Nanosized Spinel Ferrites Synthesized by Sol-Gel Autocombustion for Optimized Removal of Azo Dye from Aqueous Solution

1 “Petru Poni” Institute of Macromolecular Chemistry, Aleea Grigore Ghica Voda 41 A, 700487 Iasi, Romania 2Department of Environmental Engineering and Management, “Gheorghe Asachi” Technical University of Iasi, 73 Dimitrie Mangeron Street, 700050 Iasi, Romania 3Department of Drug Industry and Pharmaceutical Biotechnology, “Grigore T. Popa” University of Medicine and Pharmacy, 16 University Street, 700115 Iasi, Romania 4Faculty of Physics, “Alexandru Ioan Cuza” University, No. 11, Carol I Boulevard, 700506 Iasi, Romania


Introduction
The azo dyes are extensively employed as coloring agents in the industries such as textile, paper, plastic, leather, cosmetics, photographic industries, and biomedical industries.A significant part of the total amount of dyes (about 15%) are lost and discharged into the environment during dye production and dying processes [1][2][3].Numerous research reports proved that azo dyes are toxic, mutagenic, and carcinogenic compounds [4].
Different physical, chemical, and biological methods have been used to remove dyes from industrial effluents [4][5][6].
Among physical methods, adsorption is very often employed for effective treatment of wastewater.The adsorption consists in attaching of soluble pollutants on a solid material (organic or inorganic support).Therefore, different sorbents such as activated carbon, coal, fly ash, clays, silica, alumina, and chitosan have been employed in dye adsorption studies [5].Despite their good adsorption performances, the separation and recovery of these adsorbents from heterogeneous systems still remain a drawback.Recently, the magnetic separation technology has attracted attention as a feasible alternative for traditional separation technologies such as settling, centrifugation, or membrane filtration [7,8].In this line, ferrites were proposed as potential adsorbents for dyes removal due to their appropriate physical characteristics and facile separation under external magnetic fields [7][8][9][10][11].
In the present study, Congo-Red (CR) has been used to evaluate the adsorption capacity of three representative magnetic spinel ferrites with the general formula MFe 2 O 4 (M = Ni, Co, and Zn), obtained as nanosized particles by sol-gel autocombustion method.The adsorption of CR has been investigated via kinetics, equilibrium, and thermodynamic approaches.Special attention has been devoted to the response surface modeling and optimization of the adsorption process to enhance the dye removal efficiency.(M = Ni, Co, and Zn) spinel ferrite materials were prepared by sol-gel autocombustion method [12].In a typical experiment, stoichiometric amounts of metal nitrates were dissolved in distilled water with the molar ratio M 2+ /Fe 3+ of 1 : 2. The molar ratio of metallic cations to citric acid was 1 : 1.The aqueous solution of citric acid was added to the solution of nitrate salts and heated to 353 K on a water bath under stirring until a viscous gel was formed.The gel was gradually heated to 623 K when the autoignition was clearly observed.The resulting powder was sintered in two steps (at 773 K/5 h and at 973 K/5 h) in order to achieve the spinel phase formation.

Characterization Techniques.
XRD patterns of the powder samples sintered at 973 K were recorded using a Shimadzu LabX 6000 diffractometer equipped with graphite monochromator and CuK ( = 0.15406 nm) radiation.The samples were scanned from 20 to 80 ∘ (2) using a scanning rate of 0.02 ∘ /s.
The formation of spinel phase of MFe 2 O 4 ferrite was monitored by infrared spectroscopy in 4000-350 cm −1 range using a Bruker Vertex 70 FTIR spectrometer with a resolution of 2 cm −1 (KBr pellets technique).
The morphology and microstructure of ferrite samples sintered at 973 K were investigated using Hitachi High-Tech HT7700 transmission electron microscope, operated at 100 kV accelerating voltage in high-contrast mode.

