Application of response surface methodology for optimization of methyl orange adsorption by Fe-grafting sugar beet bagasse

Abstract

The adsorptive removal of methyl orange dye using a sugar beet bagasse (SBB) as agro-industrial by-product has been investigated. The adsorption potential of SBB was improved by grafting with FeCl₃·6H₂O. The dependency of removal efficiency (R) and adsorption capacity (q_e) on the level and magnitude of variables including initial pH, methyl orange concentrations, and sorbent dosage was investigated and optimized by central composite design under response surface methodology (RSM). Besides, the effect of temperature on adsorption process was evaluated in terms of thermodynamic study. The good agreement found between observed and predicted values supports and confirms the suitability of the applied model to predict adsorption state. The applied models revealed that methyl orange removal in aqueous solution was affected by all the three factors studied. By consideration of seven starting points in the response surface solutions, the best local maximum was found to be at initial solution pH 2.51, sorbent dosage of 0.37 g.L⁻¹, initial dye concentration of 100 mg.L⁻¹, removal efficiency of 51.8%, adsorption capacity of 221.5 mg.g⁻¹, and desirability of 0.692. A pseudo second-order model more accurately represented the adsorption process. Moreover, Freundlich isotherm model was superior to the Langmuir isotherm model.

Keywords

Adsorption response surface methodology sugar beet bagasse methyl orange kinetic study

Introduction

Colored sewage is as a consequence of dye usage in the several industries including dye manufacturing, textile industry, pulp and paper processing, leather tanning, battery production, and so on (Politi and Sidiras, 2012). Many dyes and their breakdown products have wide adverse effects for living organisms. Moreover, the colored wastewater reduces light penetration and then affects the photosynthetic activity of aquatic organisms (Yang et al., 2015). Azo dyes are an interesting class of compounds that are widely applied in chemical applications and industries. Although azo dyes are not strongly toxic, they can cause hypersensitivity and allergy; therefore, the presence of these dyes in water is highly undesirable (Deligeer et al., 2011; Ling et al., 2016). Hence, disposal of untreated effluents to the surrounding environment often leads problems for aquatic life and humans. To prevent any potential hazards, an effective treatment of these industrial wastewaters is needed before being discharged into the environment. Furthermore, removal of the azo dyes from the effluent is difficult because they are not easily degradable or removable by conventional wastewater treatments (Haris et al., 2010). Some methods like membrane separation (Saffaj et al., 2004), ion exchange (Wu et al., 2008), photocatalytic degradation (Lv et al., 2011), anodic oxidation (Tsantaki et al., 2012), ozone treatment (Zhang et al., 2014), biological treatment (Işık and Sponza, 2006), and adsorption (Ahmad and Hameed, 2010; Jiang et al., 2014; Liu and Zhang, 2007) have been widely applied in the process of removing dyes from aqueous solution. Among various treatment methods, adsorption is quite a promising technique for the removal of dyes due to its high efficiency, ease of handling, availability of different adsorbents, and its cost efficiency. In this regard, various adsorbents have been developed for the separation and removal of different dyes including activated carbons (Ahmad and Hameed, 2010; Oliveira et al., 2011), magnetic nanocomposites (Deligeer et al., 2011; Jiang et al., 2014; You et al., 2014), zeolites (Akgül, 2014; Hernández-Montoya et al., 2013), mesoporous materials (Lee et al., 2007; Punyapalakul and Takizawa, 2006), clays (Liu and Zhang, 2007), natural or agro-industrial by-products (Al-Ghouti et al., 2010; Haris et al., 2010; Saad et al., 2010; Subbaiah and Kim, 2016; Yu et al., 2012), and so on. In recent years, agricultural or agro-industry by-products are widely used as efficient adsorbents for improving the contaminated water and wastewaters. Sugar beet bagasse (SBB) is one of the primary agro-industrial by-products that are produced in large quantities in the world. Therefore, it can be a good candidate for developing cost-efficient adsorbents for removal of azo dyes. Response surface methodology (RSM) is a set of statistical and mathematical technique for designing experiments, building models, evaluating the relative significance of several independent variables, and determining optimum conditions for desired responses (Wantala et al., 2012). In literature, RSM based on central composite design (CCD) has been used in different applications of engineering including heavy-metal removal, dye removal, biofuel production, etc. (Auta and Hameed, 2011; Betiku and Taiwo, 2015; Dora et al., 2013; Skorupskaite et al., 2015). However, this is the first study on the optimization of methyl orange (MO) adsorption on SBB. Therefore, we decided to evaluate the MO removal potential of SBB under various operating conditions such as pH, initial MO concentrations, and sorbent dosage. The parameters for maximum removal efficiency are optimized by using CCD with RSM under (Design Expert. 7.0) software. The physicochemical characteristics of SBB are evaluated by Fourier transform infrared spectroscopy (FT-IR) and scanning electron microscopy (SEM). Moreover, Langmuir and Freundlich isotherms were applied to the equilibrium data to describe the main interactive mechanisms involved the removal process. Kinetic parameters were also calculated from the pseudo first-order and pseudo second-order models. Furthermore, thermodynamic parameters (enthalpy, entropy, and adsorption free energy), were calculated for better description of the adsorption mechanism.

