Process Optimization by a Response Surface Methodology for Adsorption of Congo Red Dye onto Exfoliated Graphite-Decorated MnFe 2 O 4 Nanocomposite: The Pivotal Role of Surface Chemistry

: Natural graphite, a locally available, eco-friendly, and low-cost carbonaceous source, can be easily transformed into exfoliated graphite (EG) with many surface functional groups via a chemical oxidation route. Combination between EG and magnetic MnFe 2 O 4 is a promising strategy to create a hybrid kind of nanocomposite (EG@MnFe 2 O 4 ) for the e ﬃ cient adsorptive removal of Congo red (CR) dye from water. Here, we reported the facile synthesis and characterization of chemical bonds of EG@MnFe 2 O 4 using several techniques such as Fourier-transform infrared spectroscopy (FT-IR), and X-ray photoelectron spectroscopy (XPS). In particular, the quantity method by Boehm titration was employed to identify the content of functional groups: Carboxylic acid (0.044 mmol / g), phenol (0.032 mmol / g), lactone (0.020 mmol / g), and total base (0.0156 mmol / g) on the surface of EG@MnFe 2 O 4 . Through the response surface methodology-optimized models, we found a clear di ﬀ erence in the adsorption capacity between EG-decorated MnFe 2 O 4 (62.0 mg / g) and MnFe 2 O 4 without EG decoration (11.1 mg / g). This result was also interpreted via a proposed mechanism to elucidate the contribution of surface functional groups of EG@MnFe 2 O 4 to adsorption e ﬃ ciency towards CR dye.


Introduction
Over the past decades, numerous synthetic dyes have been discovered, developed, and applied in industrial fields, such as textile, paper, pharmaceuticals, and food [1]. It is understandable that the increasing consumption of dyes can result in a vast volume of pollutants. Without any pretreatment measures, disposals of such contaminants could be threatening for the aquatic systems due to, for example, depletion of the penetration of light or inhibition of photosynthetic processes that may be caused by such dyes [2]. Among the emergent dyes, Congo red (CR) in terms of molecular structure presents a kind of complex azo compound constituting of many carcinogenic aromatic rings, amines, and imines ( Figure 1) [3]. Under appropriate aerobic reactions, these CR molecules are likely to react/combine with functional groups on the surface of other molecular systems in the body, raising potential risks of genetic mutation (GM) [4,5]. Therefore, treatment of persistent and non-degradable CR molecules should be a priority regardless of the huge challenges relating to cost and technologies. It has been reported that exfoliated graphene (EG), a chemically modified compound from natural graphite under oxidative conditions, can possess a series of functional groups on the surface [6][7][8]. Zheng-Hong et al. found the surface chemistry of EG containing hydroxyl (-OH), carbonyl (-C=O), and carboxylic acid (-COOH) groups [9]. Wang et al. also asserted that these groups played the main role in tailoring the chemisorption towards toxic dyes [10]. However, the main drawback of EG material is their reliance on its difficult separation from the aqueous solution during posttreatment. It is therefore reasonable to introduce a magnetic component (e.g., iron-based particles) to the EG structure, making it integrated magnetically. For standards of high magnetism, ecofriendliness, chemical stability, and tunable synthesis, MnFe2O4 is a suitable additive [11][12][13]. Combining mentioned precursors to create a novel type of EG-decorated MnFe2O4 nanocomposite affords opportunities to utilize the materials in adsorption applications.
Here, a prevalent approach to investigate and optimize the effect of input parameters, namely, response surface methodology (RSM), is adopted. The main variables consist of solution pH, CR concentration, and contact time. We attempted to interpret the optimized adsorption results based on a proposed mechanism with the contribution of surface chemistry (i.e., surface functional groups), which was analyzed by physical techniques (e.g., Fourier-transform infrared spectroscopy (FT-IR), X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray spectroscopy (EDS), and quantity of surface functional groups via Boehm titrations. Scheme 1 illustrates the total process for adsorption of CR dye onto exfoliated graphite-decorated MnFe2O4 nanocomposite. It has been reported that exfoliated graphene (EG), a chemically modified compound from natural graphite under oxidative conditions, can possess a series of functional groups on the surface [6][7][8]. Zheng-Hong et al. found the surface chemistry of EG containing hydroxyl (-OH), carbonyl (-C=O), and carboxylic acid (-COOH) groups [9]. Wang et al. also asserted that these groups played the main role in tailoring the chemisorption towards toxic dyes [10]. However, the main drawback of EG material is their reliance on its difficult separation from the aqueous solution during post-treatment. It is therefore reasonable to introduce a magnetic component (e.g., iron-based particles) to the EG structure, making it integrated magnetically. For standards of high magnetism, eco-friendliness, chemical stability, and tunable synthesis, MnFe 2 O 4 is a suitable additive [11][12][13]. Combining mentioned precursors to create a novel type of EG-decorated MnFe 2 O 4 nanocomposite affords opportunities to utilize the materials in adsorption applications.
Here, a prevalent approach to investigate and optimize the effect of input parameters, namely, response surface methodology (RSM), is adopted. The main variables consist of solution pH, CR concentration, and contact time. We attempted to interpret the optimized adsorption results based on a proposed mechanism with the contribution of surface chemistry (i.e., surface functional groups), which was analyzed by physical techniques (e.g., Fourier-transform infrared spectroscopy (FT-IR), X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray spectroscopy (EDS), and quantity of surface functional groups via Boehm titrations. Scheme 1 illustrates the total process for adsorption of CR dye onto exfoliated graphite-decorated MnFe 2 O 4 nanocomposite.

