Response surface modeling of lead (׀׀) removal by graphene oxide-Fe3O4 nanocomposite using central composite design

Background Magnetic graphene oxide (Fe3O4@SiO2-GO) nanocomposite was fabricated through a facile process and its application as an excellent adsorbent for lead (II) removal was also demonstrated by applying response surface methodology (RSM). Methods Fe3O4@SiO2-GO nanocomposite was synthesized and characterized properly. The effects of four independent variables, initial pH of solution (3.5–8.5), nanocomposite dosage (1–60 mg L−1), contact time (2–30 min), and initial lead (II) ion concentration (0.5–5 mg L−1) on the lead (II) removal efficiency were investigated and the process was optimized using RSM. Using central composite design (CCD), 44 experiments were carried out and the process response was modeled using a quadratic equation as function of the variables. Results The optimum values of the variables were found to be 6.9, 30.5 mg L−1, 16 min, and 2.49 mg L−1 for pH, adsorbent dosage, contact time, and lead (II) initial concentration, respectively. The amount of adsorbed lead (II) after 16 min was recorded as high as 505.81 mg g−1 for 90 mg L−1 initial lead (II) ion concentration. The Sips isotherm was found to provide a good fit with the adsorption data (KS = 256 L mg−1, nS = 0.57, qm = 598.4 mg g−1, and R2 = 0.984). The mean free energy Eads was 9.901 kJ/mol which confirmed the chemisorption mechanism. The kinetic study determined an appropriate compliance of experimental data with the double exponential kinetic model (R2 = 0.982). Conclusions Quadratic and reduced models were examined to correlate the variables with the removal efficiency of Fe3O4@SiO2-GO. According to the analysis of variance, the most influential factors were identified as pH and contact time. At the optimum condition, the adsorption yield was achieved up to nearly 100 %.


Background
Effluents containing Lead and other toxic metals ( ‫|‬ ‫|‬ ) are increasingly discharged into the water supplies due to the expansion of industries [1]. The maximum levels lower than 15 ppb for lead ( ‫|‬ ‫|‬ ) in drinking waters has been mandated by many environmental agencies and national standard organizations [2][3][4]. The strict limitations on discharging effluents contained lead ( ‫|‬ ‫|‬ ) to the natural water bodies are attributed to the lead ( ‫|‬ ‫|‬ ) potential health effects on children and adults [3].
Many processes such as precipitation, membrane filtration, adsorption, and ion exchange have been applied to remove lead ( ‫|‬ ‫|‬ ) and other toxic metals from the industrial effluents [5]. Only a few methods such as using functionalized adsorbents and membrane technologies can be adopted to capture low concentrations around 1 mg L −1 , which is commonly occurred in drinking water sources [6]. Although, adsorption processes are useful in removal low concentrations of metal ions from aqueous solutions, but there are two main limitations regarding to the use of them; 1. low adsorption capacity [7,8], and 2. difficult separation of adsorbent from treated water after the end of adsorption process [9][10][11].
Graphene oxide is an emerging carbon-based nonmaterial that has revealed the promising adsorptive properties [12,13]. Graphene oxide (GO) creates a highly stable aqueous dispersion which prepares an excellent situation for effective contacts with target contaminants without needing to vigorous mechanical mixing [14]. The GO flakes have high specific surface area ranging from 600 to 3500 m 2 g −1 [15,16]. The dispersibility property of GO is attributed to the plenty of hydrophilic functional groups on the GO flakes [15]. The GO flake surface contains different functional groups including epoxide and hydroxide, whereas, the edge of flakes are mainly contained a hedge of carboxylic groups [14].
Using magnetic agents like Fe 3 O 4 has been considered as a way to separate the GO nanosheets from aqueous solution when the adsorption process is finished [17,18]. Some methods employed for the adding of Fe 3 O 4 on the GO surface are generally led to form reduced GO (rGO) [19,20]. Because of the elimination of functional groups during the reduction process, rGO represents weak dispersity [14]. Hence, preserving the GO dispersibility in the aqueous solution as well as adding the magnetic property for separation purposes is under consideration.
Few literatures were reported applying non reduced Fe 3 O 4 /GO for the adsorption purposes [17,21,22]. Among them, some synthesis approaches have relied on the formation of covalent bonds between the GO sheets and Fe 3 O 4 nanoparticles [17,22] which has more stability than those methods based on physical attraction [21].
This research aimed to fabricate the covalent bond Fe 3 O 4 @SiO 2 -GO nanocomposite as a highly dispersible and easy separatable adsorbent for the elimination of lead ( ‫|‬ ‫|‬ ) from aqueous solution. Other purpose of the study was determining the optimal operational condition using response surface methodology (RSM) to achieve satisfactory lead ( ‫|‬ ‫|‬ ) removal. The conventional optimization method, which altered one variable at a time by keeping the other variables constant, is a time consuming and costly approach that can not consider the interactive effects between variables. RSM technique is an empirical statistical approach used to evaluate the relationship between a set of controlled experimental variables and observed results. It can be applied to optimize and identify the performance of adsorption process. Minimum experimental runs are achievable by using RSM. Applying RSM reduces the experiment runs and the reagents consumption. It also facilitates the execution of experiments necessary for the construction of the response surface.

