Optimization of the combined ultrasonic assisted/adsorption method for the removal of malachite green by zinc sulfide nanoparticles loaded on activated carbon: experimental design

Abstract

The aim of the present study is experimental design optimization applied to the removal of malachite green (MG) from aqueous solution by ultrasound-assisted removal onto zinc sulfide nanoparticles loaded on activated carbon (ZnS-NP-AC). The nanomaterial was characterized using different techniques such as FESEM, BET, XRD and UV-Vis measurements. The effects of variables such as pH, initial dye concentration, adsorbent dosage (g) and sonication time on MG removal were studied using central composite design (CCD) and the optimum experimental conditions were found with a desirability function (DF) combined with response surface methodology (RSM). Fitting the experimental equilibrium data to various isotherm models showed the suitability and applicability of the Langmuir model and the second-order equation model controls the kinetics of the adsorption process. A small amount of proposed adsorbent (0.025 g) is applicable for successful removal of 22 mg L⁻¹ MG (>99%) in a short time (5.0 min).

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1. Introduction

The dyes in the effluents of industries such as textile, leather, paper and plastics are a serious concern because of their adverse effects to human beings and the environment.^1,2 The dyes’ significance and importance in this associated environmental problem come from their high visibility, undesirability and recalcitrance. Therefore, their removal from such industrial effluents is a challenging requirement to produce a safe and clean environment.³

Malachite green (MG) is classified as a basic dye used in many industries (silk, wool, cotton, leather and paper) for coloring purposes; the structure is shown in Fig. 1. Furthermore, it is also employed as a therapeutic agent to treat parasites, and fungal and bacterial infections.^4,5 Despite its extensive use, MG dye has toxic properties which are known to cause injury to humans and animals by inhalation or ingestion.⁶ Therefore, the removal of MG from wastewater before discharging to the environment is necessary.

Fig. 1 Chemical structure of MG.

Many technologies have been developed for dye removal from industrial effluents including flocculation, coagulation, precipitation, biosorption, membrane filtration, electrochemical techniques and adsorption.^7–10 Among these, the adsorption technique has the advantages of a simple design, high efficiency and capacity guaranteed, ease of operation, and large scale ability of re-generable adsorbents.^11–13 Various materials such as activated carbon (AC), natural materials, polysaccharide materials, starch, bio-adsorbents and agricultural wastes have been used for the removal of dyes from solution.^14–17 AC as a non-toxic, low cost and easily available adsorbent has a relatively high surface area, porous structure, high total pore volume and large adsorption capacity. It is considered as a universal adsorbent for the removal of pollutants such as dyes from wastewater with fast adsorption kinetics.¹⁸ AC contains various reactive sites such as OH, COOH, C=O and amide groups that coincide with nanoparticle properties synergistically to improve the efficiency of an adsorption based treatment procedure. In this technique, the use of nanoscale materials with high surface areas enhances the removal percentage and adsorption capacity of AC based adsorbents. Nanoparticles typically possess notable properties such as a high number of reactive atoms, high mechanical and thermal strength, highly ordered structure and large number of vacant reactive surface sites in addition to metallic or semi-metallic behavior which can be applied to the removal of various toxic materials.^19,20

Ultrasound irradiation is well known to accelerate chemical processes due to the phenomenon of acoustic cavitation, that is, the formation, growth and collapse of micrometrical bubbles, formed by the propagation of a pressure wave through a liquid. Ultrasound, and its secondary effect cavitation (nucleation, growth and transient collapse of tiny gas bubbles), improve mass transfer through a convection pathway that emerges from physical phenomena such as micro-streaming, micro-turbulence, acoustic (or shock) waves and microjets without a significant change in equilibrium characteristics of the adsorption/desorption system.^21–23 Shock waves have the potential to create microscopic turbulence within interfacial films surrounding nearby solid particles. Acoustic streaming induced by a sonic wave is the movement of liquid, which can be considered to be the conversion of sound to kinetic energy.²⁴ Ultrasound has been proven to be a very useful tool in intensifying mass transfer processes and breaking affinities between adsorbate and adsorbent.^25,26

There are several experimental variables affecting ultrasound-assisted removal of MG. A statistically designed experiment may be preferred to decrease the number of experiments and consider interactions between variables.^27,28 Methods for the design and optimization of experiments and evaluation of the variables’ influence are needed for simultaneous optimization while considering the interaction of variables.