Chemicals and Instruments
The chemicals were commercially purchased from Merck (Kenilworth, New Jersey, USA) without any purification methods prior to the utilization. Natural graphite samples were locally purchased from Yen Bai province, Vietnam.
The D8 Advance Bruker powder diffractometer (Bruker, Billerica, MA, USA) was used to record the X-ray powder diffraction (XRD) profiles using Cu-Kα beams as excitation sources. The X-ray photoelectron spectroscopy (XPS) was performed on the ESCALab MKII spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) using Mg-Kα radiation. The characteristics of chemical bonds and functional groups were investigated using the FT-IR spectra on the Nicolet 6700 spectrophotometer (Thermo Fischer Scientific, Waltham, MA, USA). The UV-VIS spectrophotometer (Shimadzu, Kyoto, Japan) was used to determine the CR concentration at 500 nm.

Synthesis of EG
Natural graphite samples (5.0 g) was carefully added in 100 mL of mixture containing H2SO4 (96%) and H2O2 (33%) (100:7 by volume) and vigorously stirred. After the process had been finished (2 h), the solid was washed with water many times until the aqueous residual became a neutral solution. To dry the sample, the solid was placed in an oven at 110 °C overnight. The EG was formed by the microwave-assisted irradiation of the bulky powder (750 W, 10 s).

Synthesis of MnFe2O4
The production of magnetic MnFe2O4 nanoparticles was based on recent work [14]. A mixture prepared by dissolving chemicals including citric acid (93 g), ethylene glycol (140 mL), and H2O (40 mL) was heated up 80 °C beneath open air. The MnCl2·6H2O crystals (0.303 g) were slowly added into the above mixture and their temperature was allowed to rise at 130 °C during 2 h. The as-received polymeric resin was embarked on the heat-resistant furnace before being heated up at 1000 °C during 2 h. After the sample was cooled, the MnFe2O4 was stored in a desiccator.

Synthesis of EG@MnFe2O4
To prepare the EG@MnFe2O4 nanocomposite, we used the synthesized EG as a precursor. To begin with, a solution (50 mL) of citric acid (0.02 M) was slowly added into another mixture consisting of Fe(NO3)3·9H2O (0.7 g) and Mn(NO3)2·6H2O (0.25 g) in 50 mL H2O at 90 °C for 1 h under vigorous stirring. The homogeneous solution was very slowly loaded with 0.8 g EG during 30 min. Next, NH3 solution was added dropwise until a solution with pH ranging between 8 and 9 was obtained. After Scheme 1.
Process for adsorption of Congo red dye onto exfoliated graphite-decorated MnFe 2 O 4 nanocomposite.

Chemicals and Instruments
The chemicals were commercially purchased from Merck (Kenilworth, New Jersey, USA) without any purification methods prior to the utilization. Natural graphite samples were locally purchased from Yen Bai province, Vietnam.
The D8 Advance Bruker powder diffractometer (Bruker, Billerica, MA, USA) was used to record the X-ray powder diffraction (XRD) profiles using Cu-Kα beams as excitation sources. The X-ray photoelectron spectroscopy (XPS) was performed on the ESCALab MKII spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) using Mg-Kα radiation. The characteristics of chemical bonds and functional groups were investigated using the FT-IR spectra on the Nicolet 6700 spectrophotometer (Thermo Fischer Scientific, Waltham, MA, USA). The UV-VIS spectrophotometer (Shimadzu, Kyoto, Japan) was used to determine the CR concentration at 500 nm.

