Characterization and linear/nonlinear optical properties of PVA/CS/TiO₂ polymer nanocomposite films for optoelectronics applications

Abstract

Polymer composite materials combines of polyvinyl alcohol (PVA), chitosan (CS), and titanium oxide (TiO₂) were successfully synthesizing for using in optoelectronics. Successful incorporation of TiO₂ into the PVA/Chitosan (PVA/CS) blend matrix has been demonstrated by XRD, AFM, FTIR and SEM. The TiO₂ is uniformly loaded and distributed in polymer chain, as seen by SEM and AFM images. Using UV–Vis optical spectroscopy, we determine the absorption coefficient, band edge, carbon clusters numbers, and Urbach energy. The effects of TiO₂ on linear/nonlinear optical characteristics were investigated. The band gap of PVA/CS/TiO₂ is reduced when compared to PVA/CS. However, the absorbance and optical conductivity were both increased by TiO₂. After mixed PVA/CS with 2.5%, 7.5%, and 10% TiO₂, the band gap energy drops from 4.99 for PVA/CS to 4.9, 4.7, and 4.23 eV, while the Urbach tail of the blend is 1.01 eV, it enhanced to 1.45 eV, 1.72 eV, and 2.07 eV respectively. The values of relaxation time $\tau$ decrease gradually from 2.35 × 10^–5 s to 1.11 × 10^–5, 1.87 × 10^–6 to 1.69 × 10^–6 s as the concentration of TiO₂ is raised from 2.5 to 7.5% and 10%. It has been found that incorporating TiO₂ into PVA/CS enhances the synthetic composite’s optical characteristics, making the composite PVA/CS/TiO₂ it suitable for use in both energy applications and optoelectronics.

1 Introduction

Flexible composite materials are expanding rapidly to develop with suitable qualities for portable and wearable electronics devices (Althubiti et al. 2023a, b). Researchers are paying special attention to the structures, mechanical qualities, and electronic properties of polymeric films (Atta et al. 2023). Because of their special properties like portability, shape versatility, adaptability, and low cost (Alotaibi et al. 2023a; Ahmad Fauzi et al. 2022), Many researchers are looking on conductive polymer composites for usage in electronics. The composite’s exceptional properties make it suitable for use in lightweight and flexible electronics. This has led to a significant amount of focus on developing methods for making flexible composite films that incorporate conductive nanoparticle materials (Mohamed et al. 2022; Iqubal 2022). Flexible nanocomposites are becoming a novel material for a variety of energy devices (Ashour et al. 2021). Because inorganic fillers stimulate internal processes like carbonization and macromolecular dispersion, they are able to alter the optical characteristics of the polymer composite upon addition to the polymer matrix (Mohanraj et al. 2018).

PVA/Chitosan (PVA/CS) blend has high features of chemical and mechanical characteristics (Alotaibi et al. 2023b), making it a versatile additive for a wide range of uses thanks to its high degree of transparency. PVA/CS is chosen as environmentally material with hydroxyl groups for sustainable and efficient methods for preparing composites. PVA/CS has unique characteristics such soluble, inexpensive, and consequently ecofriendly (Shubha and Madhusudana Rao 2016).

The properties of PVA is modified because the alignment of ions from the dissociated filler with the polar groups of PVA, resulting in the formation of a charge-transfer complex (Abdullah et al. 2015). So, by incorporating nanofillers into PVA, the PVA chemical properties is modified (Taghizadeh and Sabouri 2013). Researchers have tried to improve PVA physical properties by lowering the host polymer’s crystalline phase by adding various nano-sized fillers to the PVA matrix (Arya et al. 2018). When crystallization is inhibited in a semi-crystalline host polymer, segmental chain mobility is enhanced (Saeed and Abdullah 2021; Hameed et al. 2021). In contrast, Chitosan is a biopolymer comprised of hydrophilic cationic linear polysaccharide. Chitosan has a distinct chemical makeup as a positively charged polyamine. Unique characteristics include film formation, gel formation, pH sensitivity, amenability to alteration and liquid absorption. These characteristics are making chitosan useful in systems and biosensors (Rosli et al. 2021).

