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

Authors: Petrisor Samoila; Corneliu Cojocaru; Igor Cretescu; Catalina Daniela Stan; Valentin Nica; Liviu Sacarescu; Valeria Harabagiu
Journal: Journal of Nanomaterials
 (2015)

---

## Abstract

Nanosized spinel ferrites MFe2O4 (M = Ni, Co, and Zn) have been prepared by sol-gel autocombustion method using citric acid as a fuel agent. The materials are characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and transmission electron microscopy (TEM). The spinel ferrites have been applied for Congo-Red (CR) dye adsorption using batch technique. Different kinetic and equilibrium models have been fitted by nonlinear regression to analyze the adsorption data. In accordance with Langmuir isotherm, the maximum adsorption capacity at 293 K is 14.06 mg/g for CoFe2O4 and 17.13 mg/g for NiFe2O4. The values of mean free energy determined from Dubinin-Radushkevich isotherm are higher than 8 (kJ mol−1), indicating a chemisorption mechanism. Based on the calculated thermodynamic parameters (free energy, enthalpy, and entropy) the adsorption of CR onto ferrites is a spontaneous and endothermic process. Response surface methodology has been applied to construct the multiple regression models for prediction of the adsorption capacity and removal efficiency. The model-based optimization has been performed using genetic algorithms and desirability function approach. The single-objective optimization has yielded a maximum value of color removal efficiency of 98.995%, using NiFe2O4 adsorbent. The multiobjective optimization has resulted in the improvement of both removal efficiency and adsorption capacity.


---

## Body

## 1. 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 [1–3]. 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 [4–6]. 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 [7–11].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 MFe2O4 (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.


## 2. Materials and Methods

### 2.1. Materials

Analytical grade Ni(NO3)2·6H2O, Co(NO3)2·6H2O, Zn(NO3)2·6H2O, Fe(NO3)3·9H2O, 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

MFe2O4 (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 M2+/Fe3+ 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.


### 2.3. 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 CuKα (λ
=
0.15406 nm) radiation. The samples were scanned from 20 to 80° (2
θ) using a scanning rate of 0.02°/s.The formation of spinel phase of MFe2O4 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.


### 2.4. 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 ofλ
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]:(1)
q
=
C
0
-
C
·
V
m
·
1000
,where q denotes the adsorption capacity (mg/g), C
0 is the initial concentration of CR in solution (mg/L), C is the final concentration of CR in solution (mg/L), V is the volume of solution (mL), and m represents the weight of the adsorbent (g). In addition, the color removal efficiency Y (%) was determined by subsequent equation [13, 14]:(2)
Y
=
1
-
C
C
0
×
100
.


## 2.1. Materials

Analytical grade Ni(NO3)2·6H2O, Co(NO3)2·6H2O, Zn(NO3)2·6H2O, Fe(NO3)3·9H2O, 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

MFe2O4 (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 M2+/Fe3+ 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.


## 2.3. 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 CuKα (λ
=
0.15406 nm) radiation. The samples were scanned from 20 to 80° (2
θ) using a scanning rate of 0.02°/s.The formation of spinel phase of MFe2O4 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.


## 2.4. 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 ofλ
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]:(1)
q
=
C
0
-
C
·
V
m
·
1000
,where q denotes the adsorption capacity (mg/g), C
0 is the initial concentration of CR in solution (mg/L), C is the final concentration of CR in solution (mg/L), V is the volume of solution (mL), and m represents the weight of the adsorbent (g). In addition, the color removal efficiency Y (%) was determined by subsequent equation [13, 14]:(2)
Y
=
1
-
C
C
0
×
100
.


## 3. Results and Discussion

### 3.1. Characterization of MFe2O4 Spinel Ferrites Sorbents

X-ray diffraction patterns of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites are shown in Figure 1. For all the analyzed materials, the most intense peaks characteristic for spinel structure were observed at 2
θ of about 35°. All peaks observed in the XRD patterns correspond to the face-centered cubic structure of pure spinels according to JCPDS cards number 44-1485, number 22-1086, and number 22-1012.Figure 1
XRD patterns of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites.The crystallite size (D
c, nm) for each sample was calculated by line broadening of the most intense (311) diffraction peak using Debye-Scherrer formula [7] (see Table 1). According to Table 1, the values of crystallite size depend on M2+ cation nature. The smallest nanosized crystallite value was found for nickel ferrite (30.6 nm), followed by zinc ferrite (34.4 nm), and cobalt containing ferrite (36.7 nm), respectively.Table 1
Summary of the experimental and calculated data obtained for MFe2O4 (M = Ni, Co, and Zn) spinel ferrites.
Spinel ferrite
a2θ
311 (degrees)
a
D
c (nm)
b
d
p
(nm)
NiFe2O4
35.68803
30.6
46
CoFe2O4
35.53905
36.7
69
ZnFe2O4
35.27044
34.4
101
aDiffraction angle (θ
311) and crystallite size (D
c), data from XRD; bparticle size, data from TEM.The FTIR spectra, in 4000–350 cm−1 range for MFe2O4 (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 ZnFe2O4 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].Figure 2
FTIR spectra of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites.The representative TEM micrographs of MFe2O4 samples are illustrated in Figure 3.Figure 3
TEM micrographs of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites (a, b, and c) and images (d, e) of magnetic separation of CoFe2O4 spinel ferrite from the aqueous solution with a permanent magnet: (d) before separation and (e) after magnetic separation.The average particle sizes (d
p, 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 CoFe2O4 spinel ferrite from the aqueous solution is shown in Figure 3(d) (before separation) and Figure 3(e) (after magnetic separation).


### 3.2. 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 Figure4. The highest adsorption performances (in terms of both color removal efficiency and adsorption capacity) were attributed to the adsorbent NiFe2O4 followed by CoFe2O4. The spinel ferrite ZnFe2O4 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 NiFe2O4 and CoFe2O4 with better sorption performances were used for the kinetics and isotherms studies.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:C
0
=
50 mg/L, SD = 1 g/L, t
=
180 min, and T
=
293 K.