Synthesis of EG
Natural graphite samples (5.0 g) was carefully added in 100 mL of mixture containing H 2 SO 4 (96%) and H 2 O 2 (33%) (100:7 by volume) and vigorously stirred. After the process had been finished (2 h), the solid was washed with water many times until the aqueous residual became a neutral solution. To dry the sample, the solid was placed in an oven at 110 • C overnight. The EG was formed by the microwave-assisted irradiation of the bulky powder (750 W, 10 s).

Synthesis of MnFe 2 O 4
The production of magnetic MnFe 2 O 4 nanoparticles was based on recent work [14]. A mixture prepared by dissolving chemicals including citric acid (93 g), ethylene glycol (140 mL), and H 2 O (40 mL) was heated up 80 • C beneath open air. The MnCl 2 ·6H 2 O crystals (0.303 g) were slowly added into the above mixture and their temperature was allowed to rise at 130 • C during 2 h. The as-received polymeric resin was embarked on the heat-resistant furnace before being heated up at 1000 • C during 2 h. After the sample was cooled, the MnFe 2 O 4 was stored in a desiccator.

Synthesis of EG@MnFe 2 O 4
To prepare the EG@MnFe 2 O 4 nanocomposite, we used the synthesized EG as a precursor. To begin with, a solution (50 mL) of citric acid (0.02 M) was slowly added into another mixture consisting of Fe(NO 3 ) 3 ·9H 2 O (0.7 g) and Mn(NO 3 ) 2 ·6H 2 O (0.25 g) in 50 mL H 2 O at 90 • C for 1 h under vigorous stirring. The homogeneous solution was very slowly loaded with 0.8 g EG during 30 min. Next, NH 3 solution was added dropwise until a solution with pH ranging between 8 and 9 was obtained. After 30 min, NH 3 was repeatedly used to adjust pH to 8, and then the sample was dehydrated at 80 • C. The solid calcination was employed at 700 • C, 2 h to obtain a black magnetic sample.

Experimental Batch
Herein, EG@MnFe 2 O 4 and MnFe 2 O 4 were used as adsorbents to compare their adsorption capacity towards CR dyes. The adsorption experiments were based on the adsorbent dose (0.05 g/L) and the volume of dye solutions (100 mL). Other parameters including solution pH, CR concentration and contact time were described by experimental design with RSM. The samples in beakers (250 mL) were agitated on a shaking table (200 rpm). After the adsorption experiments had been finished, the adsorbent was separated from aqueous solution using a simple magnet and remaining concentration was measured by the UV-VIS spectrophotometer at 500 nm. The removal efficiency (H%), adsorption capacity (Q) at equilibrium period was calculated on the basis of the concentrations before and after adsorption process by the following equations: where, C o and C t are the dye concentrations (mg/L) at the initial and final periods, respectively. V and m represent the volume of solution (mL), and weight of adsorbent (g), respectively.  (Table 1). A second-order polynomial equation in which y and x represent the response and independent variables respectively could be established to describe the relationship between the adsorption capacity and experiment conditions as follows (Equation (3)). In this study, two equations were established representing CR adsorption of two materials, EG@MnFe 2 O 4 and MnFe 2 O 4

Experimental Design with RSM
where y is the predicted response; x i and x j are the independent variables (i, j = 1, 2, 3, 4 . . . k). The parameter β o is the model constant; β i is the linear coefficient; β ii is the second-order coefficient and β ij is the interaction coefficient. The total number of experiments is defined by Equation (4). The Design-Expert ® Software Version 10 (DX10) from Stat-Ease, Inc. (Minneapolis, Minnesota, USA) was used as a means of data analysis [15]. Table 1 summarizes independent factors and associated data levels used in the real experimental attempts.

