Ultrasound Assisted Synthesis of Gadolinium Oxide-Zeolitic Imidazolate Framework-8 Nanocomposites and Their Optimization for Photocatalytic Degradation of Methyl Orange Using Response Surface Methodology

An ultrasound-assisted method was used to prepare gadolinium oxide (Gd2O3)-zeolitic imidazolate framework (ZIF)-8 nanocomposites. The surface morphology, particle size, and properties of the Gd2O3-ZIF-8 nanocomposites were examined using scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectroscopy, and ultraviolet-visible (UV-vis) spectroscopy. The synthesized Gd2O3-ZIF-8 nanocomposites were used as a catalyst to degrade methyl orange (MO) under UV light irradiation at 254 nm. The color of the aqueous MO dye solution during photocatalytic degradation was examined using color spectroscopy. Response surface methodology (RSM) using a four-factor Box-Behnken design (BBD) was used to design the experiments and optimize the photocatalytic degradation of MO. The significance of the experimental factors and their interactions were determined using analysis of variance (ANOVA). The efficiency of Gd2O3-ZIF-8 nanocomposites for the photocatalytic degradation of MO reached 98.05% within 40 min under UV irradiation at 254 nm under the experimental conditions of pH 3.3, 0.4 g/L catalyst dose, 0.0630 mM MO concentration, and 431.79 mg/L H2O2 concentration. The kinetics study showed that the MO photocatalytic degradation followed a pseudo-first-order reaction rate law.


Introduction
Azo dyes make up more than half of the dyes produced globally, and anthraquinone dyes can be found abundantly [1]. Organic dyes are commonly released into wastewater. These dyes are hazardous to the environment if they are not destroyed and cause serious pollution [2]. Therefore, it is necessary to degrade such organic dye pollutants [3].
According to their raw materials, process principles, and pollutant characteristics, dye wastewater treatment methods can be classified into various categories, which include physical adsorption, membrane separation, biodegradation, electrochemical treatment, and photocatalysis [3]. The use of advanced oxidation processes (AOPs) is a major pathway for the near-ambient degradation of wastewater pollutants because the waste water pollutants can be degraded almost completely [4].
Photocatalytic degradation of organic dyes employed on metal oxide semiconductors has received a lot of interest in recent years. Owing to its good chemical durability, high thermal stability, and low phonon energy, Gd 2 O 3 is a suitable semiconductor material for use as a photocatalyst [4]. It features a high refractive index and a suitable optical band gap, and is a potential candidate material for electronic and optoelectronic devices [4]. Gd 2 O 3 is an n-type semiconductor that can be used as a photocatalyst to degrade organic pollutants  [23,24]. The crystallite size of the Gd 2 O 3 nanowires in the synthesized Gd 2 O 3 -ZIF-8 nanocomposites was calculated using the Scherrer formula [25,26]. D = Kλ/ βcosθ (1) where D is the crystallite size, K is the Scherrer constant, λ is the X-ray wavelength (CuKα =0.15406 nm), β is the full width at half maximum intensity of the XRD peak in radians, and θ is the Bragg angle. The average crystallite size of the Gd 2 O 3 nanowires at 28.64 • in the (222) plane was 22.14 nm.
where D is the crystallite size, K is the Scherrer constant, is the X-ray wavelength (Cu =0.15406 nm), is the full width at half maximum intensity of the XRD peak in radia and is the Bragg angle. The average crystallite size of the Gd2O3 nanowires at 28.64 the (222) plane was 22.14 nm.

. Raman Spectroscopy
The Raman spectroscopy results of hybrid Gd2O3-ZIF-8 nanocomposites show prominent mode of Gd2O3 and major peaks of ZIF-8 in Figure 2 and the Raman shift ran from 200 cm −1 to 3500 cm −1 . A peak corresponding to the Fg + Ag mode of the Gd2O3 n owires was observed at 358.41 cm −1 [22,26].