Materials and methods

Chemicals

Analytical grade of hydrochloric acid (37%), sodium hydroxide (NaOH), and FeCl₃6H₂O were all purchased from Aldrich and used without further purification. Deionized distilled water was used in the preparation of all solutions. MO that also known as C.I.ACID ORANGE 52 was purchased from Merck (Germany). The chemical formula for MO is C₁₄H₁₄N₃NaO₃S with molecular weights of 327.34 g.mol⁻¹. MO molecular structure (single azo class) is shown in Scheme 1. All other reagents were of analytical grade and all glassware were cleaned by HNO₃ and rinsed with double distilled water.

Scheme 1.

Molecular structures of methyl orange (MO).

Sorbent preparation

SBB was collected from local sugar factory of Kermanshah, West of Iran. First, SBB pulverized and then washed with tap water to remove dirt and impurities and dried in the oven at 70 ℃ for 12 h. Five grams of FeCl₃·6H₂O were dissolved in 100 mL deionized water and 10 g of dry SBB was added and stirred for 4 h and kept overnight. Produced Fe-SBB was then separated by filtration and dried in an oven. Fe-SBB residue was heated in a muffle furnace at 450 ℃ for 6 h, than washed and dried. Finally, the primary SBB and Fe-SBB were tested and compared for MO removal.

Physicochemical characterization of adsorbent

FT-IR analysis was carried out on Bruker Vector 22 FT-IR Spectrometer in the range of 400–4000 cm⁻¹ employing the KBr pellet method. The structure and morphology of SBB and Fe-SBB particles were examined by SEM (MIRA3TESCAN, Czech Republic).

MO adsorption studies

Batch adsorption experiments were performed at room temperature (20 ℃) to study the effect of solution pH, initial dye concentration, and sorbent dosage. Each experiment was carried out in Erlenmeyer flasks containing 100 mL MO solution by shaking the flasks at 200 r/min for period contact time of 120 min. Samples were withdrawn at predetermined time intervals (0, 5, 15, 30, 60, 90, and 120 min) and filtered through 0.45-µm filters. The residual MO concentration in the supernatant was determined using the spectrophotometer (UVIKON) at 475 nm. To evaluate the effect of temperature on the dye adsorption, optimal process parameters (pH, sorbent dosage, and MO concentration) which were determined by the software were applied at four temperatures (20, 30, 40, and 50 ℃). The removal efficiency of the MO molecules was calculated by equation (1):

R = \frac{C_{i} - C_{e}}{C_{i}} \times 100

(1)

where R is the removal efficiency (%) of the MO, and C_i and C_e are the initial and equilibrium (residual) concentrations of MO (mg.L⁻¹), respectively.

MO adsorption capacity by SBB was determined according to equation (2):

q_{e} = V \frac{C_{i} - C_{e}}{S}

(2)

where q_e is the amount of MO adsorbed on the sorbent (mg.g⁻¹), V is the volume of dye containing solution in contact with the sorbent (L), and S is the amount of added sorbent on dry basis (g) (Ghorbani et al., 2008).

Experimentation and optimization of adsorption process

Optimum condition for the adsorption of MO by Fe-SBB was determined by means of CCD under response surface methodology (RSM). RSM has been widely used for optimization of the process variables of adsorption (Chatterjee et al., 2012; Liu et al., 2012). This method consists of a group of empirical techniques dedicated to the evaluation of relationship existing between a cluster of controlled experimental factors and measured responses according to one or more selected criteria. Optimization studies were carried out by studying the effect of three variables including Fe-SBB dosage, initial MO concentrations, and pH of solutions. The chosen independent variables used in this study were coded according to equation (3):

Z_{i} = \frac{X_{i} - X_{0}}{Δ x_{i}}

(3)

where X_i is the dimensionless coded value of the ith independent variable, X₀ is the value of X_i at the center point, and Δx_i is the step change value. The actual values of process variables and their variation limits were selected based on the values obtained in literatures (Auta and Hameed, 2011; Chatterjee et al., 2012; Pavan et al., 2007) and coded as shown in Table 1. As presented, the experimental design involved three parameters (X₁, X₂, and X₃), each at five levels, coded −1, −α, 0, + α, and +1, respectively. Factor ranges in term of (±1) levels selected by user (according to the literature) and factors in term of (±α) and (0) levels were selected by the software. MO removal efficiency (R) and MO adsorption capacity (q_e) were considered as the dependent factors (responses).

Table 1.

Independent variables and their coded levels for the CCD.

		Range and levels (coded)
Independent variables		−α	−1	0	+1	+α
pH	(X₁)	1	2	6	10	12
Sorbents dosage (g.L⁻¹)	(X₂)	1	0.1	2.6	5	6.7
MO concentration (mg.L⁻¹)	(X₃)	2.5	5	52.5	100	132.4

CCD: central composite design; MO: methyl orange.

