Open AccessArticle

TiO₂/SWCNts: Linear and Nonlinear Optical Studies for Environmental Applications

Saloua Helali

Advanced Materials Research Laboratory, Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

C 2025, 11(1), 11; https://doi.org/10.3390/c11010011

Submission received: 30 November 2024 / Revised: 13 January 2025 / Accepted: 22 January 2025 / Published: 26 January 2025

(This article belongs to the Special Issue Carbon Functionalization: From Synthesis to Applications)

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"> Figure 1
Transmittance and reflectance spectra of TiO2 and for SWCNTs/TiO2 composites for different percentages, 5%, 10%, 20%, of SWCNTs. "> Figure 2
The absorption coefficient, α, spectra of TiO2 and for 5%, 10%, 20% SWCNTs/TiO2 composites. "> Figure 3
(αhν)1/2 versus energy for (a) TiO2, (b) TiO2-(5%) SWCNTs, (c) TiO2-(10%) SWCNTs, and (d) TiO2-(20%) SWCNTs. "> Figure 4
The spectra of refractive index versus wavelength for pure TiO2 and TiO2-SWCNTs composites. "> Figure 5
The (n2 − 1)−1 vs. (hν)2 curve for pure TiO2 and for 5%, 10%, 20% SWCNTs/TiO2 composites. "> Figure 6
The relation between n2 as a function of λ2 of TiO2 and for 5%, 10%, 20% SWCNTsTiO2. "> Figure 7
The variation in (a) real part, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>, (b) imaginary part, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, of dielectric constant as a function of photon energy for TiO2 and for 5%, 10%, 20% SWCNTs-TiO2 composites. "> Figure 8
The spectra of (a) optical conductivity and (b) electrical conduction of TiO2 and for 5%, 10%, 20% SWCNTs-TiO2 composites. "> Figure 9
The variation in χ(1), χ(3), and n2 as a function of concentration of SWCNTs. "> Figure 10
The XRD patterns of pure TiO2 and 5%, 10%, 20% SWCNTs-TiO2 composites. "> Figure 11
UV–vis absorption spectra showing the photocatalytic activity of TiO2 and SWCNTs/TiO2 composites regarding photocatalytic degradation of MB in water. "> Figure 12
The variation in photocatalytic efficiency of SWCNTs-TiO2 composites. "> Figure 13
Mechanism of photocatalytic activity of SWCNTs/TiO2 composites towards degradation of MB dye. ">

Versions Notes

Abstract

A series of single-walled carbon nanotube/titanium dioxide (SWCNTs/TiO₂) composites were prepared by the incorporation of various concentrations (0, 5, 10, 20 V.%) of SWCNTs in TiO₂. The prepared solutions were successfully formed on silicon and quartz substrates using the sol–gel spin-coating approach at 600 °C in ambient air. The X-ray diffraction method was used to investigate the structure of the samples. The absorbance and transmittance data of the samples were measured using a UV–vis spectrophotometer. Through the analysis of these data, both the linear and nonlinear optical properties of the samples were examined. Wemple–DiDomenico’s single-oscillator model was used to calculate the single-oscillator energy and dispersion energy. Finally, all samples’ photocatalytic performance was studied by the photodegradation of methylene blue (MB) in an aqueous solution under UV irradiation. It is found that the photocatalytic efficiency increases when increasing the SWCNT content. This research offers a new perspective for the creation of new photocatalysts for environmental applications.

Keywords:

SWCNTs/TiO₂ composites; linear and nonlinear optics; surfaces morphology; photocatalysis

Graphical Abstract

1. Introduction

Nowadays, the development of new semiconductor photocatalysts for photocatalytic purposes has attracted significant research interest in the last two decades. Several semiconductors such as TiO₂, ZnO, Fe₂O₂, ZnS, and CdS are used as semiconductor photocatalysts due to their specific physical characteristics such as chemical stability, high dielectric constant, and high refractive index as well as their transparency in the visible light. Among them, TiO₂ semiconductors have been widely studied [1,2,3] for their interesting properties. In addition, this binary oxide seems to be a principal element for many applications including photovoltaic cells [4,5], self-cleaning surfaces [6], air purification [7], water treatment, etc. [8].

