The Degradation of Sulfamethoxazole via the Fe²⁺/Ultraviolet/Sodium Percarbonate Advanced Oxidation Process: Performance, Mechanism, and Back-Propagate–Artificial Neural Network Prediction Model

Abstract

The degradation of sulfamethoxazole (SMX) via the Fe²⁺/Ultraviolet (UV)/sodium percarbonate (SPC) system was comprehensively investigated in this study, including the performance optimization, degradation mechanism, and predicting models. The degradation condition of SMX was optimized, and it was found that appropriate amounts of $C_{{\mathrm{Fe}}^{2+}}$ (10~30 μM) and C_SPC (10 μM) under an acidic condition (pH = 4~6) were in favor of a higher degradation rate. According to probe compound experiments, it was considerable that $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$ was the primary and subordinate free radical in SMX degradation, and $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ maintained two times more than that of $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$, especially under acidic conditions. The UV direct photolysis and other active intermediates were also responsible for the SMX degradation. These active intermediates were produced via the Fe²⁺/UV/SPC system, involving ${\bullet \mathrm{HO}}_2$, ${\mathrm{HCO}}_4^{-}$, $\bullet {\mathrm{O}}_{2 }^{-}$, or ¹O₂. Furthermore, when typical anions co-existed, the degradation of SMX was negatively influenced, owing to ${\mathrm{HCO}}_3^{-}$ and ${\mathrm{CO}}_3^{2-}$ possibly consuming $\bullet \mathrm{OH}$ or H₂O₂ to compete with SMX. In addition, the prediction model was successfully established via the back-propagate artificial neural network (BP-ANN) method. The degradation rate of SMX was well forecasted via the Back-Propagate–Artificial Neural Network (BP-ANN) model, which was expressed as ${\mathrm{Y}}_{\mathrm{pre}}=\tanh (\tanh ({\mathrm{x}}_{\mathrm{i}}{\mathrm{W}}^{\mathrm{ih}}){\mathrm{W}}^{\mathrm{ho}})$. The BP-ANN model reflected the relative importance of influence factors well, which was pH > t > $C_{{\mathrm{Fe}}^{2+}}\approx C_{\mathrm{SPC}}$. Compared to the response surface method Box–Behnken design (RSM-BBD) model (R² = 0.9765, relative error = 3.08%), the BP-ANN model showed higher prediction accuracy (R² = 0.9971) and lower error (1.17%) in SMX degradation via the Fe²⁺/UV/SPC system. These findings help us to understand, in-depth, the degradation mechanism of SMX; meanwhile, they are conducive to promoting the development of the Fe²⁺/UV/SPC system in SMX degradation, especially in some practical engineering cases.

1. Introduction

In recent years, several pharmaceuticals and personal care products (PPCPs) have been frequently observed in the aqueous environment, including antibiotic drugs [1], cosmetics [2], fragrances [3], and some chemicals [4], and these products were widely used for different purposes in a large volume of consumption. Commonly, PPCPs enter into the environment via different anthropogenic activities, such as landfill leachate, sewage discharge, or livestock breeding [5]. As typical sulfonamide antibiotic drugs (SAs) in PPCPs, sulfamethoxazole (SMX) was reported with a broad spectrum of antibacterial action, which was helpful in delaying bacterial regeneration and growth by inhibiting the formation of folate [5]. The residual SMX might penetrate into the food chain to possibly discharge into surface water resources. In China, SMX had a high detection rate of 50%~60% in the aqueous environment; meanwhile, its detecting concentration in sewage wastewater, surface water, and drinking water reached 100~2500 ng/L, 60~150 ng/L, and 12 ng/L, respectively [6]. Thus, the presence of SMX in the aqueous environment might engender a threat to human and ecological health by inducing undesirable influences due to its continuous exposure, giving rise to unexpected consequences or effects according to the characteristics of pseudo-persistence and poor biodegradation. Long-term exposure to SMX would produce some toxic effects on human beings, such as vomiting, coma, or acute pulmonary edema, or it may also affect the kidneys and reproductive system [7,8]. In addition, the accumulation of SMX in the aqueous environment selectively acted on bacteria; this probably developed the effect of bacterial resistance and cross-resistance among different types of antibiotics, finally becoming a menace to human and ecological security [9,10]. Owing to insufficient knowledge in terms of the toxicity, effects, and behaviors of SMX, the study of appropriate degradation technologies is expected to rapidly develop over the next decades.

SMX is hard to remove via traditional technologies due to its stable chemical structure (Figure 1, C₁₀H₁₁N₃O₃S). In recent years, advanced oxidation processes (AOPs) have attracted increasing attention, with many SMX treatment technologies resulting in the advantages of fast degradation speeds and even the mineralization of organic matter [11]. During various AOPs for degrading SMX, oxidation via the Fenton process or by using percarbonate was performed and was recommended due to great application prospects, low investment costs, and easy operation. Commonly, this was realized by free radicals like $\bullet \mathrm{HO}$, which were produced via the catalyzing reaction of H₂O₂ and Fe²⁺ [12]. To improve the degradation efficiency, UV light was introduced into the Fenton process, namely, photo-Fenton technology [13]. However, for security concerns, H₂O₂ was not conducive to transportation and storage during practical application, which limited the development and application of Fenton or photo-Fenton on SMX degradation. Compared to H₂O₂ liquid, sodium percarbonate (SPC, 2Na₂CO₃·3H₂O₂) could be used as a dry carrier of H₂O₂ to decrease the security risks [14]; meanwhile, it was applied in a wider pH range of 4~8 [15]. It was reported that SPC was hopeful in replacing H₂O₂ to form the Fe²⁺/UV/SPC system [16], guaranteeing the degradation performance of organic pollutants in a wider pH range via the photo-Fenton process on degrading SMX in water treatment [17] or wastewater treatment [18]. To the best of our knowledge, there has been a limited number of papers studying SMX degradation via the Fe²⁺/UV/SPC process from the perspective of the oxidation mechanism and performance prediction. Especially during practical scenarios of SMX degradation, studying both parameter optimization and the free radical contributions of the Fe²⁺/UV/SPC process was inadequate, and the influence of typical inorganic ions (in natural water) on the treating performance has also not been well understood. Moreover, when SMX was not easily detected in some engineering scenarios, how to quickly obtain the degradation performance via the Fe²⁺/UV/SPC process using the prediction model needs to be further examined.

This study systematically investigated the SMX degradation by the Fe²⁺/UV/SPC process. The primary objectives of this research are to (1) assess the degradation efficiency of SMX with various operation parameters by kinetic analysis; (2) identify the contribution of primary free radicals by the competitive dynamics method to analyze the degradation mechanism; (3) evaluate the negative effect of typical anions on the degradation performance; (4) construct the prediction model of SMX degradation via two methods to compare the feasibility and accuracy, like RSM-BBD and BP-ANN.

2. Materials and Methods

2.1. Chemicals and Materials

The chemicals used in this study were given as follows, and the corresponding supplier information is exhibited in Table S1. Specifically, they are sulfamethoxazole (Na₂S₂O₄), sodium percarbonate (SPC, Na₂CO₃·1.5H₂O₂), ferrous sulfate (FeSO₄·7H₂O), sodium carbonate (Na₂CO₃), nitrobenzene (NB, C₆H₅NO₂), tert-Butanol (TBA, (CH₃)₃COH), sodium thiosulfate (Na₂S₂O₃), hydrochloric acid (HCl), sodium hydroxide (NaOH), potassium iodide (KI), potassium iodate (KIO₃), sodium bicarbonate (NaHCO₃), anhydrous sodium sulfate (Na₂SO₄), sodium thiosulfate (Na₂S₂O₃), sodium tetraborate (Na₂B₄O₇·5H₂O), sodium chloride (NaCl), phenol (PhOH, C₆H₆O), methanol (CH₃OH), and acetonitrile (CH₃CN). All the reagents were of analytic grade quality or higher and were used without further purification. The following angents were obtained from Shanghai Macklin Biochemical Technology Co., Ltd. (Shanghai, China), such as, FeSO₄·7H₂O, NB, and KIO₃. Moreover, SMX, SPC, PhOH, and KI were obtained from Shanghai Aladdin Biochemical Technology Co., Ltd. (Shanghai, China). Na₂SO₄ and TBA were obtained from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China), meanwhile, HCl, CH₃OH, and CH₃CN were purchased from Sigma-Aldrich (Shanghai) Trading Co., Ltd. NaOH, Na₂CO₃, and NaHCO₃ were achieved from Guangfu Technology Development Co., Ltd. (Tianjin, China). In addition, Na₂S₂O₃, NaCl, and Na₂B₄O₇·5H₂O were obtained from Zigaoxin Chemical Co., Ltd. (Shandong, China).

All solutions were prepared with ultra-high purity water from a Milli-Q system (PURELAB flex, Veolia, UK, resistance of 18.2 MΩ⋅cm). The SMX stock solution (10 mM) was prepared with ultrapure water without any organic co-solvent involvement, and constant stirring at room temperature was performed until complete dissolution. The stock solution of SPC and Fe²⁺ was separately prepared by dissolving Na₂CO₃·1.5H₂O₂ and FeSO₄·7H₂O, respectively.

2.2. Experimental Procedures

The SMX degradation experiments were carried out by a UV excitation device, shown in Figure 2. The UV excitation device consists of four parts: a closed photo-reactor, low-pressure mercury lamp (254 nm, 8 W), magnetic stirrer and rotor, and crystallizing disk (oxidation reactor). Turn on the UV lamp in advance to preheat and ensure uniform radiation, and add 100 mL SMX solution into the oxidation reactor. The initial pH of SMX solution was 5.2, and the pH was adjusted to 4~9 by NaOH (0.1 M) or HCl (0.1 M) whenever necessary. The calibration curve of the SMX solution is given in Figure S1. Moreover, Fe²⁺ and SPC were added concurrently to trigger the reaction under magnetic stirring conditions, and the sample (1 mL) was packed into a brown liquid phase vial for testing. If necessary, add excessive free radical inhibitors (Na₂S₂O₃, 2 mM) to stop the reaction. The vials were then placed within and analyzed immediately by the HPLC (Acquity UPLC, waters, Milford, MA, USA). We repeated all experiments and took samples at least three times.