Raman Spectroscopy
The Raman spectroscopy results of hybrid Gd 2 O 3 -ZIF-8 nanocomposites show the prominent mode of Gd 2 O 3 and major peaks of ZIF-8 in Figure 2 and the Raman shift ranges from 200 cm −1 to 3500 cm −1 . A peak corresponding to the F g + A g mode of the Gd 2 O 3 nanowires was observed at 358.41 cm −1 [22,26]. The Raman spectroscopy results of hybrid Gd2O3-ZIF-8 nanocomposites show prominent mode of Gd2O3 and major peaks of ZIF-8 in Figure 2 and the Raman shift ran from 200 cm −1 to 3500 cm −1 . A peak corresponding to the Fg + Ag mode of the Gd2O3 n owires was observed at 358.41 cm −1 [22,26].

Scanning Electron Microscopy
The SEM results of hybrid Gd 2 O 3 -ZIF-8 nanocomposites are shown in Figure 3. The SEM image of the Gd 2 O 3 shows that it had an aggregated nanowire-like shape (Figure 3a). The nanowire-like shape of Gd 2 O 3 was placed on the cubic-shaped ZIF-8 (Figure 3b,c).

Scanning Electron Microscopy
The SEM results of hybrid Gd2O3-ZIF-8 nanocomposites are shown in Figure 3. T SEM image of the Gd2O3 shows that it had an aggregated nanowire-like shape (Figure 3 The nanowire-like shape of Gd2O3 was placed on the cubic-shaped ZIF-8 (Figure 3b,c).

Investigation of Photocatalytic Activity for Degradation of MO using Gd2O3-ZIF-8 Nanocomposites
The property of light absorption was measured to identify the absorption band Gd2O3-ZIF-8 nanocomposites that corresponds to the light irradiation at 254 nm in Figu S1. The absorption peak of the Gd2O3-ZIF-8 nanocomposites was observed at 208 nm UV-vis spectroscopy in Figure S1a. The bandgap energy of Gd2O3-ZIF-8 nanocomposi was evaluated to be 4.85 eV in Figure S1b. Therefore, the photocatalyst of Gd2O3-ZIF nanocomposites could absorb light irradiation at 254 nm. Figure 4a shows the photocatalytic degradation of MO observed through UV-v spectrophotometry at constant time intervals. The UV-vis spectrophotometry data co firms that the absorption peaks of the MO solution decreased with time.
Upon UV irradiation, the electrons in the valence band of the photocatalyst mov into the conduction band. This resulted in the continuous generation of holes (h + ) in t valence band and electrons (e − ) in the conduction band. The generation of electron-ho pairs contributed to the activity of the photocatalyst. Holes with high oxidative abil

Investigation of Photocatalytic Activity for Degradation of MO using Gd 2 O 3 -ZIF-8 Nanocomposites
The property of light absorption was measured to identify the absorption band of Gd 2 O 3 -ZIF-8 nanocomposites that corresponds to the light irradiation at 254 nm in Figure S1. The absorption peak of the Gd 2 O 3 -ZIF-8 nanocomposites was observed at 208 nm in UV-vis spectroscopy in Figure S1a. The bandgap energy of Gd 2 O 3 -ZIF-8 nanocomposites was evaluated to be 4.85 eV in Figure S1b. Therefore, the photocatalyst of Gd 2 O 3 -ZIF-8 nanocomposites could absorb light irradiation at 254 nm. Figure 4a shows the photocatalytic degradation of MO observed through UV-vis spectrophotometry at constant time intervals. The UV-vis spectrophotometry data confirms that the absorption peaks of the MO solution decreased with time.
higher R 2 (0.9943) among the two examined models appears in the first-order k model, validating the underlying kinetics for MO dye degradation under ultraviole diation at 254 nm.
The linear behavior of the curve confirms that the degradation of MO follo pseudo-first-order reaction rate law as shown in Figure 4b and the value of R 2 (coef of determination) for the pseudo-first-order reaction kinetics was 0.9943.