The behavior of the system is explained by the following empirical second-order polynomial model (equation (4)):

Y = a_{0} + \sum_{i = 1}^{n} a_{i} X_{i} + \sum_{i = 1}^{n} a_{ii} X_{i}^{2} + \sum_{i = 1}^{n - 1} \sum_{j = 2}^{n} a_{ij} X_{i} X_{j} + e

(4)

where i and j are linear, quadratic coefficients, a₀ is the constant coefficient, a_i is the linear coefficient, a_ii is the interactive coefficient, and a_ij is the quadratic coefficient. The regression coefficients were then used to make statistical calculations to generate three-dimensional curves from the regression models. Design Expert software (Stat Ease, USA) was used for regression and graphical analysis of the obtained data. A 2³ CCD model was generated. This model consisted of eight factorial points, six axial points, and and central points. The 20 runs as per the experimental design obtained from Design Expert software are presented in Table 2. It is also important to check the adequacy of the developed model. The responses and the corresponding parameters have been modeled and optimized using analysis of variance (ANOVA), which has been used to identify significant variables and their individual and interactive effects on the MO removal process. Intrinsically, the optimization process involves three substantial steps, which are performing the statistically designed experiments, estimating the coefficients in a mathematical model and predicting the response, and checking the adequacy of the model. The quality of fit of the polynomial model was expressed by the coefficient of determination (R²). Significance of process variables was checked by p value and F value.

Table 2.

Experimental design in term of coded factors and results of the central composite design.

		Independent values						Responses (Y)
		Real values			Coded values			Predicted values		Observed values
Run number	Categorical factor levels	X ₁	X ₂	X ₃	X ₁	X ₂	X ₃	q_e (mg.g⁻¹)	R (%)	q_e (mg.g⁻¹)	R (%)
1	Central points	6	2.6	52.5	0	0	0	34.82	87.69	20.43	90.14
2		6	2.6	52.5	0	0	0	34.82	87.69	20.43	90.07
3		6	2.6	52.5	0	0	0	34.82	87.69	20.43	90.05
4		6	2.6	52.5	0	0	0	34.82	87.69	20.10	87.33
5		6	2.6	52.5	0	0	0	34.82	87.69	19.56	87.52
6		6	2.6	52.5	0	0	0	34.82	87.69	19.68	87.86
7	Factorial points	2	5	100	−1	1	1	18.73	90.05	14.54	73.29
8		10	5	5	1	1	−1	44.09	17.02	0.41	24.06
9		10	5	100	1	1	1	24.32	86.70	17.50	85.18
10		2	5	5	−1	1	−1	45.28	16.65	0.28	17.29
11		10	0.1	5	1	−1	−1	34.01	5.58	8.19	8.45
12		2	0.1	100	−1	−1	1	245.92	42.63	330.00	32.85
13		10	0.1	100	1	−1	1	42.67	7.43	37.50	4.04
14		2	0.1	5	−1	−1	−1	36.82	25.89	33.00	24.67
15	Axial points	1	2.6	52.5	−α	0	0	69.38	63.04	18.64	85.75
16		12	2.6	52.5	+α	0	0	6.66	24.00	0.00	0.00
17		6	1	52.5	0	−α	0	59.16	69.86	37.96	65.59
18		6	6.7	52.5	0	+α	0	27.56	71.07	6.55	75.99
19		6	2.6	2.50	0	0	−α	1.43	49.55	1.10	22.96
20		6	2.6	132.4	0	0	+α	92.74	85.96	48.79	99.41

Results and discussion

Characterization of SBB

The morphology of the sorbent was studied by SEM. Figure 1 shows the SEM images of raw SBB, Fe-SBB and Fe-SBB after MO adsorption. It can be observed that the surface morphology of raw SBB was different from that of Fe-SBB and Fe-SBB after MO adsorption. Figure 1(a) shows the structure of raw SBB at a magnification of 59,500×. It is clear that SBB particles was an assemblage of fine particles, which did not have regular and fixed shape and size and exhibit fiber-like structures with low porosity. Figure 1(b) shows that the surface layer of Fe-SBB exhibit microstructure porosity by treatment with FeCl₃·6H₂O. Microporous active sites distinguished on the surface layer of Fe-SBB may increase the specific surface area and lead to faster action of adsorption. Johar et al. (2012) indicated that under the chemical treatment conditions almost all the components that bind the fibril structure of the biomass were removed thus enabling the fibers to be separate into an individual forms. Moreover, Figure 1(c) revealed that the smooth surface of Fe-SBB became thicker and coarser after MO adsorption, which providing further evidence that MO was loaded on the surface of the sorbent.

Figure 1.

SEM images of (a) raw SBB, (b) Fe-SBB, and (c) Fe-SBB after MO adsorption.

