DOI:
10.1039/C6RA13286C
(Paper)
RSC Adv., 2016,
6, 6631166319
Simultaneous and rapid dye removal in the presence of ultrasound waves and a nano structured material: experimental design methodology, equilibrium and kinetics†
Received
22nd May 2016
, Accepted 7th July 2016
First published on 7th July 2016
Tin sulfide nanoparticles loaded on activated carbon (SnSAC) were prepared and characterized by FESEM, XRD, FTIR and EDX. Central composite design (CCD) by response surface methodology (RSM) was employed to investigate the influences of process parameters like adsorbent mass, ultrasound time, initial safranin O (SO) and methylene blue (MB) concentrations at pH of 8.0 on the simultaneous adsorption of the two dyes on the SnSAC. Analysis of variance (ANOVA) and ttest statistics were used to check the significance of the independent variables and their interactions on the adsorption efficiency. The predicted values were in good agreement with the experimental data MB (R^{2} = 0.994) and SO (R^{2} = 0.984), revealing the suitability of the constructed equations and CCD success in optimizing the adsorption process. Experimental results demonstrate high applicability and efficiency of dye removal by SnSAC with more than 95% over a very short time (12 mg L^{−1} of each dye, 0.025 g of adsorbent at pH of 8.0). The adsorption for single and binary solutions of SO and MB followed the Freundlich model and the maximum adsorption capacities for MB and SO were estimated to be 71.1 and 67.3 mg g^{−1}, respectively.
1. Introduction
Leather, textile, paper and pulp industries discharge various dyeing wastewater into rivers and lands. The dyes in water due to their high visibility are undesirable^{1} and are associated with varying damage effects to humans and animals,^{2} which take place via direct contact (eye burns), inhalation (rapid or difficult breathing) or indigestion (nausea, vomiting, mental confusion and others).^{3} SafraninO (SO, Fig. S1†) as one of most traditional synthetic dyes is used in flavoring and coloring candies and cookies,^{4} dyeing tannin, cotton, bast fibers, wool, silk, leather and paper.^{5} SO causes injuries to people like irritation to the mouth, throat, tongue, lips and pain in the stomach, which may lead to nausea, vomiting and diarrhea.^{6} Methylene blue (MB, Fig. S1†) is generally used for temporarily coloring hair, dyeing cottons and wools, coating for paper stock and as an analytical reagent.^{7–9} Different biological and physical/chemical methods like anaerobic/aerobic treatment, coagulation/flocculation, oxidation/ozonation, membrane separation and sorption are good approaches for water cleaning, while adsorption process is a successful candidate for dye removal from wastewater.
Activated carbon (AC) as an adsorbent has advantages such as low cost and nontoxic nature, but sometimes it shows a low adsorption capacity.^{10} Due to the presence of porous carbon backbone and various reactive functional groups, it is a good candidate to be impregnated and loaded with diverse nanoscaled materials.^{11} This modification can lead to enhancement in adsorption capacity by increasing reactive center and surface area.^{12} Some of the AC functional groups, –OH, –COOH, –CO and amide, are facile for loading nanoparticle on the surface, which synergistically improve their adsorption capacity of large various species.^{13–15}
Nanomaterials have been extensively studied in diverse areas for their potential applications because of specific physical and chemical properties.^{16,17} Recently, nanostructure based adsorbents have attracted great interest for removing environmental pollutants (e.g. small molecules, heavy metal ions, radionuclides, and organic chemicals),^{18} due to their large specific surface area, hollow and layered structures.^{19} Meanwhile statistical design techniques in adsorption process is effective for efficiency improvement by reducing time and overall costs via optimization of experiments.^{14,20,21}
