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. 2020 Oct 20;5(43):28305–28318. doi: 10.1021/acsomega.0c04284

Optimization and Experimental Design of the Pb2+ Adsorption Process on a Nano-Fe3O4-Based Adsorbent Using the Response Surface Methodology

Rimmy Singh 1, Rachna Bhateria 1,*
PMCID: PMC7643284  PMID: 33163814

Abstract

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Magnetic Fe3O4 nanoparticles have been used as adsorbents for the removal of heavy-metal ions. In this study, optimization of the Pb2+ adsorption process using Fe3O4 has been investigated. The adsorbent was characterized by various techniques such as transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX), and Brunauer–Emmett–Teller (BET) analysis. The influence of process variables on adsorption of Pb2+ ions in accordance with p < 0.05 was investigated and analyzed by the Box–Behnken design (BBD) matrix with five variables (pH, adsorbent dose, initial Pb2+ ion concentration, contact time, and temperature). The pH and temperature were observed to be the most significant parameters that affected the Pb2+ ion adsorption capacity from the analysis of variance (ANOVA). Conduction of 46 experiments according to BBD and a subsequent analysis of variance (ANOVA) provide information in an empirical equation for the expected response. However, a quadratic correlation was established to calculate the optimum conditions, and it was found that the R2 value (0.99) is in good agreement with adjusted R2 (0.98). The optimum process value of variables obtained by numerical optimization corresponds to pH 6, an adsorbent dose of 10 mg, and an initial Pb2+ ion concentration of 110 mg L–1 in 40 min at 40 °C adsorption temperature. A maximum of 98.4% adsorption efficiency was achieved under optimum conditions. Furthermore, the presented model with an F value of 176.7 could adequately predict the response and give appropriate information to scale up the process.

1. Introduction

For industrial development, lead (Pb2+) is a versatile and strategically significant metal as it is intrinsically associated with the automotive sector, power backup, and energy storage.1 Pb2+ and its compounds have been used in battery manufacturing, mining, refining, acid industries, smelting, etc.2,3 The extensive use of Pb2+ ions results in high levels of contamination in water and thus accumulation via the food chain. Lead is a mutagenic and teratogenic metal, and it exerts toxicological effects on the bone marrow, nervous system, kidney, and immune system, especially in children.4−10 Lead, being lethal, is the most extensive environmental pollutant due to its long-term persistence and easy transportability.11 Pb2+ occurs in organic and inorganic forms and its rate of absorption in humans mainly depends on the physicochemical nature of the exposed individual. Inorganic lead is incapable of being metabolized; hence, it gets distributed and accumulates in soft tissues and bones and is not excreted directly, whereas organic lead used in gasoline as an additive can be absorbed via the skin and respiratory tract.12 Therefore, lead is recommended as a priority pollutant on the list of the US Environmental Protection Agency (EPA),13 and the concentration of lead should be less than 10 μg L–1 in drinking water according to World Health Organisation (WHO) standards.10

Heavy-metal remediation of water involves various techniques such as membrane filtration,14 coprecipitation,15 electro-coagulation,16 reverse osmosis,17 and ion exchange.18 The above-mentioned conventional techniques possess certain limitations of sensitive operation, high energy requirements, and generation of toxic sludge.19,20 Hence, sorption methods can be alternatives for heavy-metal adsorption from wastewaters.21 In the surface adsorption process, heavy-metal ions diffuse from an aqueous solution toward the opposite charge of the adsorbent by passing the boundary layer and thus the ions are subsequently removed from the solution.22 To date, a number of adsorbents have dominated the market, with excellent mechanical properties, large surface area, facile manufacturing and regeneration, and apt pore size and structure for efficient adsorption.23 Over the years, research has been progressing rapidly on nanometal oxides that have demonstrated high reactivity and large surface-to-volume ratio. They have been designed and processed as superior adsorbents to the conventional ones. At the nanoscale, extremely attractive properties are created due to quantum effects, the dominance of interfacial phenomena, and size confinement.24

Iron oxide nanoparticles, especially magnetite (Fe3O4), have been found to be promising candidates due to their structural stability, along with high surface area and excellent removal efficiency. Magnetite NPs have unique properties as they have both trivalent (Fe3+) and divalent (Fe2+) arrangements of iron. Therefore, they have a cubic inverse spinel structure, where Fe2+ ions occupy half of the octahedral positions, whereas Fe3+ joined the lateral tetrahedral and octahedral positions. Magnetite NPs exist as both p- and -n, with a very minor band gap of 0.1 eV.25,26 These nanoparticles have a suitable framework for interaction with heavy metals such as lead (Pb2+), leading to enhanced functional properties. Recently, Rasoulzadeh et al. carried out a study on Fe3O4 NPs and chitosan-coated Fe3O4 NPs to optimize Pb2+ using the response surface methodology (RSM) and achieved a maximum of 93% removal efficiency.27 For field-based applicability, efficient adsorbents can be obtained by modeling and optimization studies.28 In another study, Fe3O4/talc NPs were fabricated to adsorb Pb2+, Ni2+, and Cu2+ ions. The process was optimized by RSM and analysis of variance (ANOVA) to achieve maximum adsorption.29 Similar adsorption studies are summarized in Table 1.

