Optimization of Adsorption Conditions Using Response Surface Methodology for Tetracycline Removal by MnFe 2 O 4 /Multi-Wall Carbon Nanotubes

: In this study, the optimal conditions and effects of external factors on tetracycline adsorption by magnetic multi-walled carbon nanotubes (MMWCNTs) were established by a response surface methodology for the ﬁrst time. Batch adsorption experiments showed that increasing the dosage and contact time effectively promoted the adsorption of tetracycline and maximum removal of 97.93–99.13% was achieved at pH 3–7. The pseudo-second-order model and Fourier-transform infrared spectroscopy spectra indicated that the mechanism of adsorption may be π – π electron interaction and cation– π electron bonding. Design Expert was utilized to develop a response surface methodology for the analysis and optimization of tetracycline adsorption by magnetic multi-walled carbon nanotubes. The Box–Behnken design (BBD) results showed that the optimization exhibited high signiﬁcance and reliability. The main effect plots and Pareto chart indicated that pH exerted a signiﬁcant individual effect on the regulation of adsorption, while 3D response surface plots and interaction effect plots exhibited a signiﬁcant antagonistic interaction between pH and contact time. A maximum tetracycline removal of 99.16% was achieved under the optimal conditions of 12 mg adsorbent dosage at pH 5.43, with an adsorption time of 120 min. Mathematical and experimental results conﬁrmed the accuracy of the established optimal conditions.


Introduction
Tetracycline (TC) is an emerging contaminant and one of the most commonly occurring antibiotics, which has been extensively utilized for medical applications due to its highly lethal effect on a variety of bacteria [1,2].TC is difficult to degrade in organisms and can even be converted into more toxic substances [2,3].Studies have shown that 70-90% of TC was excreted by humans and animals in an unmetabolized form, resulting in the occurrence of TC in various aquatic environments [4][5][6][7].TC has been detected in the wastewater generated from a variety of sources including human municipal, animal husbandry, agriculture, medical, pharmaceutical, and sewage plant drainage [8][9][10][11][12][13].TC remained in aquatic environments and has been shown to destroy microbial communities in receiving water bodies [14].TC would induce the formation of multi-resistant genes in microorganisms, resulting in resistance to TC drugs and increasing public health risks [15][16][17].
In the field of organic micropollutant treatment, the adsorption process has been certified by the U.S. Environmental Protection Agency as the most efficient treatment technology and is currently the more widely used technology.[18][19][20][21][22][23].The researchers proposed that adsorption by magnetic multi-walled carbon nanotubes (MMWCNTs) was a highly practical process due to the simplicity of design, excellent contaminant adsorption performance, and low environmental impact [24][25][26][27][28]. Previous studies have indicated that the adsorption process by MMWCNTs was capable of highly efficient removal of antibiotics [29][30][31].Although MMWCNTs could effectively remove TC, the optimization of the adsorption effect of MMWCNTs on TC and the interaction of various factors on treatment efficiency have not been documented [32,33].
According to the survey, the conditional optimization methods used in the adsorption process are listed in Table S1 [32,[34][35][36][37][38][39][40][41][42][43][44].Among the experimental methods, response surface methodology (RSM) was utilized to fit a mathematical model and experimental data, to analyze the relationship between influencing factors and response values, and to obtain the optimal operating conditions for a specific system [25,38,41,[45][46][47][48].In RSM, both Box-Behnken design (BBD) and central composite design (CCD) are plane-centered design methods.Compared with CCD, BBD is more inclined to solve the local optimal solution (the level of BBD factors is generally less than 5) [20,49,50].As one of the most commonly used response surface methods, the BBD avoided extreme conditions, and it had a moderate number of experiments, simple and efficient software operation, and high reliability and accuracy of optimization results, without massive training data for the simulation [25,29,[51][52][53].The removal rate of TC in this study was affected by three factors (pH, time, and adsorbent dosage).Apparently, BBD is more suitable for this study.In this paper, the studies on the optimization of TC removal and multiwall carbon nanotube (MWCNTs) adsorption process by RSM-BBD were summarized, which were recorded in Tables S2 and S3.Table S2 [54][55][56][57] and Table S3 [ [58][59][60][61][62][63][64][65][66] showed that BBD could improve adsorption efficiency and save resources in the fields of MWCNTs adsorbent and TC removal, respectively [54,58].At present, RSM-BBD optimization of MMWCNTs adsorption TC needs further practice.
In this study, MMWCNTs were successfully synthesized using a previously reported method for TC removal.To our knowledge, no one has ever used RSM-BBD to simulate, analyze and optimize the process of TC adsorption on MMWCNTs, using three independent variables: adsorbent dosage, pH, and time.The independent variable input values and the individual effects of the three factors were studied using batch adsorption experiments.The adsorption mechanism was established according to adsorption kinetics fitting and characterization results.Analysis of variance (ANOVA) was used to examine the significance of the model.The interactive effects of factors were assessed using response surface plots, interaction effect plots, and Pareto chart analysis, allowing the related parameters affecting removal efficiency to be statistically optimized.This study provides a feasible method for optimizing and adjusting TC adsorption conditions while enhancing the potential for the practical application of magnetic carbon nanotubes.The optimization of external conditions promotes the quality and efficiency of the TC adsorption process, providing a reference method for the improvement of TC removal efficiency.The process optimization method of TC adsorption by MMWCNTs should further adapt the actual operating conditions to increase the optimization parameters and pollutant types.
An electronic balance (BSA124S-CW, Sartorius AG, Mettler Toledo Instrument Co., Ltd., Shanghai, China) was used to weigh materials and a pH meter (PB-10, Sartorius AG) was used to determine the pH of solutions.A digital display electric constant temperature water bath (XMTD-204, Honour Instrument Shaker Co., Ltd., Tianjin, China) was used to heat carbon nanotube solutions and the iron-manganese mixture.A JJ-1 electric mixer and GL-88-b type vortex mixer (Haimen Kyling-bell Lab Instruments Co., Ltd., Haimen, China) was used for solution mixing.