Adsorption Experiments.
A stock solution of 200 mg/L was prepared by dissolving CR in distilled water.The working solutions were prepared by diluting the stock solution to the desired concentrations.The concentrations of CR in the solutions were analyzed using UV-Vis spectrophotometer (Shimadzu UV-1700 PharmaSpec) by monitoring the absorbance at the wavelength of  max = 497 nm.
The prepared ferrites were applied as adsorbents for the removal of CR from the aqueous solutions using the batch technique.For this purpose, calculated amounts of  adsorbents were added to 50 mL of working solutions, and the samples were magnetically stirred at 500 rpm for different periods of time.The adsorption experiments were carried out at naturally occurring pH 6.80 and at the different temperatures (i.e., 293 K, 313 K, and 333 K).At the end of the adsorption tests the loaded ferrites were separated using a magnet, and the resulting clear solutions were analyzed for CR concentrations.In all the experiments (screening test, kinetics, isotherms, and optimization) the adsorption capacity was determined using the following equation [13]: where  denotes the adsorption capacity (mg/g),  0 is the initial concentration of CR in solution (mg/L),  is the final concentration of CR in solution (mg/L),  is the volume of solution (mL), and  represents the weight of the adsorbent (g).In addition, the color removal efficiency  (%) was determined by subsequent equation [13,14]: The crystallite size (  , nm) for each sample was calculated by line broadening of the most intense (311) diffraction peak using Debye-Scherrer formula [7] (see    value was found for nickel ferrite (30.6 nm), followed by zinc ferrite (34.4 nm), and cobalt containing ferrite (36.7 nm), respectively.

Results and Discussion
The FTIR spectra, in 4000-350 cm −1 range for MFe 2 O 4 (M = Ni, Co, and Zn) powders heated at 973 K are shown in Figure 2. The FTIR spectra revealed only the specific bands for metal-oxygen stretching vibration from the tetrahedral site in 584-540 cm −1 range and from the octahedral site at 397-389 cm −1 .Careful observation of the ZnFe 2 O 4 IR spectra shows a supplementary third absorption band at 674 cm −1 .The presence of this band is explained by the cation exchange between the tetrahedral and octahedral spinel sites which often occurs for zinc ferrite [15].
The representative TEM micrographs of MFe 2 O 4 samples are illustrated in Figure 3.
The average particle sizes (⟨  ⟩, nm) determined from microscopy images (TEM) are reported in Table 1.For all three studied materials, TEM images prove the formation of soft agglomerates constituted of nanosized particles with irregular (nanopolyhedra) shapes.The average sizes of individual particles are of 46 nm, 69 nm, and 101 nm for nickel, cobalt, and zinc ferrites, respectively (Table 1).Note that from XRD patterns only crystallites sizes can be evaluated.In turn, the microscopy techniques are employed to determine the particle sizes and morphologies (every particle is formed by a number of crystallites).In many cases there is no direct correlation between crystallite size (determined from XRD) and particle size (determined from TEM).
The obtained spinel ferrites were easily separated from aqueous solution by means of a permanent magnet.For instance, the magnetic separation of CoFe 2 O 4 spinel ferrite from the aqueous solution is shown in Figure 3(d) (before separation) and Figure 3(e) (after magnetic separation).