In order to increase the photocatalysis activity of TiO_2, several approaches have been studied. For changing the activity of TiO₂ against illumination, this oxide has a band gap energy, which changes with the doping elements. For instance, metal transition elements such as Fe, Mn, Cu, Al, Cr, Ag, and Pt [9,10,11,12,13] have been tested. Moreover, doping with non-metal (e.g., N, C, S, P, F, etc.) [14] or co-doping with metal/metal (e.g., Zn-Cu, Fe-Ni, Ag-Mo, etc.) [15,16] or co-doping with metal/non-metal (e.g., Pt-N, Mn-P, Cu-N, etc.) [17] have been studied too, although metal doping under high absorption of the visible light may constitute a second source of pollution in water treatment [18]. Thus, doping with non-metal may be of interest to remove pollutants in water.

Recently, new types of materials such as carbon nanotubes (CNTs), grapheme, fullerenes, and graphite. Carbon nanotubes have a cylindrical structure, consisting of graphene sheets that are nanometer in diameter and micrometer in length [19,20,21]. CNTs have attracted interest because of their distinctive properties, which include high conductivity, surface area, chemical stability, and catalytic activity [21].

This study focuses on the morphological and optical evolution of SWCNTs on TiO₂ and their photocatalytic activity in the degradation of methylene blue (MB). TiO₂ is a widely used photocatalyst, but its practical application is limited by its wide band gap (~3.2 eV), which restricts photocatalytic activity to the UV region, and the rapid recombination of photogenerated electron–hole pairs. Incorporating SWCNTs into TiO₂ offers a promising solution to these challenges by enhancing charge carrier separation, increasing the surface area for photocatalytic reactions, and extending light absorption into the visible region, ultimately improving the photocatalytic efficiency of TiO₂.

In the present study, we synthesized a SWCNTs/TiO₂ composite with varying amounts of SWCNTs. UV–VIS spectrophotometer and X-ray diffraction were used to examine the morphological and optical evolutions of various concentrations of SWCNTs on TiO₂ produced via the sol–gel spin-coating process. In addition, the photocatalytic activity of the samples was tested against the photodegradation of methylene blue (MB) dye in water under UV irradiation.

2. Materials and Methods

2.1. Synthesis of SWCNTs/TiO₂ Composites

Two substrates, quartz and silicon Si (100), were utilized in the spin-coating process to deposit various thin films. Before modification, the substrates were cleaned using an ultrasonic bath and an acetone solution for ten minutes. After that, they were rinsed 3 times in deionized water and then dried at 100 °C for 10 min in an oven.

The nanocrystalline state of the TiO₂ thin films was elaborated and extensively characterized as described in [22,23]. Briefly, the TiO₂ was prepared by mixing 1 mol tetrabutyl orthotitanate, 3 mol acetic acid, 4 mol butanol, and 1 mol H₂O. The obtained solution was stirred for 60 min at room temperature.

Single-wall carbon nanotubes (SWCNTs) containing carboxylic acid functionality used in the experiment were purchased from Sigma Aldrich, St. Louis, MO, USA. The nanotubes had a diameter of about 4–5 nm and their length ranged from 0.5 μm to 1.5 μm and were marked by a COOH group. A solution of 0.1 mg/mL of SWCNTs in DMF solvent was sonicated for 30 min until the solution was visually homogeneous. The two solutions of TiO₂ and SWCNTs were prepared separately; the last one was added according to volume ratios to obtain a composition with 5, 10, and 20% V. of SWCNTs with respect to TiO₂ in the final solution product (see Table 1). The prepared solution was dropped onto cleaning substrates and then dried at 100 °C for 10 min. These substrates experienced four repetitions of the drop and dry procedures. Finally, the films were annealed in air at 600 °C (10 °C/min) for 1 h.

2.2. Characterization of SWCNTs/TiO₂ Composites

The crystallographic structure of all fabricated films was determined using X-ray diffraction (Bruker D8, Kaunas, Republic of Lithuania), with monochromator Cuα radiation of wavelength 0.154056 nm. The analysis was conducted with scanning angles in the range of 15–60° at a scan step of 1°/min. A UV–VIS spectrophotometer (UV3101PC, Athens, GA, USA) was employed to analyze the optical characteristics of the TiO₂-SWCNTs films deposited on quartz substrates.