Preparation of MMWCNTs Composites
The MMWCNTs (Size is about 10-50 nm) were prepared using a co-precipitation method previously reported by Zhao et al. [7].The specific preparation methods of MMWC-NTs, as well as Transmission Electron Microscope (Figure S1a,b), zeta potential (Figure S1c), and Fourier-transform infrared spectroscopy (Figure S1d) scanning electron microscope (Figure S1e) and Energy Dispersive X-ray spectroscopy (Figure S1f) characterization, are all provided in the Supplementary Materials.

Batch Adsorption Experiments
In this study, the dosage of adsorbent, pH, and the adsorption time were assessed as the variable factors for batch adsorption experiments.According to previously reported studies, adsorbent dosage directly affects the number of adsorption sites and the mass transfer efficiency [25,67].Due to protonation and deprotonation, the surface charge of the material and the chemical forms of organic compounds are transformed under varying pH conditions, affecting electrostatic and chemical bonding between TC and adsorbents [8,[67][68][69][70].The influence of contact time on adsorption is indicative of the adsorption reaction kinetics and can be used to establish the adsorption mechanism [4,17,70].
For the adsorption time batch experiment, 50 mL of the 20 mg/L TC solution was placed in a 150 mL conical flask, then 12 mg of MMWCNTs were accurately weighed using an electronic balance and mixed with the TC solution.The pH of the solution was maintained at 7 by adding 1 M nitric acid or sodium hydroxide in a dropwise manner as required.The conical flask was fixed in a thermostatic water bath at a temperature of 298.15 K, with continual oscillation at 140 rpm for 1500 min.Samples were collected from a conical flask for measurements at specified time points (1,2,5,8,10,15,20,25,30,45,60,90,120,720,840,960, and 1440 min).For batch experiments assessing the effects of varying pH, the maximum adsorption time was fixed at 1440 min, with the pH of the solution varying from pH 2-10, while for adsorbent dosage batch experiments, the dosage varied from 5 to 13 mg, with all other conditions remaining constant as described above.After adsorption, the adsorbent and TC solution mixture were left to stand for 30 min before 5 mL of supernatant was taken from the conical flask with a gel head dropper and filtered through a 0.45 µm cellulose filter membrane.The absorbance of the filtered sample was measured using a spectrophotometer (TC adsorption wavelength of 360 nm).The experiments were repeated in triplicate under the same conditions, with the average values used for further analysis.The solution removal rate (%) and equilibrium adsorption capacity q e (mg/g) were calculated according to Equation (1) and Equation (2), respectively.
Here, C 0 represents the initial concentration of TC before adsorption (mg/L); C e represents the concentration of TC after adsorption (mg/L); m indicates the mass of MMWCNTs (mg); and V indicates the volume of the solution.

Box-Behnken Design Model
According to the TC removal efficiency under different conditions, the range of conditions associated with higher removal rates was preliminarily determined [51].As shown in Table S4, adsorbent dosage (A), adsorption time (B), and solution pH (C) values were divided into three levels (−1, 0, 1), with adsorbent dosage levels of 6, 9, and 12 mg, adsorption time levels of 120, 300, and 480 min, and pH value levels of 4, 5, and 6.In total, 17 experiments were simulated using Design Expert (v.10.0.3) software, with TC removal efficiency set as the response (Y) for each respective variable.ANOVA and residual values were used to establish the fitness of the model, the rationality of equations, and the significance of the response [52,71].The main effect plots and Pareto chart for different factors were analyzed to assess the individual effect of each factor, with the interactions between factors then established using 3D response surface plots, Pareto chart, and interaction effect plots [26].The RSM was employed to identify the exact external condition values capable of achieving maximum removal efficiencies [72].Actual measurement values verified the predicted effect of the model.
The nonlinear quadratic model adopted for response surface analysis is shown in the Supplementary Materials.