Structural Characterization
The crystallinity profile of both MnFe 2 O 4 and EG@MnFe 2 O 4 was analyzed using the X-ray diffraction technique, which is presented in Figure 2. It is obvious that the MnFe 2 O 4 particles in Figure 2a

Structural Characterization
The crystallinity profile of both MnFe2O4 and EG@MnFe2O4 was analyzed using the X-ray diffraction technique, which is presented in Figure 2. It is obvious that the MnFe2O4 particles in Figure  2a offered a high degree of crystallinity with the presence of typical peaks at 24.4°, 34.0°, 36.7°, 50.0°, 54.5°, 62.5°, 64.8°. This observation was in line with many previous works, pointing out the successful synthesis of MnFe2O4 [16][17][18][19][20][21]. On the other hand, the EG@MnFe2O4 pattern in Figure 2b disclosed a very emergent peak at around 26.6°, corresponding to the presence of EG [7]. Although the intensity of peaks from 30° to 60° was low, the existence of MnFe2O4 in the structure of EG@MnFe2O4 could still be observed with the same position of mentioned peaks of MnFe2O4. Figure 3 also provides more information about the magnetization of EG@MnFe2O4, whose saturation magnetization value (1.5 emu/g) was found to be drastically lower than that of original MnFe2O4 [14]. Meanwhile, EDS mapping results also provided the average iron content at 6.4%. This phenomenon may be due to the decoration of non-magnetic EG, leading to a depletion in magnetization and crystallinity of original MnFe2O4. However, with an eligible magnetization, EG@MnFe2O4 can be separated from solution by inducing a magnetic field. Consequently, the EG@MnFe2O4 structure obtained a combination of EG and MnFe2O4 components [22][23][24].  Figure 3 also provides more information about the magnetization of EG@MnFe 2 O 4 , whose saturation magnetization value (1.5 emu/g) was found to be drastically lower than that of original MnFe 2 O 4 [14]. Meanwhile, EDS mapping results also provided the average iron content at 6.4%. This phenomenon may be due to the decoration of non-magnetic EG, leading to a depletion in magnetization and crystallinity of original MnFe 2 O 4 . However, with an eligible magnetization, EG@MnFe 2 O 4 can be separated from solution by inducing a magnetic field. Consequently, the EG@MnFe 2 O 4 structure obtained a combination of EG and MnFe 2 O 4 components [22][23][24].