Preparation of graphene oxide (GO)
Graphene oxide was synthesized from the graphite powder by the modified Hummers et al. method [23]. Briefly, 2.0 g of graphite powder and 2.0 g of NaNO 3 were mixed with 92 mL of H 2 SO 4 (98 %) in a flask and stirred in an ice bath vigorously for 0.5 h, and then 12.0 g of KMnO 4 was added to the above solution slowly. After stirring for 0.5 h, the ice bath was removed and the solution was stirred in a water bath at 35°C for 6 h. After that, 160 mL of the DI water was added slowly to the flask. Then, the obtained mixture was stirred at 90 0 Cfor 2 h. Afterward 400 mL of DI water was added and followed by addition of 12 mL of H 2 O 2 (30 %), Upon which the color of mixture turned to bright yellow. The obtained suspension was washed with 1:10 HCl solution (150 mL) and DI water several times to remove metal ions [24]. The resultant dispersion was sonicated at 130 KHz for 2 h and centrifuged to obtain exfoliated graphene oxide [25].

Preparation of Fe 3 O 4 @SiO 2 -NH 2
The Fe 3 O 4 magnetic nanoparticles were synthesized using a coprecipitation method [26]. For the synthesis of Fe 3 O 4 @SiO 2 -NH 2 , 1.0 g of the obtained Fe 3 O 4 MNPs was dispersed in a mixture of 40 mL ethanol and 10 mL of DI water using an ultrasonic water bath. After that, o.5 mL TEOS and 2 mL NH 3 .H 2 O (25 %) were added, and the mixture was stirred at 50°C for 6 h. The solid product was collected by an external magnetic field, washed with ethanol and dried under vacuum. In the next step, 1 g of the obtained Fe 3 O 4 @SiO 2 was dispersed in 25 mL dried toluene and treated with addition of 1 mL APTES [27]. The mixture was refluxed for 24 h under nitrogen atmosphere. The product was washed with ethanol and then dried to obtain Fe 3 O 4 @SiO 2 -NH 2 [28].

Preparation of Fe 3 O 4 @SiO 2 -GO
The condensation reaction between amine groups of Fe 3 O 4 @SiO 2 -NH 2 and carboxyl groups of GO was performed [28]. Typically, 0.2 g GO was dispersed in 50 mL DI water containing of 0.1 g NHS and 0.2 g EDC.HCl by ultrasonication for 2 h. Subsequently, 0.5 g Fe 3 O 4 @SiO 2 -NH 2 was added to the above mixture and stirred for 12 h at room temperature. The solid product was collected and washed with DI water and ethanol by magnetic separation and then dried under vacuum [17,29]. Figure 1 shows a schematic view of the synthesis process.
To confirm the stability of nanocomposite, concentration of Iron after the adsorption process was measured. As shown in Tables 2, and 3, the leaching of Iron into the aqueous solution after contact times was negligible.