Effect of Dosage
With the initial increase in dosage of MMWCNTs from 5 mg to 7 mg the removal rate increased linearly from 78% to 87% due to the increase in active sites and the high available concentration of TC (Figure 1).However, due to the agglomeration of adsorbents, further increases in adsorbent dosage led to a decline in the total adsorbent surface area and the availability of active surface sites [73].Increasing adsorbent dosages from 8 to 12 mg resulted in a smaller increase in the adsorption efficiency (<5%), with the adsorption rate becoming slower and gradually stabilizing from a dosage of 12 mg upwards, achieving a maximum TC removal rate of 99.5%.The relationship between the adsorption capacity and removal rate exhibited an inverse trend, with an increase in adsorbent dosage from 5 to 6 mg resulting in a reduction in adsorption capacity from 202.6 mg/g to 145 mg/g, with a further increase in dosage to 13 mg causing the adsorption capacity to reduce to 80 mg/g.With the increase in TC removal and adsorbent dosage, the adsorption mass transfer efficiency declined, due to TC molecules saturating the surface adsorption sites and reducing the total surface area of the adsorbent [74].The final adsorption capacity was maintained at about 83 mg/g (equilibrium adsorption capacity of 20 mg/L TC).In summary, increasing adsorbent dosage can promote TC removal, although adsorption is reduced with excessive TC concentrations.According to the experimental results, at a concentration of 20 mg/L TC, 6-12 mg was selected as the adsorbent dosage input value for RSM analysis.

Effect of pH
As shown in Figure 2, the optimal pH range for TC removal by 12 mg MMWCNTs within 24 h was pH 3-7, achieving a removal rate of 97.59-99.31%.The q e reached a maximum of 83 mg/g at pH 3 and gradually declined as the pH increased to pH 6 and above.At pH < 3.0 and >7.0, the adsorption effect of TC reached a maximum of 90-95%, with an adsorption capacity of <80 mg/g.Under different pH conditions, TCs showed different functional groups, making the adsorption effect of MMWCNTs on TCs inconsistent.In aqueous solutions, TC exhibits three pK a values of 3.3, 7.7, and 9.7 [5,75], due to its characteristics of containing electron-deficient amino and enone groups, as well as an electron-rich phenol ring [67,69].At pH < 3.3, the solution is acidic, resulting in the dimethylamine group attracting protons and TCH 3 + being the dominant component in the TC group, causing the TC molecules in the solution to exhibit cationic properties [17,76], with the potential of MMWCNTs being approximately 32 mV (Figure S1c).Despite strong interactions that resulted in the adsorption of more than 90% of TC in solution, adsorbents and contaminants are subject to electrostatic repulsion.At 3.3 < pH < 7.7, the dominant group in TC was TCH 2 0 , which has no external electrical properties, indicating that the adsorption of TC reached a peak level without the occurrence of electrostatic repulsion [4].
At pH > 7.7, TC was dominated by negatively charged TCH 2 − and TC 2− , while the potential of MMWCNTs was about −15mV due to the deprotonation of carboxyl groups on the adsorbent [10,15,[77][78][79].At pH pzc , adsorption could not be attributed to electrostatic interactions, and therefore, the removal of TC by MMWCNTs was higher at pH 3-7.The reason may be that the pH is in the range of 3-7, the TC amphiphilic form (TCH 2 0 ) exists, the TC molecules have almost no electrostatic attraction or repulsion to MMWCNTs, and the effect of pH on TC adsorption is negligible.Whereas, when the pH is less than 3 or more than 7, TC and MMWCNTs have the same charge, and a certain degree of electrostatic repulsion is generated, which is not favorable for the adsorption of TC by MMWCNTs.Based on the above analysis, the pH input value was set to 4-6 in the RSM.

