# Sensitivity Analysis with the Monte Carlo Method and Prediction of Atenolol Removal Using Modified Multiwalled Carbon Nanotubes Based on the Response Surface Method: Isotherm and Kinetics Studies

Authors: Mohammad Mehdi Amin; Nasrin Bagheri; Farzaneh Mohammadi; Bahare Dehdashti
Journal: International Journal of Chemical Engineering
 (2022)

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## Abstract

Atenolol (ATN) is aβ-blocker drug extensively used to treat arrhythmias and high blood pressure. Because the human body cannot metabolize it completely, this drug has been commonly found in many environmental matrices. In the present study, the response surface method (RSM) was used for adsorption prediction of ATN on modified multiwalled carbon nanotubes (M-MWCNTs) by NaOCl and ultrasonic. The sensitivity analysis was done by the Monte Carlo method. Sensitivity analysis was performed to determine the effective parameter by the Monte Carlo simulator. Statistical analysis of variance (ANOVA) was performed by using the nonlinear second-order model of RSM. The influential parameters including contact time (min), adsorbent dosage (g/L), pH, and the initial concentration (mg/L) of ATN were investigated, and optimal conditions were determined. Kinetic of ATN adsorption on M-MWCNTs was evaluated using pseudo-first, pseudo-second-order, and intraparticle diffusion models. Equilibrium isotherms for this system were analyzed by the ISOFIT software. As per our result, optimum conditions in the adsorption experiments were pH 7, 60 min of contact time, 0.5 mg/L ATN initial concentration, and 150 mg/L adsorbent dose. In terms of ATN removal efficiency, coefficients of R2 and adjusted R2 were 0.999 and 0.998, respectively. Sensitivity analysis also showed that contact time has the greatest effect on increasing the removal of ATN. Pseudo-first-order (R2 value of 0.99) was the best kinetic model for the adsorption of ATN, and for isotherm, BET (AICC value of 3.27) was the best model that fit the experimental data. According to the obtained results from sensitive analysis, time was the most important parameter, and after that, the adsorbent dose and pH affect positively on ATN removal efficiency. It can be concluded that the modified multiwalled carbon nanotubes can be applied as one of the best adsorbents to remove ATN from the aqueous solution.


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## Body

## 1. Introduction

β-Blockers are an important group of drugs extensively used to treat arrhythmias and high blood pressure. ATN, bisoprolol, metoprolol, sotalol, and propranolol are common kinds of β-blockers [1], among which ATN is widely used for the therapy of cardiovascular disease, hypertensive disease, infantile hemangioma [2], acute myocardial infarction [3], and decline the intensity of heart attacks. Approximately 50% of the amount ingested by humans cannot be metabolized during excretion, and it is frequently detected in urban wastewater [4]. Researchers expressed conventional wastewater treatment plants (WWTPs) including ozonation and microbial transformation [5] cannot remove ATN sufficiently. Thus, this leads to the increasing occurrence of ATN in different water bodies [2] such as surface waters, ground waters, and hospital wastewaters in the last decade [6]. Researches showed ATN concentration in the effluent was about 0.78–6.6 mg/L, whereas the admittable level is 10 ng/L [7]. Studies demonstrate that this compound is resistant to biodegradation and therefore can remain in the matrix for long time [6] and has a toxic effect on aquatic microorganisms and humans [1]. Moreover, after a chlorination process, ATN illustrated phytotoxic activity [2]. Consequently, ATN removal from aqueous solution is important. Recently, scientists use some methods for ATN removal including oxidation with UV/peroxydisulfate [8], oxidation with light [6], chlorination/UV process [9, 10], and ozonation [2]. Generation of toxic by-products [5] and high energy consumption [4] are drawbacks of the last methods.Nowadays, adsorption is widely used because of easy operation, low cost, high efficiency, and lack of toxic by-products for removal of contaminants from the aqueous solution [11]. So far, among applications of various adsorbents, carbon nanotubes (CNTs) also have been extensively used due to the large specific surface area, high porosity, and high reaction activity [11–13]. The most well-known carbon nanotubes are single-walled (SWCNTs) and multiwalled (MWCNTs) [12]. To improve performance and increase the efficiency of CNTs, two methods such as acid treatment and ultrasonication are applied [14]. MWCNTs modified by nitric acid have been used as adsorbents for removal of diclofenac from aqueous solution in China [15]. Ncibi et al. investigated the removal of antibiotic pharmaceutical from aqueous solutions by using single and multiwalled carbon nanotubes optimized by ultrasonic. They found the application of ultrasound help CNTs for omitting of drugs [16].The objective of this study was to investigate the removal of atenolol by multiwalled carbon nanotubes modified with NaOCl and ultrasonic. The equilibrium isotherms and kinetics of the ATN-M-MWCNTs adsorption system have been determined and analyzed using several adsorption models. Also, in order to determine relationships between parameters and the effects on removal of the pollutant, the RSM model was used. In the following, by using sensitivity analysis with the Monte Carlo method, impacts of the evaluated parameters on the response parameter were determined.


## 2. Materials and Methods

### 2.1. Materials

All chemicals including ATN (C14H22N2O3) with a purity of ≥98%, NaOCl (70%), HCl (≥37%), and NaOH (≥98%) were prepared from Merck Co., Germany. Raw MWCNTs (Cheap Tubes Inc., USA) was used as the base adsorbent. Table 1 provides the physical and chemical characteristics of the selected carbon nanotubes.Table 1
Specifications of MWCNTs used in this study.
CharacteristicsValuesPurity>95%Outer diameter<8 nmInner diameter2–5 nmLength>10μmSpecific surface area>500 m2·g−1Electric conductivity>100 s·cm−1Tap density0.27 g·cm−3True density2.1 g·cm−3


### 2.2. Adsorption Experiments

The preparation of adsorbent was explained in our last study [7]. The stock solution of 1,000 mg/L of atenolol was made by 100 mg of pure atenolol and deionized water. The tests were carried out under 25°C and in 100 mL dishes including 50 mL of the sample. The initial concentration of ATN for each stage of the experiment was 0.5, 1, 5, and 10 mg/L. The pH value (2, 4, 7, and 11) was managed by adding HCl or NaOH solutions and was measured by a pH meter (CyberScan pH1500, Thermo Fisher Scientific Inc., The Netherlands). The adsorbent dosages of 50, 100, 150, and 200 mg/L were added to the solutions at each stage. In order to proper mixing of the adsorbate and adsorbent, the solutions were placed on a shaker (orbital shaker, model OS 625, Germany) for 5, 20, 60, and 90 min, at the rate of 250 rpm. In all of the study steps, ATN solutions without any adsorbents were used as controls. So, ATN adsorption on the bottle wall or through evaporation was insignificant. After a certain contact time, the samples were filtered with a filter (CA0.22), and the nanoparticles were separated. After that, the samples were centrifuged at 10,000 rpm (Universal 320, Hettitech, Germany) for 10 min. Finally, ATN concentration was analyzed by the high-performance liquid chromatography (HPLC).


### 2.3. Measurements and Data Analyzing

The samples were prefiltered by the 0.45μm PTFE hydrophilic sterile filter, Membrane Solutions, MS® CA Syringe Filter Company, USA. ATN concentrations in the aqueous solution before and after the treatment were measured by the Waters HPLC, with a UV-486 detector at a wavelength of 231 nm (Waters Company, USA). The HPLC mobile phase was a combination of 0.01 M potassium dihydrogen orthophosphate with a pH value of 3.5 and acetonitrile with a volumetric ratio of 60 : 40. An isocratic method with a flow rate of 1 mL/minute and a sample injection volume of 20 μL, stationary phase (column) (250 × 4.6 mm; 5 μm) C18-Waters-Spherisorb®, and oven temperature of 25°C was used; the results of the calibration curve of atenolol within the concentration range of 0.1–10 mg/L in the water matrix revealed the linearity of the measurement method, with a correlation coefficient (R2) as large as 0.99.Shape, size, and surface morphology of MWCNTs and M-MWCNTs were investigated through transmission electron microscopy (TEM). Moreover, to determine the functional groups and formation of chemical bonds in MWCNTs and M-MWCNTs, the FTIR spectrometer was used (Bruker Optics, TENSOR 27, Netherlands).The ATN removal efficiency (E, %) and adsorption capacities (q, mg/g) of M-MWCNTs were calculated according to the following equations [17]:(1)E=Co−CeCo×100,(2)q=CO−CeVm,where Co and Ce (mg/L) are the initial and equilibrium ATN concentrations, respectively, VL is the volume of the solution, and m(g) is the mass of each used adsorbent.