Characterization
The SEM images were taken with Hitachi-S4160 scanning microscope (Tokyo, Japan) to survey the morphological pattern and surface structural aspects of GO and Fe 3 O 4 @-SiO 2 -GO nanocomposite. A Nanoscope V multimode atomic force microscope (Veeco Instruments, USA) were used to perform AFM measurements. The AFM images were taken from samples which prepared by deposition a dispersed GO/methanol solution (70 mg mL −1 ) onto a mica surface and allowing them to dry in air [25]. The images were taken under ambient condition by adjusting the instrument on the tapping mode.

Batch adsorption experiments
Using a thermostatic shaker, batch experiments were conducted in 100 mL Erlenmeyer flasks to study the removal of lead ( ‫|‬ ‫|‬ ) on the Fe 3 O 4 @SiO 2 -GO nanocomposite. The different volumes contained known quantities of asdispersed Fe 3 O 4 @SiO 2 -GO nanocomposite were added to 20 mL solution having predominated concentrations of Pb 2+ . All solutions underwent constant mixing at the 300 rpm for different contact times determined by the experimental design. After ending the adsorption process, the nanocomposite was eliminated from the aqueous solution by a magnet. The equation (1) was applied to determine the removal efficiency of lead ( ‫|‬ ‫|‬ ): Where, R (%) is the removal efficiency, C 0 and C t are the concentrations (as mg L −1 ) of lead ( ‫|‬ ‫|‬ ) at 0 and t minutes after the contact time, respectively.
The equilibrium adsorption capacity was also obtained as equation (2): Where, q e is the equilibrium capacity (mg g −1 ), x ads is the nanocomposite concentration in aqueous solution (mg L −1 ), and 1000 is converting factor (mg g −1 ). Lead ( ‫|‬ ‫|‬ ) measurements in the aqueous solution were performed by using a Spectro Arcos ICP-optical emission spectrometer (SPECTRO Analytical Instruments, Kleve, Germany) based on radial plasma observation. The Spectro Arcos has a Paschen-Runge mount which equipped with 32 linear CCD detectors. The CCD detectors supply the ability of simultaneous monitoring of line intensities at wavelengths between 130 and 770 nm.
Isotherm and kinetic constants were obtained using the Solver "add-in" with Microsoft Excel spreadsheet program [30] according to the nonlinear forms of the equations.

Experimental design
Central composite design (CCD) was used to investigate the lead ( ‫|‬ ‫|‬ ) removal. The RSM was employed to evaluate the combined effects of pH (X 1 ), GO-Fe 3 O 4 dose (X 2 ), contact time (X 3 ), and initial lead ( ‫|‬ ‫|‬ ) concentration (X 4 ) on the adsorption process. The experimental conditions of independent variables, which were derived from CCD, are summarized in Table 1. The lead ( ‫|‬ ‫|‬ ) removal efficiency (Y) were served as output responses. Applying two blocks, one cube block and one star block, total 44 experiments were carried out, consisting of 20 center points, 2 4 = 16 design point, and 2 × 4 = 8 axial points.
The details of 44 experiments are presented in Table 2. The chosen independent factors applied in the study were coded based on Eq. (3): Where, x i is a dimensionless coded value of the ith independent variable, X 0 is the center point value of X i and ΔX is the step change value. A quadratic (second order) model as shown in Eq. (4) was applied to approximate the interaction between the response (Y) and four independent variables: Where, Y represents the dependent variable (lead ( ‫|‬ ‫|‬ ) removal efficiency), b 0 is a constant value, b i , b ii , and b ij refer to the regression coefficient for linear, second order, and interactive effects, respectively, Xi, and Xj are the independent variables, c denotes the error of prediction.
The above mentioned CCD analysis plus to the statistical analysis, such as ANOVA, F-test, and t-test were obtained using R software (version 3.0.3: 2014-03-06).

