰ Moreover, with the incorporation of the BaWO₄ scrolls, the E_d values enhanced markedly from 1.30 to 2.39 eV and then declined to 0.58 eV for PS/3%BaWO₄ film, indicating a modification in the optical transition intensity of the BaWO₄-enhanced PS nanocomposite films. This induces modifications in forming the charge transfer complex between the PS matrix and the BaWO₄. ⁴² In order to determine the static refractive index values (n_o) and optical oscillator strengths (f) for PS/BaWO₄ nanocomposite films, the following equations can be utilized^59,60:

${\mathbf{n}}_{\mathit{o}}={\left(\mathbf{1}+\frac{{\mathit{E}}_{\mathit{d}}}{{\mathit{E}}_{\mathit{O}}}\right)}^{\mathbf{1}/\mathbf{2}}$

(14)

$f={\mathit{E}}_{\mathit{o}}{\mathit{E}}_{\mathit{d}}$

(15)

Figure 11.

Variation of (a) (n² − 1)⁻¹ versus (hυ)² and (b) ε_r versus λ² for all PS/BaWO₄ nanocomposite films.

Table 3.

Dispersion and oscillation parameters for all PS/BaWO₄ nanocomposite films.

	n o	f (eV) 2	E d (eV)	E o (eV)	${\mathit{\epsilon }}_{\mathit{l}}$	${\mathbf{w}}_{\mathit{p}}$ x 1013 (sec−1)	N/m* x 10 39  kg −1 m −3
PS	1.12	6.84	1.30	5.26	1.30	0.13	0.45
PS/1% BaWO4	1.17	8.52	1.78	4.79	1.46	0.23	0.81
PS/2% BaWO4	1.23	11.14	2.39	4.66	1.65	0.34	1.16
PS/3% BaWO4	1.08	1.79	0.58	3.40	1.22	0.08	0.26

As the concentration of BaWO₄ improves, the values of n_o rise sharply and then decrease for PS/3%BaWO₄ film. Compared to PS (n_o = 1.12), the values of n_o for PS/1%BaWO₄, PS/2%BaWO₄, and PS/3%BaWO₄ films are 1.17, 1.23, and 1.08, respectively. The static dielectric constant enhanced from 6.84 (eV)² to 11.14 (eV)² as the concentration of BaWO₄ increased from 0 wt% to 2 wt% and then decreased to 1.79 (eV)² for PS/3%BaWO₄ film, as presented in Table 3.

Furthermore, the equation which follows can be used to express ε_r ⁶¹ :

${\mathbf{\epsilon }}_{\mathit{r}}={\hspace{0.17em}\mathit{\epsilon }}_{\mathit{l}}-\left(\frac{{\mathit{e}}^{\mathbf{2}}}{\mathbf{4}\hspace{0.17em}{{\mathit{\pi }}^{\mathbf{2}}{\mathit{\epsilon }}_{\mathit{s}}\mathit{c}}^{\mathbf{2}}\hspace{0.17em}}\frac{\mathit{N}}{{\mathit{m}}^{*}}\right){\mathit{\lambda }}^{\mathbf{2}}$

(16)

The lattice dielectric constant ε _l and the ratio of the concentration of free carrier ions to the effective mass (N/m*) for PS/BaWO₄ nanocomposite films can be computed by calculating the intercept and slope of the linear portion in the plots of ε_r versus λ², as illustrated in Figure 11(b). Upon increasing the concentration of BaWO₄ NPs in PS, the values of ε _l rose from 1.30 to 1.65 and then dropped to 1.22 for the PS/3%BaWO₄ film. The N/m* value for PS was 0.45× 10³⁹ kg⁻¹ m⁻³. Nevertheless, this value increased to 0.81× 10³⁹ and 1.16× 10³⁹ kg⁻¹ m⁻³ for PS/1%BaWO₄ and PS/2%BaWO₄ films, respectively, and then dropped to 0.26× 10³⁹ kg⁻¹ m⁻³ for PS/3%BaWO₄ film (Table 3).

The equation presented next has been employed to determine the oscillation frequency (ω_P) for PS/BaWO₄ nanocomposite films^31,62:

${\mathit{w}}_{\mathit{P}}=\frac{{\mathit{e}}^{\mathbf{2}}}{{\mathit{\epsilon }}_{\mathit{o}}}\frac{\mathit{N}}{{\mathit{m}}^{*}}$

(17)

The oscillation frequency (ω_P) value increased from 0.13× 10¹³ sec⁻¹ for PS polymer to 0.23× 10¹³ sec⁻¹ and 0.34 × 10¹³ sec⁻¹ for PS/1%BaWO₄ and PS/2%BaWO₄ films, respectively, and then declined to 0.08× 10¹³ sec⁻¹ for PS/3%BaWO₄ film.