FT-IR spectroscopy was used to detect the presence of binding groups in the SBB and Fe-SBB (Figure 2). The absorption band for H–O–H bending vibration in water is at around 1640 cm⁻¹(An et al., 2010). The spectra show a broad band around 3000–3700 cm⁻¹, which is due to adsorbed water molecules and also O–H stretching mode (Kalapathy et al., 2000). In the SBB spectra, the absorbance peak appears in 2920 cm⁻¹ and was assigned to the C–H bond of biomass carbon structure. Moreover, the adsorption peaks aroused by other functional groups such as COOH (1740 cm^−l), COC (1050 cm⁻¹), and COH (1249 cm⁻¹) can be observed in Figure 2 (Jiang et al., 2015). Based on the obtained results from the XRF analysis (not reported here), there are some metal oxides in the SBB structure, including SiO₂ (1.3%) and Al₂O₃ (0.3%). Hence, the vibration signals around 462 and 1377 cm⁻¹ present in SBB sample are typical Si–O–Si bands attributed to the bending and Al–O, respectively (Ghorbani et al., 2013). It is valuable to note that an absorption peak appears at 540 cm⁻¹ after Fe species being grafted in SBB, but pure SBB shows no absorption at this region, indicating that the heteroatoms has been incorporated into the framework of sorbent and the Fe–O bonds have formed (Song et al., 2016).

Figure 2.

FT-IR spectra of SBB and Fe-SBB.

Comparative MO adsorption study by SBB and Fe-SBB

As preliminary experiments, the MO removal capacities of the tow different produced sorbents (SBB and Fe-SBB) were compared. The results revealed that the 9:1 Fe-SBB showed the highest dye removal potential. Therefore, this sorbent was used in all the subsequent designed experiments. The dye removal kinetics of Fe-SBB was compared with those of SBB at 1 g.L⁻¹ sorbent dosages, pH 5, and 100 mg.L⁻¹ MO concentration. The results are presented in Figure 3.

Figure 3.

Comparison of MO adsorption by SBB and Fe-SBB (sorbent dosage: 1g.L⁻¹, pH: 5, and MO concentration: 100 mg.L⁻¹).

It can be observed that the Fe-SBB sorbent has faster dye-removal kinetics and larger dye removal capacity when compared with SBB at the indicated concentration. This is attributed to the distribution of iron functional groups on the surface of SBB, thus making them kinetically more accessible for MO molecules, and increasing their binding sites available for adsorption. The adsorption can be defined as the attraction of Fe³⁺ ions to the adsorbent surface by chemical forces in addition to electrostatic forces (Hunter, 1988). Also, the formation of additional hydroxyl groups (Fe–OH) is another factor for increasing adsorption capacity.

Statistical analysis and the model fitting

RSM is more advantageous than the traditional single-parameter optimization in that it saves time, space, and raw material (Sadhukhan et al., 2016; Wu et al., 2014). There were a total of 20 runs for optimization of three individual parameters in the current CCD. By applying multiple regression analysis on the experimental data, the R response and the test variables were related by the following second-order polynomial equation equation (5)):

R = 0.62923 + 12.96674 X_{1} + 9.47698 X_{2} + 0.80794 X_{3} + 0.81240 X_{1} X_{2} - 0.0049 X_{1} X_{3} + 0.12175 X_{2} X_{3} - 1.41310 X_{1}^{2} - 2.66628 X_{2}^{2} - 0.0060 X_{3}^{2} (R 2 = 0.908)

(5)

Also, the q_e response and the test variables were related by the following linear equation (equation (6)):

q_{e} = + 44.11095 - 8.39040 X_{1} - 23.37030 X_{2} + 2.58774 X_{3} + 4.08677 X_{1} X_{2} - 0.17425 X_{1} X_{3} - 0.31682 X_{2} X_{3} (R 2 = 0.763)

(6)

The ANOVA for adsorption study of MO was used in order to confirm the goodness of the models. The significance of each term is presented in Tables 3 and 4. It is determined by the corresponding F value, p value, and sum of squares (SS). The significance of each coefficient was determined by F values and p values. Sum of squares should also be checked while considering the significance of a particular variable. As the value of SS increases, the significance of that variable also increases. Data given in Table 3 demonstrate that the regression of the R response was statistically significant at F values of 11.00 with corresponding p values of 0.0004. The “Lack of Fit” F value of the R response was 228.03. A significant lack of fit revealed that there may be some systematic variation unaccounted for in the hypothesized model (Cao et al., 2014). This was thought to be due to the exact replicate values of the independent variable in the model that provided an estimate of pure error.

Table 3.

Regression analysis using response surface quadratic model for removal efficiency (R) response.

Term	Sum of squares	df	Mean square	F	p
Model	21,851.03	9	2427.89	11.00	0.0004
X ₁	889.55	1	889.55	4.03	0.0725
X ₂	2870.76	1	2870.76	13.01	0.0048
X ₃	5034.42	1	5034.42	22.81	0.0008
X ₁ X ₂	507.08	1	507.08	2.30	0.1605
X ₁ X ₃	6.95	1	6.95	0.032	0.8627
X ₂ X ₃	1606.13	1	1606.13	7.28	0.0224
$X_{1}^{2}$	5095.32	1	5095.32	23.08	0.0007
$X_{2}^{2}$	2062.59	1	2062.59	9.34	0.0121
$X_{3}^{2}$	1647.05	1	1647.05	7.46	0.0211
Residual	2207.24	10	220.72
Lack of fit	2197.60	5	439.52	228.03	< 0.0001
Pure error	9.64	5	1.93
Cor total	24,058.27	19

Table 4.