Results and discussion
Characterization of GO-Fe 3

O 4 nanocomposite
As shown in Fig. 2, a UV-visible spectrum obtained for the GO aqueous dispersion (orange line) displays a plasmon peak at 231 nm which is related to the π → π* transitions due to the aromatic C − C bonds. Also, a hump can be detected around 300 nm approving the n → π* transitions of C = O bonds [31,32]. Gradually adding the lead ( ‫|‬ ‫|‬ ) aqueous ions into the GO dispersion resulted in producing a growing humpy pattern around 300 nm which can be attributed to the affinity between lead ( ‫|‬ ‫|‬ ) and C = O bonds relating to the carboxylic groups in the GO structure [33].
Fabricated Fe 3 O 4 @SiO 2 -GO was characterized with different techniques. Figure 3 shows the field emission SEM images of GO and Fe 3 O 4 @SiO 2 -GO. Figure 3a illustrated the fluffy nature of GO layers which turned to agglomerated morphology after the formation of covalent bonds with Fe 3 O 4 @SiO 2 -NH2 and producing Fe 3 O 4 @SiO 2 -GO (Fig. 3b). The magnetic properties of the prepared nanocomposite were characterized using vibration sample magnetization (VSM). The VSM curves (Fig. 4) shows that, the magnetic power of Fe 3 O 4 nanoparticles were dropped into the one third of original state which was due to both the SiO 2 -NH 2 coverage and the GO covalent bonds. But, the remaining 22.3 emu g −1 of saturation magnetization can still be considered as a powerful magnetic field to separate the nanocomposite from the aqueous solution, as shown in the Fig. 4d. Also, the coercivity and remanence were not observed after removing the magnetic field. From Fig. 4d, the yellow brown color of the GO dispersion revealed that the oxygenation of the graphene nanosheets has been effectively occurred during the synthesis [16,34]. After 3 months from the GO preparation, there is no any visible sign of sedimentation which shows long-term dispersibility of GO in water.
The AFM image of GO nanosheets is illustrated in Fig. 5a. Also, Fig. 5b shows the distribution of GO obtaining 210 nanosheets found in a certain area of the mica surface which confirms preparing a well distributed    Fig. 5b, the average thickness measured was 2.74 nm revealed producing few layered (1 and 2 layers) GO [35]. As shown in Fig. 5c, the thickness of a random GO sheet measured using the height profile (Line 1) in the AFM image, is about 0.75 nm. This sub-nanometer thickness confirms producing the GO monolayer [14]. Figure 6 shows the FT-IR spectra obtained for GO, Fe 3 O 4, and Fe 3 O 4 @SiO 2 -GO materials. Figure 6a depicts the characteristic features illustrated in the FT-IR spectrum for GO which are contained the adsorption bands attributed to the C-O stretching at 1055 cm −1 , the C-OH stretching at 1226 cm −1 , and the C-O carbonyl stretching at 1733 cm 1 [36][37][38]. Furthermore, the O-H hydroxide stretching vibrations appear at 3419 cm −1 . Also, the adsorbed water molecules stretching at 1621 cm −1 , although it may feature due to the skeletal vibrations of un-oxidized graphitic remnants [39,40].
As can be seen from Fig. 6b, the spectrum of the  assigned to the remaining water that was not eliminated from the surface of the Fe 3 O 4 nanoparticles [41].
As depicted in Fig. 6c, the peak at 3401 cm −1 of Fig. 5c attributed to the -NH 2 vibration. Comparing Fig. 6c with Fig. 6a, the peak at 1733 cm −1 was almost disappeared, and a new broad peak was emerged at 1641 cm-1 corresponding to C = O characteristic stretching band of the amide group. The stretching band of the amide C-N peak appears at 1230 cm −1 [42]. Meanwhile, as shown in Fig. 6c, the peaks at 802 and 1110 cm −1 were obviously observed due to the Si-O vibrations. From these findings, it is recommended that APTES functionalized Fe 3 O 4 was covalently bonded to GO through the amide linkage [22]. The reduced quadratic model was applied by omitting the variables assigned to the P-values more than 0.05 in the quadratic model [43].