To estimate the long wavelength refractive index (n_∞), the average dipole oscillator strength (S₀), and the average oscillator wavelength (λ₀), the following equations have been used and plotting 1/(n² - 1) and λ⁻² for all PS/BaWO₄ nanocomposite films (Figure 12(a)) ⁶³ :

$\frac{\mathbf{1}}{{\mathit{n}}^{\mathbf{2}}-\mathbf{1}}=\left(\frac{\mathbf{1}}{{\mathit{S}}_{\mathit{O}}{\mathit{\lambda }}_{\mathbf{0}}^{\mathbf{2}}}\right)-\left(\frac{\mathbf{1}}{{\mathit{S}}_{\mathbf{0}}}\right){\mathbf{\lambda }}^{-\mathbf{2}}$

(18)

${\mathit{n}}_{\mathit{\infty }}^{\mathbf{2}}-\mathbf{1}={\mathit{S}}_{\mathit{O}}{\mathit{\lambda }}_{\mathbf{0}}^{\mathbf{2}}$

(19)

Figure 12.

Variation of (a) 1/(n² - 1) and λ⁻² and (b) ε_i versus λ³ for all PS/BaWO₄ nanocomposite films.

The values of n_∞ and S₀ increased from 1.13 to 1.26 × 10⁻⁷ (nm)⁻¹ for pure PS to 1.19 and 20.63 × 10⁻⁷ (nm)⁻¹ for PS/1%BaWO₄ film and to 1.25 and 40.28 × 10⁻⁷ (nm)⁻¹ for PS/2%BaWO₄ film, and then declined to 1.10 and 10.06 × 10⁻⁷ (nm)⁻¹ for PS/3%BaWO₄ film. On the other hand, the average oscillator wavelength (λ₀) declined from 539.87 nm to 361.59 nm with increasing the concentration of BaWO₄ NPs and sharply increased to 433.58 nm for PS/3%BaWO₄ film, as illustrated in Table 4.

Table 4.

The values of n_∞, S₀, and λ₀, τ, and nonlinear parameters for all PS/BaWO₄ nanocomposite films.

	${\mathit{n}}_{\mathit{\infty }}$	λ o (nm)	S o x 10 −7 (nm −2 )	$\mathit{\tau }$ x 10 −3 (sec)	χ(1)	χ(3) ×10−18 esu	n2 ×10−16 esu
PS	1.13	539.87	9.26	1.8	0.019	25.44	8.56
PS/1% BaWO4	1.19	394.65	20.63	3.7	0.030	130.06	41.88
PS/2% BaWO4	1.25	361.59	40.28	6.0	0.041	471.88	144.55
PS/3% BaWO4	1.10	433.58	10.06	1.5	0.014	5.77	2.02

Furthermore, the ε_i and the relaxation time τ can be represented via the following equation ⁶⁴ :

${\mathbf{\epsilon }}_{\mathit{i}}=\frac{\mathbf{1}}{\mathbf{8}{\mathit{\pi }}^{\mathbf{3}}{\mathit{\epsilon }}_{\mathit{o}}}\left(\frac{{\mathit{e}}^{\mathbf{2}}\mathit{N}}{{\mathit{c}}^{\mathbf{3}}{\mathit{m}}^{*}\mathit{\tau }}\right){\mathit{\lambda }}^{\mathbf{3}}$

(20)

The relaxation time τ may be derived from the correlation between ε_i versus λ³ (Figure 12(b)). The relaxation time values for the PS/BaWO₄ nanocomposite films were enhanced from 1.8 × 10⁻³ sec for the PS polymer to 3.7 × 10⁻³ sec and 6.0 × 10⁻³ sec for PS/1%BaWO₄ film and PS/2%BaWO₄ film, respectively, and then decreased to 1.5 × 10⁻³ sec for PS/3%BaWO₄ film, as tabulated in Table 4.

Non-linear Optical Properties

The non-linear optical characteristics are related to the non-linear polarization response of a material to an electromagnetic wave traversing across it. Materials exhibiting elevated non-linear optical susceptibilities are desired for non-linear applications, including ultrafast optical and lasing switching devices, as well as telecommunications. The non-linear refractive index (n ₂ ), linear optical susceptibility (χ⁽¹⁾), and third-order non-linear optical susceptibility (χ⁽³⁾) for all PS/BaWO₄ nanocomposite films can be derived from the next equations:^53,65,66

${\mathit{\chi }}^{\left(\mathbf{1}\right)}={\mathit{E}}_{\mathit{d}}/\mathbf{4}\mathit{\pi }{\mathit{E}}_{\mathbf{0}}$

(21)