Structural Characterization
The crystallinity profile of both MnFe2O4 and EG@MnFe2O4 was analyzed using the X-ray diffraction technique, which is presented in Figure 2. It is obvious that the MnFe2O4 particles in Figure  2a offered a high degree of crystallinity with the presence of typical peaks at 24.4°, 34.0°, 36.7°, 50.0°, 54.5°, 62.5°, 64.8°. This observation was in line with many previous works, pointing out the successful synthesis of MnFe2O4 [16][17][18][19][20][21]. On the other hand, the EG@MnFe2O4 pattern in Figure 2b disclosed a very emergent peak at around 26.6°, corresponding to the presence of EG [7]. Although the intensity of peaks from 30° to 60° was low, the existence of MnFe2O4 in the structure of EG@MnFe2O4 could still be observed with the same position of mentioned peaks of MnFe2O4. Figure 3 also provides more information about the magnetization of EG@MnFe2O4, whose saturation magnetization value (1.5 emu/g) was found to be drastically lower than that of original MnFe2O4 [14]. Meanwhile, EDS mapping results also provided the average iron content at 6.4%. This phenomenon may be due to the decoration of non-magnetic EG, leading to a depletion in magnetization and crystallinity of original MnFe2O4. However, with an eligible magnetization, EG@MnFe2O4 can be separated from solution by inducing a magnetic field. Consequently, the EG@MnFe2O4 structure obtained a combination of EG and MnFe2O4 components [22][23][24].  To gain more insight into various types of chemical bonds on the surface of EG@MnFe 2 O 4 , the FT-IR spectra were explored. According to Figure 4 and Table 2, the hydroxyl (-OH) and amine (-NH) groups can be ascribed to a broad band at 3400 cm −1 [25]. The aldehyde/ketone/acid/ester groups (C=O) were confirmed at around 1730 cm −1 and 1639 cm −1 regions with a strong intensity [26,27]. In addition, regions at round 1520 cm −1 and 1195 cm −1 were attributable to the existence of C=C, and C-O bonds, respectively [28,29]. A peak at 1076 cm −1 could be ascribed to possible existence of primary alcohol [30]. Moreover, apart from the main peaks in EG@MnFe 2 O 4 , the spectrum of CR-loaded EG@MnFe 2 O 4 was present in Figure 2. It is clear that an emergent peak at 1346 cm −1 was of importance for C-N bond [31]. Meanwhile, three peaks at 1210 cm −1 (narrow), 1178 cm −1 (narrow), 1029 cm −1 (very strong) were devoted for the absorption of -SO 3 − groups, and at around 800 cm −1 for the ring vibrations of p-di-substituted aromatic compounds [31]. Moreover, the weak peaks at around 1580 cm −1 could be assigned to the N=N typical stretching [32]. To sum up, the EG@MnFe 2 O 4 shows a variety of chemical bonds, which were essential for adsorption. To gain more insight into various types of chemical bonds on the surface of EG@MnFe2O4, the FT-IR spectra were explored. According to Figure 4 and Table 2, the hydroxyl (-OH) and amine (-NH) groups can be ascribed to a broad band at 3400 cm −1 [25]. The aldehyde/ketone/acid/ester groups (C=O) were confirmed at around 1730 cm −1 and 1639 cm −1 regions with a strong intensity [26,27]. In addition, regions at round 1520 cm −1 and 1195 cm −1 were attributable to the existence of C=C, and C-O bonds, respectively [28,29]. A peak at 1076 cm −1 could be ascribed to possible existence of primary alcohol [30]. Moreover, apart from the main peaks in EG@MnFe2O4, the spectrum of CR-loaded EG@MnFe2O4 was present in Figure 2. It is clear that an emergent peak at 1346 cm −1 was of importance for C-N bond [31]. Meanwhile, three peaks at 1210 cm −1 (narrow), 1178 cm −1 (narrow), 1029 cm −1 (very strong) were devoted for the absorption of -SO3 − groups, and at around 800 cm −1 for the ring vibrations of p-di-substituted aromatic compounds [31]. Moreover, the weak peaks at around 1580 cm −1 could be assigned to the N=N typical stretching [32]. To sum up, the EG@MnFe2O4 shows a variety of chemical bonds, which were essential for adsorption.  Carbonyls of aldehydes (-CHO) or ketones (-C=O), lactone, esters (-COO-) or acid carboxylic (-COOH) [26] 1639 (very strong band) Conjugation lowers frequency amides (-NHCO), or N-H stretching [27] C=C bending 1520 Aromatic rings, alkenes [28] C-O stretch 1195 (strong band) Phenolic compounds or tertiary alcohol [29] 1076 Primary alcohols [30] To illustrate more information about surface functional groups, the XPS spectrum is shown in Figure 5. At a glance, the XPS survey revealed the presence of four elements for EG@MnFe2O4: Carbon (C 1s), oxygen (O 1s), iron (Fe 2p), and manganese (Mn 2p). However, among those elements, the C 1s peak was measured with high intensity. This preliminary observation can be explained mainly because EG with carbonaceous components covers overall MnFe2O4 nanoparticles, leading a vague detection of the typical MnFe2O4 signal (note that XPS sensitivity works out within a certain nanoscale depth <10 nm) [33]. This kind of pattern is commensurate with the very weak signal of MnFe2O4 in the XRD spectrum as illustrated in Figure 2.