### 3.3. Adsorption Kinetics

The adsorptions of CR onto NiFe2O4 and CoFe2O4 ferrites were studied versus time at 293 K. Figure 5 shows the amount of the dye adsorbed q
t (mg/g) against the contact time t (min) for two sorbent materials, that is, CoFe2O4 (Figure 5(a)) and NiFe2O4 (Figure 5(b)).Figure 5
Adsorption kinetics data for Congo-Red removal by ferrite sorbents and comparison of kinetic models: (a) adsorbent CoFe2O4 and (b) adsorbent NiFe2O4; experimental conditions: C
0
=
50 mg/L, SD = 1 g/L and T
=
293 K.
(a)
(b)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.Table 2
Kinetic models and the parameters for the adsorption kinetics.
Abbreviation
Kinetic model (rate equation)
Kinetic model  (nonlinear equation)
Parameters
PFO
d
q
t
d
t
=
k
1
q
e
-
q
t
q
t
=
q
e
1
-
e
-
k
1
t
q
e, k
1
PSO
d
q
t
d
t
=
k
2
q
e
-
q
t
2
q
t
=
k
2
q
e
2
t
1
+
k
2
q
e
t
q
e, k
2
PnO
d
q
t
d
t
=
k
n
q
e
-
q
t
n
q
t
=
q
e
-
n
-
1
k
n
t
+
q
e
(
1
-
n
)
1
/
(
1
-
n
)
q
e, k
n, and n
MOE
d
q
t
d
t
=
∑
i
K
i
q
e
-
q
t
i
q
t
=
q
e
1
-
e
-
K
1
t
1
-
K
2
q
e
/
(
K
1
+
K
2
q
e
)
e
-
K
1
t
q
e, K
1, and K
2
ID
d
q
t
d
t
=
k
d
2
t
q
t
=
k
d
t
+
J
k
d, JTo determine the goodness-of-fit between models’ predictions and experimental data the average relative error (ARE) function has been calculated [25]:(3)
ARE
=
100
N
∑
j
=
1
N
q
j
calc
-
q
j
exper
q
j
exper
,where q
exper denotes the experimental adsorption capacity (mg/g), q
calc is the calculated adsorption capacity (mg/g), N is the number of data within the experimental curve, and j is the integer index.The parameters of kinetic models have been determined by Gauss-Newton nonlinear regression method usingnlinfit matlab solver, and their values are reported in Table 3. The average relative error (ARE) function are also summarized in Table 3.Table 3
Kinetic parameters for Congo-Red adsorption onto spinel ferrites, determined by the nonlinear regression method.
Kinetic model and parameters
Adsorbent: CoFe2O4
Adsorbent: NiFe2O4
PFO
q
e
=
9.6461 (mg/g)
q
e
=
11.1255 (mg/g)
k
1
=
0.0527
k
1
=
0.0623
ARE  = 4.307
ARE = 2.605
PSO
q
e
=
10.5168 (mg/g)
q
e
=
11.9730 (mg/g)
k
2
=
0.0080
k
2
=
0.0089
ARE = 0.916
ARE = 0.941
PnO
q
e
=
11.198 (mg/g)
q
e
=
11.603 (mg/g)
k
n
=
2.2909
×
10
-
3
k
n
=
1.8229
×
10
-
2
n
=
2.5561
n
=
1.6539
ARE  = 0.503
ARE  = 0.745
MOE
q
e
=
10.517 (mg/g)
q
e
=
11.4637 (mg/g)
K
1
=
3.3965
×
10
-
6
K
1
=
0.0153
K
2
=
7.9652
×
10
-
3
K
2
=
0.0076
ARE  = 0.938
ARE  = 0.893
ID
k
d
=
0.5369
k
d
=
0.5879
J
=
3.2066
J
=
4.1416
ARE  = 10.624
ARE  = 11.443As one can see from Figure5, 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 n
=
2.556 (for CoFe2O4) and n
=
1.654 (for NiFe2O4). 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 CoFe2O4 and NiFe2O4, respectively. The intraparticle diffusion (ID) model shows some discrepancy between the predicted data and experimental observations with the errors of 10-11%. The kinetic data (Figure 5) suggest that NiFe2O4 ferrite is superior to CoFe2O4 for CR adsorption owing to higher values of adsorption capacity observed against the time.


### 3.4. Adsorption Isotherms

The adsorption of CR onto NiFe2O4 and CoFe2O4 has been studied against equilibrium concentration at different temperatures. From kinetic studies, the contact time has been fixed at t
=
180 min to attain the stationary adsorption (equilibrium). Figure 6 shows the amount of dye adsorbed at equilibrium q
e (mg/g) versus the equilibrium concentration C
e (mg/L) for both sorbent materials CoFe2O4 (Figure 6(a)) and NiFe2O4 (Figure 6(b)). As one can see, the adsorption of CR goes up with increment of equilibrium concentration for both cases (CoFe2O4 and NiFe2O4).Figure 6
Adsorption isotherms for Congo-Red removal by ferrite sorbents fitted by the Freundlich (solid lines) and Langmuir (dot lines) models: (a) adsorbent CoFe2O4 and (b) adsorbent NiFe2O4; experimental conditions: SD = 1 g/L and t
=
180 min.
(a)
(b)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]:(4)
q
e
=
K
F
C
e
1
/
n
F
,where C
e (mg/L) is the dye concentration in the liquid at equilibrium, q
e (mg/g) is the amount of dye adsorbed at equilibrium, K
F
[
(
m
g
/
g
)
(
L
/
g
)
1
/
n
F
] is the Freundlich constant, and n
F 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]:(5)
q
e
=
q
m
K
L
C
e
1
+
K
L
C
e
,where q
m (mg/g) is the amount of the solute adsorbed for a complete monolayer and K
L (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 CoFe2O4 and NiFe2O4.Table 4
Isotherm parameters for Congo-Red adsorption onto spinel ferrites.
Isotherm
Adsorbent: CoFe2O4
Adsorbent: NiFe2O4
T = 293 K
T = 333 K
T = 293 K
T = 333 K
Freundlich
K
F
=
4.3932
K
F
=
3.5983
K
F
=
5.7119
K
F
=
5.7563
K
F  (mg/g)
(L/g)
1
/
n
F
n
F
=
4.0025
n
F
=
5.4013
n
F
=
4.1917
n
F
=
5.2030
n
F
ARE = 3.21
ARE = 4.71
ARE = 2.79
ARE = 3.30
Langmuir
K
L
=
0.1460
K
L
=
0.2751
K
L
=
0.1746
K
L
=
0.3643
K
L (L/mg)
q
m
=
14.059
q
m
=
8.224
q
m
=
17.133
q
m
=
13.218
q
m (mg/g)
ARE = 11.72
ARE = 10.43
ARE = 12.10
ARE = 9.97
D-R
q
d
=
0.0319
q
d
=
0.0153
q
d
=
0.0380
q
d
=
0.0265
q
d (g/g)
K
D
=
0.0021
K
D
=
0.0010
K
D
=
0.0020
K
D
=
0.0011
K
D (mol2 kJ−2)
E
S
=
15.335
E
S
=
21.936
E
S
=
15.669
E
S
=
21.225
E
S (kJ mol−1)
ARE  = 4.78
ARE  = 5.51
ARE  = 4.05
ARE  = 3.69Figure6 disclosed that the adsorption of CR onto ferrites decreased with increment of temperature. This effect is more pronounced for CoFe2O4 and less significant for NiFe2O4 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 Table4. Based on D-R isotherm analysis, the mean free energy of adsorption, E
S (kJ mol−1), has been calculated [30, 31]. In our case, the values of mean free energy E
S were higher than 8 (kJ mol−1) (Table 4) suggesting that the uptake of CR onto ferrite materials was based on chemical adsorption.