Table 1. Comparison Table of Different Adsorbents with Their Experimental Details.

adsorbent adsorbent properties metal ions experimental conditions design of experiment adsorption percent (%) references
chitosan-conjugated magnetite nanobiocomposite mean size = 10 nm, monodisperse nanoparticles Pb pH = 6.1, adsorbent dose = 1.04 g L–1, contact time = 59.92 min CCD 92.15 (30)
thio-urea-functionalized magnetite ZnO/nano cellulose composite (TFZN)   Pb pH = 6.5, adsorbent dose = 40 mg, Pb concentration = 60 mg L–1, contact time = 14.5 min   99.99 (31)
T-Fe3O4 NPs with diameter less than 100 nm Pb pH = 4.5, adsorbent dose = 0.625 mg L–1, initial concentration = 32.5 g L–1, contact time = 95 min CCD 95 (32)
chitosan-coated Fe3O4 nanoparticles average size is less than 50 nm, crystalline with good uniformity Pb pH = 10.95, adsorbent dose = 5.5 mg L–1, contact time = 66.59 min, initial concentration = 0.1 g L–1   93.6 (27)
melanin-based dendrimer amine-Fe3O4 the average diameter of nanoparticles was 64.4 nm Pb initial ion concentration = 110 mg L–1, adsorbent dose = 0.49 g L–1, pH = 5, temperature = 30 °C CCD 85.6 (33)
PEG-modified Fe3O4 nanoparticles uniform spherical nanoparticles with a hydrodynamic radius of 124.1 nm Pb pH = 5, initial concentration = 11 mg L–1, temperature = 25 °C, PEG molecular weight = 2000 g mol–1, contact time = 30 min   81.39 ± 2.5 (34)
goethite/chitosan nanocomposite the average diameter is 10–60 nm Pb pH = 6, adsorbent dose = 0.05 g, initial concentration = 74.4 mg L–1 BBD 98.26 (35)
chitosan/rice husk ash/nano alumina average BET surface area = 14. 0531 nm, pore diameter = 6.80 nm Pb pH = 5, adsorbent dose = 0.01 g, initial concentration = 30 ppm, contact time = 105 min CCD 90.98 (36)
Fe3O4 nanoparticles needlelike morphology with an average size of 83.2 nm and diameter of 7.03 nm Pb pH = 6, adsorbent dose = 10 mg, initial concentration = 110 mg L–1, contact time = 40 min, temperature = 40 °C BBD 98.4 present study
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The response surface methodology (RSM) is usually aimed at a factorial design to establish optimum experimental conditions to meet regulatory requirements.37 The Box–Behnken design (BBD) facilitates the simultaneous study of experimental factors, optimization, and interactions to quantify their influence on the properties of interest in multivariate models.38 In this experimental study, the BBD matrix was applied to design experiments, propose empirical models, and determine optimum operating condition values for the studied variables (pH, initial Pb2+ concentration, adsorbent dose, contact time, and temperature) to achieve the maximum response (adsorption %).

2. Results and Discussion

2.1. Characterization of Fe3O4 Nanoparticles

The microscopic morphology of the adsorbent was characterized by a JEOL TEM-1400 transmission electron microscope (TEM). Figure 1a–c shows images acquired by TEM from pure Fe3O4 NPs that revealed the porous structure of the adsorbent. The TEM image shown in Figure 1a–c represents the needlelike morphology of the agglomerated nanoparticles. The reasons behind agglomeration may be the low dimensions, magnetic properties, and high surface energies.39 The Fe3O4 NPs comprise nanoneedles with different size distributions. The average size of the nanoparticles was 83.2 nm and the average diameter was 7.03 nm. The selected area electron diffraction (SAED) pattern revealed the polycrystalline structure of the Fe3O4 NPs (Figure 1d).

Figure 1.

Figure 1

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TEM images of synthesized nanoparticles at (a, b) 50 nm and (c) 200 nm and (d) SAED patterns of nanoparticles.

The energy-dispersive spectroscopy (EDS) peaks shown in Figure 2a correspond to iron, oxygen, and chlorine taken from the Fe3O4 NP sample, confirming the successful synthesis of the desired product. The EDS spectrum collected after adsorption of Pb2+ is represented in Figure 2b. The additional peak of lead along with iron and oxygen confirms the adsorption of Pb2+ ions on Fe3O4 NPs.

Figure 2.

Figure 2

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Collected EDX spectrum for Fe3O4 NPs (a) before and (b) after Pb2+ adsorption.