Regression analysis using response surface 2FI model for MO adsorption capacity (q_e) response.

Term	Sum of squares	df	Mean square	F value	P value
Model	73,154.03	6	12,192.34	6.99	0.0017
X ₁	10,034.38	1	10,034.38	5.75	0.0322
X ₂	16,077.84	1	16,077.84	9.22	0.0096
X ₃	14,500.10	1	14,500.10	8.31	0.0128
X ₁ X ₂	12,832.22	1	12,832.22	7.36	0.0178
X ₁ X ₃	8768.36	1	8768.36	5.03	0.0431
X ₂ X ₃	10,875.36	1	10,875.36	6.23	0.0268
Residual	22,680.56	13	1744.66
Lack of fit	22,679.82	8	2834.98	19111.09	< 0.0001
Pure error	0.74	5	0.15
Cor total	95,834.60	19

2FI: two-factor interaction; MO: methyl orange.

Data given in Table 4 demonstrate that the regression of q_e response was statistically significant at F values of 6.99 with corresponding p values of 0.0017. The “lack of fit” F value of q_e response was 19,111.09. In both models, p values are less than 0.05, which indicate that regressions are significant at 95% confidence level. It implies that the models are significant and can appropriately explain the relationship between responses (R and q_e) and independent variables. The quadratic model is found to be more significant than other models for R response. The ANOVA study suggests that initial MO concentration (p = 0.0008, SS = 5034.42, F = 22.81) has the most significant effect on dye removal (R) followed by Fe-SBB dosage (p = 0.0048, SS = 2870.76, F = 13.01). Initial solution pH (p = 0.0725) has comparatively less-significant effect on the R response. On the other hand, the two-factor interaction (2FI) model is found to be more significant for the q_e response. The ANOVA study revealed that Fe-SBB dosage (p = 0.0096, SS = 16077.84, F = 9.22) has the most significant effect on dye adsorption capacity (q_e) followed by initial MO concentration (p = 0.0128, SS = 14500.10, F = 8.31). Initial solution pH (p = 0.0322) has comparatively less-significant effect on the q_e response.

Figure 4(a) and (b) shows the relationship between actual and the predicted values of removal efficiency (R) and dye adsorption capacity (q_e) using Fe-SBB. The actual data are the original measure of MO concentration in solution that was estimated experimentally using equations (1) and (2). On the other hand, predicted values of R and q_e were generated by equations (5) and (6), respectively. The high values of coefficient demonstrated a good agreement between the calculated and observed results within the range of experiment. The value of the determination coefficient (R²) for removal efficiency was 0.9083 and adjusted determination coefficient (Adj. R²) was 0.8257. In addition, the values of the R² for dye adsorption capacity was 0.7633 and Adj. R² was 0.6541.

Figure 4.

Correlation of actual and predicted values for (a) removal efficiency (R) and (b) MO adsorption capacity (q_e).

Effect of process variables

In order to examine the interactions between the factors and responses, three-dimensional (3D) response surface plots are very helpful showing a function of two factors maintaining the other factor at a fixed level (Simsek et al., 2013). The influences of the three different process variables including initial solution pH, initial MO concentration, and sorbent dosage on removal efficiency (R) and MO adsorption capacity (q_e) as responses are shown in the 3D response surface plots (Figures 5(a) to (c) and 6(a) to (c)).

Figure 5.

3D surface plots for MO removal efficiency (R) at 120 min showing the mutual effect of (a) pH and MO concentration, (b) pH and sorbent dosage, and (c) sorbent dosage and MO concentration. MO: methyl orange.

Figure 6.

3D surface plots for MO adsorption capacity at 120 min showing the mutual effect of (a) pH and MO concentration, (b) pH and sorbent dosage, and (c) sorbent dosage and MO concentration. MO: methyl orange.

Effect of pH

According to the literature adsorption of MO usually is dependent on the pH of the solution (Mittal et al., 2007). Figure 5(a) and (b) show the interaction of pH with initial MO concentration and sorbent dosage on removal efficiency (R) response, respectively. The results show that the MO removal efficiency increased with increasing pH from 2 to 5, and then it decreased slowly with enhancement pH from 5 to 10. It seems that in this condition (pH = 5), the surface of the adsorbents was positively charged whereas the dye was negatively charged. So in this study, the effect of pH can be explained by the electrostatic interaction between the adsorbents and the MO molecules. However, with increase in pH protonation reduces, which results into retardation of adsorption. On the other hand at acidic pH, the adsorption capacity decreased due to the electrostatic repulsion between the positively charged Fe-SBB and the neutral or partially positive charges of dye. A similar trend was observed for the adsorption of acid orange by a natural pumice and Fe-coated pumice stone (Hasanzadeh et al., 2013). Obtained results in MO adsorption capacity (q_e) response by evaluating the interactions of the pH with sorbent dosage and dye concentration revealed that the maximum q_e was observed in acidic pH (Figure 6(a) and (b)).