The structural and optical properties of TiO₂ have made them a popular choice among inorganic fillers (Ullah et al. 2018). Because of their unique properties, as well as the numerous potential uses in industry, TiO₂ nanoparticles have attracted a lot of attention (Naseem et al. 2021). TiO₂ nanoparticles are widely used in different devices like sensors and solar cells. In addition, TiO₂ is a promising materials with novel characteristics for several applications such as super capacitors rechargeable batteries. The current study focuses on incorporation of conductive TiO₂ fillers into a PVA/CS matrix to improve optical efficiency. TiO₂ in polymers exhibits novel properties for usage in photonics and capacitors to store electrical charges (Begum et al. 2021).

The TiO₂ is a direct semiconductor bandgap with favorable optical properties that used in light-emitting diodes (LEDs) and solar cells (Aziz et al. 2018). TiO₂ filler is the most studied oxides has energy gap of 3.05 eV (Hadi et al. 2020), making it a direct bandgap semiconductor. In contrast, Abdullah et al. (2017) found that CO₂ conversion was significantly enhanced by TiO₂. When CO₂ is reduced via photo catalysis, the distribution of the resulting products is extremely sensitive to the band gap of the catalyst. Additionally, Aziz et al. (2019) used a solution cast approach to create a composite of chitosan/NH₄Tf/TiO₂ electrolytes. Up to 1 wt% of TiO₂ was found to increase the dielectric characteristics of composite electrolytes. Additionally, Abdullah et al. (2023) investigated TiO₂ modified the physical and electrical characteristics of PVA-NH₄NO₃. They found that the ionic conductivity is significantly improved after adding TiO₂NPs single-crystal.

The distinctive aspect of this research is the inclusion of TiO₂ into PVA/CS at varying concentrations for use in optoelectronics. FTIR, XRD, SEM, and AFM analyses all corroborate that PVA/CS/TiO₂ nanocomposites have formed successfully. Structure and linear/nonlinear optical characteristics of PVA/CS as a function of TiO₂ filler were investigated. This work shows that flexible PVA/CS/TiO₂ were successfully prepared and their linear/nonlinear characteristics were improved for use in optoelectronics devices.

2 Materials and Methods

PVA, molecular weight of 84,500–89,500 g/mol, titanium dioxide (TiO₂) of particle size of 20 nm, chitosan with a degree of deacetylation 84% were provided from Sigma-Aldrich Co., USA. The polymer solutions were prepared separately for the preparation of cross-linked PVA/CS/TiO₂ blended membranes. 1 gm of PVA is dissolving in 100 ml of deionized water at 75 °C with stirring for 1.5 h, and 1 gm of chitosan was stirred into 95 ml of acetic acid solution at room temperature. The PVA and CS were combined and stirred for 7 h. In order glutaraldehyde was used as a cross-linked the composite after various concentrations of TiO₂ were added to the solution. The TiO₂NPs were then uniformly dispersed in the PVA/CS blend by sonicating the mixtures for 40 min. Drying time was achieved by pouring the completed PVA/CS/TiO₂ mixture onto a glass Petri dish, removing any remaining air bubbles with a combination of shaking and blowing. To achieve the desired results, this process was performed multiple times to obtain 2.5%, 7.5% and 10% of TiO₂ in PVA/CS. The mean thickness of the created sheets in the range of 0.1 mm is measured with a thickness gauge (Mitutoyo 7301).

XRD (XRD-6000) in 2θ of 4° to 80° and FTIR (ATI Mattson, England) in wavelength of 500 to 4000 cm⁻¹ were used for investigating the structural characteristics of PVA/CS/TiO₂. The SEM images were captured using a FE-SEM (SEM, JEOL, Japan). The changes in surface morphology and roughness OF PVA/CS/TiO₂ are investigated with AFM. The optical spectra were given by the UV/VIS optical spectrophotometer (double-beam JascoV-670) in range of 200 to 1050 nm.