In the present work, an ultrasound assisted adsorption method as a simple, sensitive, inexpensive and rapid/assisted adsorption method followed by UV detection has been developed for removal of MG. The influence of important variables (sonication time, pH, initial MG concentration and amount of adsorbent) were investigated and optimized by central composite design (CCD) combined with response surface methodology (RSM) using the desirability function (DF) to maximize the performance achieved with this method. The results obtained from the presented models were compared with the experimental values.

Zinc sulfide nanoparticle loaded AC (ZnS-NP-AC) was synthesized and subsequently characterized via different techniques such as field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM) and UV-Vis measurements. Then the adsorption kinetics and isotherms of MG removal on this adsorbent were investigated. The adsorption rates were evaluated by fitting the experimental data to conventional kinetic models such as pseudo first and second-order and intraparticle diffusion models. The proposed sorbent is useful for quantitative adsorption of MG with high sorption capacities in a short time.

2. Experimental

2.1. Instruments and reagents

An ultrasonic bath with a heating system (Tecno-GAZ SPA Ultra Sonic System, Italy) at a frequency of 60 Hz and a power of 130 W was used for the ultrasound-assisted adsorption procedure. The pH measurements were carried out using a pH/ion meter model-686 (Metrohm, Switzerland, Swiss) and the MG concentration was determined using a Jusco UV-Vis spectrophotometer model V-530 (Jasco, Japan) at a wavelength of 619 nm.

The morphology of the ZnS-NP-AC was observed by scanning electron microscopy (SEM; Hitachi S-4160, Japan) under an acceleration voltage of 15 kV. X-ray diffraction (XRD) patterns were recorded with an automated Philips X’Pert X-ray diffractometer with Cu Kα radiation (40 kV and 30 mA) for 2θ values over 10–80°. Absorption measurements were carried out on a Perkin Elmer Lambda 25 spectrophotometer using a quartz cell with an optical path of 1 cm. The stock solution (200 mg L⁻¹) of MG was prepared by dissolving 100 mg of solid dye in 500 mL double distilled water and the working concentrations were prepared daily by suitable dilution. A BET surface analyzer (Quantachrome NOVA 2000) was used to measure nitrogen adsorption–desorption isotherms at 77 K, the samples were degassed using helium at 553 K for 3 h before this measurement.

All chemicals including malachite green, zinc acetate thioacetamide, activated carbon, NaOH, and HCl were purchased from Merck Co. (Darmstadt, Germany) with the highest purity available.

2.2. Ultrasound assisted adsorption method

The removal of dye from the solutions was investigated using ultrasound power combined with ZnS-NP-AC. The sonochemical adsorption experiment was carried out in a batch mode as follows: specified amounts of dye solution (50 mL) at known concentration (22 mg L⁻¹) and initial pH (6) with a known amount of adsorbent (0.025 g) were loaded into the flask and maintained for the desired sonication time (5.0 min). At the end of the adsorption experiment, the sample was immediately centrifuged and analyzed.

2.3. Measurements of dye uptake

The dye concentrations were determined according to a general photometry method at a maximum wavelength (619 nm) over a working concentration. The efficiency of MG removal was determined at different experimental conditions according the CCD method. The MG removal percentage was calculated using the following equation:

% MG removal = ((C₀ − C_t)/C₀) × 100 (1)

where C₀ (mg L⁻¹) and C_t (mg L⁻¹) are the concentrations of the target at time t = 0 and after time t respectively. The adsorbed MG amount (q_e (mg g⁻¹)) was calculated by the following mass balance relationship:

q_e = (C₀ − C_e)V/W (2)

where C₀ and C_e (mg L⁻¹) are the initial and equilibrium dye concentrations in aqueous solution, respectively, V (L) is the volume of the solution and W (g) is the mass of the adsorbent.