Effect of pH
As shown in Figure 2, the optimal pH range for TC removal by 12 mg MMWCNTs within 24 h was pH 3-7, achieving a removal rate of 97.59-99.31%.The qe reached a maximum of 83 mg/g at pH 3 and gradually declined as the pH increased to pH 6 and above.At pH < 3.0 and >7.0, the adsorption effect of TC reached a maximum of 90-95%, with an adsorption capacity of <80 mg/g.Under different pH conditions, TCs showed different functional groups, making the adsorption effect of MMWCNTs on TCs inconsistent.In aqueous solutions, TC exhibits three pKa values of 3.3, 7.7, and 9.7 [5,75], due to its characteristics of containing electron-deficient amino and enone groups, as well as an electronrich phenol ring [67,69].At pH < 3.3, the solution is acidic, resulting in the dimethylamine group attracting protons and TCH3 + being the dominant component in the TC group, causing the TC molecules in the solution to exhibit cationic properties [17,76], with the potential of MMWCNTs being approximately 32 mV (Figure S1c).Despite strong interactions that resulted in the adsorption of more than 90% of TC in solution, adsorbents and contaminants are subject to electrostatic repulsion.At 3.3 < pH < 7.7, the dominant group in TC was TCH2 0 , which has no external electrical properties, indicating that the adsorption of TC reached a peak level without the occurrence of electrostatic repulsion [4].At pH > 7.7, TC was dominated by negatively charged TCH2 -and TC 2-, while the potential of MMWCNTs was about −15mV due to the deprotonation of carboxyl groups on the adsorbent [10,15,[77][78][79].At pHpzc, adsorption could not be attributed to electrostatic interactions, and therefore, the removal of TC by MMWCNTs was higher at pH 3-7.The reason may be that the pH is in the range of 3-7, the TC amphiphilic form (TCH2 0 ) exists, the TC molecules have almost no electrostatic attraction or repulsion to MMWCNTs, and the effect of pH on TC adsorption is negligible.Whereas, when the pH is less than 3 or more than 7, TC and MMWCNTs have the same charge, and a certain degree of electrostatic repulsion is generated, which is not favorable for the adsorption of TC by MMWCNTs.Based on the above analysis, the pH input value was set to 4-6 in the RSM.

Effect of Time
The TC adsorption capacity of MMWCNTs increased to 82.33 mg/g, within 720 min (Figure S2).The qe of TC by MMWCNTs reached 80 mg/g prior to 200 min and remained around 83 mg/g for the remainder of the contact time, reaching adsorption equilibrium after 700 min.Within the initial 50 min of the reaction, the high concentration of TC in the solution enhanced the effect of mass transfer, with the adequate availability of adsorption The TC adsorption capacity of MMWCNTs increased to 82.33 mg/g, within 720 min (Figure S2).The q e of TC by MMWCNTs reached 80 mg/g prior to 200 min and remained around 83 mg/g for the remainder of the contact time, reaching adsorption equilibrium after 700 min.Within the initial 50 min of the reaction, the high concentration of TC in the solution enhanced the effect of mass transfer, with the adequate availability of adsorption sites providing a high probability of collision between molecules, resulting in a rapid TC adsorption rate [9,12].After MMWCNTs had rapidly adsorbed a huge amount of TC at 150 min, many of the adsorption sites were occupied and the adsorption rate declined.Therefore, based on these findings the contact time range input value for RSM analysis was 120-480 min.

Adsorption Kinetics
Figure 3 presents the results of data fitting using the pseudo-first-order, pseudo-secondorder, Elovich, Weber and Morris, and Banham models.The equations applied for the different models are provided in the supporting information, with the obtained kinetic parameters shown in Table S5.The results demonstrate that the pseudo-first-order model data fitting was good, with an R 2 of 0.944, although the adsorption capacity calculated using this model was 80.57 mg/g, which differed from the experimental results.The determination coefficients of the Elovich and Bangham models were 0.729 and 0.668, with q e values of 87.05 and 87.82 mg/g, respectively.The Weber and Morris model classified the adsorption process as being surface adsorption and slow intra-particle diffusion.However, the R 2 using the Weber and Morris model was 0.412 and the straight line failed to pass through the origin of the coordinates.The pseudo-second-order kinetic model successfully explained the experimental data (R 2 = 0.975 and q e = 84.13mg/g), indicating that the adsorption of TC by MMWCNTs may occur via chemical adsorption, due to the sharing or interchange of electrons between adsorbents and adsorbates resulting in valence forces.The chemical adsorption process can be separated into two phases, with (1) TC initially adsorbed on the surface forming a monolayer and (2) chemisorption mechanisms dominating once monolayer physical adsorption approaches saturation [17,80,81].In summary, pseudosecond-order kinetics were optimal for depicting the TC adsorption process on MMWCNTs.