Color Test of Photocatalytic Degradation of MO Dye Solution
The changes in ∆L, ∆a, ∆b, and ∆E are listed in Table 1. The increase in ∆L ind that the MO solution became whiter because of photocatalytic degradation. The ne values of ∆a and ∆b indicate that the MO solution tended to become less reddish to photocatalytic degradation. The total color change, ∆E, indicates the color diff between two colors under UV light irradiation [34,35]. Before the color of the solutio measured by a color spectrophotometer, the solution was centrifuged for 1 min to r the photocatalyst from the solution. Then, we measured the color of only liquid so Upon UV irradiation, the electrons in the valence band of the photocatalyst moved into the conduction band. This resulted in the continuous generation of holes (h + ) in the valence band and electrons (e − ) in the conduction band. The generation of electron-hole pairs contributed to the activity of the photocatalyst. Holes with high oxidative ability oxidized OH − ions into ·OH radicals in the aqueous MO solution. Valence band holes and conduction band electrons combined with hydroxide ions and oxygen to produce ·OH and ·O 2 − radicals. The ·OH and ·O 2 − radicals could act as oxidizing agents to the MO dye molecules [4,5,29]. The role of each component in the Gd 2 O 3 -ZIF-8 nanocomposites is as a co-photocatalyst due to the enhanced rate of photocaltalytic degradation of MO when Gd 2 O 3 and ZIF-8 are combined than when only Gd 2 O 3 is alone [6,26].

Kinetics Study for Photocatalytic Degradation of MO
To determine the photocatalytic kinetic model, the degradation of MO dye is examined with two kinetic models, including the first-order kinetic model and the second-order kinetic model, as expressed in the following equations. First-order kinetic model [30,31]: Second-order kinetic model [32,33]: where C 0 (mM) and C t (mM) are assigned as concentration of MO dyes at time = 0 and time = t (min −1 ), respectively. k 1 (min −1 ) and k 2 (min −1 ) represent the rate constants of firstorder and second-order, respectively. Accordingly, the fitting results from experimental investigations into two distinct kinetic models are demonstrated in Figure S2, where higher R 2 (0.9943) among the two examined models appears in the first-order kinetic model, validating the underlying kinetics for MO dye degradation under ultraviolet irradiation at 254 nm. The linear behavior of the curve confirms that the degradation of MO followed a pseudo-first-order reaction rate law as shown in Figure 4b and the value of R 2 (coefficient of determination) for the pseudo-first-order reaction kinetics was 0.9943.

Color Test of Photocatalytic Degradation of MO Dye Solution
The changes in ∆L, ∆a, ∆b, and ∆E are listed in Table 1. The increase in ∆L indicates that the MO solution became whiter because of photocatalytic degradation. The negative values of ∆a and ∆b indicate that the MO solution tended to become less reddish owing to photocatalytic degradation. The total color change, ∆E, indicates the color difference between two colors under UV light irradiation [34,35]. Before the color of the solution was measured by a color spectrophotometer, the solution was centrifuged for 1 min to remove the photocatalyst from the solution. Then, we measured the color of only liquid solution with a color spectrophotometer. Therefore, the aggregation of photocatalyst did not affect measuring the color of the solution. The color change of the MO photocatalytic degradation was measured within the range of 0 to 100. Figure 5 shows the chromaticity diagram using the calculated x and y coordinates of a given color in the CIE 1931 color space. The color of the MO solution in the CIE1931 color space changed from red to green and from yellow to blue with increasing UV light exposure time because of photocatalytic degradation. with a color spectrophotometer. Therefore, the aggregatio measuring the color of the solution. The color change of tion was measured within the range of 0 to 100. Figure 5 using the calculated x and y coordinates of a given color color of the MO solution in the CIE1931 color space chan yellow to blue with increasing UV light exposure time be tion.  Times ∆L ∆a 0 min 0 0 The photocatalytic degradation of MO using Gd 2 O 3 -ZIF-8 nanocomposites is optimized by a four-factor and three-level BBD design consisting of 27 sets of experimental data for the optimization reactions, including replication at the center point [25,36]. Four independent variables, namely the initial pH (X 1 ), catalyst dose (X 2 ), MO concentration (X 3 ), and H 2 O 2 concentration (X 4 ), were assessed. The photocatalytic degradation efficiency of MO was used as the response variable (Y). Table 2 shows the low (−1), medium (0), and high (+1) levels and the ranges of the independent variable parameters. The experimental data and response for the photocatalytic degradation of MO are shown in Table 3.
In Figure 6a, the effect of pH was investigated by varying only the pH from 3 to 7 while the other conditions remained the same. Under acidic conditions, the MO was negatively charged, and the photocatalyst surface positively charged [29]. Electrostatic attraction occurred between the MO and the photocatalyst. The transformation of the MO dye molecules to CO 2 and H 2 O under radical attack in the photocatalytic reaction was attributed to electrostatic attraction [37,38].