### 3.5. 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 CoFe2O4 sorbent were found to be Δ
G
=
-
30.861
±
2.794 kJ/mol, Δ
H
=
12.828 kJ/mol, and Δ
S
=
139.579
±
0.112 J/mol K. For CR adsorption onto NiFe2O4 sorbent, the values of the thermodynamic parameters were Δ
G
=
-
31.875
±
3.040 kJ/mol, Δ
H
=
15.301 kJ/mol, and Δ
S
=
150.725
±
2.142 J/mol K. The negative values of free energy Δ
G revealed the spontaneous nature of the adsorption process. The positive enthalpy indicated the endothermic effect of the adsorption. The positive values of entropy Δ
S disclosed the increasing of randomness at the solid/liquid interface, suggesting the affinity of CR molecules on the surface of ferrite adsorbents.


### 3.6. Response Surface Modeling of the Adsorption Process

Due to its highest sorption performances, the material NiFe2O4 was selected for modeling and optimization of the adsorption process. To this end, the response surface methodology (RSM) [32–34] 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 timet (min), initial dye concentration C
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.Table 5
Input variables and their coded and actual values used for adsorption experiments.
Input variables (factors)
Coded variables
Coded levels versus actual values
−α
-
1
0
+1
+α
Contact time,t (min)
x
1
14
30
105
180
196
Initial dye concentration,C
0 (mg/L)
x
2
13.6
20.0
50.0
80.0
86.5
Sorbent dosage (NiFe2O4), SD (g/L)
x
3
0.57
1.00
3.00
5.00
5.43
Note:α
=
1.215 (value of axial point for orthogonal CCD in case of three factors).For the investigation of the adsorption process, the central composite design (CCD) of orthogonal type was employed (Table6). Two responses were determined experimentally for each run, that is, color removal efficiency Y (%) and adsorption capacity q (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 [32–34]. The developed fitted models can be presented for coded variables (x
1, x
2, and x
3) as follows:(6)
Y
^
=
74.15
+
4.569
x
1
-
14.82
x
2
+
25.38
x
3
-
2.871
x
1
2
-
10.785
x
3
2
+
2.685
x
2
x
3
,
q
^
=
10.489
+
0.83
x
1
+
2.936
x
2
-
2.719
x
3
-
0.637
x
1
2
-
1.51
x
2
2
+
0.467
x
3
2
-
0.353
x
1
x
3
+
0.511
x
2
x
3
,subject to x
i
∈
-
α
,
α, for all i
=
1,3
¯.Table 6
Central composite design (CCD) of orthogonal type used for adsorption experiments (CR onto NiFe2O4).
Factors (controllable input variables)
Responses (experimental values)
Run
t, (min)
C
0, (mg/L)
SD, (g/L)
x
1
t
x
2
C
0
x
3
SD
Y, (%)
q, (mg/g)
1
+1
180
+1
80.0
+1
5.00
79.057
10.209
2
−1
30
+1
80.0
+1
5.00
67.367
8.628
3
+1
180
−1
20.0
+1
5.00
97.143
3.184
4
−1
30
−1
20.0
+1
5.00
95.035
3.138
5
+1
180
+1
80.0
−1
1.00
22.026
14.634
6
−1
30
+1
80.0
−1
1.00
18.094
12.117
7
+1
180
−1
20.0
−1
1.00
59.247
10.127
8
−1
30
−1
20.0
−1
1.00
48.110
8.195
9
+α
196
0
50.0
0
3.00
77.902
10.868
10
−α
14
0
50.0
0
3.00
60.478
8.390
11
0
105
+α
86.5
0
3.00
54.426
12.956
12
0
105
−α
13.6
0
3.00
95.025
3.727
13
0
105
0
50.0
+α
5.43
93.258
7.198
14
0
105
0
50.0
−α
0.57
21.775
15.317
15
0
105
0
50.0
0
3.00
73.747
10.244
16
0
105
0
50.0
0
3.00
73.305
10.350The significance of all regression coefficients in (6) was estimated using the Student t-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 P values are less than 0.0001 both models are statistically significant. The fact that the values of the coefficients of determination R
2 are high (close to 1) indicates that the observed responses are quite close to those predicted.Table 7
Analysis of variance (ANOVA) for the significance of the multiple regression models.
Source
DFa
SSb
MSc
F-value
P value
R
2
R
adj
2
Y-response (color removal efficiency)
Model
6
1.037 × 104
1.728 × 103
105.139
< 0.0001
0.986
0.977
Residual
9
147.912
16.435
Total
15
1.052 × 104
q-response (adsorption capacity)
Model
8
199.745
24.968
31.700
< 0.0001
0.973
0.942
Residual
7
5.513
0.788
Total
15
205.259
aDegree of freedom; bsum of squares; cmean square.The goodness-of-fits between predictions and experimental observations are illustrated in Figure7. Both fitted models yield well-behaved predictions for the responses Y (%) and q (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).Figure 7
Parity plot showing the agreement between experimental and calculated responses: (a) color removal efficiency and (b) adsorption capacity.
(a)
(b)The multiple regression models with actual variables have been developed by the substitution technique and may be written as follows:(7)
Y
^
=
31.205
+
0.168
t
-
0.628
C
0
+
26.63
SD
-
5.103
×
1
0
-
4
t
2
-
2.696
SD
2
+
0.045
C
0
×
SD
,
q
^
=
4.66
+
0.04
t
+
0.24
C
0
-
2.24
SD
-
1.13
×
1
0
-
4
t
2
-
1.68
×
1
0
-
3
C
0
2
+
0.12
SD
2
⋯
-
2.35
×
1
0
-
3
t
×
SD
+
8.51
×
1
0
-
3
C
0
×
SD
,subject to 14
≤
t
≤
196 (min); 13.6
≤
C
0
≤
86.5 (mg/L); 0.57
≤
S
D
≤
5.43 (g/L).The 3D plots of response surfaces showing the coupling effects of factors on responses are illustrated in Figures8-9.Figure 8
Response surface plot showing the coupling effects of SD andC
0 factors (at t
=
105 min) on (a) dye removal efficiency Y
^ (%) and (b) adsorption capacity q
^ (mg/g).
(a)
(b)Figure 9
Response surface plot showing the coupling effects oft and SD factors (at C
0
=
50 mg/L) on (a) dye removal efficiency Y
^ (%) and (b) adsorption capacity q
^ (mg/g).
(a)
(b)Figure8(a) shows that the increment of sorbent dosage (SD) variable leads to the increasing of the color removal efficiency, Y
^ (%). By contrast, the greater the dye concentration (C
0) is, the less the removal efficiency is. An interaction effect is observed between these factors, C
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 C
0. According to Figure 8(b), the increment of CR concentration (C
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 Figure9(a), the increasing of both contact time and sorbent dosage leads to higher values of color removal efficiency, Y
^ (%). 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.