It was found that the C 1s XPS spectrum in Figure 5b indicated the presence of π-π interaction 289.6 (eV), C=O (286.0 eV), C-C (284.2 eV) [34]. Meanwhile, the O 1s XPS signals in Figure 5c can be broken down into three curves with peaks at binding energies 535.1, 532.5, 530.0 eV, corresponding  Primary alcohols [30] To illustrate more information about surface functional groups, the XPS spectrum is shown in Figure 5. At a glance, the XPS survey revealed the presence of four elements for EG@MnFe 2 O 4 : Carbon (C 1s), oxygen (O 1s), iron (Fe 2p), and manganese (Mn 2p). However, among those elements, the C 1s peak was measured with high intensity. This preliminary observation can be explained mainly because EG with carbonaceous components covers overall MnFe 2 O 4 nanoparticles, leading a vague detection of the typical MnFe 2 O 4 signal (note that XPS sensitivity works out within a certain nanoscale depth <10 nm) [33]. This kind of pattern is commensurate with the very weak signal of MnFe 2 O 4 in the XRD spectrum as illustrated in Figure 2. found to be 13.5 eV, while the distance from Fe 2p1/2 to satellite position was only 8.1 eV, which represents Fe 3+ cations [35]. Mn 2p spectrum in Figure 5e shows two sub-level of spin-orbit-splits between 2p3/2 and 2p1/2 with their binding energy gap of around 11.8 eV. This distance is in close proximity to spin-orbit separation energy (~11.62 eV) of manganese (II) oxide [35]. In particular, a satellite speak appeared at 647 eV, which is nearly 6.8 eV as far as the 2p½ state, suggesting the existence of Mn 2+ in the structure of EG@MnFe2O4 [36]. To quantify the functional groups, the Boehm titration can be used. This experiment allows identification of the amount of phenolic, lactonic, carboxylic groups, and basic groups [37]. It is assumed that NaOH (a very strong base) can neutralize Brønsted acids including phenol, lactone, and carboxylic acid, Na2CO3 can neutralize lactone, and carboxylic acid, and finally, NaHCO3 can neutralize carboxylic groups [38]. According to Table 3, the EG@MnFe2O4 contains a wide range of functional groups (phenolic, lactonic, carboxylic groups, and basic groups) with the amount of 0.044, 0.032, 0.020, and 0.156 mmol/g, respectively. These functional group are obviously derived from the EG component since MnFe2O4 in absence of EG decoration failed to produce the same results. Therefore, compared with MnFe2O4 without EG, EG@MnFe2O4 can own many surface functional groups, which are responsible for enhanced adsorption of CR. The existence of functional groups on the surface of adsorbents can not only create the interaction between the adsorbent and adsorbate, but also, enhance the retention of CR molecules on the adsorbent surface; thus the more the dye molecules are captured, the better the removal efficiency is [39]. It was found that the C 1s XPS spectrum in Figure 5b indicated the presence of π-π interaction 289.6 (eV), C=O (286.0 eV), C-C (284.2 eV) [34]. Meanwhile, the O 1s XPS signals in Figure 5c can be broken down into three curves with peaks at binding energies 535.1, 532.5, 530.0 eV, corresponding to chemisorbed O, C-O/C=O, and iron oxides Fe-O [33]. Fe 2p spectrum in Figure 5d is divided into two sub levels including Fe 2p 3/2 and Fe 2p 1/2 . It is obvious that a spin-orbit separation energy was found to be 13.5 eV, while the distance from Fe 2p1/2 to satellite position was only 8.1 eV, which represents Fe 3+ cations [35]. Mn 2p spectrum in Figure 5e shows two sub-level of spin-orbit-splits between 2p 3/2 and 2p 1/2 with their binding energy gap of around 11.8 eV. This distance is in close proximity to spin-orbit separation energy (~11.62 eV) of manganese (II) oxide [35]. In particular, a satellite speak appeared at 647 eV, which is nearly 6.8 eV as far as the 2p 1 2 state, suggesting the existence of Mn 2+ in the structure of EG@MnFe 2 O 4 [36].
To quantify the functional groups, the Boehm titration can be used. This experiment allows identification of the amount of phenolic, lactonic, carboxylic groups, and basic groups [37]. It is assumed that NaOH (a very strong base) can neutralize Brønsted acids including phenol, lactone, and carboxylic acid, Na 2 CO 3 can neutralize lactone, and carboxylic acid, and finally, NaHCO 3 can neutralize carboxylic groups [38]. According to Table 3, the EG@MnFe 2 O 4 contains a wide range of functional groups (phenolic, lactonic, carboxylic groups, and basic groups) with the amount of 0.044, 0.032, 0.020, and 0.156 mmol/g, respectively. These functional group are obviously derived from the EG component since MnFe 2 O 4 in absence of EG decoration failed to produce the same results. Therefore, compared with MnFe 2 O 4 without EG, EG@MnFe 2 O 4 can own many surface functional groups, which are responsible for enhanced adsorption of CR. The existence of functional groups on the surface of adsorbents can not only create the interaction between the adsorbent and adsorbate, but also, enhance the retention of CR molecules on the adsorbent surface; thus the more the dye molecules are captured, the better the removal efficiency is [39].  Table 4. For all experiments, it is evident that CR adsorption capacities by EG@MnFe 2 O 4 were significantly higher than those by MnFe 2 O 4 materials. For example, in the last five entries, the former material offered the CR adsorption capacity at 58.21 mg/g, compared with 10.28 mg/g of MnFe 2 O 4 without EG decoration. These results could be due to the existence of EG decorated on the surface of EG@MnFe 2 O 4 , leading to an enhancement of functional groups, which greatly contribute to the adsorption. To further investigate impact of experimental conditions on adsorption, we analyzed the ANOVA results extracted from Design Expert program, as shown in Table 5. Note that: Prob. is probability, SD is standard deviations, CV is coefficient of variation, R 2 is coefficient of determination, AP is adequate precision.