### 2.4. RSM Modeling and Sensitivity Analysis

The RSM model is widely used in laboratory studies modeling [18]. This method is a complete collection of statistics methods to evaluate the parameters effect and interaction of them on response variable and to search for optimum condition [19]. In this study, the relationship between independent variables and response variables by quadratic models in the RSM model is expressed as [20](3)y=β0+∑i=1kβiX+∑i=1kβiiXi2+∑i=1k∑i≠j=1kβijXiX+ε.According to equation (3), y is the excepted response, Xi.j coded the independent variables, k is the number of variables, β0 is the model constant, βi represent the coefficients of linear variables, βii represent the coefficients of variables with quadratic, βij represent the coefficients of variables interaction, and ε is the error rate.For reliability testing, one-way analysis of variance (ANOVA) should be performed. In this model, the coefficient of determination (R2) is used to evaluate the model fit and for assessment of lack of fit in the applied F-test [21]. In this study, the finding of the experiments was entered in the RSM model as design. Moreover, the software Design Expert 11 was used for modeling.The Monte Carlo method is a computational algorithm that uses random sampling to calculate the results [22]. In the sensitivity analysis of the Monte Carlo simulation method, unlike analytical methods, the work is based on the simulation of the desired phenomenon in large numbers. For this purpose, each of the input parameters was generated in large numbers (in this study 10,000 times) by existing statistical methods and simulated, and by placing them in the created model, the response variable was also generated in the same number. To generate each input parameter, the best statistical distribution was first fitted to each of the input parameters, including contact time, adsorbent dose, ATN concentration, and pH. Table 2 provides the statistical distribution of input parameters and response variable. Then, in the statistics distribution, around 10000 data were generated for input parameters. After that, by the developed RSM model, response variable (ATN removal) was computed for any 10000 set. Finally, sensitivity of response variable to the input parameters was determined based on 10000 existing datasets by the Pearson correlation method [23]. For performance of all of the steps of sensitive analysis, the SPSS 26 software was used.Table 2
Distribution of input parameters in the model.
ParameterUnitDistributionATN concentrationmg/LWeibull (α = 0.78713, β = 3.8821)Adsorbent dosemg/LUniform (min = 50, max = 200)TimeminUniform (min = 5, max = 90)pH—Uniform (min = 2, max = 11)


### 2.5. Isotherm of Adsorption

In order to evaluate ATN adsorption by M-MWCNTs, an isotherm study was used through the optimal condition including an initial ATN concentration of 0.5, 1, 2, 5, and 10 mg/L, and the adsorbent dose of 0.15 g/L, a contact time of 60 minutes, and a pH value of 7. The water solubility (Sw) of ATN was approximated as 300 mg/L at pH 7. The isotherm fitting tool software (ISOFIT) was used in accordance with the isotherm parameters with the pilot data. ISOFIT is a software program that matches isotherm parameters to experimental data by the minimization of a weighted sum of squared error (WSSE) objective function [24]. ISOFIT supports several isotherms, containing Brunauer–Emmett–Teller (BET), Freundlich, Freundlich with linear partitioning (F-P), generalized Langmuir–Freundlich (GLF), Langmuir, Langmuir with linear partitioning (L-P), linear Polanyi with linear partitioning, and Toth [25].


### 2.6. Kinetics of Adsorption

For the analysis of the impact of contact time on the adsorption process, the adsorption kinetics was studied. The adsorption kinetics data were fitted to the pseudo-first-order, pseudo-second-order, and intraparticle diffusion kinetic models as presented in equations (4)–(6) [26]:Pseudo-first-order:(4)qt=qe1−e−K1t.Pseudo-second-order:(5)qt=K2qe2t1+K2qet.Intraparticle diffusion:(6)qt=Kpt0.5+I,WhereK1 (1/min), K2 (g/mg min), and Kp (mg/g√min) are the constants rate of the pseudo-first-order, pseudo-second-order, and intraparticle diffusion model, respectively. Meanwhile, qe and qt (mg/g) are the adsorption capacities of MWCNTs and M-MWCNTs at equilibrium and time t, respectively.


## 2.1. Materials

All chemicals including ATN (C14H22N2O3) with a purity of ≥98%, NaOCl (70%), HCl (≥37%), and NaOH (≥98%) were prepared from Merck Co., Germany. Raw MWCNTs (Cheap Tubes Inc., USA) was used as the base adsorbent. Table 1 provides the physical and chemical characteristics of the selected carbon nanotubes.Table 1
Specifications of MWCNTs used in this study.
CharacteristicsValuesPurity>95%Outer diameter<8 nmInner diameter2–5 nmLength>10μmSpecific surface area>500 m2·g−1Electric conductivity>100 s·cm−1Tap density0.27 g·cm−3True density2.1 g·cm−3


## 2.2. Adsorption Experiments

The preparation of adsorbent was explained in our last study [7]. The stock solution of 1,000 mg/L of atenolol was made by 100 mg of pure atenolol and deionized water. The tests were carried out under 25°C and in 100 mL dishes including 50 mL of the sample. The initial concentration of ATN for each stage of the experiment was 0.5, 1, 5, and 10 mg/L. The pH value (2, 4, 7, and 11) was managed by adding HCl or NaOH solutions and was measured by a pH meter (CyberScan pH1500, Thermo Fisher Scientific Inc., The Netherlands). The adsorbent dosages of 50, 100, 150, and 200 mg/L were added to the solutions at each stage. In order to proper mixing of the adsorbate and adsorbent, the solutions were placed on a shaker (orbital shaker, model OS 625, Germany) for 5, 20, 60, and 90 min, at the rate of 250 rpm. In all of the study steps, ATN solutions without any adsorbents were used as controls. So, ATN adsorption on the bottle wall or through evaporation was insignificant. After a certain contact time, the samples were filtered with a filter (CA0.22), and the nanoparticles were separated. After that, the samples were centrifuged at 10,000 rpm (Universal 320, Hettitech, Germany) for 10 min. Finally, ATN concentration was analyzed by the high-performance liquid chromatography (HPLC).


## 2.3. Measurements and Data Analyzing

The samples were prefiltered by the 0.45μm PTFE hydrophilic sterile filter, Membrane Solutions, MS® CA Syringe Filter Company, USA. ATN concentrations in the aqueous solution before and after the treatment were measured by the Waters HPLC, with a UV-486 detector at a wavelength of 231 nm (Waters Company, USA). The HPLC mobile phase was a combination of 0.01 M potassium dihydrogen orthophosphate with a pH value of 3.5 and acetonitrile with a volumetric ratio of 60 : 40. An isocratic method with a flow rate of 1 mL/minute and a sample injection volume of 20 μL, stationary phase (column) (250 × 4.6 mm; 5 μm) C18-Waters-Spherisorb®, and oven temperature of 25°C was used; the results of the calibration curve of atenolol within the concentration range of 0.1–10 mg/L in the water matrix revealed the linearity of the measurement method, with a correlation coefficient (R2) as large as 0.99.Shape, size, and surface morphology of MWCNTs and M-MWCNTs were investigated through transmission electron microscopy (TEM). Moreover, to determine the functional groups and formation of chemical bonds in MWCNTs and M-MWCNTs, the FTIR spectrometer was used (Bruker Optics, TENSOR 27, Netherlands).The ATN removal efficiency (E, %) and adsorption capacities (q, mg/g) of M-MWCNTs were calculated according to the following equations [17]:(1)E=Co−CeCo×100,(2)q=CO−CeVm,where Co and Ce (mg/L) are the initial and equilibrium ATN concentrations, respectively, VL is the volume of the solution, and m(g) is the mass of each used adsorbent.