During the degradation performance experiments, we diluted SMX stock solution into 10 μM and set the amount of ${\mathrm{Fe}}^{2+}$ and SPC to 20 μM and 10 μM, respectively. During the optimization experiments, we set the dosage of Fe²⁺ or SPC to 10~40 μM or adjusted the pH of SMX solution to 4~9. During the experiments on degradation mechanism, we selected TBA and PhOH as two probe compounds of free radical; their concentration was set as 2 mM. The excessive TBA or/and PhOH were added to SMX solution and then mixed with ${\mathrm{Fe}}^{2+}$ and SPC under UV irradiation to analyze the major components of free radicals. In addition, SMX, NB, and the mixture of PhOH and excessive TBA (PhOH + TBA) were selected as degradation substances; the contribution experiments of free radicals produced by ${\mathrm{Fe}}^{2+}$/UV/SPC process was measured. We first adjusted pH of SMX solution to 4/6/8 and then mixed it with NB and PhOH + TBA. In addition to that, we added ${\mathrm{Fe}}^{2+}$ and SPC synchronously. During the experiments of anions, four typical anions in surface water were used to analyze the negative effect on degradation performance, which consisted of ${\mathrm{Cl}}^{-}$ (1~100 mM), ${\mathrm{CO}}_3^{2-}$ (0.5~3 mM), ${\mathrm{HCO}}_3^{-}$ (0.1~1 mM), and ${\mathrm{SO}}_4^{2-}$ (0.1~5 mM).

2.3. Analytical Methods

Using the HPLC with C18 column (2.1 mm × 50 mm × 1.7 µm) to determine concentration of organic matter. The detecting conditions of SMX, NB, and PhOH were separately described as follows. As for surveying SMX and NB, the proportion of the mobile phase (V_acetonitrile:V_water) was 2:3 and 1:1, and the detection wavelength was 268 nm and 270 nm, respectively. As for measuring PhOH, the proportion of mobile phase (V_water:V_acetonitrile:V_methanol) was 10:7:3, and the detection wavelength was 263 nm. Other conditions were same; the flow rate was 0.15 mL/min, the column temperature was 30 °C, and the injection volume was 10 µL.

As for the RSM model, the interaction of the main effects (C_SPC, $C_{{\mathrm{Fe}}^{2+}}$, pH, reaction time) on response values (SMX degradation rate, %) was designed by RSM-BBD (Design-Expert 8.0.6 software).

2.4. Theoretical Calculation

2.4.1. Rate Constants and Contribution of Free Radicals

We used chemical reaction kinetics to analyze the rate constants and contribution of free radicals in the degradation of SMX with ${\mathrm{Fe}}^{2+}$/UV/SPC oxidation system. Using the NB, PhOH, and TBA as the probe compounds to investigate the steady-state concentration and the contribution rate of primary free radicals at different pH (4/6/8), the main experimental procedures were as follows.

(1) Generate amounts of ${\bullet \mathrm{CO}}_3^{-}$ with ${\mathrm{Fe}}^{2+}$/UV/SPC system. When exposed to ${\mathrm{Fe}}^{2+}$/UV/SPC system, the concentrations of SMX, PhOH, Fe²⁺, SPC, and TBA were 10 μM, 10 μM, 20 μM, 20 μM, and 2 mM, respectively. Gain the degradation rate (Y) via Equation (1) and then calculate the ln($C_{\mathrm{t}}$/$C_0$) to obtain the reaction rate constant. As the premise, ignore the reaction of SMX and PhOH; meanwhile, focus on the reaction of SPC and Fe²⁺. Firstly, obtain two apparent rate constants, $k_{\mathrm{app},\mathrm{PhOH}}$ and $k_{\mathrm{app},\mathrm{SMX}}$, by using ${\mathrm{Fe}}^{2+}$/UV/SPC system to degrade PhOH+TBA and SMX separately. Secondly, achieve two pseudo-first-order rate constants, $k_{\mathrm{d},\mathrm{PhOH}}^{*}$ and $k_{\mathrm{d},\mathrm{SMX}}^{*}$, using UV to irradiate PhOH + TBA or SMX directly. The values of $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ and $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{PhOH}}\times {\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}$ could be determined separately by Equations (2) and (3). Then, obtain the $\ln \left(\frac{\left[C_{\mathrm{SMX}}\right]}{{\left[C_{\mathrm{SMX}}\right]}_0}\right)$ and $\ln \left(\frac{\left[{\mathrm{C}}_{\mathrm{PhOH}}\right]}{{\left[C_{\mathrm{PhOH}}\right]}_0}\right)$, relying on the ln($C_{\mathrm{t}}$/$C_0$) of SMX or PhOH at 30 min. The last step was calculating the values of $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{PhOH}}$ (Equation (4)) and ${\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}$ (Equation (3)) from these previous results.

$$Y=\frac{C_0-C_{\mathrm{t}}}{C_0}\times 100\%=(1-\frac{C_{\mathrm{t}}}{C_0}) \times 100\%$$

(1)

$$k_{\mathrm{app},\mathrm{SMX}}=k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}+k_{\mathrm{d},\mathrm{SMX}}^{*}$$

(2)

$$k_{\mathrm{app},\mathrm{PhOH}}=k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{PhOH}}\times {\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}+k_{\mathrm{d},\mathrm{PhOH}}^{*}$$

(3)

$$\ln \left(\frac{{\left[C_{\mathrm{SMX}}\right]}_{\mathrm{t}}}{{\left[C_{\mathrm{SMX}}\right]}_0}\right)-k_{\mathrm{d}, \mathrm{SMX}}^{*}=\frac{k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}}{k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{PhOH}}}\left(\ln \left(\frac{{\left[C_{\mathrm{PhOH}}\right]}_{\mathrm{t}}}{{\left[C_{\mathrm{PhOH}}\right]}_0}\right)-k_{\mathrm{d},\mathrm{PhOH}}^{*}\right)$$

(4)

where $C_{\mathrm{t}}$ and $C_0$ were the concentration of degraded substance at reaction time of t and 0, respectively (μM); $k_{\mathrm{app},\mathrm{SMX}}$ and $k_{\mathrm{app},\mathrm{PhOH}}$ were the apparent rate constants for the degradation of SMX and PhOH with ${\mathrm{Fe}}^{2+}$/UV/SPC system (min⁻¹); $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ and $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{PhOH}}$ were the secondary kinetic constants for the degradation of SMX and PhOH by ${\bullet \mathrm{CO}}_3^{-}$ (min⁻¹); $k_{\mathrm{d},\mathrm{SMX}}^{*}$ and $k_{\mathrm{d},\mathrm{PhOH}}^{*}$ were the pseudo-first-order rate constants for the degradation of SMX and PhOH by the direct photolysis of UV irradiation (min⁻¹); ${\left[C_{\mathrm{SMX}}\right]}_{\mathrm{t}}$ and ${\left[C_{\mathrm{SMX}}\right]}_0$ were the SMX concentration at time t and 0, respectively (μM); ${\left[C_{\mathrm{PhOH}}\right]}_{\mathrm{t}}$ and ${\left[C_{\mathrm{PhOH}}\right]}_0$ were the PhOH concentration at time t and 0, respectively (μM); ${\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}$ was the steady-state concentration of ${\bullet \mathrm{CO}}_3^{-}$ (μM).

(2) Generate amounts of $\bullet \mathrm{OH}$ in ${\mathrm{Fe}}^{2+}$/UV/SPC system. The concentration of NB was 10 μM; other concentrations were the same, as described. As the premise, ignore the reaction of SMX and NB; meanwhile, focus on the reaction of SPC and Fe²⁺. Step one is to attain $k_{\mathrm{app},\mathrm{NB}}$ and $k_{\mathrm{app},\mathrm{SMX}}$ by using ${\mathrm{Fe}}^{2+}$/UV/SPC to degrade NB + TBA and SMX separately. Step two is to achieve $k_{\mathrm{d},\mathrm{NB}}^{\prime }$ and $k_{\mathrm{d},\mathrm{SMX}}^{\prime }$, which was realized by using UV irradiating NB + TBA or SMX directly. Step three is to calculate the value of $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ and $k_{\bullet \mathrm{OH},\mathrm{PhOH}}\times {\left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}$ separately by Equations (5) and (6). Then, obtain the $\ln \left(\frac{\left[C_{\mathrm{SMX}}\right]}{{\left[C_{\mathrm{SMX}}\right]}_0}\right)$ and $\ln \left(\frac{\left[C_{\mathrm{NB}}\right]}{{\left[C_{\mathrm{NB}}\right]}_0}\right)$, according to the ln($C_{\mathrm{t}}$/$C_0$) of SMX or NB at 30 min. Finally, calculate the value of $k_{\bullet \mathrm{OH},\mathrm{NB}}$ (Equation (7)) and ${\left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}$ (Equation (6)) from these results above.

$$k_{\mathit{app},\mathit{SMX}}=k_{\bullet \mathit{OH},\mathit{SMX}}+k_{d,\mathit{SMX}}^{*}$$

(5)

$$k_{\mathrm{app},\mathrm{NB}}=k_{\bullet \mathrm{OH},\mathrm{NB}}\times {\left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}+k_{\mathrm{d},\mathrm{NB}}^{*}$$

(6)

$$\ln \left(\frac{\left[C_{\mathrm{SMX}}\right]}{{\left[C_{\mathrm{SMX}}\right]}_0}\right)-k_{\mathrm{d}, \mathrm{SMX}}^{*}=\frac{k_{\bullet \mathrm{OH},\mathrm{SMX}}}{k_{\bullet \mathrm{OH},\mathrm{NB}}}\left(\ln \left(\frac{\left[C_{\mathrm{NB}}\right]}{{\left[C_{\mathrm{NB}}\right]}_0}\right)-k_{\mathrm{d},\mathrm{NB}}^{*}\right)$$

(7)

where $k_{\mathrm{app},\mathrm{NB}}$ is the apparent rate constant for the degradation of NB with ${\mathrm{Fe}}^{2+}$/UV/SPC system (min⁻¹); $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ and $k_{\bullet \mathrm{OH},\mathrm{NB}}$ are the secondary kinetic constants for the degradation of SMX and NB by $\bullet \mathrm{OH}$ (min⁻¹); $k_{\mathrm{d},\mathrm{NB}}^{*}$ is the pseudo-first-order rate constants for the degradation of NB by the direct photolysis of UV irradiation (min⁻¹); ${\left[C_{\mathrm{NB}}\right]}_{\mathrm{t}}$ and ${\left[C_{\mathrm{NB}}\right]}_0$ are the NB concentration at time t and 0, respectively (μM); ${\left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}$ was the steady-state concentration of $\bullet \mathrm{OH}$ (μM).