Adsorption Screening Test.
The objective of the screening test was to compare the performances of the ferrites for adsorption of Congo-Red (CR) dye from aqueous solutions under certain conditions.The results of the screening test are shown in Figure 4.The highest adsorption performances (in terms of both color removal efficiency and adsorption capacity) were attributed to the adsorbent NiFe 2 O 4 followed by CoFe 2 O 4 .The spinel ferrite ZnFe 2 O 4 disclosed the lowest sorption performances (Figure 4).The higher adsorption capacities were correlated with the smaller particle size of ferrites determined from TEM analysis.Therefore, the spinel ferrites NiFe 2 O 4 and CoFe 2 O 4 with better sorption performances were used for the kinetics and isotherms studies.Several kinetic models have been employed in this study to fit the adsorption kinetics data, namely: (1) pseudofirst order (PFO) kinetics [16,17], (2) pseudosecond order (PSO) kinetics [18], (3) pseudo-n-order (PnO) kinetics [19,20], (4) mixed 1,2-order (MOE) kinetics [21,22], and (5) intraparticle diffusion (ID) kinetics [23,24].The equations of kinetic models are summarized in Table 2.The predictions given by kinetic models have been plotted as solid, dashed and dot lines in Figure 5.
To determine the goodness-of-fit between models' predictions and experimental data the average relative error (ARE) function has been calculated [25]: where  exper denotes the experimental adsorption capacity (mg/g),  calc is the calculated adsorption capacity (mg/g),  is the number of data within the experimental curve, and  is the integer index.The parameters of kinetic models have been determined by Gauss-Newton nonlinear regression method using nlinfit matlab solver, and their values are reported in Table 3.The average relative error (ARE) function are also summarized in Table 3.
As one can see from Figure 5, the best-fitting kinetic data is given by PnO model with ARE < 0.75 (Table 3).This suggests that the orders of the rate equations (PnO) are of  = 2.556 (for CoFe 2 O 4 ) and  = 1.654 (for NiFe 2 O 4 ).Likewise, the PSO and MOE models approximate quite well the kinetic data with an average relative error less than 1% (ARE < 1).The kinetic model (PFO) fits satisfactorily the observations with the average relative errors of 4.3% and 2.6%, for CoFe 2 O 4 and NiFe 2 O 4 , respectively.The intraparticle diffusion (ID) model shows some discrepancy between the predicted data ,   , and  The equilibrium data were analyzed using the isotherm models of Freundlich and Langmuir.Freundlich model is an empirical adsorption isotherm for nonideal adsorption on heterogeneous surfaces and multisite adsorption process, which may be expressed by the following equation [26,27]: where   (mg/L) is the dye concentration in the liquid at equilibrium,   (mg/g) is the amount of dye adsorbed at q (mg/g)  equilibrium,   [(mg/g)(L/g) 1/  ] is the Freundlich constant, and   is the parameter which describes the system heterogeneity.
The basic assumption of the Langmuir theory is that adsorption takes place at specific homogeneous sites within the sorbent [28,29]: where   (mg/g) is the amount of the solute adsorbed for a complete monolayer and   (L/mg) is the Langmuir isotherm constant.
The parameters of Freundlich and Langmuir models have been calculated by means of Gauss-Newton nonlinear regression method.To estimate the goodness-of-fit for isotherms, the average relative errors (ARE) have been computed according to (3).The parameters of isotherm models as well as the values of the average relative errors are summarized in Table 4.The results reveal that Freundlich model is more suitable than Langmuir model to fit the adsorption data.This indicates the heterogeneous adsorption of CR onto magnetic sorbents CoFe 2 O 4 and NiFe 2 O 4 .
Figure 6 disclosed that the adsorption of CR onto ferrites decreased with increment of temperature.This effect is more pronounced for CoFe 2 O 4 and less significant for NiFe 2 O 4 sorbent (Figure 6).Similar trends for ferrite-dye systems were also reported by other authors [7,8].
In addition, the equilibrium adsorption data have been modeled using the Dubinin-Radushkevich (D-R) isotherm.The D-R model has been employed to distinguish between physical and chemical adsorption.The D-R isotherm parameters are reported in Table 4. Based on D-R isotherm analysis, the mean free energy of adsorption,   (kJ mol −1 ), has been calculated [30,31].In our case, the values of mean free energy   were higher than 8 (kJ mol −1 ) (Table 4) suggesting that the uptake of CR onto ferrite materials was based on chemical adsorption.

Thermodynamic Parameters.
The thermodynamic parameters for CR adsorption onto spinel ferrites have been calculated according to the methodology presented elsewhere [23].The thermodynamic parameters for CR adsorption onto CoFe 2 O 4 sorbent were found to be Δ = −30.861± 2.794 kJ/mol, Δ = 12.828 kJ/mol, and Δ = 139.579± 0.112 J/mol K.For CR adsorption onto NiFe 2 O 4 sorbent, the values of the thermodynamic parameters were Δ = −31.875± 3.040 kJ/mol, Δ = 15.301kJ/mol, and Δ = 150.725± 2.142 J/mol K.The negative values of free energy Δ revealed the spontaneous nature of the adsorption process.The positive enthalpy indicated the endothermic effect of the adsorption.The positive values of entropy Δ disclosed the increasing of randomness at the solid/liquid interface, suggesting the affinity of CR molecules on the surface of ferrite adsorbents.