According to Table 5, ANOVA data is fully listed main statistical parameters of two models, including sum of squares, degree of freedom, mean square, F-value, p-value, coefficient of determination R 2 , and adequate precision ratio (AP). To obtain the most "statistically significant level", several conditions of model parameters should be met [40][41][42]. Whereas the larger the F-value and the smaller p-value are desirable for model significance, R 2 and AP should be greater than 0.9 and 4 respectively [28]. In that case, proposed models can be considered to be statistically significant at 95% significance level. Comparing these standards with statistical parameters of both models, it is obvious that Prob. > F values were lower than 0.0001, F-values (10.75-121.02) were reliable, along with very high R 2 (0.9026-0.9909) and AP ratios (10.6995-30.2649), suggesting that both models offered an excellent degree of compatibility between predicted data and experimental data [43,44]. The R 2 reported in this study well meets the criteria of Tugba et al. who suggested that R 2 ≥ 0.80 is sufficient for model fitting [45]. Therefore, models for the adsorption of CR onto EG@MnFe 2 O 4 and MnFe 2 O 4 were well-designed, and hence eligible to predict the optimal conditions. The residual analysis (Figures 6-8) is an integral part of evaluating the model suitability. In detail, normal plots of residuals in Figure 6a,b were inclined to be "S-shape" lines rather than linear, possibly resulting in potential errors in predicting the trends of experimental data. However, Grace et al. reported that mentioned residual patterns are still eligible to analyze the transformation of the response [46]. Meanwhile, residuals versus run plots in Figure 7a,b illustrate relatively random scatters, proposing that the variance values are the constants against the residuals variables. At the same trend, Figure 8a,b show predicted and actual points distributed on the 45-degree line, therefore, it is reliable to predict the trends of models [47,48].  Three-dimensional surfaces and contour plots as shown in Figures 9-11 reflect the effect of parameters on the response [49]. Figure 9a,b demonstrated the effect of concentration and solution pH on the adsorption of CR onto EG@MnFe2O4 and MnFe2O4. It is obvious that CR adsorption capacity obtained by the former materials was significantly higher than that of the latter. In addition, both variables showed a profound impact on the adsorption capacity of CR onto EG@MnFe2O4 and MnFe2O4, leading to the respective contour plots in Figure 9c,d reaching the convergent regions in the range of investigated values. Therefore, these regions would present the optimal conditions for the adsorption of CR. Figure 10a   Three-dimensional surfaces and contour plots as shown in Figures 9-11 reflect the effect of parameters on the response [49]. Figure 9a,b demonstrated the effect of concentration and solution pH on the adsorption of CR onto EG@MnFe2O4 and MnFe2O4. It is obvious that CR adsorption capacity obtained by the former materials was significantly higher than that of the latter. In addition, both variables showed a profound impact on the adsorption capacity of CR onto EG@MnFe2O4 and MnFe2O4, leading to the respective contour plots in Figure 9c,d reaching the convergent regions in the range of investigated values. Therefore, these regions would present the optimal conditions for the adsorption of CR. Figure 10a  Three-dimensional surfaces and contour plots as shown in Figures 9-11 reflect the effect of parameters on the response [49]. Figure 9a,b demonstrated the effect of concentration and solution pH on the adsorption of CR onto EG@MnFe 2 O 4 and MnFe 2 O 4 . It is obvious that CR adsorption capacity obtained by the former materials was significantly higher than that of the latter. In addition, both variables showed a profound impact on the adsorption capacity of CR onto EG@MnFe 2 O 4 and MnFe 2 O 4 , leading to the respective contour plots in Figure 9c,d reaching the convergent regions in the range of investigated values. Therefore, these regions would present the optimal conditions for the adsorption of CR. Figure 10a Generally, pH is the most influential factor, while contact time presents a minor role in the adsorption process of CR. Contour plots in Figure 11c,d also demonstrate that the optimum pH was around 6.0.
Processes 2019, 7, 305 11 of 17 contact time on the adsorption of CR onto EG@MnFe2O4 and MnFe2O4. Generally, pH is the most influential factor, while contact time presents a minor role in the adsorption process of CR. Contour plots in Figure 11c,d also demonstrate that the optimum pH was around 6.0.   contact time on the adsorption of CR onto EG@MnFe2O4 and MnFe2O4. Generally, pH is the most influential factor, while contact time presents a minor role in the adsorption process of CR. Contour plots in Figure 11c,d also demonstrate that the optimum pH was around 6.0.       To maximize the adsorption capacity value, the optimal conditions was set up based on the RSM as summarized in Table 6. Under the optimized conditions, confirmation tests were conducted under optimized conditions to verify the suitability between proposed and actual data. Highest adsorption capacities for the EG@MnFe 2 O 4 and MnFe 2 O 4 were recorded as 62.0 and 11.1 mg/g respectively. Also, it is evident that the results obtained by tested experiments were in line with those by predicted experiments, suggesting the model design was successfully applied. Table 7 compared adsorption capacity using various adsorbents, for which this study showed the better results.