From the Brunauer–Emmett–Teller (BET) analysis, the surface area of Fe3O4 NPs was determined to be 25.37 m2 g–1 and the pore volume was 0.16 cm3 g–1. The Barrett–Joyner–Halenda (BJH) method was used to calculated the pore diameter as shown in Figure 3. Moreover, it was found that most of the pore diameters are in the range of 2–50 nm, with a peak diameter at 11.1 nm, revealing the mesoporous nature of the adsorbent.

Figure 3.

Figure 3

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Barrett–Joyner–Halenda pore size distribution for Fe3O4 NPS.

2.2. Statistical Analysis

According to ANOVA (Table 2), a higher value of F indicates that most of the variables in the response can be explained by the regression equation, and probability values (p values) less than 0.005 are considered to be statistically significant. The results compiled by ANOVA predict the adequate representation of the actual relation between the response function, i.e., removal %, and independent variables (pH, adsorbent dose, initial ion concentration, contact time, and temperature) by a second-order polynomial equation.

Table 2. Analysis of Variance (ANOVA) Results for Pb2+ Removal.

source sum of squares df mean square F value p value  
model 3696.65 20 184.83 179.76 <0.0001 significant
A—pH 1625.30 1 1625.30 1580.66 <0.0001  
B—adsorbent dose 7.30 1 7.30 7.10 0.0133  
C—initial ion conc. 1.68 1 1.68 1.63 0.2133  
D—contact time 3.89 1 3.89 3.78 0.0631  
E—-temperature 31.98 1 31.98 31.10 <0.0001  
AB 0.2025 1 0.2025 0.1969 0.6610  
AC 0.0064 1 0.0064 0.0062 0.9377  
AD 0.2401 1 0.2401 0.2335 0.6331  
AE 0.0529 1 0.0529 0.0514 0.8224  
BC 1.02 1 1.02 0.9921 0.3288  
BD 1.29 1 1.29 1.25 0.2736  
BE 0.2500 1 0.2500 0.2431 0.6263  
CD 0.7056 1 0.7056 0.6862 0.4153  
CE 3.10 1 3.10 3.01 0.0949  
DE 0.1681 1 0.1681 0.1635 0.6894  
A2 1264.55 1 1264.55 1229.82 <0.0001  
B2 11.54 1 11.54 11.22 0.0026  
C2 3.68 1 3.68 3.57 0.0703  
D2 851.01 1 851.01 827.64 <0.0001  
E2 389.12 1 389.12 378.43 <0.0001  
residual 25.71 25 1.03      
lack of fit 24.29 20 1.21 4.30 0.0563 not significant
pure error 1.41 5 0.2825      
cor total 3722.35 45        
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The empirical relation between the response, which is the amount of Pb2+ ions adsorbed per unit mass of Fe3O4 nanoparticles (mg g–1), and the independent variable is represented as Y. The positive values show the synergistic effect of variables and the negative values denote the antagonistic effect.

2.2. 1

The quadratic model was found to be significant for the Pb2+ ion adsorption mechanism. The significance of the coefficient term is dependent on the p value and the F value. The p values (prob > F) < 0.05 are significant model terms, while p values (prob > F) > 0.05 indicate insignificant terms. For response Y (% lead removal), the model terms A, B, E, A2, B2, D2, and E2 were significant. The model F value of 179.76 indicated that model terms are significant. The value for the coefficient of determination, i.e., adjusted R2 (0.98), is in good agreement with the predicted value (0.97). The results also confirmed the adequacy of the selected quadratic model.

Lack-of-fit tests and model summary statistics are summarized in Table 3. The lack of fit of the model was found to be insignificant; hence, the responses are adequately described by the regression equation.40 The goodness of fit by the regression model was evaluated by the coefficient of regression (Table 4), i.e., R2, adjusted R2, standard error of estimate, and mean absolute error. The R2 statistic indicates 93.8% of the variable Pb2+ ion removal efficiency. The adjusted R2 statistic is suitable for comparing models with different independent variables. For a significant model, the correlation coefficient should have a minimum value of 0.8.41 The standard deviation of the residuals was found to be 1.18. The “adeq precision” ratio of the model is 47.76 (adeq > 4), which indicates that the noise values to the ratio of the model are in the desirable range.42 The accuracy estimation of the regression model was evaluated by the parity plots and residual plots as shown in Figure 4a,b.

