Preparation of Fe₃O₄@SiO₂@N-TiO₂ and Its Application for Photocatalytic Degradation of Methyl Orange in Na₂SO₄ Solution

Abstract

In this paper, Fe₃O₄@SiO₂@TiO₂ and N-doped Fe₃O₄@SiO₂@N-TiO₂ photocatalysts with magnetic core-shell structures were prepared using a multi-step synthesis method. The materials were analyzed using various techniques, such as X-ray diffraction (XRD), ultraviolet-visible diffuse reflectance spectroscopy (DRS), transmission electron microscopy (TEM), field-emission scanning electron microscopy (FESEM), selected-area electron diffraction patterns (SAED), and X-ray photoelectron spectroscopy (XPS). The results indicated that the prepared samples had an anatase structure, and N was successfully doped. Fe₃O₄@SiO₂@TiO₂ and Fe₃O₄@SiO₂@N-TiO₂ with different amounts of nitrogen doping were used for the study of photocatalytic degradation of methyl orange (MO) in pure MO solution, and in MO and Na₂SO₄ (MO-Na₂SO₄) mixed solution, respectively. The average photocatalytic degradation rate of MO in pure MO solution with three different batches each of Fe₃O₄@SiO₂@TiO₂ and Fe₃O₄@SiO₂@N-TiO₂ (3 mL of NH₄OH used for doping) under high-pressure mercury lamp irradiation reached 85.25% ± 2.23% and 95.53% ± 0.53%, respectively. The average photocatalytic degradation rate of MO in the MO-Na₂SO₄ mixed solution with three different batches each of Fe₃O₄@SiO₂@TiO₂ and Fe₃O₄@SiO₂@N-TiO₂ (3 mL of NH₄OH used for doping) under the same irradiation condition reached 90.46% ± 3.33% and 97.79% ± 2.09%, respectively. The results showed that Na₂SO₄ can promote photocatalytic degradation of MO. The experiment of recycling photocatalysts showed that there was still a good degradation effect after five cycles. Finally, the first-order kinetic model and the photocatalytic degradation mechanism were investigated.

1. Introduction

With the rapid development of industrial technology, wastewater and emissions from factories are constantly released into the environment, energy is increasingly scarce today, and organic pollutants are found in natural water bodies [1,2]. Dye wastewater is complex, highly colored, toxic, and difficult to degrade, which can make wastewater treatment more difficult and has a fatal impact on the environment [3]. Usually, physical or chemical methods are used to treat dye wastewater, but the cost is relatively high. Compared with the above methods, semiconductor photocatalytic technology has the advantages of non-pollution, good effect, and simple treatment methods, and has been verified by other researchers [4,5]. Photocatalytic technology is currently an efficient method for treating environmental pollution, and further research is a very meaningful task [6,7]. TiO₂ has stable chemical properties, low cost, high activity, and nontoxicity, making it the most promising photocatalyst in semiconductor photocatalysts [8,9]. However, TiO₂ also has shortcomings, which are mainly manifested in three aspects: Firstly, the recombination rate of photogenerated electron–hole pairs is very fast, resulting in low photocatalytic activity of TiO₂ [10]. Secondly, the bandgap is wide, and the absorption range of the light is very narrow, and it can only absorb the ultraviolet range [10]. Thirdly, it is difficult to quickly separate TiO₂ from solution after photocatalytic degradation, which makes it difficult to recover the photocatalyst. If the photocatalyst cannot be recovered, it will also cause secondary pollution [11]. Therefore, how to improve the bandgap of TiO₂ to broaden the photosensitive range of light and increase the utilization rate of photocatalysts have become the focus of research in the field of photocatalysis. Currently, the main methods include metal ion doping [12,13], non-metallic doping [14,15,16], and compounding with other materials [17]. Therefore, in this paper, N-doped TiO₂ multilayer core-shell structure photocatalysts were designed, and the preparation process of the magnetic photocatalysts Fe₃O₄@SiO₂@TiO₂ and Fe₃O₄@SiO₂@N-TiO₂ was explored experimentally. The samples were characterized by transmission electron microscopy (TEM), X-ray diffraction spectroscopy (XRD), UV-VIS diffuse reflectance spectroscopy (DRS), and X-ray photoelectron spectroscopy (XPS). The photocatalytic degradation experiments of MO were also carried out in a pure MO solution and a MO-Na₂SO₄ mixed solution, respectively. The mechanism of photocatalytic degradation of MO and MO-Na₂SO₄ was meticulously examined.