Effect of initial MO concentration

The mutual effect of initial MO concentration with pH and sorbent dosage was visualized in Figure 5(a) and (c). These diagrams pointed out that the removal efficiency increased with increase in initial MO concentration from 5 to 70 mg.L⁻¹ and then relatively stable or slightly increased from 70 to 100 mg.L⁻¹. It can be supposed that a certain amount of sorbent own limited number of active adsorption sites and a corresponding saturated adsorption capacity. When the sorbent reach saturated state, all active adsorption sites are occupied, so the sorbent could not adsorb much more dye molecules. A similar result was observed for the adsorption of acid orange by a mesoporous activated carbon (Noorimotlagh et al., 2014). Through the comparison of the results of MO adsorption capacity (q_e) response (Figure 6(a) and (c)), it could be reasoned that sorbent dosage is more effective than initial dye concentration and pH. Despite, as can be seen when the initial MO concentration increases, the adsorption capacity (q_e) increased because of increasing driving force of the mass transfer and occupying the available active sites on the adsorbent by MO molecules.

Effect of sorbent dosage

The mutual effect of sorbent dosage with pH and initial MO concentration based on the fitted quadratic models is presented in Figure 5(b) and (c). It can be observed that removal efficiency (R) increased with increase of sorbent dosage from 0.1 to 4.5 g.L⁻¹ and then relatively stabled. The increased removal efficiency of MO at high sorbent dosages can be due to the increased available surface area and subsequently more adsorptive sites for an efficient adsorption (Ghorbani et al., 2008). However, when the dosage of adsorbent is 4.5 g.L⁻¹, the removal efficiency is almost complete, and over this amount, it keeps unchanged. The adsorption capacity (q_e) response as a mutual effect of sorbent dosage with pH and initial MO concentration revealed that the maximum q_e was observed in lower sorbent dosages (Figure 6(b) and (c)). This result is in agreement with other previous studies (Ahmad and Hameed, 2010; Atia et al., 2009).

Optimization and model validation

One of the main aims of this study is to find the optimum process parameters to maximize the removal efficiency (R) and adsorption capacity (q_e) of MO from the mathematical model equations developed in this study. In the optimization process, we choose the desired goal for each factor and response from the menu. The possible goals are maximize, minimize, target, within range, none (for responses only), and set to an exact value (factors only). The goals are composed into an overall desirability function. Desirability is an objective function that ranges from zero outside of the limits to one at the goal. The program explores to maximize this function. The goal searching begins at a random starting point and proceeds up the steepest slope to a maximum. There may be two or more maximums because of inflection in the response surfaces and their combination into the desirability function. A multiple response method was applied for optimization any combination of five goals, namely the initial solution pH, initial MO concentration, sorbent dosage, adsorption capacity (q_e), and removal efficiency (R). The numerical optimization found a point that maximizes the desirability function. A maximum value of R and q_e, minimum level of sorbent dosage, initial MO concentration within the range of 5–100 mg.L⁻¹ and initial solution pH within range of 2–10 were set for maximum desirability. Figure 7 shows a ramp desirability that was generated from seven optimum points via numerical optimization. By consideration of seven starting points in the response surface solutions, the best local maximum was found to be at initial solution pH 2.51, sorbent dosage of 0.37 g.L⁻¹, initial dye concentration of 100 mg.L⁻¹, removal efficiency of 51.8%, adsorption capacity of 221.5 mg.g⁻¹, and desirability of 0.692. The equilibrium time, agitation speed, and temperature were 120 min, 200 r/min, and 20 ℃, respectively. As the composite desirability is 0.697, the process has the acceptable efficiency at that operating condition.

Figure 7.

Desirability ramp for numerical optimization of five goals, namely the initial solution pH, initial MO concentration, sorbent dosage, MO adsorption capacity, and removal efficiency.

Table 5 presents a summary of the MO adsorption capacities of the various adsorbents that have been investigated. Although some materials exhibit a higher adsorption capacity of MO, the Fe-SBB with a good removal capacity is still very attractive.

Table 5.

MO adsorption capacities of various adsorbents.

Sorbent type	q_e (mg.g⁻¹)	Reference
Chitosan/Alumina composite	35.31	Zhang et al. (2012)
Iron terephthalate (MOF-235)	477	Haque et al. (2011)
Mesoporous γ-Fe₂O₃/SiO₂ nanocomposites	476	Deligeer et al. (2011)
ZnO/CuO nanocomposite immobilized on γ-Al₂O₃	341	Hassanzadeh-Tabrizi et al. (2016)
Copper sulfide nanoparticles loaded activated carbon	122	Mokhtari et al. (2016)
Fe-SBB, optimized value:	221.5	This study
Experimental value:	330	This study

MO: methyl orange.