2.4. Synthesis of zinc sulfide nanoparticles

Zinc sulfide nanoparticles (ZnS) were synthesized in an aqueous solution based on the reaction of zinc acetate (Zn(CH₃COO)₂) with thioacetamide (CH₃CSNH₂) as previously reported.²⁹ All reactions were carried out in deoxygenated water under nitrogen. In a typical synthesis, 10 mL of freshly prepared thioacetamide solution (0.1 M) was added into another solution containing Zn(CH₃COO)₂ and tri-sodium citrate (Na₃C₆H₅O₇) at a pH of 6.0 with vigorous stirring. The amounts of zinc acetate, thioacetamide, and tri-sodium citrate introduced were 0.5, 1, and 5 mmol, respectively, in a total volume of 50 mL. The resulting mixture was heated to 40 °C, and the growth of citrate-stabilized ZnS nanoparticles started gradually. After about 10 min, the solution turned milky white, which indicated the initial formation of ZnS nanoparticles. The mixture was maintained at 40 °C for 6 h and the color of the reaction solution became milky white mixed with light yellow. The ZnS nanoparticles obtained were separated from the reaction mixture by centrifugation, and washed several times with ultra-pure water and ethanol to remove impurities and tri-sodium citrate. Finally, the ZnS nanoparticles were dried in a vacuum oven (ca. 0.1 MPa) for 6 h prior to being characterized.

For the preparation of ZnS-NP-AC, 500 mL of the dispersed ZnS nanoparticles suspension (0.5 g L⁻¹) was mixed with activated carbon (10 g) in a 1000 mL flask under magnetic stirring for up to 12 h, resulting in the deposition of the ZnS nanoparticles on the activated carbon. The carbon-supported ZnS nanoparticles were then filtered and extensively washed with double distilled water. The carbon-supported ZnS nanoparticles were generally dried at 110 °C in an oven for 10 h. A mortar was used to homogeneously grind the carbon-supported ZnS nanoparticles into powder.

2.5. Central composite design

It is beneficial to evaluate and identify the most important variables with a minimum number of runs via an appropriate model. A five-level CCD was used to investigate the significance of the effects of the parameters that were designed using STATISTICA 7 (Table 1). The mathematical relationship between the four independent variables can be approximated by the second order polynomial model:³⁰where y is the predicted response (removal percentage); X_is are the independent variables (sonication time, pH, initial MG concentration and amount of adsorbent) that are known for each experimental run. The parameter β₀ is the model constant; β_i is the linear coefficient; β_ii is the quadratic coefficient and β_ij is the cross-product coefficient.

Table 1 Experimental factors and levels in the central composite design

Factors	Levels
	Low (−1)	Central (0)	High (+1)	−α	+α
(X1) sonication time (min)	2.0	3.5	5.0	0.5	6.5
(X2) pH	4	5.5	7	2.5	8.5
(X3) adsorbent dosage (g)	0.010	0.016	0.022	0.004	0.028
(X4) MG concentration (mg L^−1)	15	25	35	5	45

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Runs	X1	X2	X3	X4	Removal (%)
1	2	4	0.010	35	49.59
2	2	4	0.022	15	96.66
3	2	7	0.010	15	68.52
4	2	7	0.022	35	75.61
5	5	4	0.010	15	75.55
6	5	4	0.022	35	85.20
7	5	7	0.010	35	73.98
8	5	7	0.022	15	99.63
9 (C)	3.5	5.5	0.016	25	82.04
10 (C)	3.5	5.5	0.016	25	80.44
11	2	4	0.010	15	68.52
12	2	4	0.022	35	70.73
13	2	7	0.010	35	57.72
14	2	7	0.022	15	97.52
15	5	4	0.010	35	68.29
16	5	4	0.022	15	99.18
17	5	7	0.010	15	73.33
18	5	7	0.022	35	88.58
19 (C)	3.5	5.5	0.016	25	78.88
20 (C)	3.5	5.5	0.016	25	80.88
21	0.5	5.5	0.016	25	75.55
22	6.5	5.5	0.016	25	94.88
23	3.5	2.5	0.016	25	69.77
24	3.5	8.5	0.016	25	83.33
25	3.5	5.5	0.004	25	44.44
26	3.5	5.5	0.028	25	96.88
27	3.5	5.5	0.016	5	97.70
28	3.5	5.5	0.016	45	66.93
29 (C)	3.5	5.5	0.016	25	79.33
30 (C)	3.5	5.5	0.016	25	81.11

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Response surface methodology (RSM) is a combination of mathematical and statistical techniques followed by optimal region determination which allows the determination and evaluation of the relative significance of parameters, even in the presence of complex interactions.³¹ The modeling is performed by adjusting first or second order polynomial equations to the experimental responses obtained in the experimental design, followed by a variance analysis (ANOVA) of the model. The validated model can be plotted in a tridimensional graph, generating a surface response that corresponds to a response function which can be used to determine the best operating conditions of the process.