2. Materials and Methods

2.1. Materials and Reagents

Absolute ethanol (AR 99%), FeCl₃·6H₂O (AR 99%), sodium acetate (CH₃COONa) (AR), ammonia (NH₄OH; AR, 25–28%), tetraethyl orthosilicate (AR 98%), sodium sulphate absolute (Na₂SO₄; AR), and methyl orange (MO, AR) were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). Tetrabutyl titanate (AR 98%) and polyethylene glycol-4000 (AR) were sourced from Shanghai Macklin Biochemical Technology Co., Ltd., located in Shanghai, China. Water used during the experiment was ultrapure water.

2.2. Preparation of Nanocomposite

Fe₃O₄ was prepared using the solvothermal method. Here, 2.7 g of FeCl₃·6H₂O was dissolved in 80 mL of ethylene glycol and stirred magnetically until fully dissolved in a beaker. Then, we poured 2 g of polyethylene glycol-4000 into the above solution and stirred magnetically until it was completely dissolved. Finally, 7.2 g of sodium acetate was poured into a beaker and stirred magnetically until it was dissolved. After complete dissolution, the solution was poured into a reaction kettle and heated at 180 °C for 10 h, then washed 3 times with ethanol, placed in a vacuum drying oven, and heated at 40 °C until completely dried.

Fe₃O₄@SiO₂ was prepared using the sol-gel method. Here, 0.2 g of Fe₃O₄ powder was added into 80 mL of absolute ethanol and ultrasonically dispersed for 30 min until the Fe₃O₄ powder was fully mixed with the absolute ethanol. Next, 20 mL of ultrapure water was added into the above suspension, then 5 mL of ammonia was dropped slowly into the mixture, and the suspension was ultrasonically dispersed and mechanically stirred for 30 min and 30 min, respectively. After that, 4 mL of tetraethyl orthosilicate was dropped slowly into the above suspension, and the mixture was continually mechanically stirred for 6 h. Finally, the solution was magnetically separated by permanent magnets, the upper layer was poured out, and the black magnetic fluid was washed three times with absolute ethanol and placed into the vacuum drying box and dried at 40 °C.

Preparation of Fe₃O₄@SiO₂@TiO₂ (FS-NT (0 mL), where ‘0 mL’ represents the amount of N source in NH₄OH, which was 0 mL) nanomaterials was carried out using the sol-gel method. Here, 7 mL of tetrabutyl titanate was added dropwise into 120 mL of absolute ethanol and ultrasonically dispersed for 10 min. Then, 0.2 g of Fe₃O₄@SiO₂ was added into the above suspension and continued to be ultrasonicated for 20 min. The beaker containing the suspension was then placed in a water bath heated to a temperature of 40 °C, and the suspension was mechanically stirred for 8 h. After the reaction, the solid powder and solution in the beaker were magnetically separated with a magnet. The separated solid powder was washed three times with absolute ethanol, and then the washed powder was dried in a vacuum drying oven at 40 °C for 10 h. After drying, the FS-NT (0 mL) was placed in an atmosphere furnace for annealing. Argon was selected as the protective gas and the annealing temperature was set at 450 °C and the heating time was 3 h.