2.3. Photocatalytic Analysis

Methylene blue (MB) dye degradation in water was employed to measure the photocatalytic activity of the produced TiO₂ and 5%, 10%, 20% of SWCNTs/TiO₂ composites. The samples (area of 2 × 2 cm²) were submerged in 3 mg/mL MB aqueous solutions and exposed to UV light using a Northen Electronic lamp. For irradiation, a visible light lamp with a tungsten filament and 100 W power was used at the distance of 10 cm from the solution in a darkness box. The solution was magnetically agitated for thirty minutes in the dark to achieve an adsorption–desorption equilibrium. UV–vis absorption spectroscopy in the 400–800 nm wavelength range was used to measure the MB dye in the decomposition testing with and without samples. The photocatalytic efficiency of the TiO₂-SWCNTs sample photocatalysts was obtained from Equation (1) [24]:

e f f i c i e n c y (%) = \frac{A_{0} - A}{A_{0}} \times 100

(1)

where A and A₀ are the absorption of the MB aqueous solution with the TiO₂ thin film photocatalyst after UV irradiation and without the TiO₂ film photocatalyst, respectively.

3. Results and Discussion

3.1. Optical Characterizations of SWCNTs/TiO₂ Composites

3.1.1. Linear Optical Analysis

The optical characteristics of the TiO₂ and SWCNTs/TiO₂ samples were performed by optical transmittance and optical band gap studies. The UV–vis–NIR spectra of the SWCNTs/TiO₂ composite synthesized with various concentrations of SWCNTs (V.%) are evaluated at normal incidence in the wavelength range 300–2500 nm. The transmittance and reflectance of the TiO_2, also displayed in Figure 1, is used for comparison with the SWCNTs/TiO₂ films. It can be seen from this figure that the TiO₂ film transparency coefficient reached 87% in the visible range. In contrast, it is evident that the transmittance dropped as the concentration of SWCNTs increased. Hence, the addition of SWCNTs decreases these transparent values until reaching 60% for the sample with 20 V.% of SWCNTs. This decrease may be due to an increase in the absorption phenomenon, which leads to a lower band gap energy value, and it confirms the immobilization of SWCNTs on the TiO₂ grains.

The absorption coefficient (α) of any medium has a significant impact on its band gap. The α is essential for determining the types of transitions and the energy gap of SWCNTs/TiO₂ composites. The α for the examined films is calculated using the following equation [25]

α = \frac{1}{d} \ln (\frac{1 - R^{2}}{2 T} + \sqrt{R^{2} + \frac{1 - R^{2}}{4 T^{2}}})

(2)

where T, R, and d are the transmittance, the reflectance, and the thickness of the TiO₂-SWCNTs composites, respectively. The variations in the absorption coefficient as a function of the wavelength for the samples are represented in Figure 2.

The optical band gap energy (Eg) of pure TiO₂ and those with different concentrations of SWCNTs (V.%) composites were evaluated using the Tauc equation [22].

{(α h ν)}^{\frac{1}{m}} = A (h ν - E_{g} \pm E_{p h})

(3)

where A is a proportionality constant, Eg is the energy band gap, hυ is the photon energy, E_ph is the absorbed or the emitted phonon energy, and m is the factor related to the electron transitions. The m takes the values 2 or 3 for direct optical transitions, whereas for indirect allowed electronic transitions, m corresponds to either 1/2 or 3/2 [22,26]. Tauc plots of the samples are shown in Figure 3.

According to Equation (3), we discovered that the best linear fit for permitted indirect transitions and the relationship between (αhv)^0.5 and hv both contribute to the determination of Eg, which could be calculated by extrapolating a tangent line to the hυ axis. Table 2 summarizes the calculated values of the phonon energy and energy band gap for SWCNTs/TiO₂ composites at various SWCNT concentrations (V.%). The results show that the optical band gap increases from 3.23 eV for pure TiO₂ to 3.36 eV for 20 V.% of SWCNTs/TiO₂ composites. This increase in the band gap can be attributed to several factors, including the quantum confinement effect, interfacial interactions between SWCNTs and TiO₂, and charge transfer processes. Additionally, the incorporation of SWCNTs may influence the TiO₂ lattice structure and reduce defect states, contributing to the observed band gap widening. The band gap measurements of the SWCNTs/TiO₂ composites pointed to potential uses for them in the construction of the organic solar cell’s absorption layer.