Table 3. Lack-of-Fit Statistics and Model Summary Statistics.

lack-of-fit tests
source sum of squares df Mean square F value p value  
linear 2050.79 35 58.59 207.38 <0.0001  
2FI 2043.76 25 81.75 289.33 <0.0001  
quadratic 24.29 20 1.21 4.30 0.0563 suggested
cubic 4.28 5 0.8562 3.03 0.1245 aliased
pure error 1.41 5 0.2825      
model summary statistics
source sequential p value lack-of-fit p value adjusted R2 predicted R2  
linear 0.0002 <0.0001 0.3798 0.3020  
2FI 1.0000 <0.0001 0.1759 –0.2024  
quadratic <0.0001 0.0563 0.9876 0.9733 suggested
cubic 0.0887 0.1245 0.9931 0.9258 aliased
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Table 4. Standard Fit Statistics.

std. dev. 1.01 R2 0.9931
mean 87.89 adjusted R2 0.9876
CV (%) 1.15 predicted R2 0.9733
    adeq precision 47.7699
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Figure 4.

Figure 4

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(a) Parity plots showing the correlation between predicted and actual lead removal efficiency. (b) Plot between residuals and predicted values.

Predicted versus actual Pb2+ ion removal percent is illustrated in Figure 4a. It shows that the maximum data points near the straight line predicting the actual and predicted values are nearly identical and the regression model has predicted these values efficiently. These plots provide insight into the fit criteria for residuals. Similarly, in Figure 4b, the maximum deviation between the predicted and measured Pb2+ ion removal is below 4% and reveals a good correlation between them.

2.3. Interactive Effect of Variables and Three-Dimensional (3D) Response Surface Plots

Three-dimensional response surface plots were constructed to determine the individual and interactive effects of variables on the response. Different process variables, i.e., pH, adsorbent dose, initial ion concentration, contact time, and temperature, influenced Pb2+ ion adsorption capacity. The adsorbent dose determines the capacity of the adsorbent to remove Pb2+ ions from the solution, while the initial Pb2+ ion concentration shows a significant impact on the mass transfer resistance between the aqueous and solid phases. Meanwhile, an appropriate contact time quantifies better agitation between the adsorbent and the adsorbate. The Pb2+ ion uptake increases with an increase in the initial Pb2+ ion concentration, and the low adsorbent dose favors high adsorption. The 3D surface plots of the combined effects of pH, initial Pb2+ ion concentration, adsorbent dose, contact time, and temperature are presented in Figure 5a–j.

Figure 5.

Figure 5

Figure 5

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Three-dimensional surface plots depicting interactions among different process variables: (a) pH, adsorbent dose; (b) pH, initial Pb2+ ion concentration; (c) pH, contact time; (d) pH, temperature; (e) initial ion concentration, adsorbent dose; (f) contact time, adsorbent dose; (g) temperature, adsorbent dose; (h) contact time, initial ion concentration; (i) temperature, initial ion concentration; and (j) temperature, contact time.

Metal sorption on the surface of an adsorbent mainly depends on pH, which is related to the ionization state of the adsorbent’s functional groups and metal chemistry in the solution, which affects the availability of active sites.43Figure 5a clearly shows that the Pb2+ ion adsorption efficiency increased rapidly when pH increased from 5 to 6 and no significant increase was observed after that. The reason behind this was the competition of metal ions with hydroxyl ions to acquire adsorption sites and, therefore, the surface charge alteration led to electrostatic repulsion between the metal ions and the adsorbent, resulting in the escape of existing adsorbed ions.44 Similarly, the interactive effect of pH and the initial Pb2+ ion concentration was also evaluated (Figure 5b) and it was revealed that merely 75% Pb2+ ion adsorption occurs at 130 mg L–1 initial Pb2+ ion concentration at pH 7 when agitated for 40 min. Figure 5c depicts a 3D plot for pH and contact time. At pH 7, only 66% adsorption was achieved within 30 min and it increased as the time progressed to 40 min. Subsequently, maximum adsorption (98.5%) was achieved by the Fe3O4 NPs at 40 °C at pH 6 (Figure 5d). Furthermore, according to ANOVA, pH is a significant factor in this study as it affects the overall adsorption process.

The combined effect of adsorbent dose and initial ion concentration is represented in Figure 5e. On increasing the adsorbent dose from 5 to 15 mg L–1, the adsorption efficiency decreased by up to 96%. However, the maximum adsorption was achieved at 10 mg of Fe3O4 NP dosage. The initial increase in Pb2+ ion adsorption may be due to the large number of active sites available for adsorption. In the starting phase, where the adsorbent surface is empty, the adhering probability is high and thus sorption takes place at a higher rate. However, the subsequent adsorption rate was slow due to the saturation of active sites, and equilibrium was achieved with time.45 Furthermore, with an increase in the initial ion concentration from 90 to 130 mg L–1, the adsorption efficiency increased, with the maximum (99%) at 110 mg L–1, and declined at 130 mg L–1. The decrease in the sorption rate with increasing initial Pb2+ ion concentration may be due to the absence of active sites on Fe3O4 NPs. In fact, at lower initial concentrations, adequate numbers of sites are available to bind on, whereas relatively high metal ions are available with respect to sorption sites at higher concentrations.46