## 2.4. RSM Modeling and Sensitivity Analysis

The RSM model is widely used in laboratory studies modeling [18]. This method is a complete collection of statistics methods to evaluate the parameters effect and interaction of them on response variable and to search for optimum condition [19]. In this study, the relationship between independent variables and response variables by quadratic models in the RSM model is expressed as [20](3)y=β0+∑i=1kβiX+∑i=1kβiiXi2+∑i=1k∑i≠j=1kβijXiX+ε.According to equation (3), y is the excepted response, Xi.j coded the independent variables, k is the number of variables, β0 is the model constant, βi represent the coefficients of linear variables, βii represent the coefficients of variables with quadratic, βij represent the coefficients of variables interaction, and ε is the error rate.For reliability testing, one-way analysis of variance (ANOVA) should be performed. In this model, the coefficient of determination (R2) is used to evaluate the model fit and for assessment of lack of fit in the applied F-test [21]. In this study, the finding of the experiments was entered in the RSM model as design. Moreover, the software Design Expert 11 was used for modeling.The Monte Carlo method is a computational algorithm that uses random sampling to calculate the results [22]. In the sensitivity analysis of the Monte Carlo simulation method, unlike analytical methods, the work is based on the simulation of the desired phenomenon in large numbers. For this purpose, each of the input parameters was generated in large numbers (in this study 10,000 times) by existing statistical methods and simulated, and by placing them in the created model, the response variable was also generated in the same number. To generate each input parameter, the best statistical distribution was first fitted to each of the input parameters, including contact time, adsorbent dose, ATN concentration, and pH. Table 2 provides the statistical distribution of input parameters and response variable. Then, in the statistics distribution, around 10000 data were generated for input parameters. After that, by the developed RSM model, response variable (ATN removal) was computed for any 10000 set. Finally, sensitivity of response variable to the input parameters was determined based on 10000 existing datasets by the Pearson correlation method [23]. For performance of all of the steps of sensitive analysis, the SPSS 26 software was used.Table 2
Distribution of input parameters in the model.
ParameterUnitDistributionATN concentrationmg/LWeibull (α = 0.78713, β = 3.8821)Adsorbent dosemg/LUniform (min = 50, max = 200)TimeminUniform (min = 5, max = 90)pH—Uniform (min = 2, max = 11)


## 2.5. Isotherm of Adsorption

In order to evaluate ATN adsorption by M-MWCNTs, an isotherm study was used through the optimal condition including an initial ATN concentration of 0.5, 1, 2, 5, and 10 mg/L, and the adsorbent dose of 0.15 g/L, a contact time of 60 minutes, and a pH value of 7. The water solubility (Sw) of ATN was approximated as 300 mg/L at pH 7. The isotherm fitting tool software (ISOFIT) was used in accordance with the isotherm parameters with the pilot data. ISOFIT is a software program that matches isotherm parameters to experimental data by the minimization of a weighted sum of squared error (WSSE) objective function [24]. ISOFIT supports several isotherms, containing Brunauer–Emmett–Teller (BET), Freundlich, Freundlich with linear partitioning (F-P), generalized Langmuir–Freundlich (GLF), Langmuir, Langmuir with linear partitioning (L-P), linear Polanyi with linear partitioning, and Toth [25].


## 2.6. Kinetics of Adsorption

For the analysis of the impact of contact time on the adsorption process, the adsorption kinetics was studied. The adsorption kinetics data were fitted to the pseudo-first-order, pseudo-second-order, and intraparticle diffusion kinetic models as presented in equations (4)–(6) [26]:Pseudo-first-order:(4)qt=qe1−e−K1t.Pseudo-second-order:(5)qt=K2qe2t1+K2qet.Intraparticle diffusion:(6)qt=Kpt0.5+I,WhereK1 (1/min), K2 (g/mg min), and Kp (mg/g√min) are the constants rate of the pseudo-first-order, pseudo-second-order, and intraparticle diffusion model, respectively. Meanwhile, qe and qt (mg/g) are the adsorption capacities of MWCNTs and M-MWCNTs at equilibrium and time t, respectively.


## 3. Results and Discussion

### 3.1. Adsorbent Characteristics

Whereas chemical pretreatment of adsorbents can enhance their surface-active protons and their chemisorption capability [27], we modified MWCNTs by NaOCl solution and ultrasonication. According to the result obtained in our previous study, the optimum condition was in 30% concentration of NaOCl solution and 15 seconds ultrasonication time. Therefore, modification of MWCNTs was carried out with a 30% NaOCl solution and a contact time of 15 seconds with ultrasonic [7]. Several studies showed that MWCNTs modified by the NaOCl solution is an efficient adsorbent for the removal of some contaminants from the aqueous solution [28–31]. NaOCl solution of 30% with the balanced chlorine concentration increases the adsorbent porosity, which led to improvement in the removal efficiency. Nevertheless, NaOCl concentration of 60%, the increased chlorine oxidizes carbon nanotubes and, therewith, reduce the electrical conductivity [7]. Ultrasonic modification of the adsorbent has numerous advantages such as increased porosity, shortened length of the nanotubes, high performance, short duration, environmental soundness, and increased specific surface area of CNTs [7]. Last, researchers reported appropriate results from applying ultrasonic. Ghasemi et al. investigated adsorption and removal of Pb (II) and Cd (II) from environmental samples by an amino-functionalized silica-coated multiwalled carbon nanotube with using ultrasonic. They obtained satisfactory results (adsorption efficiencies were in the range of 98–104%) [32]. Another study compared acid functionalization of the carbon nanotube via ultrasonic and reflux mechanism, and results revealed functionalization of MWCNTs via ultrasonic bath methods is more desirable and it can result in minimum structural destruction on the surface of MWCNTs [14]. Naghizadeh et al. probed the efficiency of the ultrasonic process in the regeneration of graphene nanoparticles saturated with humic acid. They reported the maximum regeneration efficiency, at a pH of 11 and a regeneration time of 60 min, was 85.37% and 72.47% for frequencies of 60 and 37 kHz, respectively [33].