Optimization for Photocatalytic Degradation of MO Using Response Surface Methodology (RSM)
RSM was applied to predict the percentage efficiency (%) of the photocatalytic degradation of MO using the Gd2O3-ZIF-8 nanocomposites photocatalyst under the variation of four parameters, namely, the pH, catalyst dose (g/L), MO concentration (mM), and H2O2 concentration (mg/L). We obtained the predicted degradation percentage using Design Expert 11 statistical software (Stat-Ease, Minneapolis, MN, USA) in Figure S3.
As shown in Table 3, the resulting photocatalytic degradation efficiency of MO fell in the range of 32.12 to 94.79%. The quadratic polynomial regression model in Equation (4) where , , , and represent the coded values of the pH, photocatalyst dose, initial MO solution concentration, and H2O2 concentration, respectively. The accuracy of the model was verified by analysis of variance (ANOVA), and the results are presented in Table 4. The fitness of the BBD model was obtained by applying the suitability equation to the quadratic polynomial model based on the experimental data in Table 4 [15]. The obtained experimental data were scattered very closely to the trend line of the predicted data, as shown in Figure 7 [36]. The statistical parameters evaluated were the value of , the lack of fit (LOF), the p value, and the F value [42]. A regression model with a value greater than 0.9 is considered to have a high correlation between the experimental and predicted values [42]. In this study, the correlation factor obtained was 0.9988, indicating an excellent correlation and a satisfactory model for predicting the best conditions

Effect of Photocatalyst Concentration
In Figure 6b, the effect of the photocatalyst concentration was investigated by varying only the photocatalyst dose from 0.1 g/L to 0.3 g/L while the other conditions remained the same. Increasing the concentration of the photocatalyst in the MO solution may decrease the transmission of light [3]. Therefore, excess photocatalyst in solution could interfere with the photocatalytic degradation of the MO solution [36].

Effect of MO Concentration
After 40 min, the MO photocatalytic degradation efficiency decreased when the MO concentration increased from 0.0630 to 0.0105 mM (Figure 6c). Within the experimental range, the pseudo-first-order rate constant k 1 decreased with an increase in the MO concentration based on Equation (10) [3]. These results indicate that the absorption of light on the photocatalyst surface decreased at higher concentrations. Moreover, the photocatalytic degradation of MO occurred on the surface of the active sites of the photocatalyst [39].