(3) The contribution calculation of ${\bullet \mathrm{CO}}_3^{-}$ and $\bullet \mathrm{OH}$ in SMX degradation with ${\mathrm{Fe}}^{2+}$/UV/SPC system. The change in SMX degradation with reaction time is expressedby Equation (8). In addition, the contributions of ${\bullet \mathrm{CO}}_3^{-}$, $\bullet \mathrm{OH}$, and UV direct photolysis are shown by Equations (9)–(11), respectively. The effect of other intermediate oxidants on SMX degradation should be considered to calculate the total contribution (Equation (12)).

$$-\frac{\mathrm{d}{C}_{\mathrm{SMX}}}{\mathrm{dt}}=\left(k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}\times {\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}+k_{\bullet \mathrm{OH},\mathrm{SMX}}{\times \left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}+k_{\mathrm{d}, \mathrm{SMX}}^{*}+k_{\mathrm{other},\mathrm{SMX}}\right)\times C_{\mathrm{SMX}}$$

(8)

$$R_{{\bullet \mathrm{CO}}_3^{-}}=\frac{k_{\bullet {\mathrm{CO}}_3^{-},\mathrm{SMX}}{\times \left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}}{k_{\mathrm{app},\mathrm{SMX}}}\times 100\%$$

(9)

$$R_{\bullet \mathrm{OH}}=\frac{k_{\bullet \mathrm{OH},\mathrm{SMX}}{\times \left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}}{k_{\mathrm{app},\mathrm{SMX}}}\times 100\%$$

(10)

$$R_{\mathrm{UV}}=\frac{k_{\mathrm{d},\mathrm{SMX}}^{*}}{k_{\mathrm{app},\mathrm{SMX}}}\times 100\%$$

(11)

$$R_{\mathrm{total}}=R_{\bullet \mathrm{OH}}+R_{\bullet {\mathrm{CO}}_3^{-}}+R_{\mathrm{UV}}+R_{\mathrm{other}}$$

(12)

where $R_{{\bullet \mathrm{CO}}_3^{-}}$, $R_{\bullet \mathrm{OH}}$, $R_{\mathrm{UV}}$, and $R_{\mathrm{other}}$ are the contribution rate of degrading SMX by ${\bullet \mathrm{CO}}_3^{-}$, $\bullet \mathrm{OH}$, UV direct photolysis, and other substances like some oxidizing intermediates (%); $R_{\mathrm{total}}$ is the total contribution rate, selected as 100%.

2.4.2. Response Surface Model

As a parameter optimization tool, the RSM-BBD model is used to analyze the optimum conditions for the degradation of SMX by ${\mathrm{Fe}}^{2+}$/UV/SPC process. Specifically, the water quality parameter is used as the independent variable (x), and the degradation rate of SMX by ${\mathrm{Fe}}^{2+}$/UV/SPC process is the dependent variable (y) through the optimal response value of RSM-BBD. It commonly uses the second-order polynomial based on the Taylor series expansion to express the RSM-BBD model (Equation (13)).

$$\mathrm{y}={\mathsf{\beta }}_0+\sum _{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}+\sum _{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{ii}}{\mathrm{x}}_{\mathrm{i}}^2+\sum _{\mathrm{i}=1}^{\mathrm{k}}\sum _{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{ij}}{\mathrm{x}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{j}}+{\mathrm{e}}_0$$

(13)

where y is SMX degradation rate (%); ${\mathrm{x}}_{\mathrm{i}}$ and ${\mathrm{x}}_{\mathrm{j}}$ are variables; β₀ is a constant coefficient; ${\mathsf{\beta }}_{\mathrm{i}}$, ${\mathsf{\beta }}_{\mathrm{ii}}$, and β_ij are the linear coefficient, the coefficient of quadratic term, and the interaction term, respectively.

2.5. Construction of BP Neural Network Model

Artificial neural networks (ANN) are mathematical models that mimic biological neural networks, which can analyze complex objects with high precision and are applied to many aspects [19]. It commonly considers the node on ANN as one neuron, and different nodes can work concurrently. When information is input to some nodes, output results are sent to other nodes after joint processing by these nodes. In addition, obtain the final processing result until the neurons in the neural network are complete. During various neural network models, the BP-ANN is regarded as one feedforward neural network model consisting of the input, hidden, and output layers. In addition, the connections between each layer of neurons are composed of an error feature weight matrix and propagation function.

The neural network structure diagram is presented in Figure 3. In this study, the input layer has four neurons, and each one presented one influence factor during SMX degradation with the Fe²⁺/UV/SPC process, including SPC concentration (X₁), Fe²⁺ concentration (X₂), pH (X₃), and reaction time (X₄). The output layer has one neuron representing the output value, the SMX degradation rate (Y). Normalize the experimental data by Equation (14), and then use the sigmoid-tanh function (Equation (15)) as the propagation function. The random number was generated to form the eigenvalue matrix to complete the forward propagation of experimental data. After that, use the experimental data (Y_exp) and predicted value (Y_pre) of SMX degradation rate to calculate the error value and modified the eigenvalue matrix by the back-propagation that was implemented by the tanh-derived function (Equation (16)). Rely on the results of mean absolute error (MAE, Equation (17)), mean square error (MSE, Equation (18)), and the correlation coefficient (R², Equation (19)) to determine the number of hidden layer neurons, and complete the topology construction of BP-ANN model (Figure 1). Moreover, Garson’s formula (Equation (20)) was used to obtain the degree of the influence variables on the reaction.

$${\mathrm{x}}_{\mathrm{i}}=\frac{0.8({\mathrm{X}}_{\mathrm{i}}-{\mathrm{X}}_{\min })}{{\mathrm{X}}_{\max }-{\mathrm{X}}_{\min }}+0.1$$

(14)

$$\mathrm{S}\left(\mathrm{x}\right)=\frac{1}{1+{\mathrm{e}}^{-\mathrm{x}}}$$

(15)

$${\tanh }_{\mathrm{d}}\left(\mathrm{x}\right)=1-{\mathrm{x}}^2$$

(16)

$$\mathrm{MAE}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left(\left|{\mathrm{Y}}_{\mathrm{pre}}-{\mathrm{Y}}_{\exp }\right|\right)$$

(17)

$$\mathrm{MSE}=\frac{1}{\mathrm{n}}{\left(\sum _{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{Y}}_{\mathrm{pre}}-{\mathrm{Y}}_{\exp })\right)}^2$$

(18)

$${\mathrm{R}}^2=\frac{({\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{Y}}_{\exp }-\overline{{\mathrm{Y}}_{\exp }}){({\mathrm{Y}}_{\mathrm{pre}}-\overline{{\mathrm{Y}}_{\mathrm{pre}}}\left)\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left(\right({\mathrm{Y}}_{\exp }-\overline{{\mathrm{Y}}_{\exp }}){({\mathrm{Y}}_{\mathrm{pre}}-\overline{{\mathrm{Y}}_{\mathrm{pre}}}\left)\right)}^2}$$

(19)

$${\mathrm{I}}_{\mathrm{j}}=\frac{{\sum }_{\mathrm{m}=1}^{\mathrm{m}=\mathrm{Nh}}(\left(\left|{\mathrm{W}}_{\mathrm{jm}}^{\mathrm{ih}}\right|/{\sum }_{\mathrm{k}=1}^{\mathrm{k}=\mathrm{Ni}}\left|{\mathrm{W}}_{\mathrm{km}}^{\mathrm{ih}}\right|\right)\times \left|{\mathrm{W}}_{\mathrm{mn}}^{\mathrm{ho}}\right|)}{{\sum }_{\mathrm{k}=1}^{\mathrm{k}=\mathrm{Ni}}\left({\sum }_{\mathrm{m}=1}^{\mathrm{m}=\mathrm{Nh}}(\left|{\mathrm{W}}_{\mathrm{km}}^{\mathrm{ih}}\right|/{\sum }_{\mathrm{k}=1}^{\mathrm{k}=\mathrm{Ni}}\left|{\mathrm{W}}_{\mathrm{km}}^{\mathrm{ih}}\right|\times \left|{\mathrm{W}}_{\mathrm{mn}}^{\mathrm{ho}}\right|)\right)}\times 100\%$$

(20)

where x_i is the normalized value of X_i; X_max and X_min are the maximum and minimum values of X_i, respectively; I_j (%) is the relative importance of the input variable j to the Y_pre; N_i and N_h are, respectively, the numbers of neurons in the input and hidden layer; W^ih and W^ho is the connection weight of input layer–hidden layer and the hidden layer–output layer, respectively; i, h, and o correspond to the input layer, hidden layer, and output layer, respectively; k, m, and n correspond to the neurons of input layer, hidden layer, and output layer, respectively.