2.6. Desirability function

The desirability function approach (DF) is a common and established technique to discover global optimal conditions based on Derringer’s desirability function.^32,33

Each predicted response Û_i and experimental response U_i can be transformed to create a function for each individual response d_i and finally determine a global function D that should be maximized following selection of optimum values of affective variables with consideration of their interaction. Firstly, the response (U) is converted into a particular desirability function (df_i) in the range of 0 to 1. The d_i = 0 represents completely undesirable response or minimum applicability and d_i = 1 represents completely desirable or ideal response. The individual desirability scores d_is are then combined using a geometrical mean, to a single overall (global) desirability D, which is optimized to find the optimum set of input variables:

where df_i indicates the desirability of the response U_i (i = 1, 2, 3,…, n) and v_i represents the importance of responses.

The individual desirability function for the ith characteristic is computed via the following equation:

In eqn (5), α and β are the lowest and highest obtained values of the response i and w_i is the weight.

3. Results and discussion

3.1. Characterization of adsorbent

Absorption spectra measurements for the prepared ZnS nanoparticles were conducted for 1 h to 6 h intervals and the variation of absorbance value with wavelength is shown in Fig. 2a. The ZnS nanoparticle solution shows a well-resolved absorption maximum corresponding to the first electronic transition with a sufficiently narrow size distribution of ZnS nanoparticles. The shift of absorption peaks to shorter wavelengths shows the decrease in size of the nanoparticles as a consequence of the quantum confinement. The figure shows that the citrate-stabilized ZnS nanoparticles have absorption edges in the range of 290–320 nm (4.26–3.86 eV). From the absorption spectra, the energy band gap of the ZnS nanoparticles was obtained using the following relationship:³⁴

(αhν)² = A(E_g − hν) (6)

where E_g represents the nanoparticle band gap and A is a characteristic constant. A typical graph of (αhν)² versus energy (hν) for ZnS nanoparticles was plotted. By extrapolation of the linear portion of the curve respective to (αhν)² = 0, the energy band gap was determined. The straight-line characteristic of the curve shows that the ZnS nanoparticles have a direct band gap in the range of 4.26–3.86 eV, while the bulk material has a band gap of 3.67 eV.

Fig. 2 (A) Variation of absorption spectra of the ZnS nanoparticles at different time intervals and (B) the X-ray diffraction (XRD) pattern of the citrate-stabilized ZnS nanoparticles.

Fig. 2b shows the XRD pattern obtained from powdered ZnS nanoparticles synthesized at room temperature. The standard XRD pattern for ZnS (Joint Committee for Powder Diffraction Standards, JCPDS card no. 05-0566) is given at the bottom of Fig. 2b. The three broad peaks observed in the diffractogram at around 28.56°, 47.43° and 56.25° assigned to the planes (111), (220) and (311), respectively, show the cubic phase³⁵ of ZnS-NP-AC, while additional peaks corresponding to ZnO or Zn(OH)₂ were not observed. The volume average hydrodynamic diameter for the ZnS nanoparticles (determined by laser light scattering) was found to be around 60 nm with narrow size distribution (Fig. 3a). An FESEM image of the ZnS nanoparticles (Fig. 3b) reveals that the ZnS nanoparticles are semi-cubic in shape and quite uniform in size distribution (in the range of 40–70 nm). The particle size was measured directly from this FESEM image and agreed with respective approximate value determined by laser light scattering.

Fig. 3 (a) Histogram of the ZnS nanoparticle size distribution and (b) FESEM image of the ZnS nanoparticles.