A batch of Fe₃O₄@SiO₂@N-TiO₂ (FS-NT (2–5 mL), where ‘2–5 mL’ represents the amount of N source in NH₄OH, which was 2, 3, 4, and 5 mL, respectively) doped with different nitrogen contents was prepared using the sol-gel method. FS-NT (2–5 mL) with different nitrogen contents only required changing the amount of NH₄OH added, and the sample preparation process was the same. The preparation of FS-NT (2–5 mL) used the process of preparing FS-NT (3 mL) as an example. Firstly, mixture A (7 mL of tetrabutyl titanate was added into 120 mL of absolute ethanol and dispersed by ultrasound for 10 min, then 0.27 g of Fe₃O₄@SiO₂ was added into the above solution and dispersed by ultrasound for 15 min) and solution B (3 mL of NH₄OH and 2 mL of deionized water were added into 20 mL of absolute ethanol) were prepared. Then, solution B was slowly added dropwise to mixture A. The mixture of A and B was stirred for 7 h. The magnetic separation was carried out with a magnet. The obtained grey–black powder was washed three times with absolute ethanol and then the washed powder was placed in a vacuum drying oven at a drying temperature of 60 °C for 10 h. The dried samples were placed in an atmosphere furnace for annealing. Argon was chosen as the protective gas, with a heating temperature of 450 °C and a heating time of 3 h.

2.3. Characterization

The photocatalytic experimental device was a high-pressure mercury lamp (GGZ300, Shanghai Jiguang, Shanghai, China) with a light intensity of 23 mW/cm². The concentrations of MO dye were quantitatively analyzed using a TU-1950 Beijing Puxi UV-VIS spectrophotometer from Beijing, China, specifically at a peak absorption wavelength of 508 nm, both before and after conducting the photocatalytic tests. Morphological examinations of the samples were conducted using a JSM-7800 field-emission scanning electron microscope from Tokyo, Japan, operating at 3 kV. Additionally, the crystal structures of the samples were detailed through X-ray diffraction analysis using an Empyrean device from Panaco, the Netherlands, employing Cu-Kα radiation, with the 2θ scanning ranging from 10 to 80 degrees, a step length of 0.06, and a scanning speed of 4 degrees per minute. Diffuse reflectance spectra for the samples were recorded on a Shimadzu Solid Spec-3700 UV-VIS-NIR spectrophotometer from Kyoto, Japan, which was coupled with an integrating sphere and operated in a wavelength range of 200–800 nm at ambient temperature. BaSO4 served as the reference standard. XPS measurements were calibrated against the binding energy standard of C 1s at 284.8 eV using a Thermo Scientific ESCALAB 250Xi from Waltham, MA, USA. The total organic carbon (TOC) was measured in a Shimadzu TOC-L from Kyoto, Japan analyzer coupled with an autosampler.

2.4. Photodynamic Activity Test

Here, 20 mg of photocatalyst was added into 10 mL of pure MO solution at 10 mg/L and MO-Na₂SO₄ solution in a petri dish, respectively. After that, the petri dish was placed in a dark environment to reach adsorption–desorption equilibrium. The dish was then irradiated with a high-pressure mercury lamp as a light source. The calculation of the degradation rate of the dye was:

$$\eta \%=\frac{C_0-C_t}{C_0}\times 100\%$$

(1)

where C₀ (mg L⁻¹) is the initial concentration and C_t (mg L⁻¹) is the concentration at time t (min).