### 3.2. RSM Modeling

In this study, by the RSM model, nonlinear quadratic equations were fitted to the test results by multiple regression. For variable selection, parameters withp value <0.1 were kept in the model and other items were deleted. The following equation presents the ATN removal.(7)y=3.963+11.834x1−0.199x2+0.530x3−1.952x4−0.058x1x2−0.106x1x3−0.368x1x4−6.56∗10−4x2x3+0.028x2x4+0.044x3x4+0.103x12+1.398∗10−3x22,where y, x1, x2, x3, and x4 stand for the ATN removal, ATN concentration, adsorbent dose, time, and pH, respectively.The equation in terms of actual factors can be used to make predictions about the response for given levels of each factor. Here, the levels should be specified in the original units for each factor. This equation should not be used to determine the relative impact of each factor because the coefficients are scaled to accommodate the units of each factor and the intercept is not at the center of the design space. Experiment condition and the efficiency of laboratory and predicted removal are given in Table3.Table 3
Test condition and the efficiency of laboratory and predicted removal.
RunAtenolol concentration (mg/L)Adsorbent dose (mg/L)Time (min)pHAtenolol concentration at timet (mg/L)Removal (%)qe (mg/g)Predicted ATN removal (%)151009023.4930.215.130.420.515060110.180.02.6679.93105090115.7142.985.742.34101502026.6333.622.4233.855150543.7325.28.4125.160.550520.482.60.262.8712006020.2772.63.6350.0811509070.279.25.2879.291502040.8514.82.9614.410101006046.7832.232.1932.1110.52009040.180.0270.01211005110.8811.21.1212.913520020112.4950.112.5350.21410200577.0229.814.8729.7155506072.7944.244.1844.4160.51002070.4312.20.6120.3Figure1 shows the comparison of the test findings and the predicted results of the proposed model. Figure 1(a) shows the scatter plot of the actual vs. predicted response which is one of the richest forms of data visualization. Here, all the points would be close to a regressed diagonal line and represent the goodness of fit of the model. The normal probability plot of the residuals (Figure 1(b)) is approximately linearly supporting the condition that the error terms are normally distributed and there is not any recognizable outlier.Figure 1
Plot (a) predicted against experimental results and (b) normal probability plot of residuals.
(a)(b)Analysis of variance (ANOVA) was used to evaluate that the model is significant. Table4 provides the results of ANOVA analysis of the proposed model for ATN removal under the conditions considered in this study. As given in Table 4, the p value of the model is very low and less than 0.05, which shows that the second-order regression equation was significant for predicting the response variable at the appropriate level [34]. The coefficients R2, adjusted R2, predicted R2, and Adeq precision are given in Table 4. All results indicate the high capability of the model in predicting results.Table 4
ANOVA for the response surface quadratic model.
SourceF valuePp valueExplanationATN removal modelModel646.37<0.0001SignificantLack of fit1.280.3402Not significantR-squared0.9996AdjR-squared0.9981PredictedR-squared0.9833Adeq precision81.52Another way to evaluate the model is the lack of fit test. If the mathematical model is well fitted to the experimental data, the lack of fit test would be insignificant. Briefly, a model will be well fitted to the experimental data if it presents a significant regression and a nonsignificant lack of fit. In this study, the lack of fit has no significant effect; this means that the model is fitting well to all of the design points. This means that the observed errors are not meaningful and systematic, and it can even be assumed that the selected factors are appropriate for the variable response analysis [35, 36].Figure2 shows the three-dimensional (3D) plots of the trend of changes in the initial concentration of atenolol, adsorbent dose, pH, and contact time against removal efficiency according to the output of the RSM model.Figure 2
Relation between atenolol removal efficiency and the interaction terms by 3D plot: (a) interaction between pH time; (b) interaction between atenolol concentration-adsorbent dose.
(a)(b)


#### 3.2.1. Effect of pH

Figure2(a) shows the adsorption of ATN by M-MWCNTs at various pH. In this experiment pH 2, 4, 7, and 11 were studied. As given in Table 3, at each stage, all of the factors such as the pH value, contact time, ATN concentration, and adsorbent dose are variable. As shown in Figure 2(a), to increase the pH values from 2 to 11, the removal efficiency has gently increased. It was found that the best result was obtained at a pH of 11. The low adsorption at the low pH value could be due to the high concentration and high mobility of H+ ions, which competed with ATN for the adsorption sites during the sorption process [37]. Ahmadi et al. reported that the optimal pH for Ni (II) ions adsorption on MWCNTs from aqueous solution is 10. They mentioned that it could be attributed to the surface of the MWCNTs and is negatively charged. pH and the Ni (II) ions are positively charged; thus, electrostatic attraction is increased between them which enhanced the removal efficiency [38].Because removal of ATN at pH from 7 to 11 was negligible, we selected pH 7 as an optimal condition. Under low pH, the H+ ions can affect or compete against ATN for the adsorption sites. Chang et al. commented that strong and weak adsorption sites, cation exchange, and hydrogen bonding were the adsorption mechanisms for ATN removal by SAz-2 under alkaline conditions [39]. Furthermore, according to our last study on the pHZPC of the MWCNTs, which was equal to 8, the increase in adsorption of ATN at pH of 7–11 can be linked to pHZPC [40]. Researchers observed the highest adsorption of benzene, toluene, and p-Xylene at pH 7 too [37]. According to Hu et al., the highest adsorption of ATN on kaolinite occurred in neutral pH [41]. Phenol removal by MWCNTs modified with nitric acid and ultrasonic was studied. Results showed that the highest efficiency of phenol removal was at pH 11 [42]. Hadi et al. revealed that by increasing pH, adsorption of ATN on waste biomass derived activated carbon increased [26].


#### 3.2.2. Effect of Contact Time

Figure2(a) shows the changes in contact time from 5 min to 90 min and increase the ATN removal to about 40%. Increasing trend of the removal efficiency was faster to approximately 60 min, and after that, it was almost constant. This may be due to free adsorption site on nanotubes. In the start of the process, a large amount of sites are free, and as they are occupied by adsorbate, these unoccupied sites tend to decline, resulting to the equilibrium point of the process.Haro et al.’ study confirmed this result for adsorption of ATN on activated carbon [43]. Also, recently, it was reported that with an increase in contact time, removal of benzene, toluene, and p-xylene by multiwalled carbon nanotubes increased [37].


#### 3.2.3. Effect of the Initial Concentration of ATN

As shown in Figure2(b) the adsorption capacity of ATN on M-MWCNT for initial concentration of ATN from 0.5 mg/L to 1 mg/L slightly increase and after that started to decrease. For the 1 mg/L concentration of ATN, higher removal obtained, and with the enhancement of initial ATN dose, their percentage removal declined. It can be explained at lower concentrations, and ATN molecules have more chance to attach the adsorption sites because the active adsorption sites on the surface of M-MWCNTs is higher than an initial number of ATN molecules, thus removal efficiency increased [44]. With the increase of initial concentration, the limited adsorption active sites were depleted and the adsorption was in a saturated state to reach equilibrium [45]. Because the concentration of 0.5 mg/L was more economical than 1 mg/L, the difference between removal efficiency of them was trifle; therefore, further investigations were conducted by using 0.5 mg/L of ATN.


#### 3.2.4. Effect of Adsorbent Concentration

The adsorbent dosage (50–200 mg/L) as an effective factor in removal efficiency was studied. With the increase of M-MWCNTs dosage from 50 mg/L to 100 mg/L, the adsorption decreased, and after that, when M-MWCNTs dosage raised from 100 mg/L to 200 mg/L, an ascending trend was observed in ATN removal (Figure2(b)).This suggests an increase in the number of active sites, the increased contact area, and in turn the enhanced electrostatic interaction which results in the development of removal efficiency [4]. Kończyk et al. observed that with the increased MWCNT dose, due to the surface of adsorbent provided a sufficient number of binding sites for the Pb (II) ions, the adsorption efficiency increased [46]. The maximum adsorption was obtained at 150 mg/L because ATN removal at M-MWCNTs dose between 150 and 200 mg/L was negligible, and it was economical.Finally, in the current study, optimum condition was 0.5 mg/L ATN initial concentration at 60 min contact time and pH 7 and adsorbent concentration of 150 mg/L.


### 3.3. Sensitivity Analysis by Monte Carlo Simulation

Sensitivity analysis in a system means how sensitive the predicted variable at the system output is to independent input variables [47]. In this study, sensitivity analysis was performed by the Monte Carlo method. The parameters affecting ATN removal efficiency are time, adsorbent dose, ATN concentration, and pH. Based on 10,000 efficiencies calculated in the Monte Carlo method, the probability distribution diagram for ATN removal is shown in Figure 3. The response parameter followed the gamma probability distribution (scale 0.11, shape 4.73). ATN removal will remove in the range of 5–95% confidence in the range of 14.29–77.80%. Pearson correlation coefficient on 10,000 existing datasets was also used for sensitivity analysis. The test was performed at 95% confidence level in the SPSS software, and its results can be seen in the form of Tornado diagram shown in Figure 4 [48, 49]. According to these graphs, time was the most important parameter, and then, the adsorbent dose and pH had a positive effect on the removal efficiency. Initial concentration and increase of this parameter had a negative effect on pollutant removal efficiency.Figure 3
Probability distribution of Monte Carlo simulation output for ATN removal.Figure 4
Tornado diagram for sensitivity analysis by the Monte Carlo method.