Fig. 4a and b show the pore volume and pore area distribution curves of ZnS-NP-AC based on the nitrogen equilibrium adsorption isotherm at 77 K. As can be seen, the adsorbent exhibits fairly narrow pore size distribution in the mesoporous domain. The BET surface area of ZnS-NP-AC was evaluated to be 1316 m² g. The measured total pore volume for ZnS-NP-AC was 0.658 cm³ g⁻¹ while the micropore volume was 0.197 cm³ g⁻¹. As can be seen from BET analysis, ZnS-NP-AC has a porous structure and this evidence supports the idea that the enhancement of the surface area results in a good sorption capacity of such materials.

Fig. 4 Pore size distribution curves of the ZnS-NP-AC.

3.2. Central composite design (CCD)

As presented in Table 1, four independent variables (sonication time (X₁), pH (X₂), adsorbent dosage (X₃) and MG concentration (X₄)) were prescribed into three levels (low, basal and high) with coded values (−1, 0, +1) and the star points of +2 and −2 for +α and −α respectively were selected for each set of experiments. The levels of each factor are presented in Table 1. 30 experiments for the optimization were performed according to the CCD and their responses are presented in Table 1. The main, interaction and quadratic effects were evaluated in this design. To find the most important effects and interactions, analysis of variance (ANOVA) was calculated using STATISTICA 7.0 (Table 2). A p-value less than 0.05 in the ANOVA table indicates the statistical significance of an effect at 95% confidence level. An F-test was used to estimate the statistical significance of all the terms in the polynomial equation within a 95% confidence interval. Data analysis gave a semi-empirical expression of extraction recovery (ER%) with following equation:

y = 80.45 + 4.90x₁ + 2.01x₂ + 11.77x₃ − 7.11x₄ + 1.08x₁² − 1.08x₂² − 2.55x₃² − 0.92x₁x₃ + 2.87x₁x₄ + 1.44x₂x₄ − 2.28x₃x₄ (7)

Table 2 Analysis of variance (ANOVA) for CCD

Source of variation	Sum of square	Degree of freedom	Mean square	F-Value	P-Value
X1	575.796	1	575.796	419.923	0.000005
X1^2	32.250	1	32.250	23.520	0.004675
X2	97.069	1	97.069	70.792	0.000389
X2^2	32.131	1	32.131	23.433	0.004712
X3	3325.250	1	3325.250	2425.077	0.000000
X3^2	178.992	1	178.992	130.538	0.000090
X4	1214.704	1	1214.704	885.874	0.000001
X4^2	3.512	1	3.512	2.561	0.170415
X1X2	2.693	1	2.693	1.964	0.219977
X1X3	13.569	1	13.569	9.896	0.025501
X1X4	131.819	1	131.819	96.135	0.000188
X2X3	0.261	1	0.261	0.190	0.680980
X2X4	33.083	1	33.083	24.127	0.004428
X3X4	83.437	1	83.437	60.850	0.000555
Lack of fit	56.436	10	5.644	4.116	0.065902
Pure error	6.856	5	1.371
Total SS	5813.592	29

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The plot of experimental values of the removal (%) values versus those calculated from the equation indicated a good fit, as shown in Fig. 5.

Fig. 5 The experimental data versus the predicted data of normalized removal of MG.

3.3. Response surface methodology

In the next step of the design, a response surface methodology (RSM) was developed by considering all the significant interactions in the CCD to optimize the critical factors and describe the nature of the response surface in the experiment. Fig. 6 represents the relevant fitted response surfaces for the design and depicts the response surface plots of removal (%) versus significant variables. These plots were obtained for a given pair of factors at fixed and optimal values of other variables. The curvatures of these plots indicate the interactions between the variables.

Fig. 6 Response surfaces for the CCD: (a) adsorbent dosage–sonication time; (b) adsorbent dosage–pH; (c) adsorbent dosage–MG concentration; (d) sonication time–MG concentration; (e) pH–sonication time and (f) pH–MG concentration.

For the adsorbent dosage, the response surfaces plots shown in Fig. 6a–c show the changes in the percentage removal as a function of adsorbent dosage and other variables with interaction of them. The percentage removal increased with an increase in adsorbent dosage due to its high specific surface area and small particle size. At higher values, probably due to an increase in surface area and availability of more active adsorption sites, the rate of adsorption significantly increased. At lower amounts of ZnS-NP-AC, the removal percentage significantly decreased because of a higher ratio of dye molecules to vacant sites.