Materials that can be utilized in communication, such as optical cables, filters, and switches, are dependent on correct estimates of the refractive index [27]. The refractive index, n, for all samples was calculated with the aid of the extinction coefficient (k), using the following equation [26]

n = (\frac{1 + R}{1 - R}) + (\sqrt{\frac{4 R}{1 - R^{2}} - k^{2}})

(4)

k = \frac{α λ}{4 π}

(5)

Figure 4 displays the dependence of the refractive index for SWCNTs/TiO₂ composites on the wavelength in UV–Vis–NIR regions. The films’ refractive indices range from 2.6 to 7, indicating that they can be employed in a wide range of optical devices. Further, the n values decrease with an increase in the carbon nanotubes’ concentration at a higher wavelength, λ > 1000 nm, which could be clarified by the film’s discontinuity.

In the normal region, Wimple and DiDomenico have developed a single-oscillator approximation model to study the refractive index dispersion in the transparency region under the gap. Two parameters defined by the model are the dispersion energy Ed and the oscillation energy Eo [28]

n^{2} = 1 + \frac{E_{d} E_{0}}{E_{0}^{2} - {(h ν)}^{2}}

(6)

The (n² − 1)⁻¹ vs. (hν)² curve for 5, 10, and 20 V.% of SWCNT solutions is presented in Figure 5. Table 1 displays the computed E0 and Ed values for the 5, 10, and 20 V.% of SWCNT samples. As shown in Table 1, the Ed values are greater than the E0 values and that the E0 and Ed values decrease when the concentration of the SWCNT solutions increases.

The equation that follows describes the relationship between the frequency extraction at a higher frequency, Ɛ_L, and the free carrier concentration to free carrier effective mass ratio, N/m* [29]

n^{2} = ε_{L} - \frac{e^{2}}{4 π^{2} ε_{0} c^{2}} \frac{N}{m^{*}} λ^{2}

(7)

where e and ε_o are the electron charge and the permittivity for free space. Figure 6 shows the variation in n² with λ² for SWCNTs/TiO₂ composites of different concentrations of SWCNTs. The extrapolation line λ² to 0 and the appropriate line slope are used to calculate Ɛ_L and N/m* in various samples, which are then listed in Table 1. Table 1 demonstrates that the value of Ɛ_L is greater than the value of Ɛ_∝, which can be attributed to free carrier absorption [30,31].

The complex dielectric constant defines how photons and electrons interact inside a substance. The dielectric constant’s real part represents how much a substance will slow down the speed of light, while the imaginary part shows how energy from an electric field is absorbed by the material due to dipole motion. The loss factor, which is the ratio of the imaginary to the real component, can be determined by analyzing the real and imaginary components of the dielectric constant. The relationship to determine the real and imaginary components of the dielectric constant is described as follows [32]

ε = ε_{1} + i ε_{2}

(8)

ε_{1} = n^{2} - k^{2}

(9)

ε_{2} = 2 n k

(10)

The correlation between the photon energy (hν) and the real (

ε_{1}

) and imaginary (

ε_{2}

) components of the dielectric constant for TiO₂-SWCNTs composites is depicted in Figure 7. The imaginary dielectric loss has smaller values than the real dielectric constant because of the dependence on the constants of n and k. At a lower energy, both the real and imaginary dielectric constants were small and oppositely were significant at the higher energy region. Furthermore, the variation in the dielectric constant versus the photon energy creates peaks in the dielectric spectra, which represent the specific interactions between photons and electrons in the films identified in the

ε_{1}

and

ε_{2}

curves.

Another important fundamental characteristic of the material is its optical conductivity (σ_opt), which is calculated by the equation [25]

σ_{o p t} = \frac{α n c}{4 π}

(11)

where c is the speed of light. Figure 8 displays the curve of the optical conductivity vs. photon energy (hν). High optical conductivity values prove the film’s extremely high photosensitivity. The increasing σ_opt at high photon energies results in the strong absorbance of SWCNTs/TiO₂ composites and may be attributed to electron excitation by photon energy.

The electrical conductivity can be calculated using the following formula [25]:

σ_{e l e c t} = \frac{2 λ σ_{o p t}}{α}

(12)

Figure 8 illustrates the distinct profiles of σ_opt and

σ_{e l e c t}

as the photon energy increases. Also, the optical conduction values are approximately 10¹² times greater than those of the value of electrical conduction.