### 3.7. 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 NiFe2O4) has been approached via two strategies, that is, single-objective optimization (case  1) and multiobjective optimization (case  2).


#### 3.7.1. Single-Objective Optimization (Case  1)

In this case, the objective was to maximize only the color removal efficiencyY
^ (%) since this response was considered a priority from the environmental standpoint. The model-based optimization notation, for case  1, is given by(8)
max
⁡
Y
^
x
1
,
x
2
,
x
3
,
subject to:
x
i
∈
-
α
,
α
,
∀
i
=
1,3
¯
.In this study, the genetic algorithm (GA) was employed to solve the single-objective optimization problem given by (8). To this end, theoptim_ga solver was used, implemented in SciLab 5.4.1 open-source software. The optimal solution in terms of actual values of factors is t
∗
=
165 min, C
0
∗
=
13.6 mg/L, and S
D
∗
=
5.05 g/L (Table 8). Under such conditions, the predicted response is Y
^
=
105.314, and the observed response is Y
=
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 q
=
2.284 mg/g (experimental) (Table 8).Table 8
Experimental confirmation of optimal point determined by GA  (Case  1: single-objective optimization).
t
∗, (min)
C
0
∗, (mg/L)
S
D
∗, (g/L)
Y
^ predicted
q
^ predicted
Y, (%) observed
q, (mg/g) observed
165
13.6
5.05
105.314
1.728
98.995
2.284
Note. The optimal solution in terms of coded variables is x
∗ = [
0.7957
;
-
1.2150
;
1.0254
]
T.


#### 3.7.2. Multiobjective Optimization (Case  2)

For case  2, the objective was to maximize simultaneously both the color removal efficiencyY
^ (%) 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, Y
^ 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 C
0, for the fixed contact time close to the superior level (i.e., t
=
180 min). The multicriteria optimization problem may be written using the vector optimization notation as follows:(9)
max
⁡
Y
^
x
,
q
^
x
T
,
x
=
x
1
,
x
2
,
x
3
T
,
x
i
∈
-
α
,
α
,
∀
i
=
1,3
¯
.Figure 10
Overlap contour-lines plot of two response functionsY
^ and q
^ depending on the values of factors SD (g/L) and C
0 (mg/L) for a constant level of t
=
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 asnondominant solutions orPareto population (optimality). A decision-maker has to analyze the Pareto population and look for the best choice according to his priorities [35]. To solve the vector optimization problem (9), thenondominated sorting genetic algorithm-II (NSGA-II) [36] was employed using the solveroptim_nsga2 included in SciLab-5.4.1 program. The results of optimization are shown in Figure 11.Figure 11
The results of NSGA-II optimization presented in the objective space: (a) initial population and (b) Pareto population.
(a)
(b)The algorithm (NSGA-II) has randomly generated the initial population of 100 individual solutions inside of the valid region (Figure11(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 (Y
^ 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 Y
^ (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 functiond
k for each considered response y
k by converting the values of the response into the nondimensional scale ranging from 0 to 1. For the maximization of a response y
k, the corresponding individual desirability function d
k is of the-larger-the-best (LTB) type, and the conversion scheme can be written as [37]:(10)
LTB-desirability:
d
k
=
0
,
if
y
k
≤
y
k
-
,
y
k
-
y
k
-
y
k
+
-
y
k
-
W
k
,
if
y
k
-
≤
y
k
≤
y
k
+
,
1
,
if
y
k
≥
y
k
+
,where y
k is the value of the response with index k, y
k
- is the lower-bound limit of the response, y
k
+ is the upper-bound limit of the response, and W
k is the weight coefficient indicating the importance of that response. The global desirability D has been determined as the geometric mean of individual desirability functions d
k [37, 38]:(11)
D
=
∏
k
=
1
z
d
k
1
/
∑
k
W
k
,where z 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 (D
=
0.7958) is attained for Y
^
=
93.894 and 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 t
∗
=
152 min, C
0
∗
=
39 mg/L, and S
D
∗
=
4.59 g/L. The responses confirmed by experiment under such conditions are Y
=
94.579 (%) and q
=
6.450 mg/g.Table 9
Experimental confirmation of optimal point determined by NSGA-II and DFA (Case  2: multiobjective optimization).
t
∗, (min)
C
0
∗, (mg/L)
S
D
∗, (g/L)
Y
^ predict.
q
^ predict.
D desirability
Y, (%) exper.
q, (mg/g) exper.
152
39.0
4.59
93.894
7.290
0.7958
94.579
6.450
Note. The optimal solution in terms of coded variables is x
∗ = [
0.6271
;
-
0.3658
;
0.7959
]
T.Figure 12
Scatter 3D plot of Pareto population showing the global desirability into the objective space: desirability (D) versus adsorption capacity (q
^) and color removal efficiency (Y
^).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.