### 3.4. Specifications of the Adsorbent

In our last study, shape, size, and surface morphology of MWCNTs and M-MWCNTs were investigated through the transmission electron microscopy (TEM), and Fourier transform infrared (FTIR) analysis was applied to determine the functional groups and survey the chemical bonds of the modified carbon nanotubes [7]. TEM showed that after modification, ultrasonic reduced the catalytic particles on the surface and increased its specific surface area [50]. FTIR analysis demonstrated various functional groups such as hydroxyl, carboxyl, and carbonyl in raw carbon nanotubes, but in M-MWCNTs, many of the impurities were removed. The most peaks at 1566 and 2352 cm−1 in M-MWCNTs are related to the stretching vibration characteristic of C=C and C-O groups, respectively. Also, the peaks at 1708 and 1150 cm−1 are associated with the C=O group. According to the study of Pourzamani et al. that experimented modification by ozone and NaOCl, the results showed within the range of 1000–2000, 1500–2500, and 2500–3500 cm−1, the carboxylic, carbonyl, and hydroxyl functional groups have been mainly promoted, respectively [51]. In another study, after modification of MWCNT, it found that peaks at the range of 1563–1652 cm−1 were referred to the C=O group [30].


### 3.5. Adsorption Isotherms

In order to determine the most appropriate isotherm for ATN adsorption by M-MWCNTs, the ISOFIT program was used (Table5). Isotherm values of correlation between residual and normality (RN2), measured and simulated observation (Ry2), Akaike amended information criterion (AICc), and Linssen measure of nonlinearity (M2) for Freundlich, linear, Polanyi, Langmuir, L-P, and BET are given in Table 5. Based on a fairly low value of AICc, atenolol adsorption by M-MWCNTs pursued BET isotherm, and this isotherm is the best fit. The diagram of ATN removal by M-MWCNTs is shown in Figure 5.Table 5
Summary of selected diagnostics for atenolol adsorbed by M-MWCNT.
IsothermsAICCRy2RN2M2Linearity assessmentLangmuir3.3610.8832.09 × 10−4NonlinearBET3.2710.8812.08 × 10−4NonlinearLinear6.200.9980.9441.48 × 10−9LinearL-P3.3610.8802.06 × 10−4NonlinearFreundlich4.2710.8809.89 × 10−3NonlinearPolanyi partition12.010.9980.9902.22 × 10−2UncertainAICc, multimodel ranking; Ry2, correlation between measured and simulated observation; RN2, correlation between residual and normality; M2, Linssen measure of nonlinearity.Figure 5
Plot of fitted isotherm (BET) for atenolol adsorption by M-MWCNTS.It is understood which surface and distribution of sites is uniform and surface is energetically homogeneous, and there is no interaction between adsorbent and adsorbate [52]. Larous and Meniai investigated the adsorption of diclofenac by activated carbon prepared from olive stones, and their results indicate the BET isotherm is fairly better than Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) isotherms [53]. Also, this equation was fit for adsorption of a textile dye by nanosized montmorillonite (MMT)/calcium alginate (CA) composite (R2 value of 0.9855) [54].Table6 provides the parameters of BET isotherm related to ATN adsorption on M-MWCNTs, which are results from the ISOFIT software.Table 6
Selected ISOFIT postregression output.
Parameter or statisticISOFIT resultOverall quality of fitWSSE1.66 × 10−1RMSE0.235Ry1Parameter statisticsbQ01.64 × 103b1.38 × 101Parameter standard errorbQ05.203 × 101b1.409Test of assumptions Linssen (M2)M22.08 × 10−4Threshold4.73 × 10−3AssessmentLinearNormality (RN2)RN20.881Critical value0.71AssessmentNormal residualsRuns testNumber of runs4Pp value1AssessmentNo correlationDurbin–Watson test (D)D3.15PP value0.97AssessmentNo correlationIn Table6, the Linssen measure indicates significant WSSE nonlinearity near the optimal parameter values. The statistical measures such as the RN2 and Durbin–Watson test (D) show normally distributed weighted residuals with no serial autocorrelation. The ISOFIT provides two standard measures for evaluating isotherm goodness of fit, namely, the root mean squared error (RMSE, equation (8)) and the correlation between measured and fitted observations (Ry, equation (9)).(8)RMSE=WSSEm−p,(9)Ry=∑i=1mwiSi,obs−SobsavgwiSi−Savg∑i=1mwiSi,obs−Sobsavg2∑i=1mwiSi,obs−Savg2,where WSSE is the weighted sum of squared error, m is the total number of experimental observations, p is the number of isotherm parameters, wi is the weight given to observation I; Si,obs is the ith experimentally measured sorbed concentration; Si is the ith simulated sorbed concentration computed via an isotherm expression; and Sobsavg and Savg are the averages of the weighted measured and weighted isotherm simulated adsorbed concentrations, respectively [4].


### 3.6. Kinetic Studies of the Reaction

A kinetic study was performed to analyse the adsorbed amounts against contact time data by various kinetics models. The pseudo-first-order, pseudo-second-order, and intraparticle diffusion models were used to perform a kinetic study. The plotted kinetic data for ATN on MWCNT-US (Figure6) illustrate that the pseudo-first-order model better explained the adsorption of atenolol by MWCNT-US because this model has the highest correlation coefficient (R2 value of 0.9906).Figure 6
(a) Plot of pseudo-first-order, (b) pseudo-second-order, and (c) intraparticle diffusion kinetic models for ATN adsorption onto M-MWCNTs.
(a)(b)(c)Also, Table7 provides better agreement of the computed adsorption capacity relevant to the pseudo-first-order kinetic reaction. In this kinetic model, it is assumed that a various rate of adsorbate over time is directly proportional to the saturation concentration and the amount of adsorbent removed over time [55]. In the investigation of the removal of tetracycline antibiotics by a human hair-derived high surface area porous carbon material (HHC), the reaction kinetics also followed first-order kinetics (R2 values within 0.9859–0.9949) [56]. A similar result was reported by Ali et al. for the uptake of propranolol on ionic liquid iron nanocomposite adsorbent [57]. But in contrast of the results in this study, pseudo-second-order kinetic indicated the best adaptation for the removal of dyes from aqueous solutions by oxygenated functionalities enriched MWCNTs decorated with silica-coated spinel ferrite [58].Table 7
Kinetic parameters for the adsorption of ATN onto MWCNT-US.
Model typeParametersValuePseudo-first-order modelK1 (1/min)0.1636qe (mg/g)4.03R20.9906Pseudo-second-order modelK2 (1/min)0.022qe (mg/g)3.20R20.9222Intraparticle diffusionKp0.4I0.12R20.801Table8 provides the adsorption capacity of several adsorbents for some pollutants’ adsorption. As given in Table 8, MWCNT modified by NaOCl and ultrasonic can be a good alternative adsorbent for the removal of ATN and other pollutants from aqueous solutions.Table 8
Summary of similar studies.
AdsorbentAdsorbateAdsorption capacity (mg/g)ReferenceAtenololCorncob biochar-based montmorillonite composite86.86[1]TetracyclineHuman hair (carbon material)128.52[2]Ceftriaxone sodiumNanocomposite g-C3N4/MWCNT/Bi2WO6functionalized ultrasound wave22.357[3]Pb(II) ionsMWCNT functionalized by selenophosphoryl groups156.25[4]AtenololCa-montmorillonite87.89[5]TolueneMWCNT64.6[6]TetracyclinePurified and oxidized MWCNT253.3[7]TolueneSingle-wall carbon nanotubes-magnetic nanoparticles6.2–188.9[8]AtenololM-MWCNTs2.58This study