Mechanism of TC Adsorption by MMWCNTs
According to the results of FT-IR infrared spectroscopy, single-factor experiments with pH variation and adsorption kinetics results, the proposed TC adsorption mechanism (Figure S3) can be explained by the following two mechanisms: (1) π-π interactions between TC's polarity/ionization groups (including amino, carboxyl, phenol, ethanol, and
(2) The formation of cation-π bonds due to electrostatic forces between cation-induced polarized regions and the quadrupole of π-electron-rich aromatic structures [85].TC is amphoteric in a pH range of 3-7, with a cationic dimethyl amino group (pK a = 9.7), resulting in π electrons on MMWCNTs easily forming cation-π bonds.The amino and hydroxyl groups on TC molecules tend to form strong hydrogen bonds with carbon-based adsorbents [68].

Modeling and Statistical Analysis
Table 1 demonstrates the experimental design, experimental results, and the modelpredicted TC removal rate (%).The experimental results show that TC removal ranged from 73.35% to 97.88%, with an overall deviation of <3%.Kinetic analysis (Table S6) shows the results of data fitting using four models (Linear, 2FI, Quadratic, Cubic), with F-test analysis indicating that the quadratic model exhibited the highest level of significance (F-value (Fisher rate) = 22.10; p-value (prob > F) = 0.0002; F-value of the lack of fit = 0.34), indicating that most of the variation could be explained by the quadratic model regression equation [38,86].The influence of noise probability was only 0.02% with a signal-tonoise ratio of >4, while the p-value of lack of fit was 0.798, indicating that misfit error could be ignored.The calculation methods are described in detail in the Supplementary Materials.Equation (3) describes the quadratic model equation for the TC removal rate with varying dosage, contact time, and pH, with negative interaction terms (AB, BC, AC, B 2 , C 2 ) indicating an antagonistic effect on the removal rate [25].All the analyses presented in this paper were based on quadratic model analysis.
where Y represents the TC removal rate by MMWCNTs; A represents the adsorbent dosage; B represents the adsorption time; C represents the pH value.

Analysis of Variance
ANOVA was performed to verify the statistical significance of the experimental design and establish the interactions between independent variables and response effects (Table S7) [41,72].ANOVA subdivides the total variation into two components, with variation associated with either the model or experimental error [87,88].F-and p-values (prob > F, confidence interval = 95%) for the model were obtained as shown in Table S7.The F-value of the lack of fit (0.34) and the p-value (>0.05) were insignificant, proving that the second-order model with interactive effects was adequate for approximating the RSM [89].p (AB) = 0.006, p (BC) = 0 and p (C 2 ) = 0 were more significant than the other interaction terms, while the p-values of B (0.796) and B 2 (0.768) were appreciably greater than 0.05, indicating that the influence of these factors on the response value could be ignored.The accuracy of the predictions generated by the model was verified according to the R 2 (0.9660), R adj 2 (0.9223), and standard deviation (2.15).A total of 7.7% of the total variation could not be explained exclusively by the model [46,53].Overall, the ANOVA indicated that the BBD model exhibited excellent accuracy and reliability for TC adsorption by MMWCNTs [52].