Effect of H 2 O 2 Concentration
H 2 O 2 and metal oxide nanoparticles have been used to increase the photocatalytic degradation rate of MO [40]. The addition of H 2 O 2 in the presence of catalyst was studied [41]. Figure 6d shows the effect of the H 2 O 2 concentration on the photocatalytic degradation of MO. RSM was applied to predict the percentage efficiency (%) of the photocatalytic degradation of MO using the Gd 2 O 3 -ZIF-8 nanocomposites photocatalyst under the variation of four parameters, namely, the pH, catalyst dose (g/L), MO concentration (mM), and H 2 O 2 concentration (mg/L). We obtained the predicted degradation percentage using Design Expert 11 statistical software (Stat-Ease, Minneapolis, MN, USA) in Figure S3.
As shown in Table 3, the resulting photocatalytic degradation efficiency of MO fell in the range of 32.12 to 94.79%. The quadratic polynomial regression model in Equation (4) was used to obtain the degradation percentage of MO: where X 1 , X 2 , X 3 , and X 4 represent the coded values of the pH, photocatalyst dose, initial MO solution concentration, and H 2 O 2 concentration, respectively. The accuracy of the model was verified by analysis of variance (ANOVA), and the results are presented in Table 4. The fitness of the BBD model was obtained by applying the suitability equation to the quadratic polynomial model based on the experimental data in Table 4 [15]. The obtained experimental data were scattered very closely to the trend line of the predicted data, as shown in Figure 7 [36]. The statistical parameters evaluated were the value of R 2 , the lack of fit (LOF), the p value, and the F value [42]. A regression model with a R 2 value greater than 0.9 is considered to have a high correlation between the experimental and predicted values [42]. In this study, the R 2 correlation factor obtained was 0.9988, indicating an excellent correlation and a satisfactory model for predicting the best conditions for MO degradation using the Gd 2 O 3 -ZIF-8 nanocomposites. The p value is an indicator of the statistical significance and interaction ability of each variable, wherein variables with lower p values have greater significance. In the present study, ANOVA for the regression model was highly significant because of the very small p value < 0.0001, and a correspondingly large F value (710.13) was obtained. The lack of fit value obtained for the F value was 2.02 and had a larger p value (0.3762) > 0.05, indicating that the lack of fit was not significant [42][43][44][45]. Therefore, the regression model is reliable for predicting the effects of variables affecting the photocatalytic degradation of MO by the Gd 2 O 3 -ZIF-8 nanocomposites and can be used to direct the design space.  [42][43][44][45]. Therefore, the regression model is reliable for predicting the effects of variables affecting the photocatalytic degradation of MO by the Gd2O3-ZIF-8 nanocomposites and can be used to direct the design space. The linear and quadratic terms that affect the photocatalytic degradation of MO were highly significant, with p ˂ 0.0001. Meanwhile, the interaction terms X1X2 and X1X4 were significant, with p ˂ 0.0001 (Table 4) [16]. However, the interaction term X1X3 was not significant within the range assessed in this study. In Figure 6     The linear and quadratic terms that affect the photocatalytic degradation of MO were highly significant, with p < 0.0001. Meanwhile, the interaction terms X 1 X 2 and X 1 X 4 were significant, with p < 0.0001 (Table 4) [16]. However, the interaction term X 1 X 3 was not significant within the range assessed in this study. In Figure 6, the influence of a single factor on the degradation of MO was evaluated when all the other factors were maintained at the constant values for which the coded values of these factors are zero and lie between their low and high values. The pH and MO concentration negatively affected the photocatalytic degradation of MO. The efficiency of the photocatalytic degradation of MO decreased as the pH of the solution increased from 3 to 7. (X 2 ) and (X 4 ) showed a positive effect on the photocatalytic degradation. The photocatalytic degradation of MO using the Gd 2 O 3 -ZIF-8 nanocomposites showed an upward trend with an increase in (X 2 ) and (X 4 ). This increase is attributed to the increase in the number of active sites on the photocatalyst surface. In runs 1 and 23, the degradation efficiency increased from 46.93% to 75.89% when the solution pH decreased from 7 to 3. The photocatalytic degradation efficiency increased from 43.85 to 57.62% when the catalyst dose increased from 0.1 g/L in run 8 to 0.5 g/L in run 15. In addition, when the concentration of H 2 O 2 increased from 111 mg/L to 555 mg/L, the degradation efficiency increased from 32.12% to 48.63%. Meanwhile, the interaction between both factors was highly significant (p < 0.0001). This suggests that a high percentage of MO degradation can be achieved with a high H 2 O 2 concentration as well as a low pH, which can be seen from the direct proportionality between the H 2 O 2 concentration and the pH in Figure 8c,d. In addition, a high concentration of H 2 O 2 and photocatalyst at low pH increased the availability of local electrons on the surface of the photocatalyst, thereby increasing the photocatalytic degradation rate. In general, the photocatalytic degradation of MO increased when a larger amount of photocatalyst was used in the reaction because the number of active sites increased when there was a high surface-to-volume ratio. In addition, the abundant availability of active sites allowed ·OH radicals and MO to be easily adsorbed onto the surface of the photocatalyst followed by the fast exchange of electrons between the reactants. As a result, MO degradation occurred rapidly. However, a slight decline in the photocatalytic degradation percentage was observed when the amount of photocatalyst used exceeded the optimal dosage.