3. Results and Discussions

3.1. Feasibility and Mechanism of SMX Degradation Enhanced via Fe²⁺/UV/SPC System

3.1.1. Degradation Efficiency of Fe²⁺/UV/SPC System

The C_t/C₀ of SMX via the ${\mathrm{Fe}}^{2+}$/UV/SPC process was shown in Figure 4a, and the reaction rate constant (k_obs) was given in Figure 4b. When using Fe²⁺ or SPC alone in combination, the C_t/C₀ was low at 4.2%, 6.3%, and 6.2%, respectively. Moreover, their k_obs were 0.075 × 10⁻², 0.167 × 10⁻², and 0.144 × 10⁻² min⁻¹. These results demonstrated that Fe²⁺ or SPC alone could not effectively degrade SMX, and even the combination of these two components was ineffective. When using UV radiation alone, the C_SMX/C₀ and k_obs slightly raised to 17.2% and 0.585 × 10⁻² min⁻¹. When SPC was active via UV, the C_t/C₀ and k_obs were promoted to 58.1% and 3.075 × 10⁻² min⁻¹, owing to UV irradiation, and were able to directly decompose H₂O₂ molecules from SPC solution into hydroxyl radicals ($\bullet \mathrm{OH}$) or other free radical-like $\bullet {\mathrm{CO}}_3^{-}$ [20], resulting in a better degradation efficiency. In another study [21], the degradation rate of SMX was higher than 90% with the UV/SPC process due to the higher SPC dosage, which led to a higher drug cost. The same problem was found in SMX degradation with the UV/SPC process. The degradation rate was insufficient and limited when SPC was as low as 10 μM. Adding ${\mathrm{Fe}}^{2+}$ into UV/SPC, the C_t/C₀ and k_obs further improved to 84.8% and 6.304 × 10⁻² min⁻¹, respectively. In the Fe²⁺/UV/SPC process, the degradation rate and k_obs were 1.46 and 1.32 times that in the UV/SPC process, indicating that Fe²⁺ enhanced the degradation performance of SMX. In this study, the degradation efficiency was the decreased order according to the k_obs results: Fe²⁺/UV/SPC > UV/SPC > UV/Fe²⁺ > UV alone. This result displayed that the Fe²⁺/UV/SPC was more efficient than the Fenton-like (UV/SPC) process, speculating that UV light may induce the photo-Fenton reaction during SMX degradation.

In the Fe²⁺/UV/SPC process, a better degradation performance was observed in the facilitative effect of Fe²⁺ on SMX degradation, mainly due to the occurrence of a classical Fenton reaction and photo-Fenton reaction. The classical Fenton reaction (Equation (21)) [22] possibly occurred between Fe²⁺ and H₂O₂ molecules in SPC at acid pH (5.2). The photo-Fenton reaction happened between Fe²⁺ and SPC under UV radiation through the following aspects. One aspect was that the classical Fenton reaction could be photo-assisted by utilizing UV. Moreover, the Fe³⁺ produced during the classical Fenton reaction may undergo spontaneous hydrolysis in the aqueous solution to re-generate Fe²⁺ and $\bullet \mathrm{OH}$ (Equation (22)) to catalyze Fenton’s reaction [22]. Another aspect was that Fe³⁺ might transform to other forms like a mono-hydroxy complex [Fe(OH)]²⁺ with the help of photons in the photo-Fenton process due to the hydrolysis of Fe³⁺, which might occur in the aqueous solution [23]. As the pre-eminent form of Fe³⁺ under acidic conditions, the [Fe(OH)]²⁺ helped induce the generation of Fe²⁺ and $\bullet \mathrm{OH}$ through the effect of photosensitization (Equation (23)) [23]. Moreover, Na₂CO₃ in the SPC solution may consume the $\bullet \mathrm{OH}$ to form $\bullet {\mathrm{CO}}_3^{-}$ (Equations (24) and (25)) [20].

$${\mathrm{Fe}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{Fe}}^{3+}+{\mathrm{OH}}^{-}+\bullet \mathrm{OH}$$

(21)

$${\mathrm{Fe}}^{3+}+{\mathrm{H}}_2\mathrm{O}+hv\to {\mathrm{Fe}}^{2+}+{\mathrm{H}}^{+}+\bullet \mathrm{OH}$$

(22)

$${\mathrm{Fe}\left(\mathrm{OH}\right)}^{2+}+hv\to {\mathrm{Fe}}^{2+}+{\mathrm{OH}}^{-}+hv\to {\mathrm{Fe}}^{2+}+\bullet \mathrm{OH}$$

(23)

$$\bullet \mathrm{OH}+{\mathrm{CO}}_3^{2-}\to {\bullet \mathrm{CO}}_3^{-}+{\mathrm{OH}}^{-}$$

(24)

$$\bullet \mathrm{OH}+{\mathrm{HCO}}_3^{-}\to {\bullet \mathrm{CO}}_3^{-}+{\mathrm{H}}_2\mathrm{O}$$

(25)

These results speculated that there were two possible pathways for the degradation of SMX via the Fe²⁺/UV/SPC process. One pathway was direct photolysis, and the other was a free radical reaction. These free radicals ($\bullet \mathrm{OH}$ and ${\bullet \mathrm{CO}}_3^{-}$) were generated through some possible sources: the first one was the direct photolysis of SPC under UV radiation; the second pathway was hydroxyl free radicals generated by SPC and Fe²⁺ through a Fenton reaction or generated via Fe³⁺ (or iron complex) and UV radiation through photo a Fenton reaction; the third one was Na₂CO₃ in SPC-produced ${\bullet \mathrm{CO}}_3^{-}$, which consumed $\bullet \mathrm{OH}$. Compared to the UV/SPC process, adding Fe²⁺ was beneficial in promoting the generation of free radicals to enhance the SMX degradation efficiency and reaction rate.

3.1.2. Optimization Analysis of Fe²⁺/UV/SPC System

The optimal degradation performance of SMX by the Fe²⁺/UV/SPC process was investigated, including the effect of $C_{{\mathrm{Fe}}^{2+}}$, C_SPC, and pH. The degradation performance and k_obs were separately exhibited in Figure 5 and Figure S2, and the fitting Equations of k_obs are described in Table S2. As is shown in Figure 5a, the C_t/C₀ slightly increased from 83.6% to 86.2%, when $C_{{\mathrm{Fe}}^{2+}}$ increased from 10 to 30 μM. Then, the C_t/C₀ marginally decreased to 84.8% when $C_{{\mathrm{Fe}}^{2+}}$ further increased to 40 μM. The effect of $C_{{\mathrm{Fe}}^{2+}}$ on the SMX degradation efficiency was not significant, which was consistent with the results that k_obs remained close to around 6.1–6.5 × 10⁻² min⁻¹. This result illustrated that the appropriate dosage of Fe²⁺ slightly increases the SMX degradation rate due to suitable Fe²⁺ that accelerates the photo-Fenton reaction with SPC under UV radiation to produce more $\bullet \mathrm{OH}$ (Equations (14) and (15)) and $\bullet {\mathrm{CO}}_3^{-}$ (Equations (16) and (17)). Additionally, the formed Fe³⁺ and the re-generated Fe²⁺ actuated the Fenton process indirectly, which also improved the degradation of SMX. However, excessive Fe²⁺ may negatively affect the SMX degradation, owing to a significant accumulation of Fe³⁺ species that presented an inconvenience, which decelerated the degradation rate in the classical Fenton reaction (Equation (21)). In addition, excessive Fe²⁺ may also consume the free radical-like $\bullet \mathrm{OH}$ (Equation (26)) [23], or $\bullet \mathrm{OH}$ would react with itself (Equation (27)) or H₂O₂ (Equation (28)) to be quenched [20,24], resulting in the reduced degradation performance of SMX via the Fe²⁺/UV/SPC process. From a cost point of view, 10 or 20 μM was more economical than 30 μM.

$${\mathrm{Fe}}^{2+}+\bullet \mathrm{OH}\to {\mathrm{Fe}}^{3+}+{\mathrm{OH}}^{-}$$

(26)

$$\bullet \mathrm{OH}+\bullet \mathrm{OH}\to {\mathrm{H}}_2{\mathrm{O}}_2$$

(27)

$$\bullet \mathrm{OH}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\bullet \mathrm{HO}}_2+{\mathrm{Fe}}^{3+}$$

(28)