3. Results and Discussion

XRD patterns of TiO₂, Fe₃O₄, Fe₃O₄@SiO₂, and FS-NT (0, 2, 3, 4, and 5 mL) are shown in Figure 1. The prepared TiO₂ displayed good crystallinity: the diffraction peaks of TiO₂ were exhibited at 25.2°, 38.7°, 48°, 54°, 55.14°, and 62.5°, corresponding to the (101), (004), (200), (105), (211), and (204) lattice planes of TiO₂ (JCPDS No. 65-3369) [18]. The results suggest that TiO₂ has anatase crystals. The diffraction peaks of Fe₃O₄ were exhibited at 30.1°, 35.5°, 43.1°, 53.4°, 56.9°, and 62.5°, corresponding to the (220), (311), (400), (422), (511), and (440) lattice planes of the magnetite phase (JCPDS No. 02-0387) [19]. Fe₃O₄@SiO₂ maintained the characteristic diffraction peaks of Fe₃O₄ in Figure 1a. XRD patterns of FS-NT (0 mL) are shown in Figure 1a. It can be seen that compared with Fe₃O₄@SiO₂, the peak intensity of Fe₃O₄ in FS-NT decreased due to the thickness of the TiO₂ coating, and the characteristic diffraction peaks of TiO₂ appeared at 2θ = 25.2°, 38.7°, 48.1°, 54.1°, and 62.5°, corresponding to (101), (004), (200), (211), and (204) crystal planes, which indicates that TiO₂ on the surface of FS-NT (0 mL) has anatase crystal TiO₂. The XRD patterns of FS-NT (2–5 mL) are shown in Figure 1b. The intensity of the Fe₃O₄ characteristic diffraction peaks was still high, which suggests that the prepared FS-NT (2–5 mL) can provide a strong magnetic response for the subsequent magnet recovery samples. The characteristic diffraction peaks of TiO₂ appeared at 2θ = 25.2° and 48.1°, corresponding to the (101) and (200) planes of TiO₂, respectively. Compared with FS-NT (0 mL), the diffraction peaks of FS-NT (2 and 3 mL) shifted slightly toward the small-angle direction. The reason for this is that N ions are larger than O ions, and both substitutional and interstitial N ions can result in an increase in the lattice parameters of TiO₂ [20]. The possible reason for the insignificant shift of FS-NT (4 and 5 mL) is that the addition of 4 or 5 mL of NH₄OH can increase the pH of the solution and accelerate the hydrolysis of tetraethyl titanate [21], so that N ions do not or rarely enter into the lattice structure.

The TEM micrographs of FS-NT (0 mL) and FS-NT (3 mL) are shown in Figure 2a,b, where it can be seen that the nanocomposite samples clearly have a core-shell structure. The HRTEM image of FS-NT (0 mL) is shown in Figure 2c. The observed lattice spacings of 0.355 nm could be indexed to the (101) plane of TiO₂ [22], whereas those of 0.176 nm corresponded to the (422) plane of Fe₃O₄ [23]. The HRTEM image of FS-NT (3 mL) is shown in Figure 2d. The observed lattice spacings of 0.355 nm could be indexed to the (101) plane of TiO₂ [22], whereas those of 0.263 nm corresponded to the (311) plane of Fe₃O₄ [23]. Moreover, the corresponding selected-area electron diffraction (SAED) pattern (Figure 2e,f) displayed diffuse diffraction rings that were well indexed to the characteristic planes of TiO₂ and Fe₃O₄. The lattice spacings of (101) and (200) planes of FS-NT (3 mL) in Figure 2f were larger than those of FS-NT (0 mL) in Figure 2e, which may be due to the fact that N ions were larger than O ions in the lattice structure. The results are consistent with those of XRD.

Figure 3a,b show the UV-VIS DRS spectra of FS-NT (0 mL) and FS-NT (2~5 mL), respectively. The maximum of titania absorption located at 320–367 nm could be attributed to isolated Ti⁴⁺ sites in octahedral coordination [24] related to full connectivity of Ti–O–Ti linkages in Figure 3a. In Figure 3b, the maximum of titania absorption located at 336–378 nm was observed, and the UV-VIS DRS spectra of FS-NT (2~5 mL) showed a red-shifted onset of the low-energy edge, possibly due to the influence of a small amount of N. The prepared samples had strong absorption in the region at 400–800 nm due to the presence of Fe₃O₄ [18]. The DRS were converted to absorption coefficients, F(R), via the Kubelka–Munk function. The energy bandgap (E_g) of the samples was determined according to the Tauc method from the plot of (F(R)hv)² versus hv by Equation (2):

$$\alpha hv=C{(h\nu -{{\rm E}}_g)}^2$$

(2)