Optimum Condition and Model Verification
Within the experimental conditions of the parameters we used, the RSM method was to determine the optimal condition for the photocatalytic degradation of MO. Therefore, we have limited experimental conditions for the following: The pH ranges from 3 to 7, the dose of catalyst ranges from 0.1 g/L to 0.5 g/L, the concentration of MO ranges from 0.0630 mM to 0.1050 mM, and the concentration of H2O2 ranges from 111 mg/L to 555 mg/L.
The optimization function in Design Expert 11.0 was used to obtain the optimum conditions for the photocatalytic degradation of MO under four constraints: (1) The maximum photocatalytic degradation percentage was 97.24% at the initial pH of 3.3, photocatalyst dose of 0.4 g/L, MO concentration of 0.0635 mM, and H2O2 concentration of 431 mg/L. The experiment showed a photocatalytic degradation percentage of 98.05% under the optimum conditions compared with the photocatalytic degradation of 97.24% obtained from the regression model. In addition, the conditions for obtaining the highest MO photocatalytic degradation percentage at (2) the minimum weight of photocatalyst, (3) the minimum volume of H2O2, and (4) neutral pH are also listed in Table 5 [45]. The results show that the experimental design was effectively applied for optimizing the photocatalytic degradation of MO.

Optimum Condition and Model Verification
Within the experimental conditions of the parameters we used, the RSM method was to determine the optimal condition for the photocatalytic degradation of MO. Therefore, we have limited experimental conditions for the following: The pH ranges from 3 to 7, the dose of catalyst ranges from 0.1 g/L to 0.  Table 5 [45]. The results show that the experimental design was effectively applied for optimizing the photocatalytic degradation of MO.

Measurement Methods
The structure pattern and average crystallite size of Gd 2 O 3 -ZIF-8 nanocomposites were investigated using an X-ray diffractometer (Bruker, D8 ADVANCE, Karlsruhe, Germany) with a Cu Kα radiation source (0.1504 nm). The morphology of the synthesized Gd 2 O 3 -ZIF-8 nanocomposite photocatalyst was observed at an accelerating voltage of 10-20 kV using scanning electron microscopy (SEM, JEOL Ltd., JSM-6510, Tokyo, Japan). The vibrational states of the synthesized Gd 2 O 3 -ZIF-8 nanocomposites were investigated by Raman spectroscopy (532 nm excitation, BWTEK i-Raman Plus, Newark, DE, USA). Photocatalytic degradation of the MO dye was carried out using a UV lamp (Light intensity is 4 W, 254 nm) and was confirmed by UV-vis spectroscopy (Shimazu UV-1601 PC, Tokyo, Japan). The color of MO dye solution was observed using a color spectrophotometer (Colormate, Scinco, Seoul, Korea).

Preparation of Gd 2 O 3 Nanowires
Gd 2 O 3 nanowires were synthesized using the following hydrothermal procedure: 0.9 g of Gd(NO 3 ) 3 ·6H 2 O was dissolved in 25 mL of deionized water. 0.5 mL of C 2 H 5 NH 2 was then added slowly to the Gd(NO 3 ) 3 aqueous solution under vigorous stirring. The obtained white precipitate solution was heated for 12 h in an oven at 120 • C. The mixture was centrifuged several times after cooling and washed with deionized water to obtain gadolinium hydroxide. The gadolinium hydroxide was dried at 80 • C in an oven and then annealed in an electric furnace at 700 • C for 4 h in an Ar atmosphere to obtain Gd 2 O 3 [22].