As Figure 5b shows, when C_SPC increased from 10 to 40 μM, the C_t/C₀ clearly decreased from 84.8% to 59.8%. Meanwhile, the k_obs decreased from 6.304 × 10⁻² to 2.978 × 10⁻² min⁻¹, demonstrating that the degradation performance and reaction rate of the Fe²⁺/UV/SPC process were enervated by higher SPC dosage. More SPC facilitated the generation of $\bullet \mathrm{OH}$ (Equation (21)) and $\bullet {\mathrm{CO}}_3^{-}$ (Equations (24) and (25)). However, SPC and H⁺ may produce ${\mathrm{HCO}}_3^{-}$ under a pH of 5.2. It was considered that ${\mathrm{HCO}}_3^{-}$ was the $\bullet \mathrm{OH}$ scavenger in the aqueous phase (Equation (25)) [25]. On the one hand, when SPC dosage increased, more generated $\bullet \mathrm{OH}$ would be consumed by ${\mathrm{HCO}}_3^{-}$ to produce more ${\bullet \mathrm{CO}}_3^{-}$. On the other hand, the generated $\bullet {\mathrm{CO}}_3^{-}$ would continuously react with H₂O₂ molecules in the SPC solution, leading to the lessened substrate that may limit the Fenton or photo-Fenton reaction to degrade SMX. In addition, ${\mathrm{HCO}}_3^{-}$ possibly also consumed the H₂O₂ to decrease SPC concentration, resulting in the formation of more peroxymonocarbonate ions (${\mathrm{HCO}}_4^{-}$) by Equation (30) [25], which surmised that ${\mathrm{HCO}}_4^{-}$ was capable of oxidizing organic pollutants like SMX. However, the reduction–oxidation potential of ${\mathrm{HCO}}_4^{-}$ (E⁰ = 1.8 V) was lower than $\bullet \mathrm{OH}$, leading to an overall weaker oxidation capacity. Even if the produced ${\mathrm{HCO}}_4^{-}$ was high at high SPC concentrations, the SMX degradation capacity of ${\mathrm{HCO}}_4^{-}$ was not satisfied like $\bullet \mathrm{OH}$. Additionally, ${\mathrm{HCO}}_4^{-}$ with metal could form solid sedimentation or aqueous complexes [26], which diminishes the catalyst concentration (like Fe²⁺ or iron oxides) to obstruct the degradation of SXM via the Fe²⁺/UV/SPC process.

$${\bullet \mathrm{CO}}_3^{-}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\bullet \mathrm{HO}}_2+{\mathrm{HCO}}_3^{-}$$

(29)

$${\mathrm{HCO}}_3^{-}+{\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{HCO}}_4^{-}+{\mathrm{H}}_2\mathrm{O}$$

(30)

According to Figure 5c, when the initial pH increased from 4 to 9, the C_t/C₀ decreased from 86.1% to 59.0%, and the k_obs decreased from 6.010 × 10⁻² to 2.924 × 10⁻² min⁻¹, displaying that high pH affected the degradation efficiency negatively as well as the reaction rate of Fe²⁺/UV/SPC system, especially in an alkaline aqueous environment. On the one hand, solution pH affected the reduction-oxidation potential of free radicals, and acidic conditions were conducive to the catalysis of Fe²⁺ on the Fenton reaction, promoting the generation of $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$ during the Fe²⁺/UV/SPC process. The E⁰ of $\bullet \mathrm{OH}$ was 2.65-2.80 V and 1.9 V when the pH was 3 and 7, respectively [27]. It is speculated that the oxidation capacity of $\bullet \mathrm{OH}$ would decline at higher pHs like 7 and 9 in this study, meanwhile engendering the weaker degradation capacity of the Fe²⁺/UV/SPC process. On the other hand, pH also affects the abundance of ions like H₂CO₃, ${\mathrm{HCO}}_3^{-}$, and ${\mathrm{CO}}_3^{2-}$ (pK_a1 = 6.37, pK_a2 = 10.32) [28]. Thus, the generation amounts of prominent free radicals might be influenced. A high pH caused greater consumption of $\bullet \mathrm{OH}$ and ${\mathrm{H}}_2{\mathrm{O}}_2$ by ${\mathrm{HCO}}_3^{-}$ (Equations (25), (29) and (30)), reducing both $\bullet \mathrm{OH}$ amounts and the oxidization capacity of the Fe²⁺/UV/SPC process. In addition, the structural morphology of SMX was possibly affected by high pH, leading to a lower degradation rate of SMX. The SMX existed mainly as a neutral molecule (SMX⁰) at pH between pK_a1 = 2.15 and pK_a2 = 5.64, and the SMX molecular form has higher photochemical reactivity and stronger light adsorption under acidic conditions [29]. These results demonstrated that the SMX degradation was easier at acid conditions, resulting in the better degradation performance of the Fe²⁺/UV/SPC process at low pH.

The results above demonstrated that appropriate amounts of $C_{{\mathrm{Fe}}^{2+}}$ (10~30 μM) and C_SPC (10 μM) under acidic conditions (pH = 4~6) were in favor of presenting a better degradation rate of SMX via the Fe²⁺/UV/SPC process.

3.1.3. Degradation Mechanism of SMX via Fe²⁺/UV/SPC System

According to the previous study on degradation performance and optimization analysis, it was possible that $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$ played the main roles in the degradation of SMX via the Fe²⁺/UV/SPC system. Herein, relying on two probe compounds, these active free radicals were further verified by the C_t/C₀ (Figure 6) and k_obs (Figure S3 and Table S3). Commonly, the PhOH reacts with $\bullet \mathrm{OH}$ (6.0 × 10⁸ M⁻¹s⁻¹) and $\bullet {\mathrm{CO}}_3^{-}$ (2.2 × 10⁷ M⁻¹s⁻¹) at both high rates [22], and the reaction rate of TBA with $\bullet \mathrm{OH}$ was 3.8-7.6 × 10⁸ M⁻¹s⁻¹ [30]. It was considerable that PhOH was the effective quencher for both $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$, while TBA was the quencher for $\bullet \mathrm{OH}$. When pH was 4, 6, and 8, the C_t/C₀ of SMX increased to different degrees, revealing that the addition of PhOH and TBA exhibited the inhibition effect on the degradation rate of SMX in the Fe²⁺/UV/SPC process. The difference in degradation rate ($∆(Y_{\mathrm{SMX}}-Y_{\mathrm{SMX}+\mathrm{probe} \mathrm{compund}})$) between SMX and SMX + TBA or SMX + PhOH is the reflection of the inhibition effect. After adding TBA, when pH increased from 4 to 8, the decreased degradation rate was 37.1%, 28.1%, and 7.8%, respecvitvely. In addition, after adding PhOH, it was 45.1%, 45.0%, and 34.8%. Without probe compounds at pHs of 4, 6, and 8, the k_obs were 6.623, 6.010, and 3.837 × 10⁻² min⁻¹, respectively. Simultaneously, the k_obs decreased to 2.158, 2.658, and 2.755 × 10⁻² min⁻¹ after adding TBA, and the k_obs further decreased to 1.761, 1.581, and 1.320 × 10⁻² min⁻¹ after adding PhOH. It was found that the inhibitory effect of PhOH on the degradation rate and k_obs was more evident than TBA. This result speculated that both $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$ were involved in the SMX degradation via the Fe²⁺/UV/SPC system. (1) The generation pathways of $\bullet \mathrm{OH}$ were summarized as follows. The SPC in aqueous solution quickly decomposed to $\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3$ and ${\mathrm{H}}_2{\mathrm{O}}_2$ (Equation (31)), and H₂O₂ irradiated by UV would produce $\bullet \mathrm{OH}$ (Equation (32)) [31]. Additionally, the classical Fenton reaction between Fe²⁺ and H₂O₂ also produced the $\bullet \mathrm{OH}$ (Equation (21)) or through the photo-Fenton reaction via Fe²⁺ and UV radiation (Equation (22)). Furthermore, when under UV radiation, complexes like ${\mathrm{Fe}\left(\mathrm{OH}\right)}^{2+}$ (Equation (23)) or $\mathrm{HC}{\mathrm{O}}_4^{-}$ (Equation (33)) would also be decomposed to $\bullet \mathrm{HO}$ and other intermediates. (2) The $\bullet {\mathrm{CO}}_3^{-}$ mainly could be formed by two pathways; one was ${\mathrm{CO}}_3^{2-}$ or ${\mathrm{HCO}}_3^{-}$ produced via SPC decomposition reacting with $\bullet \mathrm{OH}$ (Equations (24) and (25)) [30]. The other was that intermediates like ${\mathrm{HCO}}_4^{-}$ could be decomposed into another reactive species (Equation (33)) [32,33]. (3) The PhOH could not completely inhibit the degradation of SMX by free radicals; this represented that some unstable oxidants may play an essential role in the SMX degradation besides $\bullet \mathrm{HO}$ and $\bullet {\mathrm{CO}}_3^{-}$. The possible intermediates involved are ${\bullet \mathrm{HO}}_2$ (Equations (28) and (29)), ${\mathrm{HCO}}_4^{-}$ decomposed to $\bullet \mathrm{HO}$ and $\bullet {\mathrm{CO}}_{3 }^{-}$ (Equation (30)), $\bullet {\mathrm{O}}_2^{-}$ (Equations (34)–(36)) [34], or ¹O₂ (Equations (37)–(39)) [35]. Moreover, the degradation rate difference was used to calculate the inhibition proportion of two probe compounds ($Y_{\mathrm{probe} \mathrm{compound}}^{*}=\frac{Y_{\mathrm{SMX}}-Y_{\mathrm{SMX}+\mathrm{probe} \mathrm{compund}}}{Y_{\mathrm{SMX}}}\times 100\%$) and analyze the primary free radicals produced via the Fe²⁺/UV/SPC process in SMX degradation. When pH was 4, 6, and 8, the $Y_{\mathrm{TBA}}^{*}$ was 43.1%, 33.8%, and 11.4%. Simultaneously, the $Y_{\mathrm{PhOH}}^{*}$ was 52.4%, 54.3%, and 51.3%. In addition, $Y_{\mathrm{TBA}}^{*}/Y_{\mathrm{PhOH}}^{*}$ was 82% and 62% at acidic pHs of 4 and 6. These results revealed that $\bullet \mathrm{OH}$ played a significant role in acid pH when compared to $\bullet {\mathrm{CO}}_{3 }^{-}$ in the degradation of SMX via the Fe²⁺/UV/SPC process.

$$2\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3·3{\mathrm{H}}_2{\mathrm{O}}_2\to 2\mathrm{N}{\mathrm{a}}_2\mathrm{C}{\mathrm{O}}_3+3{\mathrm{H}}_2{\mathrm{O}}_2$$

(31)

$${\mathrm{H}}_2{\mathrm{O}}_2+hv\to 2\bullet \mathrm{HO}$$

(32)

$$\mathrm{HC}{\mathrm{O}}_4^{-}\to \bullet \mathrm{HO}+\bullet {\mathrm{CO}}_3^{-}$$