## 3.1. Adsorbent Characteristics

Whereas chemical pretreatment of adsorbents can enhance their surface-active protons and their chemisorption capability [27], we modified MWCNTs by NaOCl solution and ultrasonication. According to the result obtained in our previous study, the optimum condition was in 30% concentration of NaOCl solution and 15 seconds ultrasonication time. Therefore, modification of MWCNTs was carried out with a 30% NaOCl solution and a contact time of 15 seconds with ultrasonic [7]. Several studies showed that MWCNTs modified by the NaOCl solution is an efficient adsorbent for the removal of some contaminants from the aqueous solution [28–31]. NaOCl solution of 30% with the balanced chlorine concentration increases the adsorbent porosity, which led to improvement in the removal efficiency. Nevertheless, NaOCl concentration of 60%, the increased chlorine oxidizes carbon nanotubes and, therewith, reduce the electrical conductivity [7]. Ultrasonic modification of the adsorbent has numerous advantages such as increased porosity, shortened length of the nanotubes, high performance, short duration, environmental soundness, and increased specific surface area of CNTs [7]. Last, researchers reported appropriate results from applying ultrasonic. Ghasemi et al. investigated adsorption and removal of Pb (II) and Cd (II) from environmental samples by an amino-functionalized silica-coated multiwalled carbon nanotube with using ultrasonic. They obtained satisfactory results (adsorption efficiencies were in the range of 98–104%) [32]. Another study compared acid functionalization of the carbon nanotube via ultrasonic and reflux mechanism, and results revealed functionalization of MWCNTs via ultrasonic bath methods is more desirable and it can result in minimum structural destruction on the surface of MWCNTs [14]. Naghizadeh et al. probed the efficiency of the ultrasonic process in the regeneration of graphene nanoparticles saturated with humic acid. They reported the maximum regeneration efficiency, at a pH of 11 and a regeneration time of 60 min, was 85.37% and 72.47% for frequencies of 60 and 37 kHz, respectively [33].


## 3.2. RSM Modeling

In this study, by the RSM model, nonlinear quadratic equations were fitted to the test results by multiple regression. For variable selection, parameters withp value <0.1 were kept in the model and other items were deleted. The following equation presents the ATN removal.(7)y=3.963+11.834x1−0.199x2+0.530x3−1.952x4−0.058x1x2−0.106x1x3−0.368x1x4−6.56∗10−4x2x3+0.028x2x4+0.044x3x4+0.103x12+1.398∗10−3x22,where y, x1, x2, x3, and x4 stand for the ATN removal, ATN concentration, adsorbent dose, time, and pH, respectively.The equation in terms of actual factors can be used to make predictions about the response for given levels of each factor. Here, the levels should be specified in the original units for each factor. This equation should not be used to determine the relative impact of each factor because the coefficients are scaled to accommodate the units of each factor and the intercept is not at the center of the design space. Experiment condition and the efficiency of laboratory and predicted removal are given in Table3.Table 3
Test condition and the efficiency of laboratory and predicted removal.
RunAtenolol concentration (mg/L)Adsorbent dose (mg/L)Time (min)pHAtenolol concentration at timet (mg/L)Removal (%)qe (mg/g)Predicted ATN removal (%)151009023.4930.215.130.420.515060110.180.02.6679.93105090115.7142.985.742.34101502026.6333.622.4233.855150543.7325.28.4125.160.550520.482.60.262.8712006020.2772.63.6350.0811509070.279.25.2879.291502040.8514.82.9614.410101006046.7832.232.1932.1110.52009040.180.0270.01211005110.8811.21.1212.913520020112.4950.112.5350.21410200577.0229.814.8729.7155506072.7944.244.1844.4160.51002070.4312.20.6120.3Figure1 shows the comparison of the test findings and the predicted results of the proposed model. Figure 1(a) shows the scatter plot of the actual vs. predicted response which is one of the richest forms of data visualization. Here, all the points would be close to a regressed diagonal line and represent the goodness of fit of the model. The normal probability plot of the residuals (Figure 1(b)) is approximately linearly supporting the condition that the error terms are normally distributed and there is not any recognizable outlier.Figure 1
Plot (a) predicted against experimental results and (b) normal probability plot of residuals.
(a)(b)Analysis of variance (ANOVA) was used to evaluate that the model is significant. Table4 provides the results of ANOVA analysis of the proposed model for ATN removal under the conditions considered in this study. As given in Table 4, the p value of the model is very low and less than 0.05, which shows that the second-order regression equation was significant for predicting the response variable at the appropriate level [34]. The coefficients R2, adjusted R2, predicted R2, and Adeq precision are given in Table 4. All results indicate the high capability of the model in predicting results.Table 4
ANOVA for the response surface quadratic model.
SourceF valuePp valueExplanationATN removal modelModel646.37<0.0001SignificantLack of fit1.280.3402Not significantR-squared0.9996AdjR-squared0.9981PredictedR-squared0.9833Adeq precision81.52Another way to evaluate the model is the lack of fit test. If the mathematical model is well fitted to the experimental data, the lack of fit test would be insignificant. Briefly, a model will be well fitted to the experimental data if it presents a significant regression and a nonsignificant lack of fit. In this study, the lack of fit has no significant effect; this means that the model is fitting well to all of the design points. This means that the observed errors are not meaningful and systematic, and it can even be assumed that the selected factors are appropriate for the variable response analysis [35, 36].Figure2 shows the three-dimensional (3D) plots of the trend of changes in the initial concentration of atenolol, adsorbent dose, pH, and contact time against removal efficiency according to the output of the RSM model.Figure 2
Relation between atenolol removal efficiency and the interaction terms by 3D plot: (a) interaction between pH time; (b) interaction between atenolol concentration-adsorbent dose.
(a)(b)


### 3.2.1. Effect of pH

Figure2(a) shows the adsorption of ATN by M-MWCNTs at various pH. In this experiment pH 2, 4, 7, and 11 were studied. As given in Table 3, at each stage, all of the factors such as the pH value, contact time, ATN concentration, and adsorbent dose are variable. As shown in Figure 2(a), to increase the pH values from 2 to 11, the removal efficiency has gently increased. It was found that the best result was obtained at a pH of 11. The low adsorption at the low pH value could be due to the high concentration and high mobility of H+ ions, which competed with ATN for the adsorption sites during the sorption process [37]. Ahmadi et al. reported that the optimal pH for Ni (II) ions adsorption on MWCNTs from aqueous solution is 10. They mentioned that it could be attributed to the surface of the MWCNTs and is negatively charged. pH and the Ni (II) ions are positively charged; thus, electrostatic attraction is increased between them which enhanced the removal efficiency [38].Because removal of ATN at pH from 7 to 11 was negligible, we selected pH 7 as an optimal condition. Under low pH, the H+ ions can affect or compete against ATN for the adsorption sites. Chang et al. commented that strong and weak adsorption sites, cation exchange, and hydrogen bonding were the adsorption mechanisms for ATN removal by SAz-2 under alkaline conditions [39]. Furthermore, according to our last study on the pHZPC of the MWCNTs, which was equal to 8, the increase in adsorption of ATN at pH of 7–11 can be linked to pHZPC [40]. Researchers observed the highest adsorption of benzene, toluene, and p-Xylene at pH 7 too [37]. According to Hu et al., the highest adsorption of ATN on kaolinite occurred in neutral pH [41]. Phenol removal by MWCNTs modified with nitric acid and ultrasonic was studied. Results showed that the highest efficiency of phenol removal was at pH 11 [42]. Hadi et al. revealed that by increasing pH, adsorption of ATN on waste biomass derived activated carbon increased [26].


### 3.2.2. Effect of Contact Time

Figure2(a) shows the changes in contact time from 5 min to 90 min and increase the ATN removal to about 40%. Increasing trend of the removal efficiency was faster to approximately 60 min, and after that, it was almost constant. This may be due to free adsorption site on nanotubes. In the start of the process, a large amount of sites are free, and as they are occupied by adsorbate, these unoccupied sites tend to decline, resulting to the equilibrium point of the process.Haro et al.’ study confirmed this result for adsorption of ATN on activated carbon [43]. Also, recently, it was reported that with an increase in contact time, removal of benzene, toluene, and p-xylene by multiwalled carbon nanotubes increased [37].