## 3.1. Characterization of MFe2O4 Spinel Ferrites Sorbents

X-ray diffraction patterns of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites are shown in Figure 1. For all the analyzed materials, the most intense peaks characteristic for spinel structure were observed at 2
θ of about 35°. All peaks observed in the XRD patterns correspond to the face-centered cubic structure of pure spinels according to JCPDS cards number 44-1485, number 22-1086, and number 22-1012.Figure 1
XRD patterns of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites.The crystallite size (D
c, nm) for each sample was calculated by line broadening of the most intense (311) diffraction peak using Debye-Scherrer formula [7] (see Table 1). According to Table 1, the values of crystallite size depend on M2+ cation nature. The smallest nanosized crystallite value was found for nickel ferrite (30.6 nm), followed by zinc ferrite (34.4 nm), and cobalt containing ferrite (36.7 nm), respectively.Table 1
Summary of the experimental and calculated data obtained for MFe2O4 (M = Ni, Co, and Zn) spinel ferrites.
Spinel ferrite
a2θ
311 (degrees)
a
D
c (nm)
b
d
p
(nm)
NiFe2O4
35.68803
30.6
46
CoFe2O4
35.53905
36.7
69
ZnFe2O4
35.27044
34.4
101
aDiffraction angle (θ
311) and crystallite size (D
c), data from XRD; bparticle size, data from TEM.The FTIR spectra, in 4000–350 cm−1 range for MFe2O4 (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 ZnFe2O4 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].Figure 2
FTIR spectra of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites.The representative TEM micrographs of MFe2O4 samples are illustrated in Figure 3.Figure 3
TEM micrographs of MFe2O4 (M = Ni, Co, and Zn) spinel ferrites (a, b, and c) and images (d, e) of magnetic separation of CoFe2O4 spinel ferrite from the aqueous solution with a permanent magnet: (d) before separation and (e) after magnetic separation.The average particle sizes (d
p, 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 CoFe2O4 spinel ferrite from the aqueous solution is shown in Figure 3(d) (before separation) and Figure 3(e) (after magnetic separation).


## 3.2. 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 Figure4. The highest adsorption performances (in terms of both color removal efficiency and adsorption capacity) were attributed to the adsorbent NiFe2O4 followed by CoFe2O4. The spinel ferrite ZnFe2O4 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 NiFe2O4 and CoFe2O4 with better sorption performances were used for the kinetics and isotherms studies.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:C
0
=
50 mg/L, SD = 1 g/L, t
=
180 min, and T
=
293 K.


## 3.3. Adsorption Kinetics

The adsorptions of CR onto NiFe2O4 and CoFe2O4 ferrites were studied versus time at 293 K. Figure 5 shows the amount of the dye adsorbed q
t (mg/g) against the contact time t (min) for two sorbent materials, that is, CoFe2O4 (Figure 5(a)) and NiFe2O4 (Figure 5(b)).Figure 5
Adsorption kinetics data for Congo-Red removal by ferrite sorbents and comparison of kinetic models: (a) adsorbent CoFe2O4 and (b) adsorbent NiFe2O4; experimental conditions: C
0
=
50 mg/L, SD = 1 g/L and T
=
293 K.
(a)
(b)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.Table 2
Kinetic models and the parameters for the adsorption kinetics.
Abbreviation
Kinetic model (rate equation)
Kinetic model  (nonlinear equation)
Parameters
PFO
d
q
t
d
t
=
k
1
q
e
-
q
t
q
t
=
q
e
1
-
e
-
k
1
t
q
e, k
1
PSO
d
q
t
d
t
=
k
2
q
e
-
q
t
2
q
t
=
k
2
q
e
2
t
1
+
k
2
q
e
t
q
e, k
2
PnO
d
q
t
d
t
=
k
n
q
e
-
q
t
n
q
t
=
q
e
-
n
-
1
k
n
t
+
q
e
(
1
-
n
)
1
/
(
1
-
n
)
q
e, k
n, and n
MOE
d
q
t
d
t
=
∑
i
K
i
q
e
-
q
t
i
q
t
=
q
e
1
-
e
-
K
1
t
1
-
K
2
q
e
/
(
K
1
+
K
2
q
e
)
e
-
K
1
t
q
e, K
1, and K
2
ID
d
q
t
d
t
=
k
d
2
t
q
t
=
k
d
t
+
J
k
d, JTo determine the goodness-of-fit between models’ predictions and experimental data the average relative error (ARE) function has been calculated [25]:(3)
ARE
=
100
N
∑
j
=
1
N
q
j
calc
-
q
j
exper
q
j
exper
,where q
exper denotes the experimental adsorption capacity (mg/g), q
calc is the calculated adsorption capacity (mg/g), N is the number of data within the experimental curve, and j is the integer index.The parameters of kinetic models have been determined by Gauss-Newton nonlinear regression method usingnlinfit matlab solver, and their values are reported in Table 3. The average relative error (ARE) function are also summarized in Table 3.Table 3
Kinetic parameters for Congo-Red adsorption onto spinel ferrites, determined by the nonlinear regression method.
Kinetic model and parameters
Adsorbent: CoFe2O4
Adsorbent: NiFe2O4
PFO
q
e
=
9.6461 (mg/g)
q
e
=
11.1255 (mg/g)
k
1
=
0.0527
k
1
=
0.0623
ARE  = 4.307
ARE = 2.605
PSO
q
e
=
10.5168 (mg/g)
q
e
=
11.9730 (mg/g)
k
2
=
0.0080
k
2
=
0.0089
ARE = 0.916
ARE = 0.941
PnO
q
e
=
11.198 (mg/g)
q
e
=
11.603 (mg/g)
k
n
=
2.2909
×
10
-
3
k
n
=
1.8229
×
10
-
2
n
=
2.5561
n
=
1.6539
ARE  = 0.503
ARE  = 0.745
MOE
q
e
=
10.517 (mg/g)
q
e
=
11.4637 (mg/g)
K
1
=
3.3965
×
10
-
6
K
1
=
0.0153
K
2
=
7.9652
×
10
-
3
K
2
=
0.0076
ARE  = 0.938
ARE  = 0.893
ID
k
d
=
0.5369
k
d
=
0.5879
J
=
3.2066
J
=
4.1416
ARE  = 10.624
ARE  = 11.443As one can see from Figure5, 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 n
=
2.556 (for CoFe2O4) and n
=
1.654 (for NiFe2O4). 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 CoFe2O4 and NiFe2O4, respectively. The intraparticle diffusion (ID) model shows some discrepancy between the predicted data and experimental observations with the errors of 10-11%. The kinetic data (Figure 5) suggest that NiFe2O4 ferrite is superior to CoFe2O4 for CR adsorption owing to higher values of adsorption capacity observed against the time.