Response Surface Modeling of the Adsorption Process.
Due to its highest sorption performances, the material NiFe 2 O 4 was selected for modeling and optimization of the adsorption process.To this end, the response surface methodology (RSM) [32][33][34] was employed to build the multiple regression models, which are the mathematical relationships between responses (outputs) and regressor variables (input factors) of the process under investigation.The controllable factors (regressors) employed for the experimental design of the adsorption process were the contact time  (min), initial dye concentration  0 (mg/L), and the sorbent dosage SD (g/L).For modeling purpose, the values of these factors were converted into dimensionless values, known as coded levels.The relation between actual values of factors and their coded levels is summarized in Table 5.
For the investigation of the adsorption process, the central composite design (CCD) of orthogonal type was employed (Table 6).Two responses were determined experimentally for each run, that is, color removal efficiency  (%) and adsorption capacity  (mg/g).The values of these responses are reported in Table 6.Note that all the experiments were carried out at room temperature (293 K) and naturally occurring pH 6.80.Based on the experimental design data (Table 6), two statistical models were constructed using the multiple regression method [32][33][34].The developed fitted models can be presented for coded variables ( 1 ,  2 , and  3 ) as follows: subject to   ∈ [−, ], for all  = 1, 3.
The significance of all regression coefficients in (6) was estimated using the Student -test [32].Thus, the fitted models (6) involve only the significant coefficients.Likewise, the models were validated statistically using the analysis of variance (ANOVA).The detailed description of this statistical method can be found elsewhere [33,34].The results of ANOVA are summarized in Table 7.Since the  values are less than 0.0001 both models are statistically significant.The fact that the values of the coefficients of determination  2 are high (close to 1) indicates that the observed responses are quite close to those predicted.
The goodness-of-fits between predictions and experimental observations are illustrated in Figure 7.Both fitted models yield well-behaved predictions for the responses  (%) and  (mg/g), since the data are scattered close to the bisector.Hence, the parity plot (Figure 7) is consistent with the ANOVA results (Table 7).
The multiple regression models with actual variables have been developed by the substitution technique and may be written as follows: subject to 14 ≤  ≤ 196 (min); 13.6 ≤  0 ≤ 86.5 (mg/L); 0.57 ≤ SD ≤ 5.43 (g/L).The 3D plots of response surfaces showing the coupling effects of factors on responses are illustrated in Figures 8-9.
Figure 8(a) shows that the increment of sorbent dosage (SD) variable leads to the increasing of the color removal efficiency, Ŷ (%).By contrast, the greater the dye concentration ( 0 ) is, the less the removal efficiency is.An interaction effect is observed between these factors,  0 and SD.Thus, the effect of the initial dye concentration is more significant at low levels of the sorbent dosage SD.The influence of SD variable is stronger at higher values of  0 .According to Figure 8(b), the increment of CR concentration ( 0 ) improves the values of the adsorption capacity, q (mg/g).The increasing of the sorbent dosage (SD) diminishes the adsorption capacity (q).Due to the factors' interaction, the effect of sorbent dosage is more pronounced at lower values of initial dye concentration.
As one can see from Figure 9(a), the increasing of both contact time and sorbent dosage leads to higher values of color removal efficiency, Ŷ (%).The effect of the sorbent dosage is more noticeable than the effect of the contact time.
According to Figure 9(b), the increment of the contact time leads to a gradual increasing of the adsorption capacity, q (mg/g).By contrast, as the sorbent dosage gets higher the adsorption capacity goes down.This may be related to the fact that the adsorbent material is not completely saturated with the solute at high sorbent dosages.The effect of the sorbent dosage is much more discerned than the effect of the contact time.

Optimization of the Adsorption Process.
The main objective of the experimental design and response surface modeling is to optimize the investigated process.In this work, the model-based optimization of the adsorption process (CR onto NiFe 2 O 4 ) has been approached via two strategies, that is, single-objective optimization (case 1) and multiobjective optimization (case 2).

Single-Objective Optimization (Case 1).
In this case, the objective was to maximize only the color removal efficiency Ŷ (%) since this response was considered a priority from the environmental standpoint.The model-based optimization notation, for case 1, is given by max Ŷ ( 1 ,  2 ,  3 ) , In this study, the genetic algorithm (GA) was employed to solve the single-objective optimization problem given by (8).To this end, the optim ga solver was used, implemented in SciLab 5.4.1 open-source software.The optimal solution in terms of actual values of factors is  * = 165 min,  * 0 = 13.6 mg/L, and SD * = 5.05 g/L (Table 8).Under such conditions, the predicted response is Ŷ = 105.314,and the observed response is  = 98.995%.This is the maximal value of the removal efficiency obtained in all the experiments done in this work.Note that under these conditions only the removal efficiency has been improved, while adsorption  capacity remained at the relatively low value, that is, q = 1.728 (predicted) and  = 2.284 mg/g (experimental) (Table 8).