The objectives of this study were to synthesize and characterize of tin sulfide nanoparticles loaded on active carbon (SnSAC) as well as investigate its application for simultaneous removal of cationic dyes from aqueous solution, via optimization using a central composite design (CCD). The Langmuir and Freundlich adsorption isotherms were used to model the adsorption equilibrium. Several kinetic models such as the pseudo firstorder, pseudo secondorder, intraparticle diffusion and Elovich equations were applied to investigate the dye uptake mechanisms.
2. Materials and methods
2.1. Chemicals and reagents
All chemicals including NaOH, HCl and other reagents were purchased from Merck, Germany. SafraninO (SO) and methylene blue (MB) were purchased from Sigma Aldrich and used as received. A stock solution of each dye was prepared by dissolving pure powder solid in distilled water (100 mg L^{−1}).
2.2. Preparation of adsorbent
A thioacetamide (CH_{3}CSNH_{2}) solution (10 mL, 0.1 mol L^{−1}) was added into a solution of tin(II) acetate (Sn(CH_{3}COO)_{2}) and trisodium citrate (Na_{3}C_{6}H_{5}O_{7}) at pH 6.0 with vigorously stirring and then the mixed solution was diluted to 50 mL. Heating this mixture at 40 °C leads to the slow formation and growth of citratestabilized SnS nanoparticles (milky white precipitate). After 6 h the color of the reaction solution became milky white mixed with light yellow. Then the mixture was separated by a centrifuge and the solid was washed several times with ultrapure water and ethanol to remove the impurities and trisodium citrate. Later, 500 mL of the dispersed SnS nanoparticles suspension (0.5 g L^{−1}) was mixed with 10 g activated carbon under magnetic stirring for 12 h, leading to SnS deposition on the activated carbon surface. The carbonsupported SnS nanoparticles were then dried at 110 °C in an oven for 10 h. A mortar was used to homogeneously ground the carbonsupported SnS nanoparticle powders (SnSAC).
2.3. Apparatus and instruments
The absorbance of dye solution was measured at the optimum wavelength (λ_{max}) of 662 and 518 nm for MB and SO, respectively, using a UVVis spectrophotometer (Perkin Elmer Lambda 25). The spectra of Fourier transform infrared spectroscopy (FTIR) of the adsorbent were obtained using a spectrometer (FTIR 68, JASCO, Japan) in the range of 4000–400 cm^{−1}. An Xray diffractometer (XRD, Philips PW 1800, Nederland) using Cu Kα radiation (40 kV, 40 mA) was used for identification of the structural phase. The surface structures of the adsorbent were obtained using a field emission scanning electron microscope (FESEM, Hitachi S4160, Japan). Chemical composition of the adsorbent was performed by Oxford INCA II energy dispersive Xray field emission scanning electron microscopy (FESEMEDS). An ultrasound bath system with a working frequency of 40 kHz and 130 W power (TecnoGAZ SPA Ultra Sonic System) was used to assist the adsorption of dyes from water onto SnSAC. A Metrohm 686 pH meter (Switzerland) with a glass combination electrode was used throughout this study.
2.4. Ultrasonicassisted adsorption procedure
The stock solutions (100 mg L^{−1}) of SO and MB were diluted to obtain standard solutions in a range of 4 to 20 mg L^{−1}. SnSAC at 0.003–0.0271 g and 50 mL binarycomponent solution were shaken and mixed completely by sonication over 0.5 to 6.5 min with a water bath to control temperature at 25 °C. The liquid and solid phases were separated by centrifuging at 3500 rpm for 3 min, while dye concentration was determined spectrophotometrically at 518 and 662 nm for SO and MB, respectively. The calibration graph of absorbance versus concentration obeyed a linear Lambert–Beer relationship. Removal efficiency expressed as percent adsorption of dyes was determined using the following equation:^{22} 
 (1) 
where C_{0} and C_{e} are the initial and final concentrations of dye (mg L^{−1}), respectively.
The extent of adsorption at equilibrium (q_{e}, mg g^{−1}) was calculated from the initial and equilibrium dye concentrations in solution based on the mass balance equation as,^{19}