### 3.2.3. Effect of the Initial Concentration of ATN

As shown in Figure2(b) the adsorption capacity of ATN on M-MWCNT for initial concentration of ATN from 0.5 mg/L to 1 mg/L slightly increase and after that started to decrease. For the 1 mg/L concentration of ATN, higher removal obtained, and with the enhancement of initial ATN dose, their percentage removal declined. It can be explained at lower concentrations, and ATN molecules have more chance to attach the adsorption sites because the active adsorption sites on the surface of M-MWCNTs is higher than an initial number of ATN molecules, thus removal efficiency increased [44]. With the increase of initial concentration, the limited adsorption active sites were depleted and the adsorption was in a saturated state to reach equilibrium [45]. Because the concentration of 0.5 mg/L was more economical than 1 mg/L, the difference between removal efficiency of them was trifle; therefore, further investigations were conducted by using 0.5 mg/L of ATN.


### 3.2.4. Effect of Adsorbent Concentration

The adsorbent dosage (50–200 mg/L) as an effective factor in removal efficiency was studied. With the increase of M-MWCNTs dosage from 50 mg/L to 100 mg/L, the adsorption decreased, and after that, when M-MWCNTs dosage raised from 100 mg/L to 200 mg/L, an ascending trend was observed in ATN removal (Figure2(b)).This suggests an increase in the number of active sites, the increased contact area, and in turn the enhanced electrostatic interaction which results in the development of removal efficiency [4]. Kończyk et al. observed that with the increased MWCNT dose, due to the surface of adsorbent provided a sufficient number of binding sites for the Pb (II) ions, the adsorption efficiency increased [46]. The maximum adsorption was obtained at 150 mg/L because ATN removal at M-MWCNTs dose between 150 and 200 mg/L was negligible, and it was economical.Finally, in the current study, optimum condition was 0.5 mg/L ATN initial concentration at 60 min contact time and pH 7 and adsorbent concentration of 150 mg/L.


## 3.2.1. Effect of pH

Figure2(a) shows the adsorption of ATN by M-MWCNTs at various pH. In this experiment pH 2, 4, 7, and 11 were studied. As given in Table 3, at each stage, all of the factors such as the pH value, contact time, ATN concentration, and adsorbent dose are variable. As shown in Figure 2(a), to increase the pH values from 2 to 11, the removal efficiency has gently increased. It was found that the best result was obtained at a pH of 11. The low adsorption at the low pH value could be due to the high concentration and high mobility of H+ ions, which competed with ATN for the adsorption sites during the sorption process [37]. Ahmadi et al. reported that the optimal pH for Ni (II) ions adsorption on MWCNTs from aqueous solution is 10. They mentioned that it could be attributed to the surface of the MWCNTs and is negatively charged. pH and the Ni (II) ions are positively charged; thus, electrostatic attraction is increased between them which enhanced the removal efficiency [38].Because removal of ATN at pH from 7 to 11 was negligible, we selected pH 7 as an optimal condition. Under low pH, the H+ ions can affect or compete against ATN for the adsorption sites. Chang et al. commented that strong and weak adsorption sites, cation exchange, and hydrogen bonding were the adsorption mechanisms for ATN removal by SAz-2 under alkaline conditions [39]. Furthermore, according to our last study on the pHZPC of the MWCNTs, which was equal to 8, the increase in adsorption of ATN at pH of 7–11 can be linked to pHZPC [40]. Researchers observed the highest adsorption of benzene, toluene, and p-Xylene at pH 7 too [37]. According to Hu et al., the highest adsorption of ATN on kaolinite occurred in neutral pH [41]. Phenol removal by MWCNTs modified with nitric acid and ultrasonic was studied. Results showed that the highest efficiency of phenol removal was at pH 11 [42]. Hadi et al. revealed that by increasing pH, adsorption of ATN on waste biomass derived activated carbon increased [26].


## 3.2.2. Effect of Contact Time

Figure2(a) shows the changes in contact time from 5 min to 90 min and increase the ATN removal to about 40%. Increasing trend of the removal efficiency was faster to approximately 60 min, and after that, it was almost constant. This may be due to free adsorption site on nanotubes. In the start of the process, a large amount of sites are free, and as they are occupied by adsorbate, these unoccupied sites tend to decline, resulting to the equilibrium point of the process.Haro et al.’ study confirmed this result for adsorption of ATN on activated carbon [43]. Also, recently, it was reported that with an increase in contact time, removal of benzene, toluene, and p-xylene by multiwalled carbon nanotubes increased [37].


## 3.2.3. Effect of the Initial Concentration of ATN

As shown in Figure2(b) the adsorption capacity of ATN on M-MWCNT for initial concentration of ATN from 0.5 mg/L to 1 mg/L slightly increase and after that started to decrease. For the 1 mg/L concentration of ATN, higher removal obtained, and with the enhancement of initial ATN dose, their percentage removal declined. It can be explained at lower concentrations, and ATN molecules have more chance to attach the adsorption sites because the active adsorption sites on the surface of M-MWCNTs is higher than an initial number of ATN molecules, thus removal efficiency increased [44]. With the increase of initial concentration, the limited adsorption active sites were depleted and the adsorption was in a saturated state to reach equilibrium [45]. Because the concentration of 0.5 mg/L was more economical than 1 mg/L, the difference between removal efficiency of them was trifle; therefore, further investigations were conducted by using 0.5 mg/L of ATN.


## 3.2.4. Effect of Adsorbent Concentration

The adsorbent dosage (50–200 mg/L) as an effective factor in removal efficiency was studied. With the increase of M-MWCNTs dosage from 50 mg/L to 100 mg/L, the adsorption decreased, and after that, when M-MWCNTs dosage raised from 100 mg/L to 200 mg/L, an ascending trend was observed in ATN removal (Figure2(b)).This suggests an increase in the number of active sites, the increased contact area, and in turn the enhanced electrostatic interaction which results in the development of removal efficiency [4]. Kończyk et al. observed that with the increased MWCNT dose, due to the surface of adsorbent provided a sufficient number of binding sites for the Pb (II) ions, the adsorption efficiency increased [46]. The maximum adsorption was obtained at 150 mg/L because ATN removal at M-MWCNTs dose between 150 and 200 mg/L was negligible, and it was economical.Finally, in the current study, optimum condition was 0.5 mg/L ATN initial concentration at 60 min contact time and pH 7 and adsorbent concentration of 150 mg/L.


## 3.3. Sensitivity Analysis by Monte Carlo Simulation

Sensitivity analysis in a system means how sensitive the predicted variable at the system output is to independent input variables [47]. In this study, sensitivity analysis was performed by the Monte Carlo method. The parameters affecting ATN removal efficiency are time, adsorbent dose, ATN concentration, and pH. Based on 10,000 efficiencies calculated in the Monte Carlo method, the probability distribution diagram for ATN removal is shown in Figure 3. The response parameter followed the gamma probability distribution (scale 0.11, shape 4.73). ATN removal will remove in the range of 5–95% confidence in the range of 14.29–77.80%. Pearson correlation coefficient on 10,000 existing datasets was also used for sensitivity analysis. The test was performed at 95% confidence level in the SPSS software, and its results can be seen in the form of Tornado diagram shown in Figure 4 [48, 49]. According to these graphs, time was the most important parameter, and then, the adsorbent dose and pH had a positive effect on the removal efficiency. Initial concentration and increase of this parameter had a negative effect on pollutant removal efficiency.Figure 3
Probability distribution of Monte Carlo simulation output for ATN removal.Figure 4
Tornado diagram for sensitivity analysis by the Monte Carlo method.


## 3.4. Specifications of the Adsorbent

In our last study, shape, size, and surface morphology of MWCNTs and M-MWCNTs were investigated through the transmission electron microscopy (TEM), and Fourier transform infrared (FTIR) analysis was applied to determine the functional groups and survey the chemical bonds of the modified carbon nanotubes [7]. TEM showed that after modification, ultrasonic reduced the catalytic particles on the surface and increased its specific surface area [50]. FTIR analysis demonstrated various functional groups such as hydroxyl, carboxyl, and carbonyl in raw carbon nanotubes, but in M-MWCNTs, many of the impurities were removed. The most peaks at 1566 and 2352 cm−1 in M-MWCNTs are related to the stretching vibration characteristic of C=C and C-O groups, respectively. Also, the peaks at 1708 and 1150 cm−1 are associated with the C=O group. According to the study of Pourzamani et al. that experimented modification by ozone and NaOCl, the results showed within the range of 1000–2000, 1500–2500, and 2500–3500 cm−1, the carboxylic, carbonyl, and hydroxyl functional groups have been mainly promoted, respectively [51]. In another study, after modification of MWCNT, it found that peaks at the range of 1563–1652 cm−1 were referred to the C=O group [30].