The bandgaps are shown in Figure 3c,d. The values of bandgaps of FS-NT (0 mL), FS-NT (2 mL), FS-NT (3 mL), FS-NT (4 mL), and FS-NT (5 mL) were 2.92 eV, 2.76 eV, 2.67 eV, 2.6 eV, and 2.52 eV, respectively. Compared with FS-NT (0 mL), FS-NT (2–5 mL) had a smaller bandgap, and although the light absorption range was in the ultraviolet range, it was still expanded. The reason for this is that N atoms in FS-NT (2–5 mL) replaced some O atoms in the lattice of TiO₂ and formed a O-Ti-N bond, which created an additional energy level and further reduced the bandgap width. This result is consistent with the literature [25,26].

The chemical state of FS-NT (0 mL) and FS-NT (3 mL) was investigated using XPS analysis, as shown in Figure 4. Figure 4a,b present the N 1s spectra of FS-NT (0 mL) and FS-NT (3 mL), respectively. In Figure 4a,b, binding energy of 401.55 eV was attributed to the surface molecularly chemisorbed dinitrogen [27], while binding energy of 400 eV may be attributed to the presence of NH₄OH (N-H) [28], possibly due to the presence of NH₄OH in the Fe₃O₄@SiO₂ residual during the preparation process. In Figure 4b, compared with FS-NT (0 mL), two additional peaks of binding energy were observed at 396.8eV and 405.4eV, respectively. N 1s peaks at 396.8 eV were attributed to substitutional nitrogen (O-Ti-N) [27,29,30], while a binding energy of 405.4eV may be attributed to interstitial nitrogen [29,31,32]. The results are consistent with those of XRD and SAED. Figure 4c shows the Ti 2p XPS spectra of FS-NT (0 mL). The binding energies at 458.8 and 464.5 eV were associated with Ti⁴⁺ 2p_3/2 and Ti⁴⁺ 2p_1/2, respectively, as confirmed by the spin orbit splitting of 5.7 eV [33]. Therefore, it could be inferred that titanium ion was in the form of Ti⁴⁺, and Ti³⁺ did not exist in the FS-NT. Figure 4d shows the binding energies of 458.6 and 464.3 eV corresponding to Ti⁴⁺ 2p_3/2 and Ti⁴⁺ 2p_1/2 for FS-NT (3 mL), respectively. It can be clearly seen that Ti 2p peak values of FS-NT (3 mL) were smaller than those of FS-NT (0 mL), which may be due to N substituting for O, causing a decrease in the binding energy. The derived electronic interaction between Ti and N anions resulted in partial electron transfer from N to Ti. At the same time, the electron density of Ti was also increasing due to the fact that the electronegative energy of N was less than that of O. This revealed that N was incorporated into TiO₂ and replaced O [34]. In the O 1s XPS spectra, the presence of Ti-O and surface-adsorbed O₂ or OH^– can be confirmed by the deconvoluted peaks at binding energies of 530.2 and 532.7 eV in Figure 4e,f [34,35], respectively.