Response surface methodology model analysis
The values of the determination coefficient (multiple R 2 ) shown in Tables 4 and 5 indicated that 87.9 and 86.3 % of the variability in the response could be explained by the quadratic and reduced quadratic models, respectively.
If there have been various terms in the model and also the sample size has not been very large, the adjusted correlation coefficient (adjusted R 2 ) may represent values considerably smaller than the multiple correlation coefficients (Multiple R 2 ) [44]. In this experiment, the adjusted correlation coefficient value (adjusted R 2 = 0.836) are also noticeable to support the high significance of the models and approves a satisfactory adjustment for the reduced quadratic model to the experimental data [45][46][47].
The values of the determination coefficient (multiple R 2 ) shown in Tables 4 and 5 indicated that 87.9 and 86.3 % of the variability in the response could be explained by the quadratic and reduced quadratic models, respectively. As revealed from Tables 4 and 5, the "lack of fit (LOF)" values were 0.337 and 0.355 for the quadratic and reduced quadratic models, respectively. The insignificant values of LOF (>0.05) and the significant P-values for both models prove that applying models is eligible to interpret the lead ( ‫|‬ ‫|‬ ) removal process and also, the reduced model is the better choice because of the higher adjusted R 2 (0.836) and the higher value obtained for LOF (0.355) [43,46]. Table 6 represents the regression analysis obtained from the reduced quadratic model. As shown, the significant of each coefficient was determined by P-value. Also, Values of "Prob > |t|" less than 0.05 in Table 6 indicate that all the model terms are significant. The bigger amounts of the t-values beside the smaller amounts of P-values show the more significant of the corresponding coefficients [46]. Based on the t-and P -value results, pH and time can be considered as the substantial effective factors on the lead ( ‫|‬ ‫|‬ ) adsorption. The effect of each model term, also, can be observed from the coefficient estimate values represented in Table 6.
Contour plots depicted in Fig. 7 are the graphical illustrations of the regression analysis (Table 6) which represent the simultaneous effects of adsorbent-pH (a), time-pH (b), and time-adsorbent (c) on lead ( ‫|‬ ‫|‬ ) removal efficiency as the response factor. As noted above, the interaction effects of pH (X 1 ) and Fe 3 O 4 @-SiO 2 -GO dose (X 2 ) on the lead ( ‫|‬ ‫|‬ ) removal is shown in Fig. 7a. The contact time and lead ( ‫|‬ ‫|‬ ) initial concentration were fixed constant at 16 min and 2.49 mg/L, respectively. As shown, the lead ( ‫|‬ ‫|‬ ) removal increased with increasing the Fe 3 O 4 @SiO 2 -GO dosage. The maximum lead ( ‫|‬ ‫|‬ ) removal was obtained in the range of pH from 6.5 to 8.5. In that range, the lead ( ‫|‬ ‫|‬ ) removal was independent from the adsorbent dosage. In the pH values between 3-6.5, almost a direct relationship between pH and lead ( ‫|‬ ‫|‬ ) removal was observed.
The effects of pH (X 1 ) and contact time (X 3 ) on lead ( ‫|‬ ‫|‬ ) removal are shown in Fig. 7b. The adsorbent dose and lead ( ‫|‬ ‫|‬ ) initial concentration were fixed constant at 30.5 mg/L and 2.49 mg/L, respectively. It is inferred from Fig. 7b that around the neutral pH, the lead ( ‫|‬ ‫|‬ ) removal process was almost completed during the contact time up to 10 min. But for pH values less than 4, after the contact time more than 30 min, the removal efficiency near 70 % was achieved.
The effects of Fe 3 O 4 @SiO 2 -GO dosage (X 2 ) and contact time (X 3 ) on lead ( ‫|‬ ‫|‬ ) removal can be observed in Fig. 7c. The pH and lead ( ‫|‬ ‫|‬ ) initial concentration were fixed constant at 6 and 2.49 mg/L, respectively. Figure 7b shows that, for the adsorbent doses more than 40 mg/L, regardless the contact time, the lead ( ‫|‬ ‫|‬ ) removal efficiency revealed the levels permanently beyond 95 %.
Lead ( ‫|‬ ‫|‬ ) removal showed to be very sensitive to changes in the pH both in low and high adsorbent dose. The removal capacity of Fe 3 O 4 @SiO 2 -GO nanocomposite was rapidly increased when the pH increased from 3.5 to 8.5; as it was also reported by Madadrang [15]. pH influences both the surface charges of the functional groups on the surface of graphene oxide and also the species of lead ion in the aqueous solution [48].  Increasing the protonation of functional groups on graphene oxide surface would be happen at acidic conditions and electropositivity of Fe 3 O 4 @SiO 2 -GO surface would retard the adsorption rate, and finally, the removal efficiency of lead ( ‫|‬ ‫|‬ ) can be reduced [18]. As inferred from Fig. 7a-b, when pH is less than 5, the lead ( ‫|‬ ‫|‬ ) removal efficiency was weak. However, the adsorption of lead ( ‫|‬ ‫|‬ ) was enhanced with the increasing pH from 5 to 8.5. Normally, the adsorption capacities of metal ions for most carbon based nanomaterials would increase with increases in the pH value. In this case, lead ( ‫|‬ ‫|‬ ) can be adsorbed onto the graphene oxide surface by reacting lead ( ‫|‬ ‫|‬ ) with − COOH and − OH groups [15,49]. As shown in the contour plot exhibited in Fig. 7c, regardless the adsorbent dose, more than 75 % of lead ( ‫|‬ ‫|‬ ) adsorption was achieved during the contact time less than 10 min and the adsorption process was completely done after passing twenty minutes. These findings revealed that the fast adsorption rate of the lead ( ‫|‬ ‫|‬ ) can be attributed to the high affinity of lead ( ‫|‬ ‫|‬ ) ions to the hydroxide (−OH), epoxide (−O−) and carboxylic (−COOH) groups on the GO nanosheets [15,50,51].
The optimum values of pH, adsorbent dose, and contact time determined by applying the reduced quadratic model were 6.9, 30.49 mg/L, and 16.01 min, respectively. The optimum concentration of initial lead ( ‫|‬ ‫|‬ ) was not obtained from the reduced quadratic model because it was omitted from the model. But the results of quadratic model suggested 2.49 mg L −1 as the optimum value. Further studies such as isotherm and kinetic experiments were investigated according to the abovementioned optimum values obtained from the model.