Main Effect of Variables
The main effect of variables represents the regulatory effect of a specific individual factor on the response value [25].The main effect plot for varying dosage (Figure S6a) demonstrated that an increase in adsorbent dosage from 6 to 12 mg resulted in an increase in the average removal rate from 86.08% to 89.39%, while the curve slope decreased with increasing dosage from 0.778 (6-9 mg) to 0.325 (9-12 mg), indicating that the promotive effect of dosage on the removal rate decreased with increasing dosage levels.Initial increases in adsorbent dosage increase the surface area available for TC adsorption.However, at an adsorbent dosage of 13 mg, the q e of the adsorbent was close to the equilibrium adsorption capacity of 83 mg/g, leading to a decrease in the main effect of this factor.According to the results of variance analysis, the p-values of A and A 2 were 0.082 and 0.065, respectively.Pareto chart analysis showed that the contributions of A and A 2 to the removal rate were 0.41% and 0.39%, respectively, indicating that the effect of dosage on the removal of TC was weak.
The main effect plot for pH (Figure S6b) indicated that the TC removal rate increased rapidly from 83.33% (pH 4) to 92.16% (pH 5), then decreased to 83.73% (pH 6), with the slope of the curve altering by 200%, while the intersection angle between the curve and reference line was the largest compared with the other two factors.Variance analysis showed a p-value for pH of 0.066 (<0.05) and a p-value for pH 2 of 0, indicating a strong individual effect.According to Figure S1c, the pH pzc of MMWCNTs was 4-5, with TCH 2 0 being the dominant species at pH 5, indicating that adsorption was far greater than electrostatic repulsion.Once the pH value deviates from pH pzc , a small portion of TCH -groups on TC molecules will repel the adsorbent surface.Therefore, compared with contact time and dosage, the pH value exhibited the most significant individual effect on the rate of TC removal by MMWCNTs.
The main effect plot for adsorption time (Figure S6c) was drawn from the average TC removal rate values at 120, 300, and 480 min in 17 groups of experiments, according to the RSM.Before the 300 min, the curve slope was 0.0014, running almost parallel to the reference line, with the removal rate changing by 0.25%.After 480 min, the average TC removal rate increased to 90.58%.Variance analysis demonstrated that contact time exerted a low effect on TC removal (p-value for time = 0.796, p-value for time 2 = 0.768).Due to the affinity among adsorbates and adsorbents and the excessive concentration of TC, the high mass transfer efficiency resulted in the adsorption equilibrium being reached within a short time and the adsorption time indicating a weak individual effect on the removal rate.
The standardized Pareto chart (Figure 4) indicated the influence of the items in Equation (3) on TC removal [26,90].The results showed that the most significant factors affecting TC adsorption by MMWCNTs were pH 2 (standardization effect = 8.27%) and pH-time (standardization effect = 10.13%)interactions, indicating an acceptable level of agreement with the observed results shown in Table S7 (p-value for pH 2 and pH-time = 0).These results validate the previously established conclusion, that the individual effect of pH was the most significant (pH (4.53%), pH 2 (8.27%), pH-time (10.13%), and pH-dosage (4.06%)).
being the dominant species at pH 5, indicating that adsorption was far greater than electrostatic repulsion.Once the pH value deviates from pHpzc, a small portion of TCH -groups on TC molecules will repel the adsorbent surface.Therefore, compared with contact time and dosage, the pH value exhibited the most significant individual effect on the rate of TC removal by MMWCNTs.
The main effect plot for adsorption time (Figure S6c) was drawn from the average TC removal rate values at 120, 300, and 480 min in 17 groups of experiments, according to the RSM.Before the 300 min, the curve slope was 0.0014, running almost parallel to the reference line, with the removal rate changing by 0.25%.After 480 min, the average TC removal rate increased to 90.58%.Variance analysis demonstrated that contact time exerted a low effect on TC removal (p-value for time = 0.796, p-value for time 2 = 0.768).Due to the affinity among adsorbates and adsorbents and the excessive concentration of TC, the high mass transfer efficiency resulted in the adsorption equilibrium being reached within a short time and the adsorption time indicating a weak individual effect on the removal rate.
The standardized Pareto chart (Figure 4) indicated the influence of the items in Equation (3) on TC removal [26,90].The results showed that the most significant factors affecting TC adsorption by MMWCNTs were pH 2 (standardization effect = 8.27%) and pH-time (standardization effect = 10.13%)interactions, indicating an acceptable level of agreement with the observed results shown in Table S7 (p-value for pH 2 and pH-time = 0).These results validate the previously established conclusion, that the individual effect of pH was the most significant (pH (4.53%), pH 2 (8.27%), pH-time (10.13%), and pH-dosage (4.06%)).

Interaction of Contact Time and Adsorbent Dosage
To understand the interactions of various factors on removal, contour plots, 3D response surface plots, and interaction effect plots were constructed according to the proposed regression model (Equation ( 2)) [91].Figure 5a,b show contour plots and response surface plots for adsorption time and adsorbent dosage.As the adsorbent dosage increased from 6 to 12 mg and the contact time was extended from 120 to 480 min, the TC removal rate gradually increased.TC removal reached a maximum of 97% in 480 min at an adsorbent dosage of 6 mg and 120 min at an adsorbent dosage of 12 mg.The lowest adsorption efficiency (86%) occurred at a dosage of 6 mg and a contact time of 120 min, with the extension of adsorption time increasing the collision probability for TC molecules and the adsorbent, while the rise in adsorbent dosage increases the accessibility of the exchangeable surface adsorption sites.When a maximum contact time and dosage were applied (480 min contact time and 12 mg dosage), the adsorption efficiency decreased (92%) due to the antagonistic effect of time and dosage.Figure S7 shows an interaction effect plot for time and dosage, which was utilized to describe the dynamic interaction between various factors.From 120 to 300 min, the curves intersected, and the slope varied from 0.036 at 6 mg, and −0.044 at 9 mg, to 0.069 at 12 mg, indicating a distinct interaction between the time and dosage.In the Pareto chart (Figure 4), the interactive contribution of time and dosage on the removal rate was 4.06% > 2.57% (minimum statistically significant effect magnitude), indicating the significance of time-dosage interactions.In summary, the interactive effect of adsorbent dosage and contact time on TC removal was significant and substantial (p-value = 0.006, Table S7).(The color changes from blue to red, indicating that the removal rate is getting higher and higher).