The photocatalytic activity of the samples was studied by detecting the UV-VIS spectra of MO dye after the photocatalytic degradation reaction under the same conditions. Figure 5a shows the UV-VIS absorption spectra of MO before (Co) and after photocatalytic degradation by FS-NT (0 and 2–5 mL) in pure MO solution. The results indicate that the photocatalytic effect was best when 3 mL of NH₄OH was used as the nitrogen-doping source. Figure 5b shows UV-VIS absorption spectra of MO with an initial concentration of 10 mg L⁻¹ under different illumination times during the photocatalytic degradation of MO using a random batch of FS-NT (3 mL). Figure 5c shows the average degradation rate of MO degraded by three batches of FS-NT (0 and 2–5 mL), and the experimental results of the three different batches were averaged and standard errors were added. In a dark environment, dye in water was removed by adsorption, and the removal rates of MO by FS-NT (0 and 2–5 mL) were 10.05%, 9.34%, 10.91%, 8.33%, and 7.84%, respectively. The results showed that the average degradation rate of MO degraded by three different batches of FS-NT (3 mL) reached 95.53% ± 0.53% within 32 min under irradiation conditions, and this degradation effect was better than that of other samples. The results suggest that proper non-metallic doping can improve the photocatalytic ability of TiO₂. The photocatalytic activity of some related materials for MO is presented in

Table 1. The photocatalytic activity of related materials [36,37,38].

Material	Initial Concentration of MO (mg/L)	Light Source	Amount of Catalyst per mL (mg)	Degradation Time (min) and Degradation Rate	Cyclic Degradation Rate
ATT-SnO2-TiO2	20	High-pressure mercury lamp	1	30 (99%)	non
ZnO/TiO2	16	High-pressure mercury lamp	0.3	100 (98%)	non
Pt-TiO2/zeolite	20	High-pressure mercury lamp	2	90 (99%)	non
FS-NT (3 mL)	10	High-pressure mercury lamp	2	32 (95.53% ± 0.53%)	92%

. Although there are differences in the materials [36,37,38], the photocatalytic degradation rate of FS-NT (3 mL) was commendable. The degradation effect of FS-NT (3 mL) in 32 min was favorable. In particular, the degradation rate was still 92% in recycling.

The recovered FS-NT (0 and 3 mL) was used to degrade MO under the same experimental conditions. Figure 6 shows the photocatalytic activity of the recycled FS-NT (0 and 3 mL). The first to fifth cycle experiments corresponded to horizontal coordinates of 0–32 min, 32–64 min, 64–96 min, 96–128 min, and 128–160 min, respectively. The degradation rates of MO degraded by a batch of FS-NT (0 mL) recovered for the five cycles were 89.25%, 80.68%, 75.48%, 84.47%, and 86.30%, as shown in Figure 6a, respectively, and the average degradation rate was 83.24%. The degradation rates of MO degraded by a batch of FS-NT (3 mL) recovered for the five cycles were 94.44%, 91.92%, 91.91%, 90.09%, and 92.20%, as shown in Figure 6b, respectively, and the average degradation rate was 92.11% for the five cycles. The results indicate that the FS-NT (3 mL) photocatalyst exhibited better degradation performance through magnetic recovery. In the second, third, and fourth cycle experiments, the possible reason for the decrease in the degradation rate was the production of insoluble intermediates on the surface of the photocatalyst during the cyclic degradation process [18]. The insoluble intermediates hindered the contact between the photocatalyst and the dye and reduced the absorption of the light by the photocatalyst surface, which resulted in a decrease in photocatalytic activity. In order to improve the degradation effect of cycle test, at the end of the third cycle of the experiment, the photocatalyst was self-cleaning. The self-cleaning process was as follows: the recovered photocatalyst was placed in deionized water and illuminated with a high-pressure mercury lamp for about 1 h, then washed by deionized water and dried.