 (2) 
where
V is the volume (mL) of solution and
W is the amount (g) of adsorbent. The adsorption isotherm was evaluated using dye concentrations
viz. 12 mg L
^{−1} in single and binary systems at temperature of 25 °C and the optimum solution pH = 8.0.
The kinetics of dye adsorption was studied at temperature of 25 °C for a fixed dye concentration (12 mg L^{−1}) at solution pH of 8.0. The extent of dye adsorbed (q_{t}) at each preselected time interval (t) was evaluated together with that at equilibrium (q_{e}).
2.5. Experimental design
Optimum conditions corresponding to efficient adsorption of SO and MB onto SnSAC were determined by means of central composite design (CCD) under response surface methodology (RSM) to evaluate the relationship between cluster of controlled experimental factors and respective responses according to one or more selected criteria. In this work, the optimization studies were carried out by studying the effects of four variables including adsorbent mass, sonication time, MB and SO concentrations which were coded according to eqn (3):^{10} 
 (3) 
where X is the coded variables, x is the actual variables. The behavior of the system is explained by the empirical secondorder polynomial model. The DesignExpert 7.0.0 (StatEase, Inc., Minneapolis, MN, USA) software was used for regression and graphical analysis of the obtained data. A design of 31 experiments was achieved for the four factors i.e. sixteen factorial points, eight axial (star) points and seven replicates at central points. The optimum values of the selected variables were obtained by solving the regression equation at desired values of the process responses. Each of the parameters was coded at five levels: −α, −1, 0, +1 and +α, while their interval and level in coded values corresponding to RSM and final responses assigned to each point for both dyes are given in Table 1.
Table 1 The central composite experimental design and the response for the yield of dye adsorption
Factors 
Unit 
Levels 
−α 
Low (−1) 
Central (0) 
High (+1) 
+α 
Experimental values of response. Predicted values of response by RSM proposed model. 
A: adsorbent mass 
g 
0.003 
0.009 
0.015 
0.021 
0.0027 
B: ultrasound time 
min 
0.5 
2.0 
3.5 
5 
6.5 
C: MB concentration 
mg L^{−1} 
4 
8 
12 
16 
20 
D: SO concentration 
mg L^{−1} 
4 
8 
12 
16 
20 
Run 
Factors 
R% MB 
R% SO 
A 
B 
C 
D 
Observed^{a} 
Predicted^{b} 
Observed^{a} 
Predicted^{b} 
1 
0.009 
2 
8 
8 
90.0 
88.5 
61.9 
60.6 
2 
0.021 
2 
8 
8 
98.0 
98.3 
90.2 
92.1 
3 
0.009 
5 
8 
8 
91.8 
92.2 
62.9 
65.0 
4 
0.021 
5 
8 
8 
98.0 
98.4 
94.7 
95.0 
5 
0.009 
2 
16 
8 
52.4 
52.1 
58.0 
62.0 
6 
0.021 
2 
16 
8 
80.0 
79.2 
93.6 
89.6 
7 
0.009 
5 
16 
8 
65.4 
65.2 
68.1 
68.6 
8 
0.021 
5 
16 
8 
90.1 
88.9 
94.6 
95.0 
9 
0.009 
2 
8 
16 
84.6 
85.2 
34.3 
36.2 
10 
0.021 
2 
8 
16 
97.0 
97.4 
66.2 
63.6 
11 
0.009 
5 
8 
16 
88.3 
89.3 
44.1 
46.1 
12 
0.021 
5 
8 
16 
98.3 
98.0 
73.9 
72.0 
13 
0.009 
2 
16 
16 
57.7 
57.4 
42.7 
40.3 
14 
0.021 
2 
16 
16 
88.0 
87.0 
64.0 
63.9 
15 
0.009 
5 
16 
16 
71.9 
70.9 
52.2 
52.4 
16 
0.021 
5 
16 
16 
95.3 
97.0 
75.2 
74.4 
17 
0.003 
3.5 
12 
12 
61.1 
61.6 
49.7 
46.2 
18 
0.027 
3.5 
12 
12 
97.4 
97.5 
96.1 
99.7 
19 
0.015 
0.5 
12 
12 
79.6 
80.8 
50.2 
51.6 
20 
0.015 
6.5 
12 
12 
95.1 
94.5 
67.8 
66.5 
21 
0.015 
3.5 
4 
12 
98.4 
97.6 
72.1 
70.9 
22 
0.015 
3.5 
20 
12 
58.8 
60.2 
73.5 
74.7 
23 
0.015 
3.5 
12 
4 
86.3 
87.7 
88.5 
86.7 
24 
0.015 
3.5 
12 
20 
93.2 
92.5 
40.2 
42.0 
25 
0.015 
3.5 
12 
12 
94.4 
91.5 
72.1 
70.4 
26 
0.015 
3.5 
12 
12 
89.7 
91.5 
68.2 
70.4 
27 
0.015 
3.5 
12 
12 
91.0 
91.5 
72.9 
70.4 
28 
0.015 
3.5 
12 
12 
91.9 
91.5 
69.9 
70.4 
29 
0.015 
3.5 
12 
12 
90.7 
91.5 
67.8 
70.4 
30 
0.015 
3.5 
12 
12 
92.1 
91.5 
72.6 
70.4 
31 
0.015 
3.5 
12 
12 
90.5 
91.5 
69.6 
70.4 
3. Results and discussion
3.1. Characterization of the adsorbent
The FESEM micrograph of SnSAC (Fig. 1a) shows aggregation of SnS nanoparticles due to their extremely small dimensions and high surface energy, while energydispersive Xray spectroscopy (EDX) from different sample spots (Fig. 1b and c) confirm the presence of C, Sn and S in elemental composition of the SnSAC. Fig. 2a shows XRD pattern of SnSAC. A prominent peak was observed at 2θ = 29.95°, which corresponds to the (1 1 1) reflection plane of SnS and the other peaks at 2θ = 22.46°, 24.93°, 27.47°, 28.33°, 39.00°, 43.12°, 44.56°, 48.82°, 50.27°, 54.96° and 68.38° are corresponding to the (1 2 0), (1 2 0), (0 2 1), (1 0 1), (1 3 1), (1 4 2), (0 0 2), (2 1 1), (1 1 2), (1 2 2) and (2 1 2) reflection planes of SnS, respectively. The patterns suggest SnS (JCPDS: 390354) has the herzenbergite orthorhombic structure (lattice parameters, a = 4.3137 Å, b = 11.2583 Å and c = 3.9958 Å), where the Sn and S are tightly bonded in a layer. This implies that the particles are polycrystalline SnS with a strong (1 1 1) reflection plane. The preferred orientation of the particles is due to the growth process controlled by nucleation. The particle size from the XRD pattern was found around 48 nm. In the XRD spectrum, no characteristic peaks were observed for other impurities such as SnS_{2}, Sn_{2}S_{3}, and Sn_{3}S_{4}, implying the formation of singlephase mono sulphide. Fig. 2b shows FTIR spectrum of SnSAC with strong and sharp bands at 615, 1000–1200 and 2354 cm^{−1}, which are attributed to the characteristic peaks of SnS.^{23,24} Also, a doublet band was observed at 1047 and 1087 cm^{−1}, which is due to SO_{3} stretching. Another broad band appears at 3250–3500 cm^{−1}, ascribing to OH stretching vibration. The FTIR and XRD confirm the presence of SnS nanoparticles.