Interaction of Adsorbent Dosage and pH
Figure 5c,d are contour and 3D response surface plots for pH and adsorbent dosage.The results show that the removal rate initially increased and then decreased with the rise in pH from 4 to 6. TC removal occurred monotonically (86-93%) with increasing dosage from 6 to 12 mg.The peak TC removal rate (92%) occurred at pH 5 and a dosage of 12 mg, which was attributed to the π-π electron interactions and cationic-π electron bonds between MMWCNTs and TC molecules at pH pzc (with weak electrostatic repulsion).The results indicate that increasing dosage does not affect the relationship between pH and the TC removal rate, and neither does increasing pH affect the relationship between dosage and the TC removal rate, verifying the insignificance of pH and adsorbent dosage interactions.As shown by the pH and adsorbent dosage interaction plot (Figure S7), with increasing pH, TC removal initially increased to a maximum level (90-95%) and then decreased to 85%.The three interaction curves demonstrate that the variation in adsorbent dosage did not alter the overall trend, although the removal effect could be improved.At pH 5-6, the slope fluctuated from 8.27 (6 mg) to 6.919 (9 mg) to 12.02 (12 mg), indicating the low level of interaction between pH and adsorbent dosage.The same result was shown by the Pareto chart (Figure 4), where the contribution of interaction between pH and the adsorbent dose was only 3%.Therefore, the interactive effect of dosage and pH on TC removal was low (p-value = 0.024, Table S7).

Interaction of Contact Time and pH
Figure 5e,f display the contour plot and response surface plot for the pH and contact time of adsorption efficiency.The maximum percentage of TC removal was achieved at 480 min and pH 4.5.At pH levels < 5, a significant increase in the amount adsorbed was observed from 120 to 480 min, while the opposite trend was observed at pH levels > 5. Similarly, within 300 min, the adsorption effect increased with higher pH values (from 80% to 94%), while from 300 to 480 min, the adsorption effect decreased with increasing pH values from 4 (96%) to 6 (82%), further proving the antagonistic interaction between pH and contact time.Therefore, simultaneous increases in pH and contact time significantly reduced the TC adsorption effect.As shown by the pH and time interaction plot (Figure S7), in which from 120 to 480 min the varying pH initially increased from 4 to 6 the TC removal rate (73.35-93.19%)at a pH of 4 and then decreased the removal rate (97.28-75.54%)at a pH of 6, verifying the occurrence of antagonistic interactions.Pareto chart analysis revealed that pH-contact time contributed 10.13% to the removal rate and ANOVA (F-value = 93.62,p-value = 0) demonstrated that the interaction between pH and contact time was most significant compared with the other interaction terms.

Validation of Box-Behnken Design Optimization
To determine the practical application effect of RSM-BBD on the parameter optimization of TC adsorption by MMWCNTs, the optimum conditions for TC removal by the MMWCNTs adsorbent were investigated with varying adsorbent dosage, pH, and adsorption time [51].
Design Expert software suggested that pH 5.4, an adsorbent dosage of 12 mg, and contact time of 120 min, were the optimum conditions to achieve a maximum TC removal by MMWCNTs of 99.16%, with desirability of 0.984.
Table 2 shows the validation results for 10 groups of different experimental conditions simulated by Design Expert software (v.10.0.3).The experimental results show that the TC removal rate reached 98.86% under optimal conditions, with an error level of 0.3%.The overall error of the 10 groups of experiments was <1%, proving the accuracy of the model prediction.Overall, RSM-BBD was found to reliably simulate TC adsorption by MMWCNTs, allowing effective method optimization.

Concluding Remarks
In this study, RSM-BBD was employed to establish a quadratic polynomial model to analyze the TC adsorption process by MMWCNTs, in terms of dosage, pH, and time.The main conclusions are as follows: (1) ANOVA established a high level of significance (F-value = 22.1, p-value < 0.05), fitness (R 2 = 0.966 and R adj 2 = 0.922), and accuracy (the residual fit the normal probability distribution) of the model.( 2) From the analysis of the Pareto Diagram and main effect diagram, the promoting effect of dose on removal rate decreases with the increase in dose level, and the effect on TC is weak.Main effect plots demonstrated that in the pH range from 4 to 6, the average removal curve slope changed by 200%, with the effect of pH on TC removal being the most significant (contribution of pH 2 on removal = 8.27%, F-value = 69.60,p-value = 0).(3) The pseudo-second-order model was successfully applied to explain the adsorption kinetics (R 2 = 0.975 and q e = 84.1 mg/g).The TC adsorption mechanism involved π-π electronic interaction and cation-π electronic bonding.(4) The response surface plots, Pareto chart, and variance analysis established that the strongest antagonistic interaction occurred between contact time and pH (contribution of time-pH = 10.13%,F-value = 93.62,p-value = 0).In addition, the correlations of pH with dosage and dosage with time were not significant.(5) The maximum TC removal efficiency of 99.16% was achieved at an adsorbent dosage of 12 mg, pH 5.4, within 120 min, and desirability = 0.984.The verification experiment results indicated that the actual removal under optimal conditions was 98.86%, indicating that the RSM-BBD model could effectively be used for optimizing TC adsorption by MMWCNTs.The optimization method used in this paper determined the optimal adsorption conditions and the influence of external factors, promoting the industrial application of MMWCNTs.S1: Optimization methods of various adsorption processes; Table S2: Current status of BBD-RSM in the optimization of TC adsorption process with different adsorbents; Table S3: Current status of BBD-RSM in the optimization of MWCNTs adsorption process with different adsorbents; Table S4: The experimental factors, levels and coded values for TC removal experiment, including three factors and three response levels; Table S5: Parameters of kinetic models for the adsorption of TC by MMWCNTs; Table S6: Statistical analysis of the effectiveness of models for modeling the process of TC adsorption by MnFe2O4/MWCNTs (confidence interval = 95%); Table S7: Analysis of variance (ANOVA) for TC removal according to the response surface quadratic model (confidence interval: 95%).