The UV-VIS absorption spectra of MO degraded by FS-NT (0 and 2–5 mL) in MO-Na₂SO₄ mixed solution are shown in Figure 7a. The results suggest that the photocatalytic degradation effect of FS-NT (3 mL) was the best. Figure 7b shows UV-VIS absorption spectra of MO degraded by a random batch of FS-NT (3 mL) in MO-Na₂SO₄ mixed solution at different degradation times. Figure 7c shows the average degradation rate of MO degraded by three different batches of FS-NT (0 and 2–5 mL) in MO-Na₂SO₄ mixed solution, and the experimental results of the three different batches were averaged and standard errors were added. In a dark environment, the removal rates of MO-Na₂SO₄ by FS-NT (0 and 2–5 mL) were 10.51%, 10.74%, 11.42%, 8.83%, and 8.53%, respectively. The results showed that the average degradation rate of MO using three different batches of FS-NT (3 mL) in MO-Na₂SO₄ mixed solution reached 97.79% ± 2.09% within 32 min under irradiation conditions. The results indicate that the FS-NT (3 mL) photocatalyst exhibited better degradation performance in the MO-Na₂SO₄ mixed solution. It was found that when FS-NT has an appropriate amount of N, Na₂SO₄ can promote photocatalytic degradation. The possible reason is that Na₂SO₄ can improve the separation efficiency of photogenerated electron–hole pairs and promote the formation of free radicals with high activity [39]. The pH value of the MO solution was 4.0, and the pH value of the MO-Na₂SO₄ mixed solution was 6.22. MO is an anionic molecule that exhibits higher adsorption efficiency on the photocatalyst at lower pH values, which is very beneficial to photocatalytic degradation. After the addition of Na₂SO₄, the increase in pH was not conducive to adsorption, but SO₄^2– reacted with h⁺ to form SO₄^–·, which enhanced the photocatalytic activity of the photocatalyst and improved the photocatalytic degradation effect [39,40].

In order to study the effect of photocatalyst recycling in the MO-Na₂SO₄ mixed solution, the photocatalytic degradation of MO degraded by recycled FS-NT (0 and 3 mL) was studied. The degradation rate of MO using a batch of recycled FS-NT (0 mL) in the MO-Na₂SO₄ mixed solution is shown in Figure 8a, and the average degradation rate of MO for the five-cycle experiment was 91.38%. Figure 8b shows the degradation rate of MO by a batch of FS-NT (3 mL) recovered in the MO-Na₂SO₄ mixed solution, and the average degradation rate was 98.78%. It was found that in the MO-Na₂SO₄ mixed solution, the recovered FS-NT (3 mL) showed better photocatalytic degradation than recovered FS-NT (0 mL). The photocatalytic degradation effect of the recycled FS-NT (3 mL) and the recycled FS-NT (0 mL) in the MO-Na₂SO₄ mixed solution was better than that in the pure MO solution, respectively. The results indicate that the photocatalytic activity of FS-NT (3 mL) was very stable.

The first-order kinetic model is given by the following:

$$\ln (\frac{C_0}{C_t})=kt$$

(3)

where t (minutes) is the reaction time, k is the rate constant, and C₀ (mg L⁻¹) and C_t (mg L⁻¹) are the same as those in Equation (1).

As shown in Figure 9, the kinetic curves were highly linear, and the correlation coefficients (R²) was close to 1. This means that the photocatalytic reaction followed the first-order reaction kinetic model. The initial rate constant k was obtained using experimental data up to 24 min of simulated irradiation because subsequent data seemed to deviate from the linear plot of ln(C₀/C_t) vs. t, owing to the decreasing MO concentration in the bulk solution. The rate constant k of FS-NT (0 mL) and FS-NT (3 mL) in pure MO solution were calculated to be 0.0575 and 0.08114 min⁻¹, respectively. By comparing the k values, it was evident that N doping could improve photocatalytic activity. The corresponding degradation rate constant k values of FS-NT (0 mL) and FS-NT (3 mL) in the MO-Na₂SO₄ mixed solution were calculated to be 0.07334 and 0.08209 min⁻¹, respectively. The results indicate that FS-NT (3 mL) showed better performance in the MO-Na₂SO₄ mixed solution. Comparing the k values of the MO and MO-Na₂SO₄ tests, it was seen that Na₂SO₄ could accelerate the reaction rate.