(33)

$${\bullet \mathrm{HO}}_2\to {\mathrm{H}}^{+}+\bullet {\mathrm{O}}_2^{-}$$

(34)

$${\bullet \mathrm{HO}}_2+\bullet \mathrm{OH}\to {\mathrm{H}}_2\mathrm{O}+\bullet {\mathrm{O}}_2^{-}$$

(35)

$${\bullet \mathrm{HO}}_2+\mathrm{C}{\mathrm{O}}_3^{2-}\to \bullet {\mathrm{O}}_2^{-}+\mathrm{H}{\mathrm{CO}}_3^{-}$$

(36)

$${\bullet \mathrm{HO}}_2+\bullet {\mathrm{O}}_2^{-}\to {}^1{\mathrm{O}}_2+\mathrm{H}{\mathrm{O}}_2^{-}$$

(37)

$$\bullet \mathrm{OH}+\bullet {\mathrm{O}}_2^{-}\to {}^1{\mathrm{O}}_2+\mathrm{H}{\mathrm{O}}^{-}$$

(38)

$${\bullet \mathrm{HO}}_2+{\bullet \mathrm{HO}}_2\to {}^1{\mathrm{O}}_2+{\mathrm{H}}_2{\mathrm{O}}_2$$

(39)

In order to investigate the contribution rate of $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$ in SMX degradation via the Fe²⁺/UV/SPC system, the second-order rate constants of SMX with $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_3^{-}$ were determined. In addition to the results of Figures S4 and S5, the calculated $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ and $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ is shown in Figure 7a. It was found that the $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ increased from 2.33 × 10⁸ to 4.73 × 10⁸ M⁻¹s⁻¹; meanwhile, the $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ decreased from 6.07 × 10⁸ to 5.32 × 10⁸ M⁻¹s⁻¹, when pH rose from 4 to 8. The $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ was maintained until two times that of $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$, even though $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ and $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ were in the same order of magnitude. These results illustrated that $\bullet \mathrm{OH}$ was more accessible to a reaction with SMX than $\bullet {\mathrm{CO}}_3^{-}$, especially in acidic conditions. It was reported that $\bullet {\mathrm{CO}}_3^{-}$ could react with substituted anilines with a reaction rate of 10⁷~10⁸ M⁻¹s⁻¹ [36] or react with pesticides with a reaction rate of 10⁵~10⁷ M⁻¹s⁻¹ [37]. When pH was 4~8, the $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ kept higher than 2.33 × 10⁸ M⁻¹s⁻¹, demonstrating that the $\bullet {\mathrm{CO}}_3^{-}$ also showed high oxidation characteristics in SMX degradation.

The ${\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}$ and ${\left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}$ in SMX degradation were exhibited in Figure 7b. When pH was 4~8, the ${\left[{\bullet \mathrm{CO}}_3^{-}\right]}_{\mathrm{ss}}$ decreased from 8.26 × 10⁻¹³ to 4.24 × 10⁻¹³ M, and the ${\left[\bullet \mathrm{OH}\right]}_{\mathrm{ss}}$ also declined from 1.16 × 10⁻¹³ to 5.65 × 10⁻¹⁴ M. These results displayed that the generation amounts of both ${\bullet \mathrm{CO}}_3^{-}$ and $\bullet \mathrm{OH}$ produced via the Fe²⁺/UV/SPC system was higher in acidic conditions, which was beneficial to the degradation of SMX and was consistent with the result of Figure 7c. It was caused by the fact that Fe²⁺ and H₂O₂ were conducive to the Fenton (Equation (21)) or photo-Fenton reaction (Equations (22) and (23)), which promoted the generation of $\bullet \mathrm{OH}$ in acidic conditions. Moreover, at alkaline conditions, the produced Fe²⁺ or Fe(OH)²⁺ quickly accumulated (Equations (21) and (22)), which possibly led to the consumption of $\bullet \mathrm{OH}$ (Equation (26)) or the generation of ${\bullet \mathrm{CO}}_3^{-}$ becoming difficult (Equation (24)) [38].

The contribution of free radicals in SMX degradation via the Fe²⁺/UV/SPC system is displayed in Figure 7c. The $R_{\bullet \mathrm{OH}}$ decreased from 62.9% to 46.3%, meanwhile, $R_{{\bullet \mathrm{CO}}_3^{-}}$ increased from 17.3% to 31.5%, and the sums of R_UV and R_other remained at about 20~22% when pH increased from 4 to 8. In the SMX degradation, $\bullet \mathrm{OH}$ made the greatest contribution to the degradation, and ${\bullet \mathrm{CO}}_3^{-}$ played an important role in degrading SMX simultaneously. Additionally, the effect of UV direct photolysis and other active intermediates was also responsible for the SMX degradation. These active intermediates might be produced via the Fe²⁺/UV/SPC system, involving ${\bullet \mathrm{HO}}_2$, ${\mathrm{HCO}}_4^{-}$, $\bullet {\mathrm{O}}_{2 }^{-}$, or ¹O₂. With the increase in pH, the contribution of $\bullet \mathrm{OH}$ to SMX was negatively correlated, while $\bullet {\mathrm{CO}}_{3 }^{-}$ was positively correlated, demonstrating that acidic conditions were more conducive to making $\bullet \mathrm{OH}$ work in the degradation. These results regarding the contribution rate in Figure 5 confirmed the implication in Figure 4.

3.1.4. Influence of Anions on the SMX Degradation via Fe²⁺/UV/SPC System

The effect of typical anions on SMX degradation via the Fe²⁺/UV/SPC system was exhibited in Figure 8, and the corresponding K_obs was given in Figure S6a and Table S4. As Figure 8a displays, the degradation rate of SMX slightly decreased from 84.8% to 82.1% when Cl⁻ raised to 0.1 mM. Then, it remained around 83.9% when ${\mathrm{Cl}}^{-}$ further raised to 0.5~10 mM. Additionally, the K_obs slightly decreased from 6.304 to 5.857 × 10⁻² min⁻¹ and kept around 6.141 × 10⁻² min⁻¹. Adding ${\mathrm{Cl}}^{-}$ to Fe²⁺/UV/SPC process, the ${\mathrm{Cl}}^{-}$ would consume $\bullet \mathrm{OH}$ to generate $\bullet \mathrm{ClO}{\mathrm{H}}^{-}$ (Equation (40)), which further transformed to $\bullet \mathrm{Cl}$ (Equation (41)) or ${\bullet \mathrm{Cl}}_2^{-}$ (Equation (42)) [38]. The activity of $\bullet \mathrm{ClO}{\mathrm{H}}^{-}$ (K_obs = 4.3 × 10⁹ M⁻¹s⁻¹), $\bullet \mathrm{Cl}$ (K_obs = 3.2 × 10¹⁰ M⁻¹s⁻¹), or ${\bullet \mathrm{Cl}}_2^{-}$ (K_obs = 7.8 × 10⁹ M⁻¹s⁻¹) was weaker than $\bullet \mathrm{OH}$, leading to a slightly decreased SMX degradation rate.

According to Figure 8b, the degradation rate of SMX decreased from 84.8% to 53.6% when ${\mathrm{HCO}}_3^{-}$ was raised to 0.3 mM. Then, the degradation rate of SMX increased to 82.5% when ${\mathrm{HCO}}_3^{-}$ was further raised to 1 mM. Simultaneously, the K_obs decreased from 6.304 to 1.845 × 10⁻² M⁻¹s⁻¹, then raised to 2.925 × 10⁻² M⁻¹s⁻¹. The negative effect of ${\mathrm{HCO}}_3^{-}$ on the SMX degradation presented at a dosage of 0.1~0.3 mM, owing to ${\mathrm{HCO}}_3^{-}$, would consume the $\bullet \mathrm{OH}$ or ${\mathrm{H}}_2{\mathrm{O}}_2$ to produce ${\bullet \mathrm{CO}}_3^{-}$ (Equation (25)) or ${\mathrm{HCO}}_4^{-}$ (Equation (30)). However, excessive ${\mathrm{HCO}}_3^{-}$ would undergo a hydrolysis reaction, leading to the consumption of H⁺ and high pH. This possibly induced the precipitation of Fe(OH)₃. Also, this affected the Fenton reaction or photo-Fenton reaction to produce $\bullet \mathrm{OH}.$ Nevertheless, the generation quantity of ${\bullet \mathrm{CO}}_3^{-}$ and ${\mathrm{HCO}}_4^{-}$ would increase, or ${\mathrm{HCO}}_4^{-}$ would decompose to $\bullet \mathrm{OH}$ and ${\bullet \mathrm{CO}}_3^{-}$ (Equation (33)). A large amount of ${\bullet \mathrm{CO}}_3^{-}$ may become the main active substance of the Fe²⁺/UV/SPC process for SMX degradation in this situation.

$$\bullet \mathrm{OH}+{\mathrm{Cl}}^{-}\to \bullet \mathrm{Cl}\mathrm{O}{\mathrm{H}}^{-}$$

(40)

$$\bullet \mathrm{ClO}{\mathrm{H}}^{-}+{\mathrm{H}}^{+}+{\mathrm{Cl}}^{-}\leftrightarrow \bullet \mathrm{Cl}+{\mathrm{H}}_2\mathrm{O}$$

(41)

$$\bullet \mathrm{Cl}+{\mathrm{Cl}}^{-}\leftrightarrow {\bullet \mathrm{Cl}}_2^{-}$$

(42)