 Fig. 1 (a) SEM image and (b and c) EDX images of the SnSAC.  

 Fig. 2 (a) XRD spectra, (b) FTIR spectra of the SnSAC and (c) the effect of solution pH on dye adsorption onto adsorbent (C_{0} = 8 mg L^{−1}, adsorbent mass = 0.021 g, sonication time = 4 min and T = 25 °C).  
3.2. Effect of solution pH
Solution pH is one of the important parameters controlling dye adsorption. Its effect on SO and MB adsorption onto SnSAC in binary systems at a pH range of 2.0–12.0 is shown in Fig. 2c. Increasing pH from 2.0 to 12.0 leads to enhanced dye removal from 60 to 95%, which is related to the fact that cationic dyes take a positive charge in water. Thus, in acidic solutions (lower pH), the positively charged surface of a sorbent tends to hinder the adsorption of cationic dyes, while pH rising causes dye adsorption due to an enhanced electrostatic force^{25} of the adsorbent with negative charge at pH > pH_{ZPC}. The maximum adsorption of SO and MB takes place at around pH 8.0, which was selected for all further adsorption experiments.
3.3. Statistical analysis
The experiments were conducted according to the design matrix and the corresponding results are listed in Table 1. The quadratic equations for prediction of the optimum point were obtained according to the CCD and input variables as follows: 
Y_{R% MB} = 98.7 + 1842.0A + 1.8B − 3.3C − 1.2D − 97.3AB + 181.0AC + 25.3AD + 0.4BC + 0.02BD + 0.2CD − 82750.0A^{2} − 0.4B^{2} − 0.2C^{2} − 0.02D^{2}
 (4) 