Fig. 6b, e and f present the interaction of pH with adsorption dosage, sonication time and initial MG concentration, respectively. The removal percentage of MG was observed to increase with an increase in pH. This is probably due to the fact that at a low initial pH, as a result of protonation of the functional groups, the ZnS-NP-AC surface gets positively charged, and the strong repulsive forces between the cationic dye molecules and adsorbent surface lead to a significant decrease in the dye removal percentage. The increase in the initial pH leads to deprotonation of the active adsorption sites on the AC surface, such as OH and COOH, via electrostatic interaction and/or hydrogen bonding, which leads to adsorption of the MG molecule.

As shown in Fig. 6a, d and e it can be concluded that the maximum adsorption of MG could be achieved when the sonication time was increased. A quick establishment of an equilibrium and rapid adsorption show the efficiency of ultrasound power in terms of its usage in wastewater treatment. The results showed that the initial adsorption rate is very rapid because of the high available surface area and vacant sites of the adsorbent due to dispersion of the adsorbent in solution by ultrasonic power.

The effects of initial MG concentration on its removal percentage and the interaction of this with some other factors are shown in Fig. 6c, d and f. It was seen that in spite of the increase in the amount of dye uptake, the removal efficiency was decreased, and at lower dye concentrations the ratio of solute concentration to adsorbent sites is lower, which causes an increase in dye removal. At higher concentrations, the lower adsorption yield is due to the saturation of the adsorption sites. On the other hand, the percentage removal of dye was higher at lower initial dye concentrations and lower at higher initial concentrations, which clearly indicates that the adsorption of MG from aqueous solution was dependent on its initial concentration.

3.4. Optimization of CCD by DF for the extraction procedure

The profile for predicted values and desirability options in the STATISTICA 7.0 software is used for the optimization process (Fig. 7). Profiling the desirability of responses involves specifying the DF for each dependent variable (removal percentage) by assigning predicted values. The scale in the range of 0.0 (undesirable) to 1.0 (very desirable) is used to obtain a global function (D) that should be maximized according to efficient selection and optimization of designed variables. The CCD design matrix results (Table 1) show the maximum (99.63%) and minimum (44.45%) adsorption of MG. According to these values, DF settings for each dependent variable of the removal percentage are depicted on the right hand side of Fig. 7: desirability of 1.0 was assigned for maximum removal (99.63%), 0.0 for minimum (44.45%) and 0.5 for half adsorption (72.04%). On the left hand side of Fig. 7 (bottom) the individual desirability scores are illustrated for the calculation of the removal percentage. Since a desirability of 1.0 was selected as the target value, the overall response obtained from these plots with the current level of each variable in the model is depicted at the top (left) of Fig. 7. Quick observation of the figures immediately reveals that variables affect the response and its desirability simultaneously. On the basis of these calculations and a desirability score of 1.0, maximum recovery (99.5%) was obtained at optimum conditions set as: 5.0 min of sonication time, pH 6, 0.025 g of adsorbent and an initial MG concentration of 22 mg L⁻¹. The validity of duplicate concurrent experiments at the optimized values of all the parameters was investigated. The results are closely co-related with the data obtained from desirability optimization analysis using CCD.

Fig. 7 Profiles for predicated values and desirability function for the removal percentage of MG. The dashed line indicates current values after optimization.