Figure 5f shows the effect of adsorbent dose and contact time on Pb2+ ion adsorption. The adsorption rate increased with an increase in agitation time from 30 to 40 min and achieved the maximum sorption. The Pb2+ ion adsorption rate increased up to 40 min and thereafter no further increase was observed with contact time (Figure 5h,j). The adsorption rate was higher at the initial agitation time as a greater number of binding sites were available for adsorption. However, with time, a higher amount of Pb2+ ions got adsorbed on the Fe3O4 surface and hence the surface area decreased.47 The significance of contact time clearly identifies the possible speed of binding and sorption process of the studied metal ions by the adsorbent, thus obtaining the optimal time for the entire elimination of metal ions. However, in the initial phase, the active sites were vacant and the concentration gradient of the solute was high, while as the agitation time increased, the Pb2+ ion uptake decreased due to lack of availability of sorption sites and metal ion concentration.48 As the adsorbent dose and temperature were increased from 5 to 15 mg and 35 to 45 °C, respectively, the Pb2+ ion removal percent decreased as shown in Figure 5g. Moreover, as the agitation time for interaction was increased from 30 to 40 min, the Pb2+ adsorption efficiency also increased. The effect of the initial Pb2+ ion concentration and temperature on adsorption is displayed in Figure 5i, which shows that an increase in temperature results in increased sorption up to 40 °C and a further increase in temperature results in a decreased sorption rate. Moreover, at 35 °C, the adsorption rate was nearly constant, while the removal rate was minimum at 45 °C when agitated for 30 min.

2.4. Confirmation and Validation of the Model

Optimization is carried out for processes involving multiple responses to produce the desirable value of variables that are considered simultaneously. The aim of numerical optimization is to produce the maximum response for all of the runs analyzed under these conditions. The conditions chosen are the minimum adsorbent dose and the maximum initial Pb2+ ion concentration for the maximum response. The optimum conditions include a magnetite dose of 10 mg, contact time of 40 min, temperature of 40 °C, and initial Pb2+ ion concentration of 110 mg L–1 with 98.4% Pb2+ ion removal. The perturbation plot for these constraints is given in Figure 6.

Figure 6.

Figure 6

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Perturbation graph.

2.5. Adsorption Isotherm

2.5.1. Redlich–Peterson Isotherm

Redlich–Pesterson is a hybrid isotherm with features of both Langmuir and Freundlich isotherms.49 Redlich and Peterson suggested a “three-parameter adsorption isotherm equation50 in 1959, unanimously called the Redlich–Peterson (R–P) isotherm equation (or model)”. The equation compensates for imperfections of Langmuir and Freundlich isotherm equations in some adsorption systems. The linear form of the R–P equation is given as follows

2.5.1. 2

A plot of ln (Ce/qe) versus ln Ce (Figure 7a) enables the determination of Redlich–Peterson constants, where β is the slope and A is the intercept,51−55 where A is also a constant and β is an exponent and it ranges from 0 to 1. If β is equal to 1, the equation reduces to the Langmuir isotherm equation, whereas β equal to 0 favors the Freundlich isotherm. The Redlich–Peterson (R–P) isotherm model was applied to understand the interaction mechanism of Pb2+ ion adsorption on magnetite nanoparticles. However, the accuracy of RP interpretations rigidly depends on the method of fitting.56 From Table 5, it is clear that the interpreted RP model is in agreement with experimental data on the basis of the β value for magnetite nanoparticles, which is lower than 1 (308, 318, 328 K), i.e., 0.13–0.51.57

Figure 7.

Figure 7

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(a) Redlich–Peterson isotherm model, (b) Elovich’s isotherm model, and (c) D–R isotherm.

Table 5. Isotherm Models and Their Calculated Parameters.
isotherm parameter 298 K 308 K 318 K 328 K
D–R isotherm qm (mg g–1) maximum adsorption capacity 14.01 11.58 10.48 11.82
KDR × 10–7 (mol2 kJ–2) D–R isotherm constant 4.844 5.882 5.293 7.163
R2 coefficient of correlation 0.91 0.91 0.91 0.88
Redlich–Peterson isotherm β exponent 2.047 0.344 0.134 0.516
A (mg L–1) constant 0.112 0.748 0.715 0.942
R2 coefficient of correlation 0.90 0.52 0.51 0.26
Elovich’s isotherm qm (mg g–1) Elovich’s maximum adsorption capacity 24.39 10.38 26.73 5.58
Ke constant 1.058 1.218 1.068 1.682
R2 coefficient of correlation 0.12 0.84 0.81 0.66
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2.5.2. Dubinin–Radushkevich Isotherm

The D–R isotherm is an empirical model generally used to express the adsorption process with a Gaussian energy distribution onto a heterogeneous surface.58 This isotherm was basically used to distinguish between physical and chemical adsorption of metal ions59 with its free energy, E, per molecule of adsorbate. The equation to compute E is given as follows

2.5.2. 3

where KDR is the isotherm constant in eq 3 and the E parameter (eq 4) can be correlated by the given equation

2.5.2. 4

where R is the gas constant (8.314 J mol–1 K–1), T is the absolute temperature, and Ce is the equilibrium concentration of the adsorbate (mg L–1). A ln qe versus E2 curve was plotted and the values of parameters qm and KDR were computed from the following equation

2.5.2. 5

The type of adsorption, i.e., physical or chemical, is determined by the DR isotherm model. By plotting ln qe against E2 (Figure 7b), the values of qm and KDR can be obtained using the intercept and slope60 (Table 5).