${\mathit{\chi }}^{\left(\mathbf{3}\right)}=\mathbf{6.82}\times {\mathbf{10}}^{-\mathbf{15}}\hspace{0.17em}{\left({\mathit{E}}_{\mathit{d}}/{\mathit{E}}_{\mathbf{0}}\right)}^{\mathbf{4}}\hspace{0.17em}e.s.u.$

(22)

${\mathit{n}}_{\mathbf{2}}=\mathbf{12}\mathit{\pi }{\mathit{\chi }}^{\left(\mathbf{3}\right)}/{\mathit{n}}_{\mathbf{0}}$

(23)

Increasing the BaWO₄ concentration from 0% to 2% in PS polymer resulted in the increase of χ⁽¹⁾ from 0.019 to 0.041, and χ⁽³⁾ increased from 25.44 × 10⁻¹⁸ esu to 471.88 × 10⁻¹⁸ esu, and the n₂ increased from 8.56 × 10⁻¹⁶ esu to 144.55 × 10⁻¹⁶ esu. At the same time, the values of χ⁽¹⁾, χ⁽³⁾, and n₂ decreased to 0.014, 5.77 × 10⁻¹⁸ esu, and 2.02 × 10⁻¹⁶ esu, respectively, for the PS/3%BaWO₄ film, as illustrated in Table 3.

Conclusion

This work explores the effect of BaWO₄ NPs with varying concentrations (0, 1, 2, and 3 wt%) on the optical properties of the PS polymer. The XRD pattern indicates the formation of pure single-phase BaWO₄ NPs with a tetragonal structure and crystallite size of 39 nm. The uniform scroll-like shape of the synthesized BaWO₄ is shown in the SEM image. The XRD patterns of the PS/BaWO₄ nanocomposite films confirmed the growth of BaWO₄ NPs in the PS matrix. The optical results showed a gradual rise in optical absorbance of the PS with the rising concentration ratio of BaWO₄ scrolls. Moreover, the direct energy gap values ( $E_g^{dir}$ ) were determined to be 3.88, 3.85, 3.73, and 3.71 eV for PS, PS/1%BaWO₄, PS/2%BaWO₄, and PS/3%BaWO₄ nanocomposite films. The computed value of the Urbach energy for PS film was found to be 1.25 eV, and it rose to 1.38, 1.43, and 1.54 eV for the PS/1%BaWO₄, PS/2% BaWO₄, and PS/3% BaWO₄ nanocomposite films, respectively. Furthermore, the extinction coefficient (K_o) values exhibit an increasing trend following the addition of the BaWO₄ with varying ratios. The refractive index of the PS/1% BaWO₄ and PS/2% BaWO₄ films is higher than that of pure PS, while the PS/3% BaWO₄ film experiences a reduction. In addition, the E_o values dropped from 5.26 eV to 3.40 eV with a higher concentration of the BaWO₄ scrolls. While incorporating the BaWO₄ NPs, the E_d values enhanced markedly from 1.30 to 2.39 eV and then declined to 0.58 eV for the PS/3%BaWO₄ film. The N/m* value was concluded to be 0.45× 10³⁹ kg⁻¹ m⁻³ for PS, which increased to 0.81× 10³⁹ and 1.16× 10³⁹ kg⁻¹ m⁻³ for PS/1%BaWO₄ and PS/2%BaWO₄ films, respectively, and then dropped to 0.26× 10³⁹ kg⁻¹ m⁻³ for PS/3%BaWO₄ film. The relaxation time values enhanced from 1.8 × 10⁻³ sec for the PS polymer to 3.7 × 10⁻³ sec and 6.0 × 10⁻³ sec for PS/1%BaWO₄ film and PS/2%BaWO₄ film, respectively, and then decreased to 1.5 × 10⁻³ sec for PS/3%BaWO₄ film. Increasing the BaWO₄ concentration from 0% to 2% in PS polymer resulted in the increase of χ⁽¹⁾ from 0.019 to 0.041, and χ⁽³⁾ increased from 25.44 × 10⁻¹⁸ esu to 471.88 × 10⁻¹⁸ esu, and the n₂ increased from 8.56 × 10⁻¹⁶ esu to 144.55 × 10⁻¹⁶ esu. At the same time, the values of χ⁽¹⁾, χ⁽³⁾, and n₂ decreased to 0.014, 5.77 × 10⁻¹⁸ esu, and 2.02 × 10⁻¹⁶ esu for the PS/3%BaWO₄ film. The optical results suggested that the PS/1% BaWO₄ and PS/2% BaWO₄ films can be utilized in photonic devices, anti-reflective coatings, and waveguide technology. The PS/3% BaWO₄ film can be employed in applications that depend on the rapid transmission of optical signals, such as optical communications.