Y_{R% SO} = 41.4 + 2844A + 8.2B − 0.9C − 1.2D − 41.4AB − 40.1AC − 42.0AD + 0.1BC + 0.2BD + 0.04CD + 1717A^{2} − 1.3B^{2} + 0.04C^{2} − 0.1D^{2}
 (5) 
where Y is the dye adsorption efficiency (R% of SO and MB), A, B, C and D are representing adsorbent mass, ultrasound time, initial SO and MB concentrations, respectively. The analyses of variance (ANOVA) (Table S1†) suggest that the model equation derived by RSM could be used to describe the dye removal by SnSAC adsorbent. It is wellknown that a corresponding variable is more significant if its absolute pvalue is smaller than 0.05. The calculated Fvalues corresponding to MB and SO adsorption response models are 185.9 and 70.2, respectively, exceeding the tabulated Fvalue (F_{0.05}(14, 16) = 2.37) at the 5% level and justify significant differences.^{26} The lackoffit p values of 0.62 for MB and 0.15 for SO, respectively, suggest the applicability and efficiency of the models for good representation of experimental data at various conditions.^{27} A high RSquared (R^{2}) value (close to 1) ensures a satisfactory adjustment of the quadratic model and the experimental data.^{28} As presented in Table S1,† the models present high R^{2} values of 99.4 and 98.4% for MB and SO removal, respectively, indicating good agreement between the experimental and predicted results. Also, the predR^{2} values of 97.6 and 92.2% for MB and SO, respectively, have reasonable and good agreement with the adjR^{2} values of 98.8 and 97.0% for MB and SO, respectively. The model's adequate precision (signal to noise ratio) was 25.43, indicating adequate signal and also demonstrating the usability of models to navigate the design space. Fig. 3a–d shows that the predicted values were close to the experimental results of MB and SO adsorption. Fig. 3e and f shows that the residuals were close to the straight line and scattered randomly around with no particular pattern and abnormal adsorption behavior.^{25} The ratios of signal to noise are greater than 4 at 46.61 and 31.87 for MB and SO, respectively, further confirming that these models can be used to navigate the design space.

 Fig. 3 (a and b) Predicted vs. experimental, (c and d) residuals vs. run number and (e and f) normal probability plot of residuals dyes removal efficiency.  
3.4. Effect of variables as response surface and counter plots
The relationship between independent and dependent variables is illustrated in threedimensional representations of the response surfaces. The higher values of MB removal efficiencies were obtained by the increases in agitation time and SnSAC mass (Fig. 4a). The maximum dye removal was found at 4 min sonication.

 Fig. 4 The response surface plots (a) showing simultaneous influence of adsorbent mass and ultrasound time on MB adsorption (b) showing the interaction between adsorbent mass and SO concentration on SO adsorption and (c) showing the interaction between ultrasound time and SO concentration.  
The increased initial dye concentrations also lead to enhancement of adsorption rate and strong dye removal percentage (Fig. 4b). Meanwhile, a larger sonication time enhanced adsorbent dispersion into solution via ultrasonic power and improved adsorption efficiency (Fig. 4c).
3.5. Optimizations using the desirability function
The maximum adsorption efficiencies of MB and SO dyes on SnSAC and the corresponding optimal experimental conditions were determined using the desirability function by the Design expert software (Fig. 5) and confirmed by further experiments. The optimum conditions were found to be pH 6.0, 3.5 min sonication, 0.025 g SnSAC, and 12 mg L^{−1} of MB and SO, giving the maximum MB and SO removal efficiencies of 98.2 and 95.6%, respectively. The predicted optimum conditions were checked experimentally by running six experiments under the same conditions at 25 °C, revealing that MB and SO adsorption efficiencies were 97.6 ± 0.3% and 94.2 ± 0.7%, respectively. The high agreement between replicated results with predicted values strongly supports high reliability and efficiency of the central composite design for the evaluation and optimization of the adsorption variables on removal efficiency of MB and SO.