Kinetics, adsorption isotherms, and thermodynamic studies

Kinetic study. The kinetic study explains the rate of adsorption of MO on Fe-SBB. The pseudo-first-order and pseudo-second-order models are often used to fit the adsorption rate data. The comparison is done between the experimental data, calculated data, and the regression coefficient (R²). The pseudo-first-order kinetic model is expressed in equation (7):

\ln (q_{e} - q_{t}) = \ln q_{e} - K_{1} t

(7)

Based on equilibrium adsorption, the pseudo-second-order kinetic equation is expressed as equation (8):

\frac{t}{q_{t}} = \frac{1}{K_{2} q_{e}^{2}} + \frac{t}{q_{e}}

(8)

where q_t is the amount of MO adsorbed at time t (mg.g⁻¹), q_e is the amount of MO adsorbed per unit mass of adsorbent at equilibrium (mg.g⁻¹), and K₁ and K₂ are the rate constants (min⁻¹).

The pseudo-first-order considers the rate of occupation of sorption sites to be in proportion to the number of unoccupied sites. A straight line of ln (q_e − q_t) versus t (min) indicates application of the pseudo-first-order kinetics model. In a true pseudo-first-order process, −K₁ and ln q_e parameters should be equal to the slope and intercept of ln (q_e − q_t) versus t, respectively. On the other hand, the parameters of q_e and K₂ can be calculated by a curve-fitting program from the slope and intercept of t/q_t versus t plots, respectively. Linear plots revealed that pseudo-second-order regression coefficient R² has values greater than that of the pseudo-first-order regression. So, the obtained results indicate that the kinetic is pseudo-second-order kinetics of adsorption. Similar kinetic results have also been reported for the adsorption of acid blue 193 on to BTMA-bentonite (Özcan et al., 2005) and the real tannery effluent on to activated carbon prepared from an agricultural by-product (Baccar et al., 2013). All data regarding the pseudo-first-order and pseudo-second-order kinetics are shown in Table 6. Rapid adsorption was observed during the first 5 min of contact time was enough to reach the equilibrium state. The value of correlation coefficient (R²) is greater than 0.993 and best describe the reaction obeying second order.

Table 6.

Kinetic parameters for adsorption rate expressions.

C_i (mg.L⁻¹)	$q_{e}^{\exp .}$ (mg.g⁻¹)	Pseudo-first-order			Pseudo-second-order
C_i (mg.L⁻¹)	$q_{e}^{\exp .}$ (mg.g⁻¹)	q_e1 (mg.g⁻¹)	−K₁ (min⁻¹)	R ²	q_e2 (mg.g⁻¹)	K₂ (min⁻¹)	R ²
5	13.699	6.527	0.019	0.805	13.736	0.334	0.993
25	32.314	10.087	0.020	0.709	31.847	0.064	0.997
50	53.446	20.867	0.022	0.741	52.083	0.054	0.993
100	74.392	34.658	0.026	0.847	73.529	0.045	0.995
135	89.392	29.897	0.029	0.856	89.286	0.020	0.999

C_i: initial MO concentration; $q_{e}^{\exp .}$ : experimental value; q_e1 and q_e2: calculated values; K₁ and K₂: rate constants.

Adsorption isotherms. For the optimization of adsorption process parameters, Langmuir and Freundlich isotherm models were used to analyze the experiment data. Freundlich (1907) isotherm can be used for non-ideal multilayer adsorption of inorganic and organic components in a solution that involves heterogeneous sorption. This model is commonly written as in equation (9):

q_{e} = K_{f} C_{e}^{1 / 1 n n}

(9)

where q_e is the equilibrium adsorption capacity of the Fe-SBB (mg.g⁻¹), C_e is the equilibrium concentration of MO (mg.L⁻¹) ,and K_f (mg.L⁻¹) and 1/n are constants related to the sorption capacity and intensity, respectively. Nonlinear regression analysis was carried out in Sigma Plot 12.0 software in order to determine K_f and n values (Figure 8).

Figure 8.

Langmuir and Freundlich isotherms for adsorption of MO on Fe-SBB with a sorbent dosage of 0.37 g.L⁻¹ and pH level of 2.51.

The Langmuir (1918) model is valid for monolayer sorption on surfaces containing a finite number of identical sorption sites and the model is written as in equation (10):

q_{e} = \frac{q_{\max} b C_{e}}{1 + b C_{e}}

(10)

where q_e is the equilibrium sorption capacity of Fe-SBB (mg.g⁻¹), C_e is the equilibrium concentration of MO (mg.L⁻¹), q_max is the maximum amount of MO adsorbed (mg.g⁻¹) and b is the constant that is referred to the bonding energy of sorption (mg.L⁻¹). In addition, nonlinear regression analysis was performed in Sigma Plot 12.0 software in order to determine b and q_max values (Figure 8). The formation of the isotherm is the first tentative tool used to diagnose the nature of the adsorption process. The isotherms have been classified by Giles et al. (1974), into four main groups: L, S, H, and C. The experimental adsorption isotherm for the adsorption of the MO dye onto the Fe-SBB is presented in Figure 8. According to the cited classification, the isotherm for the MO displayed an L curve pattern. The isotherm had a concavity toward the abscissa axis, which indicated that as more sites in the substrate are filled, it becomes more difficult for a fresh solute molecule to find an adsorption site (Cabrita et al., 2010). The isotherm parameters and linear regression coefficient (R²) values are shown in Table 7. The results indicated that the Freundlich model employed to describe the heterogeneous systems fitted well, compared with the Langmuir model. Furthermore, the maximum adsorption capacity of MO by Fe-SBB was 127.097 mg.g⁻¹.