3.5. Adsorption equilibrium study

Generally, an equilibrium adsorption isotherm is used to give useful information about the mechanism, properties and tendency of adsorbent toward each dye. The data obtained during an equilibrium study has been fitted to various adsorption isotherm equations such as Langmuir, Freundlich, Temkin and Dubinin–Radushkevich (D–R) isotherms to investigate the equilibrium characteristics of the adsorption process.^36–41 The constant parameters and correlation coefficients (R²) obtained from the plots of known equations for Langmuir, Freundlich, Tempkin and D–R are summarized in Table 3. Based on the linear form of the Langmuir isotherm model³⁶ (according to Table 3), the values of K_L (the Langmuir adsorption constant (L mg⁻¹)) and Q_m (theoretical maximum adsorption capacity (mg g⁻¹)) were obtained from the intercept and slope of the plot of C_e/q_e vs. C_e, respectively (Fig. 8a). A high correlation coefficient (0.9998) shows the applicability of the Langmuir model for the interpretation of the experimental data. Parameters of the Freundlich isotherm model such as K_F ((mg g⁻¹)/(mg L⁻¹)^1/n) and n (the capacity and intensity of the adsorption) were calculated from the intercept and slope of the linear plot of ln q_e versus ln C_e, respectively (Fig. 8b) and their values are presented in Table 3. The value of 1/n for the Freundlich isotherm (0.237) shows the high tendency of MG for adsorption onto ZnS-NP-AC, while the lower R² value (0.8496) show its unsuitability for fitting the experimental data.

Table 3 Isotherm constant parameters and correlation coefficients calculated for the adsorption of MG onto 0.025 g of ZnS-NP-AC

Isotherm	Equation	Parameters	Value of parameters
Langmuir	Ce/qe = 1/(KaQm) + Ce/Qm	Qm (mg g^−1)	51.55
		Ka (L mg^−1)	12.12
		R^2	0.9998
Freundlich	ln qe = ln KF + (1/n)ln Ce	1/n	0.237
		KF (L mg^−1)	37.02
		R^2	0.8496
Tempkin	qe = B1 ln KT + B1 ln Ce	B1	5.499
		KT (L mg^−1)	1478.37
		R^2	0.929
Dubinin–Radushkevich (D–R)	ln qe = ln Qs − Bε^2	Qs (mg g^−1)	40.90
		B (mol^2 kJ^−2)	8 × 10^−9
		R^2	0.8812

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Fig. 8 Plot of equilibrium isotherms for the adsorption of MG dye onto ZnS-NP-AC: (a) Langmuir; (b) Freundlich; (c) Temkin and (d) Dubinin–Radushkevich isotherms.

The heat of the adsorption and the adsorbent–adsorbate interaction were evaluated using the Tempkin isotherm model.⁴¹ B is the Tempkin constant related to the heat of the adsorption (J mol⁻¹), T is the absolute temperature (K), R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), and K_T is the equilibrium binding constant (L mg⁻¹). The values of the Tempkin constants and the correlation coefficient are lower than the Langmuir values (Fig. 8c).

Another adsorption isotherm, the D–R model, was applied to estimate the porosity apparent free energy and the characteristics of adsorption. In the D–R isotherm K (mol² kJ⁻²) is a constant related to the adsorption energy, Q_m (mg g⁻¹) is the theoretical saturation capacity, and ε is the Polanyi potential. The slope of the plot of ln q_e versus ε² gives K and the intercept yields the Q_m value. The mean free energy of the adsorption (E), defined as the free energy change when one mole of ion is transferred from the solution to the surface of the sorbent, can be calculated. The value of the correlation coefficient obtained from the D–R model is lower than the other isotherms values mentioned above (Fig. 8d). In this case, the D–R equation represents a poorer fit of the experimental data than the other isotherm equations. Among various isotherm models, the best usable model is Langmuir, due to the charge of the adsorbent and adsorbate hindered from multilayer adsorption.

3.6. Adsorption kinetic modeling

The experimental kinetic data of MG were correlated by kinetic models including pseudo first and second-order and intraparticle diffusion to study the rate and mechanism of the adsorption process. Table 4 summarizes the properties of each model. The pseudo first-order model (Lagergren model),⁴² according to the equation listed in Table 4 by plotting the values of log(q_e − q_t) versus t, may give a linear relationship from which k₁ and q_e values can be determined from the slope and intercept of the obtained line, respectively (Fig. 9a).

Table 4 Kinetic parameters for the adsorption of MG onto ZnS-NP-AC

Model	Equation	Parameters	Value of parameters
First-order kinetic	log(qe − qt) = log(qe) − (k1/2.303)t	k1	0.6347
		qe (calc)	15.696
		R^2	0.9818
Second-order kinetic	(t/qt) = 1/(k2qe^2) + 1/qe(t)	k2	0.162
		qe (calc)	43.859
		R^2	0.9990
Intraparticle diffusion	qt = Kdifft^1/2 + C	Kdiff	7.452
		C	27.599
		R^2	0.9229
		qe (exp)	43.734

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Fig. 9 Kinetic plots for the adsorption of MG dye onto ZnS-NP-AC: (a) pseudo first-order kinetic plot; (b) pseudo second-order kinetic plot; and (c) intraparticle diffusion model.