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Figure 1 .
Figure 1.Effect of adsorbent dosage on the Tetracycline (TC) removal rate and adsorption capacity of magnetic multi-walled carbon nanotubes (MMWCNTs).Reaction conditions included an initial TC concentration of 20 mg/L, pH 7.0 ± 0.1, contact time of 1440 min, and reaction temperature of 298.15 K. (The black data points in the graph represent the removal rate and the red data points represent the qe.)

Figure 1 .
Figure 1.Effect of adsorbent dosage on the Tetracycline (TC) removal rate and adsorption capacity of magnetic multi-walled carbon nanotubes (MMWCNTs).Reaction conditions included an initial TC concentration of 20 mg/L, pH 7.0 ± 0.1, contact time of 1440 min, and reaction temperature of 298.15 K. (The black data points in the graph represent the removal rate and the red data points represent the q e. ).Water 2023, 15, x FOR PEER REVIEW 6 of 18

Figure 2 .
Figure 2. Effect of pH on the TC removal rate and adsorption capacity of MMWCNTs.Reaction conditions included an initial TC concentration of 20 mg/L, adsorbent dosage of 12 mg, contact time of 1440 min, and reaction temperature of 298.15 K. (The red data points in the graph represent the removal rate and the black data points represent the qe.)

Figure 2 .
Figure 2. Effect of pH on the TC removal rate and adsorption capacity of MMWCNTs.Reaction conditions included an initial TC concentration of 20 mg/L, adsorbent dosage of 12 mg, contact time of 1440 min, and reaction temperature of 298.15 K. (The red data points in the graph represent the removal rate and the black data points represent the q e. ).

Water 2023 , 18 Figure 3 .
Figure 3. Experimental data of adsorption kinetic and nonlinear fitting of the pseudo-first-order, pseudo-second-order, Elovich, Weber and Morris, and Banham models for TC adsorption.Reaction conditions included an initial TC concentration of 20 mg/L, adsorbent dosage of 12 mg, pH 7.0 ± 0.1, and reaction temperature of 298.15 K.

Figure 3 .
Figure 3. Experimental data of adsorption kinetic and nonlinear fitting of the pseudo-first-order, pseudo-second-order, Elovich, Weber and Morris, and Banham models for TC adsorption.Reaction conditions included an initial TC concentration of 20 mg/L, adsorbent dosage of 12 mg, pH 7.0 ± 0.1, and reaction temperature of 298.15 K.

Figure 4 .
Figure 4. Pareto chart of the interactive effect of experimental factors (dosage, time and pH) with TC removal as the corresponding variable (α = 0.05).

Figure 5 .
Figure 5. Interaction of dosage, time, and pH on TC removal efficiency: (a) Contour plot of time and dosage (pH 5); (b) Response surface plot of time and dosage (pH 5); (c) Contour plot of pH and dosage coefficient of each component; Figure S5: Residual diagnostic chart of TC adsorption test results: (a) Normal % probability versus internally studentized residuals; (b) Residuals versus predicted values; (c) Residuals versus run number; (d) Plot of model predicted value versus actual experimental value; Figure S6: Main effect plots for (a) Dosage; (b) pH and (c) Reaction time for the response surface method; Figure S7: Interaction plot of dosage, reaction time and pH; Table

Table 1 .
Experimental factor level values with experimental and predicted TC removal values at each factor level.

Table 2 .
Experimental design conditions and the TC removal response (%) of each run.Initial TC concentration: 20 mg/L and temperature: 298.15 K.