Table 7.

Isotherm parameters for the adsorption of MO on Fe-SBB.

Langmuir			Freundlich
q _max	b	R ²	K _f	n	R ²
127.097	0.021	0.991	7.374	1.854	0.994

Thermodynamic study. The thermodynamic parameters can be determined using the distribution coefficient (K) that is dependent on temperature. The change in free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) associated with the adsorption process were calculated by equation (11) (Chen and Wang, 2006):

\ln K = \frac{Δ S \circ}{R} - \frac{Δ H \circ}{RT}

(11)

where R is the universal gas constant (8.314 J.mol⁻¹.K⁻¹) and T is the temperature (K). According to equation (11), ΔH° and ΔS° can be calculated by a curve-fitting program from the slope and intercept of van't Hoff plot of ln K versus 1/T, respectively. The distribution coefficient (K) is calculated from the concentration of MO in the initial concentration (C_i) and that of MO in the supernatant (C_e) after filtration according to the following equation (Wang et al., 2005):

K = \frac{C_{i} - C_{e}}{C_{e}} \times \frac{V}{m}

(12)

where V is the volume of the solution (mL), and m is the mass of the sorbent (g). The Gibbs free energy, ΔG°, of specific adsorption was calculated from the well-known equation:

Δ G \circ = Δ H \circ - T Δ S \circ

(13)

The data calculated from equations (11) to (13) are presented in Table 8. The adsorption of MO molecules decreased with an increase of temperature. This might be due to the fact that the interaction between the MO molecules and the adsorption sites of Fe-SBB was lower at higher temperatures. Also, the positive values of ΔH° indicate the endothermic behavior of the adsorption reaction of MO molecules. The ΔG° for the values adsorption process were −13.073, −13.518, −13.963, and −14.408 kJ.mol⁻¹ at 293, 303, 313, and 323 K, respectively. The negative ΔG° values at different temperatures were due to the fact that the adsorption process is feasible and thermodynamically spontaneous. The negative value of ΔG° that increased with an increase in temperature indicated less efficient adsorption of MO at higher temperature. The degree of spontaneity of the reaction increases with increasing temperature, mainly owing to chemisorption rather than physisorption. The negative values of entropy change (ΔS°) suggest decreased randomness at the solid/solution interface during the sorption MO onto Fe-SBB.

Table 8.

Thermodynamic parameters of MO adsorption on Fe-SBB at different temperatures in Kelvin (with initial MO concentration of 100 mg.L⁻¹, sorbent dosage of 0.37 g.L⁻¹, and pH level of 2.51).

ΔH˚ (J.mol⁻¹)	−ΔS° (J.mol⁻¹.K⁻¹)	−ΔG° (kJmol⁻¹)				R ²
ΔH˚ (J.mol⁻¹)	−ΔS° (J.mol⁻¹.K⁻¹)	293 K	303 K	313 K	323 K	R ²
29.938	44.515	13.073	13.518	13.963	14.408	0.894

Conclusion

The Fe-SBB prepared by pretreatment of SBB (as an agro-industry by-product) by FeCl₃·6H₂O was found to be an efficient adsorbent for the removal of MO molecules from aqueous solutions. FT-IR and SEM analysis were used for characterization of the adsorbent. These analyses showed that SBB particles exhibit non-spherical and fiber-like structures with low porosity. On the other hand, when the SBB treated by the FeCl₃, iron ions were reacted by the surface of the sorbent and microporous active sites distinguished on the surface layer of Fe-SBB. The RSM was utilized to create optimum process condition for MO molecules adsorption. The operating parameters, initial pH of the solution, initial dye concentration, and sorbent dosage are recognized effective on the removal efficiency (R) and adsorption capacity (q_e) of MO. The optimal conditions were pH of 2.51, initial MO concentration of 100 mg.L⁻¹, and sorbent dosage of 0.37 g.L⁻¹, under which the R and q_e were 51.8% and 221.5 mg.g⁻¹, respectively. Also, this study indicated that temperature was an effective parameter for the removal of MO molecules from aqueous solutions under optimal conditions. The kinetics, adsorption isotherms, and thermodynamic studies were considered. The equilibrium data were best explained by the Freundlich isotherm. The kinetics process can be successfully described and well fitted to the pseudo-second-order kinetic model. The thermodynamic parameter studies, i.e., the ΔG° negative values were due to the fact that the adsorption process is feasible and thermodynamically spontaneous and the positive value of ΔH° (29.93 J.mol⁻¹) shows that the process is endothermic, while the value of ΔS° (44.51 J.mol⁻¹.K⁻¹) is negative and predicts the decreased randomness at the solid/liquid interface during the adsorption of MO.

Footnotes

Acknowledgements

The authors wish to thank Mr Hoshyar Gavilian for his assistance (lab technicians of environment laboratory) at environmental science departments.

Declaration of Conflicting Interests

The author(s) declared no potential conflict of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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