Adsorption isotherms
In order to investigate the adsorption equilibrium of lead ( ‫|‬ ‫|‬ ), isotherm models consisting of Langmuir (Eq. 5), Freundlich (Eq. 6), and Sips (Eq. 7) were applied. The original forms (nonlinear) of models can be expressed as follows: Where, q e is the amount of lead ( ‫|‬ ‫|‬ ) adsorbed on the absorbent at equilibrium (mg g −1 ), C e describes the equilibrium lead ( ‫|‬ ‫|‬ ) concentration (mg L −1 ), K L is the Langmuir adsorption constant (L mg −1 ) and q m denotes the maximum adsorption capacity attributeing to the complete monolayer coverage of the adsorbent (mg g −1 ). K F is the Freundlich constant related to the maximum sorption capacity (mg g −1 ), also, n F is the Frendlich constant related to the heterogeneity factor. K S (L g −1 ) is the affinity constant and n S denotes the surface heterogeneity. If n S value is equal to the unity, the Sips isotherm is turned to the Langmuir isotherm, and consequently, the homogeneous adsorption can be modeled. Also, any deviation of n S value from the unity (more than or less than unity) predicts the heterogeneous surface [52,53].
The adsorption mechanism can be expressed by applying Dubinin-Radushkevich isotherm (Eq.8) which is based on the potential theory and assumes a Gaussian energy distribution.
Where, ε is the Polanyi potential given by: The B DR constant (mol 2 /J 2 ) is related to the mean free energy E ads of the adsorption per molecule when it is transferred to the surface from infinity of the bulk phase.
Plotting the isotherm models versus the experimental results are depicted in Fig. 8a. The parameters of isotherm models can be observed in Fig. 8b. These parameters were determined according to the nonlinear regression by plotting q e versus C e assisted by Solver Add-Ins MS Excel [30].
The Sips model includes three parameters and has the capability to apply for both the homogeneous and heterogeneous systems [54]. The Sips model (Eq. 5) integrates parameters from both the Langmuir and the Freundlich isotherm. The heterogeneous surface of adsorbent can be considered if the deviation of n S value from the unity be occurred [53,55]. However, the Sips isotherm moves toward a constant level at high concentrations whereas a pattern of Freundlich model can be observed at low concentrations [55].
According to the experimental data, the maximum adsorption uptake (q m ) was 505.8 mg g −1 which indicates the adsorption capacity higher than those reported by studies applying magnetic GO as lead ( ‫|‬ ‫|‬ ) adsorbent [56] and is comparable with the studies using pristine GO [15,49,57]. The maximum adsorption uptake (q m ) obtained from Sips isotherm model was found to be 598.4 mg g −1 which was more than the values achieved both from the Langmuir model and the experimental data (q m.Langmuir = 497.8 mg g −1 , q m , exp = 505.8 mg g −1 ). This indicates that the Sips model overestimates the q m value which can be due to the heterogeneity characteristic considered in the Sips model. As shown in Fig. 8b, the deviation of n S value from the unity (n S = 0.57) as well as the n F value more than unity (n F = 4.28) can be assigned to the crosslinking effects beside the amount of functionalities such as -COOH and -OH on the adsorbent surface (see FTIR-spectra in Fig. 6). The isotherm curves were L-shaped, which shows the high affinity of surface groups towards lead ( ‫|‬ ‫|‬ ) ions both at low and high concentrations [55]. As revealed from Fig. 8b, the mean free energy E ads was 9.901 Kj/mol which seems to be the evidence of predomination the chemisorption mechanism [58].
Where, q t and q e are the sorption capacity (mg g −1 ) at time t and at the equilibrium time, respectively. k 1 and k 2 are the pseudo-first-order and pseudo-second-order rate constants, respectively. D 1 and D 2 (mg L −1 ) are the rapid and slow steps, K D1 and K D2 (min −1 ) are constants controlling the mechanism of slow and rapid phases, respectively. x ads is the adsorbent dosage (g L −1 ). Figure 9a presents the nonlinear curves attributed to the kinetic models by applying equations 11, 12, and 13. Also, the kinetic parameters of lead ( ‫|‬ ‫|‬ ) removal were illustrated in Fig. 9b.
According to the regression coefficient values of kinetic models, it was found that the double exponential kinetic model (R 2 = 0.982) obtains a better description to predict the kinetic data of lead ( ‫|‬ ‫|‬ ) than both pseudo-first-order and pseudo-secondorder models. The values of constant parameters of double-exponential kinetic model revealed that the both external diffusion and internal diffusion have substantial effects on the lead ( ‫|‬ ‫|‬ ) sorption using Fe 3 O 4 @SiO 2 -GO nanocomposite [50].