In Figure 8c, the effect of ${\mathrm{CO}}_3^{2-}$ on SMX degradation was similar to ${\mathrm{HCO}}_3^{-}$. The degradation rate and K_obs obviously decreased to 46.3% and 2.010 × 10⁻² M⁻¹s⁻¹, when ${\mathrm{CO}}_3^{2-}$ increased to 0.5 mM. When ${\mathrm{CO}}_3^{2-}$ further raised from 1 to 3 mM, the degradation rate gradually increased from 47.3% to 58.4% and 75.1%; meanwhile, the K_obs showed the same trend and finally increased to 2.921 × 10⁻² M⁻¹s⁻¹. Similar to ${\mathrm{HCO}}_3^{-}$, the consumption of $\bullet \mathrm{OH}$ (Equation (24)) or H₂O₂ (Equation (29)) by ${\mathrm{CO}}_3^{2-}$ actuated the formation of ${\bullet \mathrm{CO}}_3^{-}$ and ${\bullet \mathrm{HO}}_2$, leading to a lower degradation rate of SMX. When adding excessive ${\mathrm{CO}}_3^{2-}$, such as in a quantity of 3 mM, the hydrolysis reaction of ${\mathrm{CO}}_3^{2-}$ also induced a high pH like ${\mathrm{HCO}}_3^{-}$, which was beneficial in producing large amounts of ${\bullet \mathrm{CO}}_3^{-}$ to guarantee the SMX degradation, even though the consumption of $\bullet \mathrm{OH}$ was also very huge. As Figure 8d showed, the degradation rate of SMX was maintained at 82.7~83.5%, and K_obs was kept around 5.734~6.099 × 10⁻² M⁻¹s⁻¹. These results illustrated that the degradation capability of the Fe²⁺/UV/PDS system was not inhibited too much by ${\mathrm{SO}}_4^{2-}$, owing to ${\mathrm{SO}}_4^{2-}$ having little effect on pH or active free radicals.

3.2. Predictions Models for the SMX Degradation via Fe²⁺/UV/SPC System

In some practical scenarios, many experiments are commonly necessary to determine the optimal conditions for SMX degradation by the Fe²⁺/UV/SPC system, which will hinder the promotion of the Fe²⁺/UV/SPC system in practical engineering. Therefore, it is necessary to study some convenient modes to predict the degradation rate of SMX in the Fe²⁺/UV/SPC process. In this section, two models were established for predicting SMX degradation by the Fe²⁺/UV/SPC process involving RSM-BBD and BP-ANN.

3.2.1. Evaluation of RSM-BBD Model

W selected four influence factors as the parameters of RSM-BBD, consisting of $C_{{\mathrm{Fe}}^{2+}}$, C_SPC, pH, and reaction time (t), to investigate the interaction influence of these factors on SMX degradation performance. The design matrix (variables and codes) and the corresponding response values of the RSM-BBD model are given in Table S5, and the interaction effect is exhibited in Figure 9. Using Design-Expert 8.0.6 software to construct the second-order polynomial regression equation (Equation (43)), where $\mathrm{y}$ was the predicted value of SMX degradation rate via the Fe²⁺/UV/SPC process, ${\mathrm{x}}_1$, ${\mathrm{x}}_2$, ${\mathrm{x}}_3$, and ${\mathrm{x}}_4$, respectively, referred to C_SPC, $C_{{\mathrm{Fe}}^{2+}}$, pH, and t.

$$\mathrm{y}=65.20-7.46{\mathrm{x}}_1+6.76{\mathrm{x}}_2-15{\mathrm{x}}_3+14.42{\mathrm{x}}_4-2.40{\mathrm{x}}_1{\mathrm{x}}_2-4.93{\mathrm{x}}_1{\mathrm{x}}_3-0.75{\mathrm{x}}_1{\mathrm{x}}_4+3.75{\mathrm{x}}_2{\mathrm{x}}_3 -0.025{\mathrm{x}}_2{\mathrm{x}}_4+3.75{\mathrm{x}}_3{\mathrm{x}}_4-1.69{\mathrm{x}}_1^2-3.29{\mathrm{x}}_2^2+8.15{\mathrm{x}}_3^2-8.35{\mathrm{x}}_4^2$$

(43)

The variance parameters of the RSM-BBD model were given in

Table 1. Variance parameters of the RSM-BBD model in SMX degradation via Fe²⁺/UV/SPC system.

Type	Quadratic Sum	DOF	MSE	F	p	Significance
Model	7818	14	558.43	43.42	<0.0001	significant
${\mathrm{x}}_1$ (CSPC)	667.52	1	667.52	51.9	<0.0001	significant
${\mathrm{x}}_2$ ($C_{{\mathrm{Fe}}^{2+}}$)	548.1	1	548.1	42.61	<0.0001	significant
${\mathrm{x}}_3$ (pH)	2700	1	2700	209.91	<0.0001	significant
${\mathrm{x}}_4$ (t)	2494.08	1	2494.08	193.9	<0.0001	significant
${\mathrm{x}}_1{\mathrm{x}}_2$	23.04	1	23.04	1.79	0.2021
${\mathrm{x}}_1{\mathrm{x}}_3$	97.02	1	97.02	7.54	0.0158	significant
${\mathrm{x}}_1{\mathrm{x}}_4$	2.25	1	2.25	0.17	0.6821
${\mathrm{x}}_2{\mathrm{x}}_3$	56.25	1	56.25	4.37	0.0552
${\mathrm{x}}_2{\mathrm{x}}_4$	0.0025	1	0.0025	0.000194	0.9891
${\mathrm{x}}_3{\mathrm{x}}_4$	57	1	57	4.43	0.0538
${\mathrm{x}}_1^2$	18.56	1	18.56	1.44	0.2496
${\mathrm{x}}_2^2$	70.28	1	70.28	5.46	0.0348	significant
${\mathrm{x}}_3^2$	430.41	1	430.41	33.46	<0.0001	significant
${\mathrm{x}}_4^2$	452.71	1	452.71	35.2	<0.0001	significant
Residual error	180.08	14	12.86
Disfitting term	159.28	10	15.93	3.06	0.146	insignificant
Pure error	20.8	4	5.2
Sum	7998.07	28

, including quadratic sum, degree of freedom (DOF), mean square error (MSE), F value, and p-value. The F value and p-value of the RSM-BBD model were 43.42 and <0.0001, demonstrating that this regression equation was highly significant and could describe the mathematical relationship between four influence factors and response values of the SMX degradation rate. The coefficient of variation was 5.69% (<10%), and the signal-to-noise ratio was 22.809 (>4), showing that the RSM-BBD model was stable and reasonable. The R² and adj-R² were 0.9780 and 0.9550, respectively, reflecting that the relative error between the predicted and actual values was small. It was found that significant items of the model consisted of ${\mathrm{x}}_1$, ${\mathrm{x}}_2$, ${\mathrm{x}}_3$, ${\mathrm{x}}_4$, ${\mathrm{x}}_1{\mathrm{x}}_3$, ${\mathrm{x}}_1^2$, ${\mathrm{x}}_2^2$, ${\mathrm{x}}_3^2$, and ${\mathrm{x}}_4^2$. Relying on the F values, the influence of four factors on SMX degradation was determined, and the order was pH > t > C_SPC > $C_{{\mathrm{Fe}}^{2+}}$. Additionally, the significance test of the RSM-BBD model and coefficients were carried out to obtain the p-value, and the interaction effect was considered significant when p-value < 0.05. The significance of ${\mathrm{x}}_1{\mathrm{x}}_3$ demonstrated that the interaction effect of C_SPC and pH on the SMX degradation was significant.

To further analyze the interaction effect of four factors on SMX degradation, the 3D response surface diagram is exhibited in Figure 9. Figure 9a shows the convex surface; the degradation rate of SMX increased with the higher $C_{{\mathrm{Fe}}^{2+}}$ (30 μM) and lower C_SPC (20 μM). This result was consistent with the previous result shown in Section 3.1.2 due to suitable $C_{{\mathrm{Fe}}^{2+}}$ accelerating the photo-Fenton reaction to produce more $\bullet \mathrm{OH}$ (Equations (14) and (15)) and $\bullet {\mathrm{CO}}_3^{-}$ (Equations (16) and (17)) to enhance the SMX degradation. Meanwhile, a large amount C_SPC would produce more ${\bullet \mathrm{CO}}_3^{-}$ and ${\mathrm{HCO}}_4^{-}$, leading to unsatisfactory degradation performance, which is not as good as $\bullet \mathrm{OH}$. Figure 9b exhibited an irregular surface and presented a better degradation rate with a lower C_SPC (20 μM) and acid pH (4.0). The pH obviously affected the decomposition of SPC, and an acidic condition was inclined to produce more $\bullet \mathrm{OH}$. Figure 9c presented a concave surface, acidic pH, and higher $C_{{\mathrm{Fe}}^{2+}}$, which were beneficial in ensuring a high degradation rate of SMX. Fe²⁺ was quickly transformed into Fe³⁺ at an alkaline pH and then precipitated. This consumption of Fe²⁺ was not conducive to the Fenton reaction and the photo-Fenton reaction, resulting in the degradation rate of SMX being affected. Figure 9d–f all show that a longer reaction time interacted with low C_SPC, high $C_{{\mathrm{Fe}}^{2+}}$, and an acidic pH, respectively, to ensure an adequate reaction and better SMX degradation.

3.2.2. Evaluation of BP-ANN Model

The BP-ANN model was constructed using the experimental data collected from SMX degradation via the Fe²⁺/UV/SPC process. The MSE of neuron numbers in different hidden layers is shown in Figure 10a, and the training iteration of the BP-ANN model is exhibited in Figure 10b. We used 29 experimental values of the SMX degradation rate (Table S5) to constitute the data sets and randomly divided the data sets into two parts, including 24 training sets and 5 verification sets. Selecting the appropriate number of hidden layer neurons is necessary to determine the performance of the BP-ANN model. Too few hidden layer neurons would lead to insufficient fitting, and too many neurons would cause overfitting. Therefore, continuous training was necessary to meet the accuracy requirements in order to avoid mismatched fitting or overfitting in the training process. The number of hidden layer neurons were adjusted to 1~10 to determine the optimal number. As can be seen from Figure 10a, the number of hidden layers greatly influenced the MSE of the BP-ANN model, and the MSE value decreased with the increased number of neurons in the hidden layer. It was obvious that eight neurons in the hidden layer were the optimal value, and the corresponding MSE was the lowest at 0.015. This result indicated that the BP-ANN model had the highest accuracy and best predictability at this time; herein, the topology structure of the BP-ANN model was determined as 4-8-1.