Photocatalytic Activity of MO Degradation using Gd 2 O 3 -ZIF-8 Nanocomposites
The photocatalytic degradation of MO by the Gd 2 O 3 -ZIF-8 nanocomposites was performed in an aqueous MO dye solution under UV irradiation at 254 nm.
The initial pH values were adjusted to 3, 5, and 7 using 1 M aqueous HCl solution. The photocatalyst was added to the prepared MO solution and kept under constant stirring in the dark for adsorption. After adsorption-desorption equilibrium was reached between the MO dye and the catalyst in the solution for 30 min, the solution was irradiated under UV light at 254 nm with regular intervals, after which the photocatalytic degradation of MO was observed by UV-vis spectrophotometry. The photocatalytic degradation efficiency was measured using the following equation (Equation (5)) [21,47]: where C 0 is the initial MO concentration after adsorption-desorption equilibrium has been reached under dark conditions (t = 0), and C is the MO concentration after 40 min. The values for the photocatalytic degradation of MO are shown in Table 2.

Evaluation of Color Change during Photocatalytic Degradation of MO
The CIELAB method was used to determine the color parameters L, a, and b. L indicates the lightness, and a and b are the chromaticity coordinates. The a parameter represents the red (+) to green (−) components. The b parameter represents the yellow (+) to blue (−) components. L can vary from white (100) to black (0) [48]. The colors of the initial and final solutions were measured using a color spectrophotometer. The total color change (∆E) for each solution was calculated as follows: ∆L = L 0 − L t (8) ∆E = (∆a 2 + ∆b 2 + ∆L 2 ) 1/2 (9) where a 0 , b 0 , and L 0 are the initial color parameters; a t , b t , and L t the final parameters at the reaction time t (min); and ∆a, ∆b, and ∆L are the differences between the initial and final parameter values [34,35].

Experimental Design with RSM
The experimental design was based on the Box-Behnken design (BBD) with four factors at three levels. Table 1 shows the independent variables, experimental ranges, and coded levels of the tested variables in the BBD. The initial pH (X 1 ), dose of catalyst (X 2 ), concentration of MO (X 3 ), and concentration of H 2 O 2 (X 4 ) were selected as the independent variables. The predicted photocatalytic degradation efficiency of MO (Y) was used as the dependent variable. A quadratic polynomial equation (Equation (10)) was used to fit the response variables [20,45]: where β 0 is a constant coefficient, β i are the linear interaction coefficients, β ii are the quadratic interaction coefficients, β ij are the cross-factor interaction coefficients, k is the number of factors investigated in the experiment, and X i , and X j are independent variables [45]. In the analysis of variance (ANOVA), the significance and suitability of the model were assessed using the lack of fit (LOF), F value, p value, and coefficient of determination (R 2 ). Surface plots (3D) and contour plots (2D) of MO photocatalytic degradation efficiency (%) were employed to demonstrate the effect of two interaction variables on the response (% degradation) based on the model Equation (10).

Conclusions
In this study, Gd 2 O 3 -ZIF-8 nanocomposites were successfully prepared using an ultrasound-assisted synthesis method and characterized by XRD, Raman spectroscopy, SEM, and UV-vis spectroscopy. The photocatalytic degradation of MO using Gd 2 O 3 -ZIF-8 nanocomposites as catalyst under various conditions was studied in detail. The color changes between the initial and final Lab values were confirmed in the coordinate diagram. The optimization of the MO photocatalytic degradation process was studied using response surface methodology based on the Box-Behnken design. The proposed regression model was highly reliable. Under optimal conditions (pH 3.3, 431 mg/L of H 2 O 2 , 0.0635 mM of MO, and 0.4 g/L of photocatalyst), the photocatalytic degradation percentage of MO was 98.05% after 40 min. The photocatalytic degradation of MO using Gd 2 O 3 -ZIF-8 nanocomposites was found to follow the pseudo-first-order kinetics rate law.