 Fig. 5 Desirability ramp for numerical optimization of four independent variables, adsorbent mass, ultrasound time, MB concentration and initial SO concentration.  
3.6. Kinetic modelling of dye adsorption
The pseudo firstorder (eqn (6)), secondorder kinetic (eqn (7)), Elovich (eqn (8)) and intraparticle diffusion (eqn (9)) models were used to describe the adsorption kinetics of dyes onto SnSAC (Table 2).^{29–32} 
 (6) 

 (7) 
where q_{e} and q_{t} represent the adsorption capacities (mg g^{−1}) of SnSAC at equilibrium and at a particular time t (min), respectively. k_{1} and k_{2} are the firstorder and secondorder kinetic rate constants.
Table 2 Obtained kinetic model parameters for the adsorption of dyes onto SnSAC (C_{0} = 12 mg L^{−1}, adsorbent mass = 0.025 g, pH = 6.0, sonication time = 0.5–7.0 min and T = 25 °C)
Model 
Parameters 
0.025 g adsorbent 
Single component 
Multicomponent 
MB 
SO 
MB 
SO 
Pseudo first kinetic 
K_{1} 
0.37 
0.74 
1.26 
0.84 
q_{e(calc)} 
4.31 
1.06 
41.5 
13.7 
R^{2} 
0.724 
0.619 
0.959 
0.950 
Pseudo second kinetic 
K_{2} 
0.22 
0.36 
0.072 
0.27 
q_{e(calc)} 
24.3 
23.9 
25.4 
23.5 
R^{2} 
0.999 
0.999 
0.999 
0.999 
Intraparticle diffusion 
K_{dif} (mg g^{−1} min^{−1/2}) 
2.37 
2.87 
5.28 
3.26 
C (mg g^{−1}) 
17.9 
16.6 
10.3 
15.0 
R^{2} 
0.868 
0.794 
0.867 
0.831 
Elovich 
β (g mg^{−1}) 
0.521 
0.422 
0.235 
0.375 
α (mg g^{−1} min^{−1}) 
65.6 
70.4 
85.2 
71.1 
R^{2} 
0.968 
0.925 
0.962 
0.948 
Experimental data 
q_{e(exp)} (mg g^{−1}) 
23.8 
23.6 
23.5 
23.1 
The R^{2} of the first and second order kinetic models were compared to check the suitable model for dye adsorption onto SnSAC. The deviation of equilibrium adsorption capacity (q_{e}) obtained from the models and the experimental values was also calculated.

 (8) 
α is the initial adsorption rate and
β is related to the extent of surface coverage and the activation energy for chemisorptions.

q_{t} = K_{dif}t^{1/2} + C
 (9) 
where
K_{dif} is the intraparticle diffusion rate constant, and
C is a constant about the thickness of the boundary layer. According to the model, if the regression of q
_{t} vs. t^{1/2} is linear and passes through the origin, then intraparticle diffusion is the sole ratelimiting step and the adsorption process is controlled by intraparticle diffusion.
Based on the correlation coefficients, the adsorption of SO and MB is best described by the pseudosecond order equation (Table 2).
As shown in Table 2, the k_{2} values calculated for single system are comparatively higher than those for binary system, suggesting a lower affinity for adsorbent exchange sites. The R^{2} value (Table 2) for this model was far from the unity, which shows that the intraparticle diffusion model is not applicable.
3.7. Equilibrium isotherms for dye adsorption
The experimental data were fitted to the Langmuir and Freundlich models. In the Langmuir sorption model, sorption of sorbate takes places at specific homogeneous sites within the adsorbent and valid for monolayer sorption onto adsorbents.^{33} The expression of the Langmuir model is given by the following equation:^{34} 
 (10) 
where C_{e} is the equilibrium dye concentration in the solution (mg L^{−1}), k_{L} is the Langmuir sorption constant (L mg^{−1}), and Q_{m} is the theoretical maximum sorption capacity (mg g^{−1}). The values of the constants of Langmuir model along with the regression coefficient (R^{2}) are presented in Table 3.
Table 3 Parameters of investigated adsorption models for adsorption of dyes from aqueous solution onto SnSAC (C_{0} = 5–30 mg L^{−1}, adsorbent mass = 0.025 g, pH = 6.0, sonication time = 3.5 min and T = 25 °C)
Isotherm 
Parameters 
Single component 
Multicomponent 
MB 
SO 
MB 
SO 
Langmuir 
Q_{m} (mg g^{−1}) 
71.0 
67.3 
53.9 
40.3 
K_{a} (L mg^{−1}) 
70.3 
1.65 
3.06 
5.97 
R^{2} 
0.964 
0.949 
0.985 
0.988 
Freundlich 
1/n 
0.473 
0.488 
0.276 
0.198 
K_{F} (L mg^{−1}) 
10.7 
1.46 
4.65 
4.37 
R^{2} 
0.998 
0.995 
0.998 
0.998 
The Freundlich equation can be described by assuming a heterogeneous surface with adsorption on each class of sites. Freundlich proposed the equation as:^{35}