3.1.2. Nonlinear Optical Analysis

It is recognized that studies of nonlinear optical characteristics can give a comprehensive account of how light interacts in nonlinear media. Third-order nonlinear optical analysis offers the ability to modify the characteristics of light’s transmission through a medium and change the frequency of its color. The nonlinear refractive index, n₂, the linear optical susceptibility, χ⁽¹⁾, and the third order of nonlinear polarizability parameter, χ^(3), can be offered by Miller’s principles as represented by the equations [29]

χ^{(1)} = \frac{(n^{2} - 1)}{4 π}

(13)

χ^{(3)} = A {(χ^{(1)})}^{4} = \frac{A {(n^{2} - 1)}^{4}}{{(4 π)}^{4}}

(14)

n_{2} = \frac{12 χ^{(3)}}{n}

(15)

where A is a constant, A = 1.7 × 10⁻¹⁰. The variations in n₂, χ⁽¹⁾, and χ⁽³⁾ for all produced TiO₂-SWCNT films at various SWCNT concentrations are shown in Figure 9. The value of nonlinear optical parameters n₂, χ⁽¹⁾, and χ⁽³⁾ was found to decrease with the addition of SWCNTs. While the nonlinear refractive index values vary from 0.64 × 10⁻¹⁰ to 2.24 × 10⁻¹⁰ esu, the third order of nonlinear polarizability values range from 0.58 × 10⁻¹¹ to 1.74 × 10⁻¹¹ esu. The results confirm that TiO₂-SWCNTs films are appropriate for an array of optical switching devices.

3.2. X-Ray Diffraction Analysis

Figure 10 displays the diffraction spectra of both the pure TiO₂ and SWCNTs/TiO₂ composites. The XRD pattern of the pure TiO₂ film reveals peaks at 2θ values of 25.3°, 37.7°, 38.5°, 48.0°, 52.8°, 55.0°, and 62.6°. These peaks are assigned to the crystal planes of the tetragonal anatase phase, which are (101), (004), (112), (200), (105), (211), and (213) [24]. However, SWCNT-related peaks were located at three major angles assigned at 26.04, 44.12, and 53.81, corresponding to the (0 0 2), (1 0 0), and (0 0 4) planes, as detailed in previous studies [33,34]. The SWCNT addition to TiO₂ demonstrates that the plane (1 0 1) of the TiO₂ phase overlaps with (0 0 2) of SWCNTs, and the TiO₂ particles are still in their pristine phase in the SWCNTs-TiO₂ composites. Moreover, the intensity of the samples’ XRD peaks indicates that the formed nanoparticles are polycrystalline [35]. The crystallite’s size can be determined using the Scherrer equation [36].

D = \frac{0.9 λ}{β c o s θ}

(16)

where D is the crystallite’s grain size, λ is the X-ray wavelength, β is the broadening of diffraction estimated at half the maximum intensity, and θ is the angle of diffraction. From this relationship, we note that the larger the crystallite sizes, the sharper and narrower the peak would be. The variation in the size of the grains decreases with the SWCNT concentration (V.%), as shown in Table 3. The crystallite size decreases from 39.6 nm for pure TiO₂ to 36.78 for (20 V.%) SWCNTs-TiO₂ composites. This change in the grain size can be explained by the fact that carbon nanotubes were immobilized on TiO₂ grains using the acid groups on the SWCNTs and they do not form a new particle.

3.3. Photocatalytic Activity Tests

The photocatalytic degradation of MB dye by the SWCNTs/TiO₂ composites was used for the self-clearing procedure. The process is based on SWCNTs-TiO₂ composites as semiconductor photocatalysts immersed in aqueous MB solution and then exposed to UV radiation. The transfer of electrons in the conduction band, the holes in the valance band, and the formation of the radicals (^•O₂⁻) and (^•OH) were explained by several studies [37,38,39]. Figure 11 presents the UV–vis absorption spectra of 3 mg/mL MB in water with the pure TiO₂ film and SWCNTs/TiO₂ composite films with different amounts of SWCNTs on TiO₂. It is commonly recognized that the most frequently seen absorption peak in the MB solution, which is indicative of the MB dye, is situated at 664 nm [38]. The optical absorption spectra clearly demonstrated that the intensity of the characteristic absorption peak decreases with the increasing SWCNT concentration, showing an improvement in the photocatalytic activity towards the degradation of MB in water.