2.5.3. Elovich’s Isotherm

The equation that defines this model is based on a kinetic principle that assumes that adsorption sites increase exponentially with adsorption; this implies multilayer adsorption.61 The equation was first developed to describe the kinetics of chemisorption of gas onto solids.62 The linear forms of the Elovich model are expressed as follows63

2.5.3. 6

The slope and intercept of the plot of ln (qe/Ce) versus qe (Figure 7c) give Elovich’s maximum adsorption capacity and Elovich’s constant. The coefficient of regression (R2) for Elovich’s isotherm ranges from 0.12 to 0.84 (Table 5).

2.6. Principal Component Analysis (PCA)

PCA was the most widely used multivariate statistical analysis technique. PCA is a data dimension reduction technique that intends to explain most of the variance in the data with a small number of independent variables (termed “principal components”).64 With PCA, an orthogonal transformation method is used to identify the first principal component accounting for the largest possible variance in the original data. Then, each succeeding component is identified with the constraint that it is orthogonal to all preceding components. It is often conducted by eigenvalue decomposition in a matrix operation. The eigenvectors with the highest eigenvalue are the principal components (PCs) of the data set.65

The individual and combined effects of parameters of Pb2+ ion adsorption are explained using principal component analysis (see Table 6). The bold numbers in Table 6 represent high correlation values. By conducting 46 adsorption experiments, the effect of pH, adsorbent dose, initial concentration, contact time, and temperature on Pb2+ ion adsorption by Fe3O4 nanoparticles was studied (see Table 8). The calibration data basically consists of matrix X of dimension 46 × 5 and a response vector of dimension 46 × 1 (adsorption % in this case). The adsorption data presented by only two principal components captures most of the variance. The biplot for the first and second principal components (PC1 and PC2) is shown in Figure 8. PCA was carried out as outlined in the literature66 using the Origin 2020b version.

Table 6. Correlation Table of Principal Components.

  coefficients of PC1 coefficients of PC2 coefficients of PC3 coefficients of PC4 coefficients of PC5
A (pH) 0.69755 –0.1374 0.088 0 0.01526
B (adsorbent dose) 0.04676 0.38308 –0.29219 –0.15775 0.85943
C (initial concentration) 0.02241 0.6853 0.72506 0.0107 –0.05943
D (contact time) –0.03413 –0.18783 0.19243 0.90738 0.31941
E (temperature) 0.09785 0.57398 –0.58664 0.38944 –0.39445
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Table 8. BBD Design Matrix for Model.

  factors
 adsorption (%)
run A B C D E observed values predicted values
1 7 10 90 40 40 76.15 76.05
2 6 10 110 40 40 99.00 98.45
3 5 10 110 30 40 86.00 86.37
4 5 10 110 50 40 86.23 86.87
5 7 10 130 40 40 75.20 75.33
6 6 10 110 50 45 80.98 80.78
7 6 10 130 40 45 89.19 88.51
8 7 15 110 40 40 73.88 74.74
9 5 15 110 40 40 96.00 94.45
10 6 10 110 40 40 98.50 98.45
11 7 10 110 50 40 68.15 67.20
12 6 15 130 40 40 95.00 95.15
13 7 10 110 40 45 67.80 68.13
14 5 5 110 40 40 98.02 96.25
15 6 5 110 50 40 88.47 89.17
16 6 5 110 40 45 89.52 90.14
17 6 15 110 50 40 85.67 86.68
18 6 10 110 40 40 98.55 98.45
19 5 10 110 40 45 88.20 88.52
20 5 10 90 40 40 95.39 96.13
21 6 10 90 40 45 92.52 90.92
22 5 10 130 40 40 94.60 95.56
23 6 10 110 40 40 98.00 98.45
24 6 10 90 50 40 88.92 89.17
25 6 10 130 30 40 87.90 87.53
26 6 15 90 40 40 97.19 96.81
27 5 10 110 40 35 90.83 91.12
28 6 10 90 30 40 86.03 87.34
29 6 5 130 40 40 96.67 97.51
30 7 10 110 30 40 66.94 65.73
31 7 10 110 40 35 70.89 71.19
32 6 10 130 40 35 92.71 93.10
33 7 5 110 40 40 75.00 75.64
34 6 10 110 30 35 82.00 82.62
35 6 10 110 40 40 99.00 98.45
36 6 15 110 40 45 87.51 88.29
37 6 10 90 40 35 92.52 91.99
38 6 10 110 50 35 84.03 84.01
39 6 10 130 50 40 89.11 87.68
40 6 15 110 30 40 87.25 86.83
41 6 10 110 40 40 97.68 98.45
42 6 15 110 40 35 92.06 91.62
43 6 5 90 40 40 96.84 97.15
44 6 5 110 40 35 93.07 92.47
45 6 5 110 30 40 87.78 87.05
46 6 10 110 30 45 79.77 80.20
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Figure 8.