Proposed Mechanism
Based on optimized conditions via RSM models, it was revealed that CR adsorption capacity of EG@MnFe 2 O 4 was approximately six-fold higher than that of MnFe 2 O 4 . This result can be explained due to the role of chemical functional groups on the surface of EG@MnFe 2 O 4 [56]. As previously mentioned, EG@MnFe 2 O 4 is proved to contain many kinds of functional groups including carboxylic acid, lactone, phenol, and base groups, which are non-existent in MnFe 2 O 4 ( Table 3). During the adsorption process, the presence of functional groups may contribute to the interaction with CR molecules [56]. As a result, the CR molecules were more easily captured on the surface of EG@MnFe 2 O 4 than on the surface of MnFe 2 O 4 .
Herein, we propose several kinds of plausible mechanism including H-bonding, and π-π interaction ( Figure 12). It is known that CR molecules are constituted of aromatic rings, amines (-NH 2 ) and imines (-N=N-) as shown in Figure 1, while the four mentioned functional groups contain both H-donors (hydrogen atoms belonging to groups such as -OH, -NH 2 , -C 6 H 4 OH) and H-acceptors (electron-rich oxygen or nitrogen atoms such as -CHO, N=N, -COO − ). Therefore, a H-bond type can be formed between these CR molecules and functional groups, enhancing the adsorption efficiency [57,58]. In addition, the EG@MnFe 2 O 4 is decorated with the outer EG layer. Because the EG is the carbonaceous source that abundantly contains aromatic rings in the structure. As a result, π-π interaction can be formed between aromatic rings of CR molecules and EG layers of EG@MnFe 2 O 4 material, leading to an improvement in adsorption capacity.
In MnFe 2 O 4 , the adsorption of CR may be attributable to the existence of weak forces including "oxygen-metal" bridge and van der Waals [59]. It was reported that the electron-rich atoms such as oxygen can interact with a metal/oxides site to form an intermediate bridge called "oxygen-metal" [59]. Because these kinds of force are weak, the adsorption of CR over MnFe 2 O 4 was unconducive.

Conclusions
The EG@MnFe2O4 has been successfully synthesized and characterized. The XPS, FT-IR and Boehm titration results indicated that EG@MnFe2O4 contains various kind of functional groups with carboxylic acid (0.044 mmol/g), phenol (0.032 mmol/g), lactone (0.020 mmol/g), and total base (0.156 mmol/g) on the surface. In addition, EG@MnFe2O4 and MnFe2O4 were used to absorb the CR dye from water via the experimental design by RSM for three parameters: Solution pH (4.3-7.7), CR concentration (43.2-76.8 mg/L) and contact time. The quadratic regression models were proved to be statistically significant at 95% significance level. Verification of the optimized results revealed that the CR adsorption capacity onto EG@MnFe2O4 (62.0 mg/g) was significantly higher than that onto MnFe2O4 (11.1 mg/g). To explain these results, the plausible mechanisms including H-bonding, and π-π interaction were proposed based on the Boehm titration results, assuming that functional groups on the surface of EG@MnFe2O4 play a crucial role in enhancing the adsorption of CR dye.