Conclusions
Magnetic Fe 3 O 4 @SiO 2 -GO nanocomposite was synthesized and applied to elimination the lead ( ‫|‬ ‫|‬ ) from aqueous solution. Due to the high loading capacity of GO for metal ions, Fe 3 O 4 @SiO 2 -GO revealed excellent performance in treatment the lead ( ‫|‬ ‫|‬ ) contaminated waters. The removal process was found to be quick and facile, and the lead ( ‫|‬ ‫|‬ ) adsorption process was almost completed up to 10 min contact time.
Main advantages of Fe 3 O 4 @SiO 2 -GO nanocomposite include quick separation performed by using an external magnetic field and the noticeable lead ( ‫|‬ ‫|‬ ) removal capacity (506 mg g −1 ).
A central composite design (CCD) was applied to investigate the effects of four adsorption variables, namely pH, adsorbent dose, contact time, and initial lead ion concentration on the removal efficiency of lead ( ‫|‬ ‫|‬ ). Both the quadratic and reduced quadratic models were applied to correlate the variables to the response values. Results from the analysis of response surfaces indicated that pH, time, and the adsorbent dose were found to have significant effects on the removal efficiency of lead ( ‫|‬ ‫|‬ ). The optimization of process was performed and the experimental values were found to be agreed satisfactorily with the predicted values. The adsorption isotherms and kinetics were also investigated. Equilibrium adsorption data had best fit by the Sips isotherm model and chemisorption mechanism was predominated. Kinetic studies indicated that the doubleexponential kinetic model is the preferred model to explain the equilibrium adsorption over the time.