The photocatalytic efficiency of the TiO₂ films coated with different amounts of SWCNTs is illustrated in Figure 12. It can be seen that small amounts of SWCNTs in titanium dioxide (5%) can improve their photocatalytic activity under the UV range. This figure indeed shows that the photocatalytic efficiency increases from 13.63% to 31.93 after adding 20% (V.%) of SWCNTs/TiO₂ composites. The photocatalytic efficiency increased with SWCNT loading up to 10% but showed no significant improvement at 20% loading. Higher concentrations of SWCNTs cause more light scattering, which lowers the effective light penetration into the TiO₂ matrix and accounts for this discovery. Additionally, excess SWCNTs could decrease the overall efficiency by serving as recombination sites for photogenerated charge carriers. Because it balances better light absorption, increased charge separation, and reduced recombination losses, 10% SWCNT loading is therefore the ideal concentration.

3.4. Mechanism of the Photocatalytic Activity of SWCNTs/TiO₂ Composites

Several studies of photocatalytic activity using CNTs/TiO₂ confirm that the absorption effect is not the mechanism of degradation of the MB solution but the relation between SWCNTs and TiO₂ particles, which play a crucial role in the electron transfer. An SWCNT is a molecule with a nano-cylinder structure, which can provide free carrier charges at room temperature and the electron can move freely through the structure. The photocatalytic activity of SWCNTs/TiO₂ composites is depicted in Figure 13, which illustrates the schematic mechanism based on a previous work on the photocatalytic activity of TiO₂ [37,38,39]. Using the last property of SWCNTs could absorb the photo-induced electron into the conduction band of the TiO₂ nanoparticles by UV irradiation. Meanwhile, the electron in the conduction band reacts with molecular oxygen to produce superoxide radical anions (^•O₂⁻). The photogenerated holes in the valence band migrate to the surface of TiO₂ and then react with adsorbed water molecules, forming hydroxyl radicals (^•OH). As we are aware, the degradation of the organic compound is based on the formation of both the radical groups (superoxide radical ion ^•O₂⁻ and hydroxyl radical ^•OH) [39,40,41]. Consequently, the mechanism of SWCNTs/TiO₂ composites may be explained by the following equations:

SWCNT/TiO₂ → SWCNT⁺/TiO₂⁻

(17)

SWCNT⁺/TiO₂⁻ + O₂ → SWCNT⁺/TiO₂ + ^•O₂⁻

(18)

SWCNT⁺/TiO₂ → SWCNT/TiO₂⁺

(19)

SWCNT/TiO₂⁺ + H₂O → SWCNT/TiO₂ + H⁺ + ^•OH

(20)

4. Conclusions

This work addresses the issues of the deposition at different concentrations of SWCNTs (5, 10, 20) into TiO₂ films by using the sol–gel spin-coating method. The XRD results confirm the presence of SWCNTs in TiO₂ thin films, and the crystallite size increases in terms of the SWCNT content. The linear and nonlinear optical characteristics of TiO₂-SWCNTs films of varied concentrations of SWCNTs are examined. The transition type of films is an indirect permitted transition with mean values equal to 3.23, 3.43, 3.4, and 3.36 eV for TiO₂, TiO₂-5% SWCNTs, TiO₂-10% SWCNTs, and TiO₂-20% SWCNTs, respectively. These values enabled the utilization of the produced materials for organic solar cell devices. The refractive index was in the range from 2.6 to 7, indicating that they can be employed in a wide range of optical devices. The values of the dielectric constant are larger than the values of the dielectric loss for the analyzed media. Additionally, the nonlinear characteristics were assessed, and it was shown that when the SWCNT concentrations increased, the susceptibility (3) varied from 0.58 × 10⁻¹¹ to 1.74 × 10⁻¹¹ esu while the n2 values changed from 0.64 × 10⁻¹⁰ to 2.24 × 10⁻¹⁰ esu. It was found that TiO₂-SWCNTs composites enhanced the photocatalytic activity. Indeed, the photocatalytic efficiency increases from 13.63% for pureTiO₂ film to 31.93 for 20% (V.%) SWCNTs/TiO₂ composites. Even though SWCNTs/TiO₂ composites show great promise for improving photocatalytic efficiency, their use in real-world environments presents several challenges, including the materials’ long-term stability, the economic viability of synthesizing these composites, the viability of large-scale production, and reproducibility in manufacturing processes while maintaining cost-effectiveness remains a major obstacle. Addressing these challenges, SWCNTs/TiO₂ composites could be integrated with other advanced materials, such as metal–organic frameworks (MOFs) or conducting polymers, to further enhance their photocatalytic efficiency and selectivity.