3 Results and Discussion

Figure 1 investigates the XRD of PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂. The pure PVA/CS spectrum shows diffraction peak at 20.1°, while the XRD of PVA/CS/TiO₂ show other new diffraction peaks at 25.4°. The XRD show a further reduction in the PVA/CS diffraction peak of 20.1° by increasing TiO₂. This decrease in PVA/CS crystallinity indicated the interaction between the PVA/CS chains and TiO₂. The changes of FWHM of PVA/CS peak at 20.1° have proved a good interaction of the PVA/CS and TiO₂. The crystallite size (D) of the pure TiO₂ is calcuated using the simple Debye–Scherrer (Atta et al. 2021).

$$\mathrm{D}= \frac{0.94\uplambda }{\mathrm{\beta cos\theta }}$$

(1)

$\lambda$ is the wavelength, $\theta$ is the diffraction angle, and $\beta$ is refer to FWHM. The crystallite size D, is determined of 35.2 nm

Fig. 1

XRD pattern of PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂ films

The FTIR spectra of synthesized PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂ are presented in Fig. 2. Broad peaks at 3290 cm⁻¹ of PVA/CS could be attributed to –OH groups (Chhabra et al. 2020) and another at 2930 cm⁻¹ for C–H stretching (Ismail et al. 2012). The other peaks at 1640 cm⁻¹ attributed to vibrational C=C (Borhade and Uphade 2012). Beaks at ~ 1410 and 1080 cm⁻¹ refers respectively to the –OH and C=O stretching. The band 908 cm⁻¹ is assigned to C–C stretching and 825 cm⁻¹ for CH₂ stretches. Due to the interaction between TiO₂ and PVA/CS levels, a slight shift of the peaks were seen (Sayyah et al. 2015). Moreover, due to charge transport complexes, PVA/CS /TiO₂ composite films have a different intensity than pure PVA/CS (Khmissi et al. 2016). When nanoparticles were added, these bands’ locations were seen to shift from red to blue, clearly showing a change in the interactions between intermolecular hydrogen bonds and confirming the complexation between the polymer and the nanoparticles.

Fig. 2

FTIR of PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂ films

The SEM images show homogeneous morphology of PVA (Shi et al. 2015) with smooth surface and structure (Fig. 3a). Figure 3b–d are show SEM images of 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂ films, respectively. These images demonstrated the formation of nanocomposites with roughly shaped pores of varying sizes. The combination of PVA and TiO₂ is investigated the homogeneous surface morphologies. The bonding between the PVA chain and TiO₂ is due to this coalescence between polymer and TiO₂. Circular spots are uniformly distributed across the surface, forming fine discharge channels (Masid Roy et al. 2017). This suggests the formation of PVA/CS/TiO₂ nanocomposites. The scanning electron microscopy show TiO₂ nanoparticles are agglomerated uniformly in PVA/CS. Results from the FE-SEM analysis corroborate the XRD findings of a robust interaction between the polymer blend and TiO₂. Clearly, the PVA in these images has a thickness of around 90 um. TiO₂ nanoparticles fill the polymeric spaces in PVA, drawing the PVA chains closer together to form a dense hybrid structure.

Fig. 3

SEM of a PVA/CS, b 0.025TiO₂, c 0.075TiO₂ and d 0.1TiO₂ films

Topographical views of PVA/CS and PVA/CS/TiO₂ in 2D were indicated in Fig. 4a, b, while 3D representations are shown in Fig. 4c, d, respectively. When compared with the PVA/TiO₂, which is characterized by nano convolutions, the topography of PVA is relatively smooth, according to AFM pictures. Addition of TiO₂ in PVA/CS is causes an increase in surface roughness, demonstrating that the mixed of TiO₂ in PVA/CA blend. Although PVA possesses hydrophilic channels, they have been constricted to provide a surface with a low roughness and high smoothness. Hydrophilic channels in PVA/CS blend are efficiently covered by the extra TiO₂ nanoparticles, making the PVA/CS/TiO₂ composite is rougher.