Figure 10 shows the schematic diagram of the photocatalytic degradation mechanism of MO in pure MO solution. Photogenerated holes (h⁺) can oxidize OH^– and H₂O molecules to produce ·OH and ·O₂^–. Photogenerated electrons (e⁻) can indeed react with dissolved oxygen in water, leading to the formation of superoxide radicals ·O₂^–, which can react with H₂O to form ·OH [41]. As shown in Figure 10, doping with appropriate N content may introduce lattice defects and oxygen vacancies in the photocatalyst. These lattice defects and oxygen vacancies can enhance the visible light absorption ability of photocatalysts, which can improve the photocatalytic degradation effect [42]. The TOC of MO was 5.395 mg/L in pure MO solution, 3.425 mg/L after degradation by FS-NT (0 mL) in pure MO solution, and 5.089 mg/L after degradation by FS-NT (3 mL) in pure MO solution. Combined with the results of Figure 5, the results suggest that FS-NT (3 mL) has good decolorization ability, but its ability to completely degrade MO is weak.

Figure 11 shows the schematic diagram of the photocatalytic degradation mechanism of MO in the MO-Na₂SO₄ mixed solution. Under high-pressure mercury lamp irradiation, on the one hand, ·OH and ·O₂^– were produced, and on the other hand, SO₄^2– was adsorbed on the surface of the photocatalyst, and SO₄^2– reacted with h⁺ to produce SO₄^–·, as shown in Figure 11. Thus, SO₄^–· and ·OH jointly participated in the redox reaction. Dye will be oxidized by free radicals in solution or on the surface of the photocatalyst and SO₄^–·, which will increase the reaction rate [39]. The synergistic effect of N doping and SO₄^–· further enhanced the photocatalytic degradation effect in the MO-Na₂SO₄ mixed solution, as shown in Figure 11.

4. Conclusions

Fe₃O₄@SiO₂@TiO₂ (FS-NT (0 mL)) and N-doped Fe₃O₄@SiO₂@N-TiO₂ (FS-NT (2–5 mL)) photocatalysts with magnetic core-shell structures were prepared using a multi-step synthesis method. The prepared materials were characterized by DRS, XRD, FESEM, XPS, TEM, and SAED. The results of the characterizations showed that the prepared samples had an anatase structure, and N was successfully doped. FS-NT (0 mL) and FS-NT (2–5 mL) with different amounts of nitrogen doping were used for the study of photocatalytic degradation of methyl orange (MO) in a pure MO solution and a MO-Na₂SO₄ mixed solution, respectively. Under high-pressure mercury lamp irradiation, the average photocatalytic degradation rate of MO in the pure MO solution using three different batches each of FS-NT (0 mL) and FS-NT (3 mL) for the first time reached 85.25% ± 2.23% and 95.53% ± 0.53%, respectively. The average photocatalytic degradation rate of MO in the MO-Na₂SO₄ mixed solution using three different batches each of FS-NT (0 mL) and FS-NT (3 mL) for the first time under the same irradiation conditions reached 90.46% ± 3.33% and 97.79% ± 2.09%, respectively. The results showed that Na₂SO₄ can promote photocatalytic degradation of MO by FS-NT (0 mL) and FS-NT (3 mL). The reason for this may be that SO₄⁻· was produced by the interaction with h⁺, and SO₄⁻· can degrade MO. The experiment of recycling photocatalysts showed that there was still a good degradation effect after five cycles. The results of the recycle experiment indicated that the FS-NT (3 mL) photocatalyst exhibited better degradation performance in the MO solution and MO-Na₂SO₄ mixed solution, respectively. Finally, the first-order kinetic model and the photocatalytic degradation mechanism showed that the synergistic effects of N doping and SO₄^–· can enhance the photocatalytic degradation effect of MO in the MO-Na₂SO₄ mixed solution. The FS-NT photocatalyst can be magnetically recycled and reused without pollution to the environment; thus, it has broad development prospects in wastewater treatment.