Funding

This research received no external funding.

Data Availability Statement

All relevant data are available within the article.

Acknowledgments

The author would like to thank Haythem Gamoudi, Khouloud Sahli and E.F.M.El-Zaidia for their help.

Conflicts of Interest

The author declares no conflicts of interest.

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Figure 1. Transmittance and reflectance spectra of TiO₂ and for SWCNTs/TiO₂ composites for different percentages, 5%, 10%, 20%, of SWCNTs.

Figure 2. The absorption coefficient, α, spectra of TiO₂ and for 5%, 10%, 20% SWCNTs/TiO₂ composites.

Figure 3. (αhν)^1/2 versus energy for (a) TiO₂, (b) TiO₂-(5%) SWCNTs, (c) TiO₂-(10%) SWCNTs, and (d) TiO₂-(20%) SWCNTs.

Figure 4. The spectra of refractive index versus wavelength for pure TiO₂ and TiO₂-SWCNTs composites.

Figure 5. The (n² − 1)⁻¹ vs. (hν)² curve for pure TiO₂ and for 5%, 10%, 20% SWCNTs/TiO₂ composites.

Figure 6. The relation between n² as a function of λ² of TiO₂ and for 5%, 10%, 20% SWCNTsTiO₂.

Figure 7. The variation in (a) real part,

ε_{1}

, (b) imaginary part,

ε_{2}

, of dielectric constant as a function of photon energy for TiO₂ and for 5%, 10%, 20% SWCNTs-TiO₂ composites.

Figure 7. The variation in (a) real part,

ε_{1}

, (b) imaginary part,

ε_{2}

, of dielectric constant as a function of photon energy for TiO₂ and for 5%, 10%, 20% SWCNTs-TiO₂ composites.

Figure 8. The spectra of (a) optical conductivity and (b) electrical conduction of TiO₂ and for 5%, 10%, 20% SWCNTs-TiO₂ composites.

Figure 9. The variation in χ⁽¹⁾, χ⁽³⁾, and n₂ as a function of concentration of SWCNTs.

Figure 10. The XRD patterns of pure TiO₂ and 5%, 10%, 20% SWCNTs-TiO₂ composites.

Figure 11. UV–vis absorption spectra showing the photocatalytic activity of TiO₂ and SWCNTs/TiO₂ composites regarding photocatalytic degradation of MB in water.

Figure 12. The variation in photocatalytic efficiency of SWCNTs-TiO₂ composites.

Figure 13. Mechanism of photocatalytic activity of SWCNTs/TiO₂ composites towards degradation of MB dye.

Table 1. Stoichiometric calculation for preparation of SWCNTs/TiO₂ composites.

Samples	Volume of TiO₂ (mL)	Volume of SWCNTs (mL)
S1 (pure TiO₂)	10	0
S2 (5% SWCNTs)	9.5	0.5
S3 (10% SWCNTs)	9	1
S4 (20% SWCNTs)	8	2

Table 2. The dispersion parameters of pure TiO₂ and for 5%, 10%, 20% of SWCNTs/TiO₂ composites.

	E_g^{ind allowed}		E_d	E_o	ε_oo	ε_L	N/m* ×(10⁴⁷ gm⁻¹cm⁻³)
	E_g1 (eV)	E_ph (meV)	E_d	E_o	ε_oo	ε_L	N/m* ×(10⁴⁷ gm⁻¹cm⁻³)
Pure TiO₂	3.23	325	14.36	2.02	6.96	10.65	5.7
TiO₂ + 5% SWCNTs	3.43	180	12.78	1.96	7.49	10.05	6.16
TiO₂ + 10% SWCNTs	3.4	175	10.67	1.79	6.96	9.65	5.63
TiO₂ + 20% SWCNTs	3.36	118	8.16	1.6	5.88	8.42	5.39

Table 3. The crystallite size L (nm) values are calculated from the Scherrer plot.

	L (nm)
Pure TiO₂	39.6
TiO₂ + 5% SWCNTs	38.32
TiO₂ + 10% SWCNTs	38.25
TiO₂ + 20% SWCNTs	36.78

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TiO₂/SWCNts: Linear and Nonlinear Optical Studies for Environmental Applications

Abstract

1. Introduction