Moreover, we optimized the BP-ANN model by training a large number of samples. Based on the topology structure of 4-8-1, we set the training steps as 10,000 times, the step length as 10, the learning rate as 0.5, and the momentum factor constant as 0.1. When the target error was at the magnitude order of 10⁻² after 10,000 times of iterative training calculation, the training of the BP-ANN model was completed. In Figure 10b, the training error curve shows that the MSE was 0.235 × 10⁻², which met the accuracy requirement of the target error. The final BP-ANN model of SMX degradation via the Fe²⁺/UV/SPC process was given in Equation (44); meanwhile, the ${\mathrm{W}}^{\mathrm{ih}}$ and ${\mathrm{W}}^{\mathrm{ho}}$ were expressed in Equations (45) and (46), respectively.

$${\mathrm{Y}}_{\mathrm{pre}}=\tanh (\tanh ({\mathrm{x}}_{\mathrm{i}}{\mathrm{W}}^{\mathrm{ih}}){\mathrm{W}}^{\mathrm{ho}})$$

(44)

$${\mathrm{W}}^{\mathrm{ih}}=\left[\begin{array}{cc}\begin{array}{ccc}0.443& -0.309& -0.434\\ -0.020& 0.299& -0.805\\ -0.103& 0.167& 0.019\end{array}& \begin{array}{c}0.175\\ 0.313\\ -1.937\end{array}\\ \begin{array}{ccc}-1.334& -0.502& 1.900\\ -0.685& -1.380& -0.208\\ \begin{array}{c}-0.009\\ \begin{array}{c}-1.053\\ 1.547\end{array}\end{array}& \begin{array}{c}0.507\\ \begin{array}{c}0.501\\ -0.566\end{array}\end{array}& \begin{array}{c}2.594\\ -1.101\\ 1.893\end{array}\end{array}& \begin{array}{c}-0.479\\ -0.184\\ \begin{array}{c}0.512\\ -0.462\\ 1.389\end{array}\end{array}\end{array}\right]$$

(45)

$${\mathrm{W}}^{\mathrm{ho}}=\left[\begin{array}{c}0.500\\ 0.913\\ \begin{array}{c}-0.576\\ 0.590\\ \begin{array}{c}-1.080\\ -1.780\\ \begin{array}{c}1.376\\ 2.401\end{array}\end{array}\end{array}\end{array}\right]$$

(46)

Commonly, Garson’s formula is used to obtain the influence degree of variables on the reaction [39]. In this study, according to the weight matrix of the eigenvalues predicted by the BP-ANN model, the relative importance (I_j) of each input variable (C_SPC, $C_{{\mathrm{Fe}}^{2+}}$, pH, t) to the response value was determined, and the weight matrix of eigenvalues was presented in

Table 2. Input layer–hidden layer connection weight (w^ih) and connection weights of the hidden layer and output layer (w^ho).

Wih					Who
Hidden Layer	CSPC	${\mathit{C}}_{{\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}}$	pH	t
1	0.443	−0.309	−0.434	0.175	0.500
2	−0.020	0.299	−0.805	0.313	0.913
3	−0.103	0.167	0.019	−1.937	−0.576
4	−1.334	−0.502	1.900	−0.479	0.590
5	−0.658	−1.380	−0.208	−0.184	−1.080
6	−0.009	0.507	2.594	0.512	−1.780
7	−1.053	0.501	−1.101	−0.462	1.376
8	1.547	−0.566	1.893	1.389	2.401

. Depending on Equation (20), the calculated I_j of C_SPC, $C_{{\mathrm{Fe}}^{2+}}$, pH, and t was 20.00%, 20.04%, 35.55%, and 24.42%, respectively. The order of relative importance was pH > t > $C_{{\mathrm{Fe}}^{2+}}\approx C_{\mathrm{SPC}}$. This result indicated that pH and t both played essential roles in SMX degradation via the Fe²⁺/UV/SPC process, which was consistent with the RSM model.

The prediction comparison of the RSM-BBD model and BP-ANN model was displayed in Figure 11a,b. The linear regression fittings R² of the two models were separate as 0.9765 and 0.9971, indicating that the RSM-BBD model and BP-ANN model both had a good ability to predict the SMX degradation via the Fe²⁺/UV/SPC process. The MAE and MSE of the BP-ANN model were 0.47 and 0.80. Meanwhile, the MAE and MSE of the RSM-BBD model were 2.11 and 6.21 when calculated by Equations (17) and (18). Based on the above analysis, the optimal theoretical conditions of the RSM-BBD model for predicting the SMX degradation rate were described as follows: $C_{{\mathrm{Fe}}^{2+}}$ = 28.15 μM, C_SPC = 20 μM, pH = 4, t = 26.8 min. Synchronously, the corresponding maximum degradation rate of SMX was 95.3%, and the experimental values fitted well with the predicted values due to the relative error of 3.08%. Additionally, for the BP-ANN model, the highest degradation rate of SMX was 96.18% after 15 iterations, and the optimal conditions were as follows: $C_{{\mathrm{Fe}}^{2+}}$ = 25.62 μM, C_SPC = 17.24 μM, pH = 4.2, t = 25.42 min. However, the relative error of the predicted and experimental values was only 1.17%. From the perspective of higher accuracy and lower error, the BP-ANN model had a better predicting capacity than the RSM-BBD model in forecasting the degradation performance of SMX via the Fe²⁺/UV/SPC system. Some studies [40] pointed out that the accuracy of the ANN model was higher than the RSM model when studying NOx removal in liquefied natural gas evaporation systems. This was consistent with our study that the BP-ANN model showed more significance in predicting the degradation performance of SXM. The BP-ANN model was conducive to obtaining the predicted value of the SMX degradation rate quickly and accurately when the experimental data were hard to collect. Synchronously, it was helpful to promote the development of the Fe²⁺/UV/SPC system in practical application.

4. Conclusions

In this research, the comprehensive assessment of the Fe²⁺/UV/SPC system on degrading SMX was carried out through the following aspects, involving performance optimization, degradation mechanism, and prediction model. The SMX could be effectively degraded via the Fe²⁺/UV/SPC system when adding appropriate amounts of $C_{{\mathrm{Fe}}^{2+}}$ (10~30 μM) and C_SPC (10 μM) under acidic conditions (pH = 4~6). Relying on probe compounds of TBA, PhOH, and NB, the results revealed that $\bullet \mathrm{OH}$ and $\bullet {\mathrm{CO}}_{3 }^{-}$ separately played the major and subordinate role in the degradation of SMX via the Fe²⁺/UV/SPC process, especially at acidic pHs. The $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ and $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$ was in the same order of magnitude, but the $k_{\bullet \mathrm{OH},\mathrm{SMX}}$ kept higher than 2.33 × 10⁸ M⁻¹s⁻¹, which was almost two times that of $k_{{\bullet \mathrm{CO}}_3^{-},\mathrm{SMX}}$. When pH increased from 4 to 8, the contribution rate of $\bullet \mathrm{OH}$ decreased from 62.9% to 46.3%; meanwhile, the contribution rate of $\bullet {\mathrm{CO}}_3^{-}$ increased from 17.3% to 31.5%. Simultaneously, the contribution of UV direct photolysis and other active intermediates remained at about 20~22%. These active intermediates might be produced via the Fe²⁺/UV/SPC system in SMX degradation, involving ${\bullet \mathrm{HO}}_2$, ${\mathrm{HCO}}_4^{-}$, $\bullet {\mathrm{O}}_{2 }^{-}$, or ¹O₂. Additionally, as compared with Cl⁻ and ${\mathrm{SO}}_4^{2-}$, ${\mathrm{HCO}}_3^{-}$ (0.1~0.5 mM) and ${\mathrm{CO}}_3^{2-}$ (0.5~3 mM) negatively affected the degradation rate, possibly due to their consumption of $\bullet \mathrm{OH}$ or H₂O₂ to inhibit the SMX degradation. Furthermore, two prediction models were successfully constructed by investigating four influence factors, such as $C_{{\mathrm{Fe}}^{2+}}$, C_SPC, pH, and t. The RSM-BBD model displayed the interaction effect of influence factors well, through the second-order polynomial regression equation (Equation (43)). The BP-ANN model was expressed as ${\mathrm{Y}}_{\mathrm{pre}}=\tanh (\tanh ({\mathrm{x}}_{\mathrm{i}}{\mathrm{W}}^{\mathrm{ih}}){\mathrm{W}}^{\mathrm{ho}})$, and the BP-ANN model exhibited significant capability in forecasting the SMX degradation rate in terms of higher accuracy and lower error. The BP-ANN model also reflected the relative importance well; pH > t > $C_{{\mathrm{Fe}}^{2+}}\approx C_{\mathrm{SPC}}$. When $C_{{\mathrm{Fe}}^{2+}}$ = 25.62 μM, C_SPC = 17.24 μM, pH = 4.2, t = 25.42 min, the predicted degradation rate of SMX was 96.18%, and the relative error of the predicted value and experimental value was only 1.17%. These findings help foster an in-depth understanding of the degradation mechanism of SMX, and they were conducive to the promotion of the development of the Fe²⁺/UV/SPC process in SMX degradation, especially in some practical scenarios.