Fig. 4

2D AFM a PVA/CS, b 0.1TiO₂, 3D images of c PVA/CS and d 0.1TiO₂ films

Figure 5a shows the absorbance of PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂ films. The band gap absorption of TiO₂ and absorption structural defects is both responsible for the uniform absorption behavior observed across all samples, which has an absorption peak around 650 nm. The TiO₂ content of the composite all have a significant impact on the absorption peak strength. As shown in Fig. 5a, the intensity are enhanced as the TiO₂ percentage was raised from 0.025 to 0.10. The findings are consistent with SEM findings and XRD data. The high peak with TiO₂ compared to PVA/CS is also demonstrated by the absence of a shift in the absorption peaks with increasing TiO₂. It is shown that the encapsulation of TiO₂ effects on the formation of TiO₂ and PVA/CS chains (Rao et al. 2012). The absorption coefficients ($\alpha$) of PVA/CS/TiO₂ films is given by

Fig. 5

a Absorbance with λ, b $\alpha$ versus $h\upnu$, c band gap with $h\upnu$ d ln ($\alpha$) with $h\upnu$

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

(2)

A is absorbance and d is thickness. In Fig. 5b, the $\alpha$ is plotted with incident photon energy ($h\upnu$). The $\alpha$ is rise as the TiO₂ content is increased. This change could be a result of the TiO₂ addition induced level changes (Taha et al. 2019). When 2.5%, 7.5%, and 10% TiO₂ are added, the absorption edge of PVA/CS drops from 4.77 eV to 4.66, 4.21, and 3.81 eV, respectively. Tauc’s relation is used to estimate the optical gap E_g by.

$$\alpha h\upnu =A {(h\upnu -{\mathrm{E}}_{g})}^{m}$$

(3)

Absorption constant is denoted by A, energy bandgap by E_g, and optical transition type by m. The relationship of ($\alpha$ hv)² and photon energy (hv) is used to estimate the band gap E_g. This is achieved by extrapolating the straight line sections of the graphs to zero absorption, as in Fig. 5c and detailed in Table 1. The E_g is decreased as the TiO₂ increased. After being mixed with 2.5%, 7.5%, and 10% TiO₂, the E_g of the polymer drops from 4.99 to 4.9, 4.7, and 4.23 eV, respectively. Due to an enhancement of charge-carrier, the energy gap is varied by TiO₂. Taha et al. (2019), investigated the addition of nickel oxide (NiO) to PVC, and nearly the found the same behaviour. As NiONPs content increased and states were produced inside the optical band gap, they discovered the band gap shrank. This confirmed the miscibility of TiO₂ and PVA chains. Using relation E_g = 34.4/N, the optical gap E_g is used to estimate carbon cluster number (N) (Zaki et al. 2017). Table 1 displays the predicted N values for PVA/CS and PVA/CS/TiO₂. By increasing the TiO₂ content from 2.5 to 7.5% and 10%, the N value for PVA/CS rises from 166 to 172, 178 and 188. TiO₂ contributes to a lower band gap and higher N. The Urbach’s tail is given according to formula (Zaki et al. 2017).

$$\alpha \left(\upnu \right)={\mathrm{\alpha }}_{o} {\mathrm{e}}^{h\upnu /{\mathrm{E}}_{u}}$$

(4)

where ${\mathrm{\alpha }}_{o}$ is a constant and E_u is the band tail. As a result, the band tail of polymer and polymer/TiO₂ films is determined by plotting ln ($\alpha$) with photon energy, as in Fig. 5d. The band tail of the polymer blend and composite samples was estimated using the inverse slope of the linear portions of these graphs, and the results are shown in Table 1. The predicted Urbach tail of the blend is 1.01 eV, it increases to 1.45 eV, 1.72 eV, and 2.07 eV by increasing TiO₂ to 2.5%, 7.5%, and 10% of TiO₂, respectively. Increases in the TiO₂ content of the composite are associated with an increase in Urbach tail values, which is indicative of changes in disorder state. Furthermore, the structural characteristics of the blend were altered by TiO₂, which enhanced the optical properties. Graphene oxide (fGO) embedded in PVC exhibits similar behavior, the Urbach energies increasing with increased graphene oxides as a result of disorder in the nanocomposite (Taha and Saleh 2018).