Figure 8

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PCA biplot for Pb2+ adsorption parameters.

For visual interpretation of the data trend, a scatter plot of the samples was obtained using PC1 and PC2 of the data matrix. Accordingly, separation of process pH, adsorbent dose, initial concentration, contact time, and temperature can be seen. The variable contact time negatively influenced the PC1 (i.e., pH), while temperature, adsorbent dose, and initial concentration positively influenced the PC1. In contrast, PC1 negatively influenced the PC2 (i.e., adsorbent dose). The points shown in the PCA plot that are geometrically close to one another indicate the similarity of the patterns that represent these points. The vector orientation, which describes the variables in factor space indicating increased trend of these variables and the vector length, is proportional to the square of correlation values. The angles between corresponding variables depict the degree of correlation, i.e., smaller angles represent high correlation.67

A dendrogram is a hierarchical clustering of large amounts of information in a visual form that is easy to understand. On the basis of Euclidean distance, major clustering groups can be evaluated. The horizontal axis of a dendrogram represents dissimilarity or distance between clusters, whereas the vertical axis represents clusters. A dendrogram begins with each run in a separate cluster and at every step, the two most similar clusters join into a single new cluster. In the above dendrogram (Figure 9), two cluster groups A and B were found to be prominent. Cluster A includes eight experimental runs (1, 28, 20, 43, 37, 26, 21, and 24), while cluster B comprises 38 experimental runs (2, 35, 10, 18, 23, 41, 14, 9, 27, 42, 44, 16, 19, 36, 4, 17, 38, 15, 6, 3, 40, 34, 45, 46, 8, 31, 33, 13, 11, 30, 5, 7, 12, 22, 32, 29, 39, and 25). Both these clusters A and B are grouped on the basis of their initial concentrations. Cluster A has experimental runs with 90 mg L–1 initial Pb2+ ion concentration, whereas group B consists of experimental runs with 110 mg L–1 initial Pb2+ ion concentration.

Figure 9.

Figure 9

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Hierarchal mapping of Pb2+ adsorption by a dendrogram.

3. Conclusions

This experimental work has detailed the probability of RSM for evaluating the interactive effect of five process variables on Pb2+ ion adsorption using Fe3O4 NPs as adsorbents. The mean size of the synthesized nanoparticles was 83.2 nm, and they had a needlelike morphology. This study was carried out to correlate the combined influence of different variables including adsorbent dose, pH, initial Pb2+ ion concentration, temperature, and contact time using the Box–Behnken design. On summarizing the results, RSM was found to be a highly applicable method for optimization of Pb2+ adsorption parameters. In fact, ANOVA showed a high coefficient of regression, i.e., R2 = 0.99, and confirmed that experimental data fit well to the model. Furthermore, pH and temperature are significant terms with p value < 0.0001 in the model that have crucial control over the Pb2+ ion adsorption process. The results also revealed that the adsorption rate decreased gradually with an increase in the adsorbent dose and temperature. Fe3O4 NPs could be promising adsorbents and the given RSM model could effectively predict the response with a maximum of 98.4% adsorption efficiency and provide information for process scale-up.

4. Experimental Section

4.1. Chemicals

Ferric chloride hexahydrate (FeCl3·6H2O) and sodium hydroxide (NaOH) were purchased from the Central Drug House, New Delhi, India. Sodium borohydride (NaBH4), ethanol, and lead nitrate (Pb (NO3)2) were purchased from Merck, India. All reagents were used intact as received, without further purification. Double-distilled water was used throughout the experiments for preparing synthetic stock solutions. The pH of the solution was adjusted using 0.1 M HCl and 0.1 M NaOH with a pH meter (Mettler Toledo AG, FEP 20). The initial and equilibrium Pb2+ concentrations were analyzed by an inductively coupled plasma mass spectrometer (ICPMS) (Agilent’s 7900 ICPMS).

4.2. Adsorbent Preparation

The magnetic Fe3O4 nanoparticles used in this study were synthesized by the sodium borohydride (NaBH4) chemical reduction method. The synthesis process was carried out in four steps: (i) 0.54 g of ferric chloride hexahydrate (FeCl3·6H2O) was dissolved in 30 mL of ethanol–water solution (4/1) (v/v), (ii) 100 mL of 0.1 M NaBH4 was added to the solution dropwise with stirring, (iii) black precipitates were formed and were separated, and (iv) the synthesized NPs were dried for 5 h at 90 °C.