## 3.4. Adsorption Isotherms

The adsorption of CR onto NiFe2O4 and CoFe2O4 has been studied against equilibrium concentration at different temperatures. From kinetic studies, the contact time has been fixed at t
=
180 min to attain the stationary adsorption (equilibrium). Figure 6 shows the amount of dye adsorbed at equilibrium q
e (mg/g) versus the equilibrium concentration C
e (mg/L) for both sorbent materials CoFe2O4 (Figure 6(a)) and NiFe2O4 (Figure 6(b)). As one can see, the adsorption of CR goes up with increment of equilibrium concentration for both cases (CoFe2O4 and NiFe2O4).Figure 6
Adsorption isotherms for Congo-Red removal by ferrite sorbents fitted by the Freundlich (solid lines) and Langmuir (dot lines) models: (a) adsorbent CoFe2O4 and (b) adsorbent NiFe2O4; experimental conditions: SD = 1 g/L and t
=
180 min.
(a)
(b)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]:(4)
q
e
=
K
F
C
e
1
/
n
F
,where C
e (mg/L) is the dye concentration in the liquid at equilibrium, q
e (mg/g) is the amount of dye adsorbed at equilibrium, K
F
[
(
m
g
/
g
)
(
L
/
g
)
1
/
n
F
] is the Freundlich constant, and n
F 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]:(5)
q
e
=
q
m
K
L
C
e
1
+
K
L
C
e
,where q
m (mg/g) is the amount of the solute adsorbed for a complete monolayer and K
L (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 CoFe2O4 and NiFe2O4.Table 4
Isotherm parameters for Congo-Red adsorption onto spinel ferrites.
Isotherm
Adsorbent: CoFe2O4
Adsorbent: NiFe2O4
T = 293 K
T = 333 K
T = 293 K
T = 333 K
Freundlich
K
F
=
4.3932
K
F
=
3.5983
K
F
=
5.7119
K
F
=
5.7563
K
F  (mg/g)
(L/g)
1
/
n
F
n
F
=
4.0025
n
F
=
5.4013
n
F
=
4.1917
n
F
=
5.2030
n
F
ARE = 3.21
ARE = 4.71
ARE = 2.79
ARE = 3.30
Langmuir
K
L
=
0.1460
K
L
=
0.2751
K
L
=
0.1746
K
L
=
0.3643
K
L (L/mg)
q
m
=
14.059
q
m
=
8.224
q
m
=
17.133
q
m
=
13.218
q
m (mg/g)
ARE = 11.72
ARE = 10.43
ARE = 12.10
ARE = 9.97
D-R
q
d
=
0.0319
q
d
=
0.0153
q
d
=
0.0380
q
d
=
0.0265
q
d (g/g)
K
D
=
0.0021
K
D
=
0.0010
K
D
=
0.0020
K
D
=
0.0011
K
D (mol2 kJ−2)
E
S
=
15.335
E
S
=
21.936
E
S
=
15.669
E
S
=
21.225
E
S (kJ mol−1)
ARE  = 4.78
ARE  = 5.51
ARE  = 4.05
ARE  = 3.69Figure6 disclosed that the adsorption of CR onto ferrites decreased with increment of temperature. This effect is more pronounced for CoFe2O4 and less significant for NiFe2O4 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 Table4. Based on D-R isotherm analysis, the mean free energy of adsorption, E
S (kJ mol−1), has been calculated [30, 31]. In our case, the values of mean free energy E
S were higher than 8 (kJ mol−1) (Table 4) suggesting that the uptake of CR onto ferrite materials was based on chemical adsorption.


## 3.5. 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 CoFe2O4 sorbent were found to be Δ
G
=
-
30.861
±
2.794 kJ/mol, Δ
H
=
12.828 kJ/mol, and Δ
S
=
139.579
±
0.112 J/mol K. For CR adsorption onto NiFe2O4 sorbent, the values of the thermodynamic parameters were Δ
G
=
-
31.875
±
3.040 kJ/mol, Δ
H
=
15.301 kJ/mol, and Δ
S
=
150.725
±
2.142 J/mol K. The negative values of free energy Δ
G revealed the spontaneous nature of the adsorption process. The positive enthalpy indicated the endothermic effect of the adsorption. The positive values of entropy Δ
S disclosed the increasing of randomness at the solid/liquid interface, suggesting the affinity of CR molecules on the surface of ferrite adsorbents.


## 3.6. Response Surface Modeling of the Adsorption Process

Due to its highest sorption performances, the material NiFe2O4 was selected for modeling and optimization of the adsorption process. To this end, the response surface methodology (RSM) [32–34] 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 timet (min), initial dye concentration C
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.Table 5
Input variables and their coded and actual values used for adsorption experiments.
Input variables (factors)
Coded variables
Coded levels versus actual values
−α
-
1
0
+1
+α
Contact time,t (min)
x
1
14
30
105
180
196
Initial dye concentration,C
0 (mg/L)
x
2
13.6
20.0
50.0
80.0
86.5
Sorbent dosage (NiFe2O4), SD (g/L)
x
3
0.57
1.00
3.00
5.00
5.43
Note:α
=
1.215 (value of axial point for orthogonal CCD in case of three factors).For the investigation of the adsorption process, the central composite design (CCD) of orthogonal type was employed (Table6). Two responses were determined experimentally for each run, that is, color removal efficiency Y (%) and adsorption capacity q (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 [32–34]. The developed fitted models can be presented for coded variables (x
1, x
2, and x
3) as follows:(6)
Y
^
=
74.15
+
4.569
x
1
-
14.82
x
2
+
25.38
x
3
-
2.871
x
1
2
-
10.785
x
3
2
+
2.685
x
2
x
3
,
q
^
=
10.489
+
0.83
x
1
+
2.936
x
2
-
2.719
x
3
-
0.637
x
1
2
-
1.51
x
2
2
+
0.467
x
3
2
-
0.353
x
1
x
3
+
0.511
x
2
x
3
,subject to x
i
∈
-
α
,
α, for all i
=
1,3
¯.Table 6
Central composite design (CCD) of orthogonal type used for adsorption experiments (CR onto NiFe2O4).
Factors (controllable input variables)
Responses (experimental values)
Run
t, (min)
C
0, (mg/L)
SD, (g/L)
x
1
t
x
2
C
0
x
3
SD
Y, (%)
q, (mg/g)
1
+1
180
+1
80.0
+1
5.00
79.057
10.209
2
−1
30
+1
80.0
+1
5.00
67.367
8.628
3
+1
180
−1
20.0
+1
5.00
97.143
3.184
4
−1
30
−1
20.0
+1
5.00
95.035
3.138
5
+1
180
+1
80.0
−1
1.00
22.026
14.634
6
−1
30
+1
80.0
−1
1.00
18.094
12.117
7
+1
180
−1
20.0
−1
1.00
59.247
10.127
8
−1
30
−1
20.0
−1
1.00
48.110
8.195
9
+α
196
0
50.0
0
3.00
77.902
10.868
10
−α
14
0
50.0
0
3.00
60.478
8.390
11
0
105
+α
86.5
0
3.00
54.426
12.956
12
0
105
−α
13.6
0
3.00
95.025
3.727
13
0
105
0
50.0
+α
5.43
93.258
7.198
14
0
105
0
50.0
−α
0.57
21.775
15.317
15
0
105
0
50.0
0
3.00
73.747
10.244
16
0
105
0
50.0
0
3.00
73.305
10.350The significance of all regression coefficients in (6) was estimated using the Student t-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 P values are less than 0.0001 both models are statistically significant. The fact that the values of the coefficients of determination R
2 are high (close to 1) indicates that the observed responses are quite close to those predicted.Table 7
Analysis of variance (ANOVA) for the significance of the multiple regression models.
Source
DFa
SSb
MSc
F-value
P value
R
2
R
adj
2
Y-response (color removal efficiency)
Model
6
1.037 × 104
1.728 × 103
105.139
< 0.0001
0.986
0.977
Residual
9
147.912
16.435
Total
15
1.052 × 104
q-response (adsorption capacity)
Model
8
199.745
24.968
31.700
< 0.0001
0.973
0.942
Residual
7
5.513
0.788
Total
15
205.259
aDegree of freedom; bsum of squares; cmean square.The goodness-of-fits between predictions and experimental observations are illustrated in Figure7. Both fitted models yield well-behaved predictions for the responses Y (%) and q (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).Figure 7
Parity plot showing the agreement between experimental and calculated responses: (a) color removal efficiency and (b) adsorption capacity.
(a)
(b)The multiple regression models with actual variables have been developed by the substitution technique and may be written as follows:(7)
Y
^
=
31.205
+
0.168
t
-
0.628
C
0
+
26.63
SD
-
5.103
×
1
0
-
4
t
2
-
2.696
SD
2
+
0.045
C
0
×
SD
,
q
^
=
4.66
+
0.04
t
+
0.24
C
0
-
2.24
SD
-
1.13
×
1
0
-
4
t
2
-
1.68
×
1
0
-
3
C
0
2
+
0.12
SD
2
⋯
-
2.35
×
1
0
-
3
t
×
SD
+
8.51
×
1
0
-
3
C
0
×
SD
,subject to 14
≤
t
≤
196 (min); 13.6
≤
C
0
≤
86.5 (mg/L); 0.57
≤
S
D
≤
5.43 (g/L).The 3D plots of response surfaces showing the coupling effects of factors on responses are illustrated in Figures8-9.Figure 8
Response surface plot showing the coupling effects of SD andC
0 factors (at t
=
105 min) on (a) dye removal efficiency Y
^ (%) and (b) adsorption capacity q
^ (mg/g).
(a)
(b)Figure 9
Response surface plot showing the coupling effects oft and SD factors (at C
0
=
50 mg/L) on (a) dye removal efficiency Y
^ (%) and (b) adsorption capacity q
^ (mg/g).
(a)
(b)Figure8(a) shows that the increment of sorbent dosage (SD) variable leads to the increasing of the color removal efficiency, Y
^ (%). By contrast, the greater the dye concentration (C
0) is, the less the removal efficiency is. An interaction effect is observed between these factors, C
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 C
0. According to Figure 8(b), the increment of CR concentration (C
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 Figure9(a), the increasing of both contact time and sorbent dosage leads to higher values of color removal efficiency, Y
^ (%). 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.