Table 1 E_e, E_u and E_g values of PVA/CS, 0.25TiO₂, 0.75TiO₂, and 0.1TiO₂

The extinction coefficient (K₀) is given by (Kakil et al. 2018)

$${K}_{o}=\frac{\mathrm{\alpha \lambda }}{4\uppi }$$

(5)

The K₀ of PVA/CS/TiO₂ are plotted with photon energy in Fig. 6a. It is crucial to understand that the increase in defects leads to an enhancement in the absorbance coefficient, which in turn raises K_o for composite samples. The reflectance of the samples with wavelengths is shown in Fig. 6b. The reflectance of PVA/CS/TiO₂ changes with wavelength. The composite’s reflectivity also changed as the TiO₂ content was increased. The refractive index (n) is given by (Alrowaili et al. 2021).

Fig. 6

Variation of a K_o with $h\upnu$, b R with $\uplambda$, c refractive index with $\uplambda$, and d the optical conductivity with $\uplambda$, for PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂

$$n=\frac{(1+R)}{(1-R)}+\sqrt{\frac{4R}{{\left(1-R\right)}^{2}}}-{{K}_{o}}^{2}$$

(6)

The index of pure PVA/CS and PVA/CS/TiO₂ nanocomposite samples is shown in Fig. 6c. The index n rises with wavelength in both pure and composite films. The refractive index gradually changed after pure PVA/CS was mixed with 2.5%, 7.5%, and 10% TiO₂. Covalent bonds can be formed between different chains thanks to the composite’s increased TiO₂ (Obasi et al. 2019). The optical conductivity of PVA/CS and PVA/CS/TiO₂ given by Banerjee and Kumar (2011).

$${\upsigma }_{opt}=\frac{\alpha nc}{4\pi }$$

(7)

Figure 6d shows the optical conductivity with wavelength. Because of the density of the concentrated states in the band structure, the conductivity of the films rises. Similar effects are seen when SnO₂ is added to PVC polymers, where higher concentrations of SnO₂ result in higher optical conductivities (Taha et al. 2018).

Real ${\varepsilon }_{r}$ and imaginary ${\upvarepsilon }_{i}$ are the two terms that make up a material’s complex dielectric constant, which is one of its most crucial characteristics (Donya et al. 2020).

$$\upvarepsilon ={\varepsilon }_{r}+i{\upvarepsilon }_{i}$$

(8)

The next formula is to estimate the ${\varepsilon }_{r}$ (Abd El-Rahman et al. 2019).

$${\upvarepsilon }_{r}={n}^{2}-{{K}_{o}}^{2}$$

(9)

The real component (${\varepsilon }_{r}$) is changes with wavelength as shown in Fig. 7a. As was already mentioned, adding TiO₂ to the PVA/CS results in the formation of covalent bonds between individual chains, leading to an enhanced in the loss of photon energy. The fictitious component, which represents the energy dissipation caused by the motion of the dipole moment, is also obtained from relation (Rasheed et al. 2019).

Fig. 7

a real and b imaginary constants with $\uplambda$, for PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂

$${\upvarepsilon }_{i}=2 n {K}_{o}$$

(10)

The ${\upvarepsilon }_{i}$ versus wavelength of PVA/CS/TiO₂ is shown in Fig. 7b.

Thus, the dispersion of refractive index is alternatively investigated by using the single oscillator model (Wemple DiDomenicon model) by Equation (Abdullah et al. 2022).

$$\frac{1}{{n}^{2}-1}=\frac{{E}_{O}}{{E}_{d}}-\frac{1}{{E}_{O} {E}_{d}}{\left(h\upnu \right)}^{2}$$

(11)

E_o denotes the singular oscillating energy and E_d the dispersion energy.

The relationship between (n²−1)⁻¹ and (hv)² of the pure PVA/CS and PVA/CS/TiO₂ films is depicted in Fig. 8a. The intercept and slope of the linear fitting component are used to calculate E₀ and E_d. Additionally, PVA/CS and PVA/CS/TiO₂ refractive static index values were provided by Al-Zahrani et al. (2015).