4.3. Characterization

Transmission electron microscopy (JEOL JEM-1400) was used to study the morphology of nanoparticles and attached selected area electron diffraction (SAED) was used to study the crystallinity of the sample. A small amount of sample was mounted on a copper grid and analyzed by TEM to capture bright-field images at different magnification scales. Energy-dispersive spectroscopy (EDS) was also performed to analyze the elemental composition of the sample before and after Pb2+ adsorption. The Brunauer–Emmett–Teller (BET) model was used to calculate the surface area of the nanoparticles, and pore size distribution was determined using the Barrett–Joyner–Halenda (BJH) model isotherm (Autosorb 1Q-C-MP).

4.4. Adsorption Experiment

For the batch experimental study, optimization of the dependent parameters such as adsorbent dose (10–60 mg), Pb2+ ion concentration (10–150 mg L–1), agitation time (20–60 min), pH (2–9), and temperature (15–55 °C) was conducted. Optimum conditions obtained from batch experiments were used for the experimental design of process variables in BBD RSM. Furthermore, to optimize the experimental conditions and collection of data for isothermal studies, batch experiments were carried out in a 250 mL Erlenmeyer flask with 10 mg of Fe3O4 nanoparticles in 100 mL of Pb2+ ion aqueous solution at different concentrations (30, 70, 110, 130 mg L–1) for an equilibrium time of 40 min. The pH of the solution was adjusted to 6. The residual Pb2+ ion concentration in the samples was analyzed by inductively coupled plasma mass spectroscopy (ICP-MS) to obtain the final concentration. The percentage of Pb2+ ion adsorption68 and capacity69 were computed using eqs 7 and 8, respectively

4.4. 7
4.4. 8

where C0 is the initial Pb2+ ion concentration, Ce is the Pb2+ ion concentration at equilibrium, V is the volume of the solution, m is the mass of the adsorbent, and qe is the adsorption capacity.

4.5. Experimental Design: Methodology

For the process optimization of Pb2+ ion adsorption, the experimental design was created by the response surface methodology on the basis of optimum conditions obtained from batch experiments. It is based on mathematical and statistical techniques to fit a polynomial equation to the experimental data. This method is well applied to a response influenced by various parameters.70 In the present experimental investigation, the process variables that estimated Pb2+ removal efficiency were pH, adsorbent dose (mg), initial Pb2+ ion concentration (mg L–1), contact time (min), and temperature (°C). As RSM is an efficient statistical mathematical approach, it uses quantitative data of apt experiments for the design of a set of experiments and optimization of process variables to achieve the maximum response. A three-level five-factor Box–Behnken design (BBD) was used to optimize five variables. The response surface model generates an empirical equation for describing the corresponding quantity of the process.71 The BBD is “an independent, rotatable quadratic design with no embedded factorial or fractional factorial points where the variable combinations are at the midpoints of the edges of the variable space and at the center”.72 It is ensured by the BBD that not all of the factors are at high levels at the same time. Hence, significant interaction can be identified for batch studies.72−75

Preliminary experiments revealed the significant variables that affect the Pb2+ adsorption including pH, adsorbent dose, Pb2+ ion concentration, contact time, and temperature. Different ranges adjusted for process variables (A, B, C, D, E) at three different levels (coded as −1, 0, +1) for low, intermediate, and high values, respectively, are summarized in Table 7.

Table 7. Factors and Low–High Levels in the BBD–RSM Design.

  levels
factors low (−1) central (0) high (+1)
A—pH 5 6 7
B—adsorbent dose (mg L–1) 5 10 15
C—initial ion concentration (mg L–1) 90 110 130
D—contact time (min) 30 40 50
E—-temperature (°C) 35 40 45
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According to the RSM statistical matrix, 46 runs were generated to set up the experimental design (Table 8). Using a nonlinear regression method and second-order polynomial, experimental data was fit to identify significant coefficient terms. The response surface methodology gives the empirical relationship between the response function and the independent variables. The quadratic response model is based on all linear terms, square terms, and linear interaction terms according to the following equation76

4.5. 9

where Y denotes the predicted response (Pb2+ removal efficiency), b0 is the model constant, bi is the linear coefficient, bii is the quadratic effect of the input factor xii, and bij is the linear interaction effect between the input factors xi and xj.

The response function coefficients of experimental data were determined by regression. The standard polynomial quadratic equation was used to approximate the response function for lead removal (%).37 To analyze the adequacy of the proposed model, analysis of variance (ANOVA) was performed. ANOVA evaluates the suitability of the response functions and the significance of the effects of independent variables.

Acknowledgments

Central Research Facility, IIT Delhi (CRF-IITD), is gratefully acknowledged for their facility of ICPMS.

The authors declare no competing financial interest.

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