## 3.5. Adsorption Isotherms

In order to determine the most appropriate isotherm for ATN adsorption by M-MWCNTs, the ISOFIT program was used (Table5). Isotherm values of correlation between residual and normality (RN2), measured and simulated observation (Ry2), Akaike amended information criterion (AICc), and Linssen measure of nonlinearity (M2) for Freundlich, linear, Polanyi, Langmuir, L-P, and BET are given in Table 5. Based on a fairly low value of AICc, atenolol adsorption by M-MWCNTs pursued BET isotherm, and this isotherm is the best fit. The diagram of ATN removal by M-MWCNTs is shown in Figure 5.Table 5
Summary of selected diagnostics for atenolol adsorbed by M-MWCNT.
IsothermsAICCRy2RN2M2Linearity assessmentLangmuir3.3610.8832.09 × 10−4NonlinearBET3.2710.8812.08 × 10−4NonlinearLinear6.200.9980.9441.48 × 10−9LinearL-P3.3610.8802.06 × 10−4NonlinearFreundlich4.2710.8809.89 × 10−3NonlinearPolanyi partition12.010.9980.9902.22 × 10−2UncertainAICc, multimodel ranking; Ry2, correlation between measured and simulated observation; RN2, correlation between residual and normality; M2, Linssen measure of nonlinearity.Figure 5
Plot of fitted isotherm (BET) for atenolol adsorption by M-MWCNTS.It is understood which surface and distribution of sites is uniform and surface is energetically homogeneous, and there is no interaction between adsorbent and adsorbate [52]. Larous and Meniai investigated the adsorption of diclofenac by activated carbon prepared from olive stones, and their results indicate the BET isotherm is fairly better than Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) isotherms [53]. Also, this equation was fit for adsorption of a textile dye by nanosized montmorillonite (MMT)/calcium alginate (CA) composite (R2 value of 0.9855) [54].Table6 provides the parameters of BET isotherm related to ATN adsorption on M-MWCNTs, which are results from the ISOFIT software.Table 6
Selected ISOFIT postregression output.
Parameter or statisticISOFIT resultOverall quality of fitWSSE1.66 × 10−1RMSE0.235Ry1Parameter statisticsbQ01.64 × 103b1.38 × 101Parameter standard errorbQ05.203 × 101b1.409Test of assumptions Linssen (M2)M22.08 × 10−4Threshold4.73 × 10−3AssessmentLinearNormality (RN2)RN20.881Critical value0.71AssessmentNormal residualsRuns testNumber of runs4Pp value1AssessmentNo correlationDurbin–Watson test (D)D3.15PP value0.97AssessmentNo correlationIn Table6, the Linssen measure indicates significant WSSE nonlinearity near the optimal parameter values. The statistical measures such as the RN2 and Durbin–Watson test (D) show normally distributed weighted residuals with no serial autocorrelation. The ISOFIT provides two standard measures for evaluating isotherm goodness of fit, namely, the root mean squared error (RMSE, equation (8)) and the correlation between measured and fitted observations (Ry, equation (9)).(8)RMSE=WSSEm−p,(9)Ry=∑i=1mwiSi,obs−SobsavgwiSi−Savg∑i=1mwiSi,obs−Sobsavg2∑i=1mwiSi,obs−Savg2,where WSSE is the weighted sum of squared error, m is the total number of experimental observations, p is the number of isotherm parameters, wi is the weight given to observation I; Si,obs is the ith experimentally measured sorbed concentration; Si is the ith simulated sorbed concentration computed via an isotherm expression; and Sobsavg and Savg are the averages of the weighted measured and weighted isotherm simulated adsorbed concentrations, respectively [4].


## 3.6. Kinetic Studies of the Reaction

A kinetic study was performed to analyse the adsorbed amounts against contact time data by various kinetics models. The pseudo-first-order, pseudo-second-order, and intraparticle diffusion models were used to perform a kinetic study. The plotted kinetic data for ATN on MWCNT-US (Figure6) illustrate that the pseudo-first-order model better explained the adsorption of atenolol by MWCNT-US because this model has the highest correlation coefficient (R2 value of 0.9906).Figure 6
(a) Plot of pseudo-first-order, (b) pseudo-second-order, and (c) intraparticle diffusion kinetic models for ATN adsorption onto M-MWCNTs.
(a)(b)(c)Also, Table7 provides better agreement of the computed adsorption capacity relevant to the pseudo-first-order kinetic reaction. In this kinetic model, it is assumed that a various rate of adsorbate over time is directly proportional to the saturation concentration and the amount of adsorbent removed over time [55]. In the investigation of the removal of tetracycline antibiotics by a human hair-derived high surface area porous carbon material (HHC), the reaction kinetics also followed first-order kinetics (R2 values within 0.9859–0.9949) [56]. A similar result was reported by Ali et al. for the uptake of propranolol on ionic liquid iron nanocomposite adsorbent [57]. But in contrast of the results in this study, pseudo-second-order kinetic indicated the best adaptation for the removal of dyes from aqueous solutions by oxygenated functionalities enriched MWCNTs decorated with silica-coated spinel ferrite [58].Table 7
Kinetic parameters for the adsorption of ATN onto MWCNT-US.
Model typeParametersValuePseudo-first-order modelK1 (1/min)0.1636qe (mg/g)4.03R20.9906Pseudo-second-order modelK2 (1/min)0.022qe (mg/g)3.20R20.9222Intraparticle diffusionKp0.4I0.12R20.801Table8 provides the adsorption capacity of several adsorbents for some pollutants’ adsorption. As given in Table 8, MWCNT modified by NaOCl and ultrasonic can be a good alternative adsorbent for the removal of ATN and other pollutants from aqueous solutions.Table 8
Summary of similar studies.
AdsorbentAdsorbateAdsorption capacity (mg/g)ReferenceAtenololCorncob biochar-based montmorillonite composite86.86[1]TetracyclineHuman hair (carbon material)128.52[2]Ceftriaxone sodiumNanocomposite g-C3N4/MWCNT/Bi2WO6functionalized ultrasound wave22.357[3]Pb(II) ionsMWCNT functionalized by selenophosphoryl groups156.25[4]AtenololCa-montmorillonite87.89[5]TolueneMWCNT64.6[6]TetracyclinePurified and oxidized MWCNT253.3[7]TolueneSingle-wall carbon nanotubes-magnetic nanoparticles6.2–188.9[8]AtenololM-MWCNTs2.58This study


## 4. Conclusion

Through the removal efficiency analysis of ATN via M-MWCNTs, we found an increase in the adsorbent dose and pH cause increasing of ATN removal efficiency. Time ascending to 60 min promotes the removal efficiency, and after that, it was almost constant. Initial ATN concentration had a negative effect on the removal efficiency. Results showed M-MWCNT is a high-performance adsorbent for removing ATN from the aqueous solution. According to the obtained results from sensitivity analysis, time was the most important parameter, and after that, the adsorbent dose and pH affect positively on ATN removal efficiency.The kinetic investigation demonstrated that the adsorption process followed the pseudo-first-order model. The result of the isotherm study showed that the process was fitted to the BET model.Adsorption with M-MWCNT proved to be an efficient method for removing atenolol because this method has high removal efficiency. This method is relatively easy, fast, and eco-friendly. Also, it is possible to reuse MWCNTs, and even their modified mode can be utilized as a new method.



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*Source: 4613023-2022-06-08.xml*