## 3.7. 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 NiFe2O4) has been approached via two strategies, that is, single-objective optimization (case  1) and multiobjective optimization (case  2).


### 3.7.1. Single-Objective Optimization (Case  1)

In this case, the objective was to maximize only the color removal efficiencyY
^ (%) since this response was considered a priority from the environmental standpoint. The model-based optimization notation, for case  1, is given by(8)
max
⁡
Y
^
x
1
,
x
2
,
x
3
,
subject to:
x
i
∈
-
α
,
α
,
∀
i
=
1,3
¯
.In this study, the genetic algorithm (GA) was employed to solve the single-objective optimization problem given by (8). To this end, theoptim_ga solver was used, implemented in SciLab 5.4.1 open-source software. The optimal solution in terms of actual values of factors is t
∗
=
165 min, C
0
∗
=
13.6 mg/L, and S
D
∗
=
5.05 g/L (Table 8). Under such conditions, the predicted response is Y
^
=
105.314, and the observed response is Y
=
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 q
=
2.284 mg/g (experimental) (Table 8).Table 8
Experimental confirmation of optimal point determined by GA  (Case  1: single-objective optimization).
t
∗, (min)
C
0
∗, (mg/L)
S
D
∗, (g/L)
Y
^ predicted
q
^ predicted
Y, (%) observed
q, (mg/g) observed
165
13.6
5.05
105.314
1.728
98.995
2.284
Note. The optimal solution in terms of coded variables is x
∗ = [
0.7957
;
-
1.2150
;
1.0254
]
T.


### 3.7.2. Multiobjective Optimization (Case  2)

For case  2, the objective was to maximize simultaneously both the color removal efficiencyY
^ (%) 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, Y
^ 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 C
0, for the fixed contact time close to the superior level (i.e., t
=
180 min). The multicriteria optimization problem may be written using the vector optimization notation as follows:(9)
max
⁡
Y
^
x
,
q
^
x
T
,
x
=
x
1
,
x
2
,
x
3
T
,
x
i
∈
-
α
,
α
,
∀
i
=
1,3
¯
.Figure 10
Overlap contour-lines plot of two response functionsY
^ and q
^ depending on the values of factors SD (g/L) and C
0 (mg/L) for a constant level of t
=
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 asnondominant solutions orPareto population (optimality). A decision-maker has to analyze the Pareto population and look for the best choice according to his priorities [35]. To solve the vector optimization problem (9), thenondominated sorting genetic algorithm-II (NSGA-II) [36] was employed using the solveroptim_nsga2 included in SciLab-5.4.1 program. The results of optimization are shown in Figure 11.Figure 11
The results of NSGA-II optimization presented in the objective space: (a) initial population and (b) Pareto population.
(a)
(b)The algorithm (NSGA-II) has randomly generated the initial population of 100 individual solutions inside of the valid region (Figure11(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 (Y
^ 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 Y
^ (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 functiond
k for each considered response y
k by converting the values of the response into the nondimensional scale ranging from 0 to 1. For the maximization of a response y
k, the corresponding individual desirability function d
k is of the-larger-the-best (LTB) type, and the conversion scheme can be written as [37]:(10)
LTB-desirability:
d
k
=
0
,
if
y
k
≤
y
k
-
,
y
k
-
y
k
-
y
k
+
-
y
k
-
W
k
,
if
y
k
-
≤
y
k
≤
y
k
+
,
1
,
if
y
k
≥
y
k
+
,where y
k is the value of the response with index k, y
k
- is the lower-bound limit of the response, y
k
+ is the upper-bound limit of the response, and W
k is the weight coefficient indicating the importance of that response. The global desirability D has been determined as the geometric mean of individual desirability functions d
k [37, 38]:(11)
D
=
∏
k
=
1
z
d
k
1
/
∑
k
W
k
,where z 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 (D
=
0.7958) is attained for Y
^
=
93.894 and 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 t
∗
=
152 min, C
0
∗
=
39 mg/L, and S
D
∗
=
4.59 g/L. The responses confirmed by experiment under such conditions are Y
=
94.579 (%) and q
=
6.450 mg/g.Table 9
Experimental confirmation of optimal point determined by NSGA-II and DFA (Case  2: multiobjective optimization).
t
∗, (min)
C
0
∗, (mg/L)
S
D
∗, (g/L)
Y
^ predict.
q
^ predict.
D desirability
Y, (%) exper.
q, (mg/g) exper.
152
39.0
4.59
93.894
7.290
0.7958
94.579
6.450
Note. The optimal solution in terms of coded variables is x
∗ = [
0.6271
;
-
0.3658
;
0.7959
]
T.Figure 12
Scatter 3D plot of Pareto population showing the global desirability into the objective space: desirability (D) versus adsorption capacity (q
^) and color removal efficiency (Y
^).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.