Fig. 8

a (n²−1)⁻¹ against (hυ)², b ε_r against λ², c (n²− 1)⁻¹ against λ⁻², and d ε_i against λ³, PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂

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

(12)

Hence, the (ε_∞) of the PVA/CS /TiO₂ were estimated by ε_∞ = (n_o)². Table 2 summarizes the E_o, E_d, and n_o, for both PVA/CS/TiO₂ films. Including TiO₂ into the polymer with 2.5%, 7.5%, and 10%, is changed E₀ from 2.47 eV (E_o = 0.495E_g) for the pure PVA/CS to 2.42 eV (E_o = 0.494E_g), 2.55(E_o = 0.543E_g) and 2.65 eV (E_oo = 0.626E_g). This indirect in relation between E_g and E_o is due to the aggregation of TiO₂ in the composite for high concentration of TiO₂. The dispersion energy E_d enhanced from 3.38 to 3.56, 4.46, 5.89 eV. In addition, as indicated in Table 2, the statically refractive index n₀ is 1.53 for PVA/CS and it changed to 1.51, 1.66, 1.81 when the TiO₂ concentration is increased from 2.5 to 7.5% and 10% respectively.

Table 2 n_o, E_d, E_0, ε_∞, ε_l, and N/m* for PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂

Dielectric constants are calculated using the Spitzer-Fan approach, which (N/m*) to identify the dielectric constant using (El-Nahass et al. 2009).

$${\upvarepsilon }_{r}={\varepsilon }_{l}-\left(\frac{{e}^{2}}{4 {{\pi }^{2}{\varepsilon }_{s}c}^{2} }\frac{N}{{m}^{*}}\right){\lambda }^{2}$$

(13)

The constant s is the dielectric free space constant, c is the speed of light, and e is the charge of an electron. Hence, Fig. 8b depicts the λ² and ${\varepsilon }_{r}$ for the PVA/CS and PVA/CS/TiO₂. Table 3 displays the slope and interception of the straight sections of the detour, derived from the PVA/CS and PVA/CS/TiO₂ composites, respectively. The resonant plasma frequency (W_p) is determined by (Hamad 2013).

Table 3 W_p, λ_o, S_o, n_∞, and $\tau$ of PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂

$${\mathrm{W}}_{p}=\frac{{e}^{2}}{{\varepsilon }_{o}} \times \frac{N}{{m}^{*}}$$

(14)

The addition of 2.5%, 7.5%, and 10% TiO₂ in PVA/CS led to an increase in N/m*, and Wp values. Additionally, medium oscillator (λ_o), the long refractive index (n_∞), and oscillator length intensity (S_o) are determined using the single-term Sellmeier oscillator method (Alwan 2012).

$${(n}_{\infty }^{2}-1)/({n}^{2}-1)=1-\left(\frac{{\lambda }_{o}}{\lambda }\right)^{2}$$

(15)

Hence, the relationship of (n²−1)⁻¹ and λ⁻² at longer-wavelength is shown in Fig. 8c. As stated in Table 3, it is possible to estimate n_∞ and λ₀ from the intercept and slope of the linear portion of the detour, respectively. Thus, we can approximate S₀ values as (El Sayed et al. 2014).

$${S}_{o}={(n}_{\infty }^{2}-1)/{{(\lambda }_{o})}^{2}$$

(16)

The values of n_∞ increase, but the value of S₀ decreases, as the TiO₂ load increases. In the Drude model, ${\upvarepsilon }_{i}$ is calculated using the following formula (Saadeddin et al. 2007).

$${\upvarepsilon }_{i}=\frac{1}{4{\pi }^{3}{\varepsilon }_{o}}\left(\frac{{e}^{2}N}{{c}^{3}{m}^{*}\tau }\right){\lambda }^{3}$$

(17)