Multiobjective Optimization (Case 2).
For case 2, the objective was to maximize simultaneously both the color removal efficiency Ŷ (%) and the adsorption capacity q (mg/g).Firstly, the region of interest (i.e., desirability zone close to the optimum) has been identified by visual inspection of the contour overlap plot shown in Figure 10.Herein, the superposition of the two response functions is depicted, that is, Ŷ and q (predicted responses).According to Figure 10, the responses are conflicting; that is, the increment of one response leads to a decrease in the value of another objective.The desirability region (colored yellow zone in Figure 10) corresponds to high SD and low  0 , for the fixed contact time close to the superior level (i.e.,  = 180 min).The multicriteria optimization problem may be written using the vector optimization notation as follows: Ŷ (%) q (mg/g) Figure 10: Overlap contour-lines plot of two response functions Ŷ and q depending on the values of factors SD (g/L) and  0 (mg/L) for a constant level of  = 180 (min).
For solving the multiattribute optimization problem (9), one must find a set of solutions that satisfies both objectives.Such set of possible optimal solutions is known as nondominant solutions or Pareto population (optimality).A decisionmaker has to analyze the Pareto population and look for the best choice according to his priorities [35].To solve the vector optimization problem (9), the nondominated sorting genetic algorithm-II (NSGA-II) [36] was employed using the solver optim nsga2 included in SciLab-5.4.1 program.The results of optimization are shown in Figure 11.
The algorithm (NSGA-II) has randomly generated the initial population of 100 individual solutions inside of the valid region (Figure 11(a)).According to heuristic calculations, a set of the equivalent solutions (Pareto optimality) has been found as illustrated in Figure 11(b).The Pareto population involves many individual solutions (about 100), since the responses are conflicting and both objectives ( Ŷ and q) are treated with the same importance.To choose an optimal solution for experimental confirmation, the desirability function approach (DFA) has been employed additionally.In this respect, the individual solutions from Pareto optimality have been checked for the desirability by assigning different importance for responses.Thus, the response Ŷ (color removal efficiency) has been considered more important than the response q (adsorption capacity) for the calculation of the desirability.
The desirability function approach deals with the calculation of individual desirability function   for each considered response   by converting the values of the response into the nondimensional scale ranging from 0 to 1.For the maximization of a response   , the corresponding individual desirability function   is of the-larger-the-best (LTB) type, and the conversion scheme can be written as [37]: LTB-desirability: where   is the value of the response with index ,  −  is the lower-bound limit of the response,  +  is the upper-bound limit of the response, and   is the weight coefficient indicating the importance of that response.The global desirability  has been determined as the geometric mean of individual desirability functions   [37,38]: where  is the number of responses.The global desirability was calculated according to (11) for all individual solutions   from Pareto population.Figure 12 shows the scatter 3D plot of Pareto population into the desirability-objectives space.A maximum value of desirability ( = 0.7958) is attained for Ŷ = 93.894and q = 7.290.This point has been selected as the optimal solution for experimental confirmation.The results of confirmation run are reported in Table 9.The optimum conditions in terms of controllable variables are  * = 152 min,  * 0 = 39 mg/L, and SD * = 4.59 g/L.The responses confirmed by experiment under such conditions are  = 94.579(%) and  = 6.450 mg/g.The comparisons of the results from single and multiobjective optimization strategies reveal that the removal efficiency, for case 2, is smaller with 4.5%.In turn, the adsorption capacity is about 3-fold higher.The optimal solution derived from single-objective optimization (case 1) is more suitable if the aim of decontamination is to obtain the maximal removal efficiency.The optimum point determined by multiobjective strategy (case 2) is more appropriate for the enhanced adsorption accomplished in a shorter time and with a smaller sorbent amount.

Conclusions
In this work, the nanosized spinel ferrites MFe 2 O 4 (M = Ni, Co, and Zn) were obtained by sol-gel autocombustion method.The XRD analysis and FTIR spectroscopy confirmed the pure spinel phase formation for all the ferrite samples sintered at 973 K.The presence of nanometric particles and a low degree of agglomeration were observed by TEM.
The obtained ferrite materials were applied for Congo-Red (CR) adsorption from aqueous solutions.The screening test revealed that the most efficient adsorbents for CR removal were NiFe

3. 3 .
Adsorption Kinetics.The adsorptions of CR onto NiFe 2 O 4 and CoFe 2 O 4 ferrites were studied versus time at 293 K. Figure 5 shows the amount of the dye adsorbed   (mg/g) against the contact time  (min) for two sorbent materials, that is, CoFe 2 O 4 (Figure 5(a)) and NiFe 2 O 4 (Figure 5(b)).