 (11) 
where
K_{F} is a constant indicative of the relative adsorption capacity of the adsorbent (mg g
^{−1}) and the constant, 1/
n indicates the intensity of the adsorption.
The validity of the isotherm models was tested by comparing the experimental and calculated data. Based on correlation coefficients (R^{2}) (Table 3), it is noted that the Freundlich equation gives the best fit. The values of 1/n between 0.1 < 1/n < 1.0 represent good adsorption of dyes onto SnSAC.^{36} The ultimate adsorption capacity of the adsorbent can be calculated by substituting the required equilibrium concentration in the Freundlich equation.
3.8. Comparison of SnSAC with other adsorbents
The monolayer adsorption capacity (Q_{max}) and contact time of various other adsorbents reported in literature are shown in Table 4. It is obvious that the SnSAC synthesized in this work exhibits a much higher Q_{max} and lower contact time, which suggests that the assynthesized nanoparticles can be considered as a promising adsorbent for the removal of MB and SO dyes from wastewater.
Table 4 Comparison of maximum equilibrium sorption capacity of dyes on different adsorbents
Adsorbent 
Dye 
Adsorption capacity (Q_{max} (mg g^{−1})) 
Contact time (min) 
Ref. 
MWCNTs filled with Fe_{2}O_{3} particles 
MB 
42.9 
60 
37 
Ag nanoparticles loaded on activated carbon 
MB 
71.4 
15 
38 
NiS nanoparticles loaded on activated carbon 
MB 
52.0 
5.5 
39 
CuO nanoparticles loaded on activated carbon 
MB 
10.5 
15 
40 
Graphene nanosheet/magnetite (Fe_{3}O_{4}) composite 
MB 
43.8 
20 
9 
MgO decked multi layered graphene 
SO 
137.6 
120 
41 
Mesoporous MCM41 
SO 
68.8 
120 
42 
NiSnanoparticles loaded on activated carbon 
SO 
53.2 
5.5 
39 
Activated carbon 
SO 
19.0 
3.0 
43 
ZnOnanorods loaded on activated carbon 
SO 
55.2 
3.0 
43 
Activated carbon 
MB 
33.6 

This work 
SO 
29.7 
3.5 
SnSAC 
MB 
71.0 
SO 
67.2 

4. Conclusions
This study shows RSM and central composite design were successfully employed for experimental design. Satisfactory empirical models were obtained to correlate MB and SO removal percentages to their initial concentration, adsorbent mass and ultrasound time. The process optimization for maximum adsorption of the dyes identified the process conditions (pH 8.0, 0.025 g SnSAC, and 12 mg L^{−1} of each dye). Moreover, the kinetic studies showed the best fit with pseudosecond order rate equation. Besides, the adsorption equilibrium showed the best fitting with the Freundlich isotherm equation.
Acknowledgements
The authors thank the Research Council of Shahrekord University and the University of Yasouj, Iran for all supports provided.
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Footnote 
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra13286c 

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