The values for, the relaxation time, are thus calculated by plotting the relationship between ${\upvarepsilon }_{i}$ and ${\lambda }^{3}$, as shown in Fig. 8d, and are tabulated below. The values of $\tau$ decrease gradually from 2.35 × 10^–5 s to 1.11 × 10^–5, 1.87 × 10^–6 to 1.69 × 10^–6 s as the concentration of TiO₂ is raised from 2.5 to 7.5% and 10%. Based on these findings, it is clear that incorporating TiO₂ filler into PVA/CS results in nanocomposite films with enhanced properties, making TiO₂/ PVA/CS films a practical choice for use in energy devices. Nonlinear optical (NLO) responsiveness of a material pattern is described by the following formula (Frumar et al. 2003):

$$P={X}^{(1)}E+{\mathrm{X}}^{(2)}{E}^{2}+{\mathrm{X}}^{\left(3\right)}{E}^{3}$$

(18)

P represents the polarization, ${X}^{(1)}$ represents the first linear susceptibility, ${X}^{(2)}$ represents the second NLO susceptibility, and ${X}^{(3)}$ is the third NLO. Both ${X}^{(1)}$ and ${X}^{(3)}$ are calculated using (Ticha and Tichy 2002).

$${X}^{(1)}=\frac{({n}^{2}-1)}{4\pi }$$

(19)

and

$${X}^{(3)}=A{({X}^{\left(1\right)})}^{4}$$

(20)

The refractive index given by:

$$n\left(\lambda \right)={n}_{o}\left(\lambda \right)+{n}_{2}\left({E}^{2}\right)$$

(21)

The n₂ is estimated by (Kanis et al. 1991).

$${n}_{2}=\frac{12\pi {X}^{(3)}}{{n}_{o}}$$

(22)

Figure 9a, b demonstrate the relationship between ${X}^{(1)}$ and ${X}^{(3)}$ and for pure PVA/CS and PVA/CS/TiO₂ composites samples, respectively. As the percentage of TiO₂ in the composite increased, so did the amounts of ${X}^{(1)}$ and ${X}^{(3)}$. The introduction of TiO₂ causes an increase in local polarizabilities, which originates from the defects’ centers (Ali et al. 2021). Non-linear refractive index versus wavelength for PVA/CS and PVA/CS /TiO₂ samples is also depicted in Fig. 9c. Notably, ${n}_{2}$ quantities grow in a linear fashion with increasing TiO₂ content in the composite, mirroring the behavior observed for Atta et al. (2023). Based on these results, it is clear that the PVA/CS /TiO₂ nanocomposite film is preferable to pure PVA/CS when it comes to nonlinear optical applications and optoelectronic devices.

Fig. 9

a $X$⁽¹⁾, b $X$⁽³⁾, and c n₂ versus the wavelength λ for PVA/CS, 0.025TiO₂, 0.075TiO₂, and 0.1TiO₂

4 Conclusion

The XRD, SEM, AFM and FTIR results verify the successful fabrication of PVA/CS/TiO₂ nanocomposites samples. The SEM images showed that the TiO₂ had been successfully integrated onto the PVA, with average particle sizes ranging in 90 nm. The FTIR analysis further revealed that the TiO₂ nanoparticles were dispersed throughout the PVA/CS matrix. Surface morphological changes in TiO₂/PVA/CS have been attributed to the introduction of defects and chain session process. The optical characteristics are also evaluated for both PVA/CS and PVA/CS/TiO₂. The addition of 2.5%, 7.5%, and 10% TiO₂ to pure PVA/CS reduced the band gap energy from 4.99 to 4.9 eV, 4.7 eV, and 4.23 eV, respectively. Moreover, the oscillating energy E₀ changed from 2.47 for the pure PVA/CS to 2.42 eV, 2.55 and 2.65 eV and the dispersion energy E_d increased from 3.38 to 3.56, 4.46, 5.89 eV The linear/nonlinear optical parameters of the influence of TiO₂ were determined. Based on these results, PVA/CS /TiO₂ films with different concentrations of TiO₂ nanoparticles are superior characteristics compared to PVA/CS to be used in energy-related applications.