The sorption kinetics may be described by a pseudo second-order model.⁴³ In contrast to a first-order model, the plot of t/q_t versus t for the pseudo second-order kinetic model gives a straight line with a high correlation coefficient. From this k₂ and the equilibrium adsorption capacity (q_e) were calculated from the intercept and slope, respectively (Fig. 9b). The values of R² and closeness of the experimental and theoretical adsorption capacity (q_e) values show the applicability of the second-order model to explain and interpret the experimental data (Table 4). The R² value for the pseudo second-order kinetic model was found to be higher (0.999) and the calculated q_e value is close to the experimental adsorption capacity value.

The final process possibility was explored using an intraparticle diffusion model based on diffusive mass transfer and adsorption rate expressed in terms of the square root of time (t).^44,45 The values of K_diff and C were calculated from the slope and intercept of the plot of q_t versus t^1/2 (Fig. 9c). The C value is related to the thickness of the boundary layer and K_diff is the intraparticle diffusion rate constant (mg g⁻¹ min^−1/2). The values of K_diff and C were obtained from the final linear portion and their values are presented in Table 4. Since, the intraparticle curve did not pass through the origin; one can notice that in addition to the intraparticle diffusion model another stage such as the pseudo second-order kinetic model acts to control the adsorption process.

3.7. Comparison with literature

The performance of the proposed method has been compared with other methods and some adsorbents (Table 5). The adsorption capacity and contact time for the proposed method in comparison with all of the adsorbents are preferable and superior to the literature which shows a satisfactory removal performance for MG.^6,46–49 The ultrasonic-assisted enhancement of removal could be attributed to the high-speed microjets and high-pressure shock waves during the violent collapse of cavitation bubbles. Thoroughly mixing the adsorbent led to a significant reduction in mass transfer under similar conditions in the absence of ultrasonic power. It was found that the removal percentage under optimum conditions in the absence of ultrasonic power was lower than 60%, which significantly enhanced to 99% with the use of ultrasonic power.

Table 5 Comparison of the removal of dyes by different methods and adsorbents

Adsorbent	Adsorbate	Adsorption capacity (mg g^−1)	Concentration (mg L^−1)	Contact time (min)	Ref.
Raw coffee beans	MG	55.3	50	30	7
Hydrilla verticillata biomass	MG	69.88	200	150	46
Ricinus communis	MG	27.78	50	90	47
Brown-rotted pine wood	MG	42.43	7.0	>600	48
Zeolite	MG	23.90	50	240	49
ZnS-NP-AC	MG	51.55	22	5.0	This work

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4. Conclusion

In the present study, the analytical utility of experimental design for the evaluation of optimum conditions for the removal of MG in aqueous solution by ZnS-NP-AC coupled with ultrasound assisted adsorption method has been investigated. It was observed that ZnS-NP-AC is an efficient adsorbent for the removal of MG. The combination of ultrasonic power in addition to the application of ZnS-NP-AC is an efficient, fast and sensitive adsorption method for the removal of MG. The influences of experimental parameters on the removal percentage were investigated using CCD combined with RSM. Fitting the experimental equilibrium data showed the suitability and applicability of the Langmuir model with the second-order equation model to control the kinetics of the adsorption process. The optimum operating variables (0.025 g adsorbent, 5.0 min contact time, pH 6 and 22 mg L⁻¹ MG) to obtain maximum MG removal (>99%) were determined by DF. An advantage of this method is the use of a nontoxic adsorbent for the removal of a large amount of MG in a short time via a simple procedure. The developed procedure provided many advantages such as high percentage removal, simplicity, stability and ease of operatation.

Acknowledgements

The authors express their appreciation to the Graduate School and Research Council of the University of Yasouj for the financial support of this work. The author acknowledges financial support from the Iran National Science Foundation (INSF-No.: 92039361).

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