## 3.7.1. Single-Objective Optimization (Case  1)

In this case, the objective was to maximize only the color removal efficiencyY
^ (%) since this response was considered a priority from the environmental standpoint. The model-based optimization notation, for case  1, is given by(8)
max
⁡
Y
^
x
1
,
x
2
,
x
3
,
subject to:
x
i
∈
-
α
,
α
,
∀
i
=
1,3
¯
.In this study, the genetic algorithm (GA) was employed to solve the single-objective optimization problem given by (8). To this end, theoptim_ga solver was used, implemented in SciLab 5.4.1 open-source software. The optimal solution in terms of actual values of factors is t
∗
=
165 min, C
0
∗
=
13.6 mg/L, and S
D
∗
=
5.05 g/L (Table 8). Under such conditions, the predicted response is Y
^
=
105.314, and the observed response is Y
=
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 q
=
2.284 mg/g (experimental) (Table 8).Table 8
Experimental confirmation of optimal point determined by GA  (Case  1: single-objective optimization).
t
∗, (min)
C
0
∗, (mg/L)
S
D
∗, (g/L)
Y
^ predicted
q
^ predicted
Y, (%) observed
q, (mg/g) observed
165
13.6
5.05
105.314
1.728
98.995
2.284
Note. The optimal solution in terms of coded variables is x
∗ = [
0.7957
;
-
1.2150
;
1.0254
]
T.


## 3.7.2. Multiobjective Optimization (Case  2)

For case  2, the objective was to maximize simultaneously both the color removal efficiencyY
^ (%) 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, Y
^ 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 C
0, for the fixed contact time close to the superior level (i.e., t
=
180 min). The multicriteria optimization problem may be written using the vector optimization notation as follows:(9)
max
⁡
Y
^
x
,
q
^
x
T
,
x
=
x
1
,
x
2
,
x
3
T
,
x
i
∈
-
α
,
α
,
∀
i
=
1,3
¯
.Figure 10
Overlap contour-lines plot of two response functionsY
^ and q
^ depending on the values of factors SD (g/L) and C
0 (mg/L) for a constant level of t
=
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 asnondominant solutions orPareto population (optimality). A decision-maker has to analyze the Pareto population and look for the best choice according to his priorities [35]. To solve the vector optimization problem (9), thenondominated sorting genetic algorithm-II (NSGA-II) [36] was employed using the solveroptim_nsga2 included in SciLab-5.4.1 program. The results of optimization are shown in Figure 11.Figure 11
The results of NSGA-II optimization presented in the objective space: (a) initial population and (b) Pareto population.
(a)
(b)The algorithm (NSGA-II) has randomly generated the initial population of 100 individual solutions inside of the valid region (Figure11(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 (Y
^ 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 Y
^ (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 functiond
k for each considered response y
k by converting the values of the response into the nondimensional scale ranging from 0 to 1. For the maximization of a response y
k, the corresponding individual desirability function d
k is of the-larger-the-best (LTB) type, and the conversion scheme can be written as [37]:(10)
LTB-desirability:
d
k
=
0
,
if
y
k
≤
y
k
-
,
y
k
-
y
k
-
y
k
+
-
y
k
-
W
k
,
if
y
k
-
≤
y
k
≤
y
k
+
,
1
,
if
y
k
≥
y
k
+
,where y
k is the value of the response with index k, y
k
- is the lower-bound limit of the response, y
k
+ is the upper-bound limit of the response, and W
k is the weight coefficient indicating the importance of that response. The global desirability D has been determined as the geometric mean of individual desirability functions d
k [37, 38]:(11)
D
=
∏
k
=
1
z
d
k
1
/
∑
k
W
k
,where z 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 (D
=
0.7958) is attained for Y
^
=
93.894 and 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 t
∗
=
152 min, C
0
∗
=
39 mg/L, and S
D
∗
=
4.59 g/L. The responses confirmed by experiment under such conditions are Y
=
94.579 (%) and q
=
6.450 mg/g.Table 9
Experimental confirmation of optimal point determined by NSGA-II and DFA (Case  2: multiobjective optimization).
t
∗, (min)
C
0
∗, (mg/L)
S
D
∗, (g/L)
Y
^ predict.
q
^ predict.
D desirability
Y, (%) exper.
q, (mg/g) exper.
152
39.0
4.59
93.894
7.290
0.7958
94.579
6.450
Note. The optimal solution in terms of coded variables is x
∗ = [
0.6271
;
-
0.3658
;
0.7959
]
T.Figure 12
Scatter 3D plot of Pareto population showing the global desirability into the objective space: desirability (D) versus adsorption capacity (q
^) and color removal efficiency (Y
^).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.


## 4. Conclusions

In this work, the nanosized spinel ferrites MFe2O4 (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 NiFe2O4 followed by CoFe2O4. The adsorption kinetics disclosed that the data were best fitted by PnO model, suggesting that the most appropriate orders for the rate equations were n
=
1.654 (for NiFe2O4) and n
=
2.556 (for CoFe2O4). 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 CoFe2O4 and 17.13 mg/g for NiFe2O4. The values of mean free energy E
S determined from Dubinin-Radushkevich (D-R) isotherm suggested the chemical adsorption mechanism.The response surface methodology was employed for modeling and optimization of the process to enhance CR adsorption onto NiFe2O4. The optimum point resulted from single-objective optimization was confirmed by experiment giving the maximal value of color removal efficiency of Y
=
98.995
%. The multiobjective optimization done by NSGA-II and DFA methods led to the improved values of both color removal efficiency and adsorption capacity, that is, 94.579% and 6.45 mg/g, respectively.



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*Source: 713802-2015-06-07.xml*