Figure 3 :
Figure 3: TEM micrographs of MFe 2 O 4 (M = Ni, Co, and Zn) spinel ferrites (a, b, and c) and images (d, e) of magnetic separation of CoFe 2 O 4 spinel ferrite from the aqueous solution with a permanent magnet: (d) before separation and (e) after magnetic separation.

Figure 4 :
Figure 4: Screening test for CR dye adsorption using different ferrite adsorbents showing the adsorption capacity and color removal efficiency determined under the following conditions:  0 = 50 mg/L, SD = 1 g/L,  = 180 min, and  = 293 K.

Figure 7 :Figure 8 :
Figure 7: Parity plot showing the agreement between experimental and calculated responses: (a) color removal efficiency and (b) adsorption capacity.

Figure 9 :
Figure 9: Response surface plot showing the coupling effects of  and SD factors (at  0 = 50 mg/L) on (a) dye removal efficiency Ŷ (%) and (b) adsorption capacity q (mg/g).

Figure 11 :
Figure 11: The results of NSGA-II optimization presented in the objective space: (a) initial population and (b) Pareto population.

Note.Figure 12 :
Figure 12: Scatter 3D plot of Pareto population showing the global desirability into the objective space: desirability () versus adsorption capacity (q) and color removal efficiency ( Ŷ).

2 O 4
followed by CoFe 2 O 4 .The adsorption kinetics disclosed that the data were best fitted by PnO model, suggesting that the most appropriate orders for the rate equations were  = 1.654 (for NiFe 2 O 4 ) and  = 2.556 (for CoFe 2 O 4 ).The Freundlich isotherm model showed the best agreement with the experimental data, suggesting the heterogeneous adsorption of CR onto magnetic sorbents.The maximum adsorption capacity at 293 K was 14.06 mg/g for CoFe 2 O 4 and 17.13 mg/g for NiFe 2 O 4 .The values of mean 2.1.Materials.Analytical gradeNi(NO 3 ) 2 ⋅6H 2 O, Co(NO 3 ) 2 ⋅6H 2 O, Zn(NO 3 ) 2 ⋅6H 2 O, Fe(NO 3 ) 3 ⋅9H 2 O,citric acid monohydrate, and Congo-Red azo dye were purchased from Sigma-Aldrich and used without further purification.2.2.Synthesis of Nanosized Spinel Ferrites Sorbents.MFe 2 O 4

Table 1 :
).According to Table 1, the values of crystallite size depend on M 2+ cation nature.The smallest nanosized crystallite Summary of the experimental and calculated data obtained for MFe 2 O 4 (M = Ni, Co, and Zn) spinel ferrites.

Table 2 :
Kinetic models and the parameters for the adsorption kinetics.Abbreviation Kinetic model (rate equation) Kinetic model (nonlinear equation) Parameters PFO and  2 As one can see, the adsorption of CR goes up with increment of equilibrium concentration for both cases (CoFe 2 O 4 and NiFe 2 O 4 ).
2 O 4 and CoFe 2 O 4 has been studied against equilibrium concentration at different temperatures.From kinetic studies, the contact time has been fixed at  = 180 min to attain the stationary adsorption (equilibrium).Figure6shows the amount of dye adsorbed at equilibrium   (mg/g) versus the equilibrium concentration   (mg/L) for both sorbent materials CoFe 2 O 4 (Figure6(a)) and NiFe 2 O 4 (Figure 6(b)).

Table 3 :
Kinetic parameters for Congo-Red adsorption onto spinel ferrites, determined by the nonlinear regression method.

Table 5 :
Input variables and their coded and actual values used for adsorption experiments.
Note:  = 1.215 (value of axial point for orthogonal CCD in case of three factors).

Table 6 :
Central composite design (CCD) of orthogonal type used for adsorption experiments (CR onto NiFe 2 O 4 ).

Table 7 :
Analysis of variance (ANOVA) for the significance of the multiple regression models.
a Degree of freedom; b sum of squares; c mean square.

Table 8 :
Experimental confirmation of optimal point determined by GA (Case 1: single-objective optimization).

Table 9 :
Experimental confirmation of optimal point determined by NSGA-II and DFA (Case 2: multiobjective optimization).