Adsorption of reactive red dye (RR-120) on nanoadsorbent O-carboxymethylchitosan/γ-Fe₂O₃: kinetic, equilibrium and factorial design studies

Abstract

In this study, a novel magnetically separable nanoadsorbent, consisting of a γ-Fe₂O₃ and O-carboxymethylchitosan (O-CM), was synthesized in a three-step procedure. The structure of O-CM was characterized by Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TG), vibrating-sample magnetometer (VSM), and transmission electron microscope (SEM). Adsorption features of the magnetic nanoadsorbent were evaluated using the dye reactive red 120 (RR120). The isotherms, kinetics, and thermodynamics of the dye adsorption were studied in various experimental conditions, i.e., initial dye concentration, contact time, solution pH and temperature. The effects of pH, initial dye concentration and temperature were investigated by the 3³ Box–Behnken factorial experimental design method, and the statistical approach analysis of variance was used to optimize the operating conditions. The results obtained fitted well to the Langmuir–Freundlich model, and the kinetics of the adsorption process were found to follow the pseudo-second-order kinetics. The thermodynamic study was conducted by calculating a number of thermodynamic parameters, such as the standard changes in ΔG°, ΔH° and ΔS°. The high sensitivity of the magnetic nanoadsorbent to the external magnetic field culminates in its efficient and easy separation and good adsorption ability, demonstrating great potential in the application of water treatment.

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1 Introduction

Many industrial processes use synthetic dyes in the production of textiles, paper, leather, plastic, food, etc. To meet industrial demand, it is estimated that 1.6 million tons of dyes are produced annually, and 10–15% of this volume is discarded as wastewater.¹ As a result, dyes are major water pollutants.² Azo reactive dyes are the most common compounds, comprising around 60–70% of the total amount of dyes used by companies in different industries.³ Among the azo dyes, reactive dyes are the most widely used dyes in the textile industry, and are believed to be the most problematic chemicals among textile industry effluents; due to their high water-solubility and low degradability.⁴ They are often also stable, resistant to degradation, toxic, carcinogenic and mutagenic; due to their complicated chemical structure, and can cause serious health problems such as allergy and dermatological diseases.⁵

Dye wastewater is typically treated using coagulation–flocculation, aerobic or anaerobic treatment, electrochemical treatment, membrane filtration, or adsorption methods.⁶ Adsorption is the most popular of these methods, due to the effectiveness and simplicity of the process. Most commercial systems use activated carbon as adsorbent to remove dyes in water, due to its good adsorption capacity. However, its widespread use is limited by its high cost. In order to decrease the cost of treatment, some attempts have been made to find low cost alternative adsorbents.⁷

Chitosan is characterized as an excellent biosorbent presenting abundance, non-toxicity, hydrophilicity, biodegradability, biocompatibility and low cost. Since the primary research work of Muzzarelli in 1969, numerous papers have been published regarding the use of chitosan as adsorbent for decontamination of wastewaters. Another widely-known advantage of chitosan is the existence of modifiable positions in its chemical structure.⁸ Therefore, chitosan derivatives, such as carboxymethylated chitosan, may be suitable candidates as biosorbents for water treatment because they are usually compatible with all pH ranges.⁹

Magnetic nanoparticles can make the separation process simple and fast, because it can be easily collected by an external magnetic field without additional centrifugation or filtration.^10–13 Recently, several researchers have reported on magnetic nanoparticles containing chitosan derivatives, and their application in dye removal.^10,14–20

In this study, we report the synthesis and characterization of O-carboxymethylchitosan/γ-Fe₂O₃ nanoparticles (O-CM), and its use in the removal of azo dye Reactive Red 120 (RR120) from aqueous solution. This work involves batch studies of equilibrium and kinetics of adsorption in different pH and temperature conditions, and also factorial design, to predict adsorption on an industrial scale.

2 Experimental

2.1 Materials

Chitosan (viscosimetric molecular weight of 2.5 × 10⁵ g mol⁻¹, and deacetylation degree of 85%) was obtained from Purifarma (São Paulo). The dye Reactive Red 120 (Procion Red HE-3B; molecular formula: C₄₄H₂₄C₁₂N₁₄O₂₀S₆Na₆; molecular weight 1469.98 g mol⁻¹) was kindly donated by Trento Brasil Beneficiamento Têxtil (Nova Trento, Brazil). All the other reagents used were of analytic grade, and were used without purification.

2.2 Synthesis of O-carboxymethylchitosan (O-C)

Sodium hydroxide (27 g) was dissolved in distilled water (120 mL) and isopropanol (180 mL). Next, chitosan (20 g) was added. This mixture was stirred for one hour at 0 °C and stored at the same temperature for 24 hours. A solution of monochloroacetic acid (30 g) in isopropanol (40 mL) was then dripped onto the previously prepared mixture, maintaining the temperature at 0 °C. The reaction was maintained at this temperature for approximately 48 hours and then stopped by adding 70% ethanol (400 mL). The resulting mixture was then filtered, washed with ethanol 70% and dried under vacuum for 24.⁹

After O-C in the salt form (10 g) was dissolved in approximately 700 mL of distilled water. Next, 25% glutaraldehyde (8 mL) was slowly added, and the mixture was stirred for 3 hours. The pH was then adjusted to precipitate crosslinked O-C. Finally, the mixture was filtered with acetone and dried under vacuum for 24 h.

2.3 Synthesis of magnetic nanoparticles

Crosslinked O-C (7 g), FeSO₄·7H₂O (7 g) and NH₂OH·HCl (1.75 g) were dispersed in distilled water (700 mL) and the mixture was stirred for 2 h at room temperature to absorb iron ions within the O-C particles. Next, NaNO₂ (0.060 g), dissolved in water (10 mL), was added to the particle suspension and stirred for 15 min to oxidize the Fe²⁺ for Fe³⁺. After 4.94 g of Fe(NH₄)₂(SO₄)₂·6H₂O dissolved in water (100 mL), were added to the previous dispersion, the pH was adjusted to 9.0 and the mixture was stirred and heated for 30 minutes at 60 °C. The O-C magnetic (O-CM) was filtered, washed with distilled water, 95% ethanol, and acetone, and dried under vacuum for 24 h.

2.4 Characterization

O-CM was characterized by transmission electron microscopy (TEM), using a Titan Cubed 80-300 FEI Cs image corrected instrument and X-ray diffractometer with Fe Kα radiation. Mössbauer spectrometry measurements were performed at 77 K using a source of ⁵⁷Co in Rh matrix; the spectra were fitted with the Mosfit program, assuming a Lorentzian shape of the lines. Magnetization measurements were carried out using a vibrating sample magnetometer of PPMS (Quantum Design) in the temperature range 2–300 K and field range ±50 kOe.

The FTIR spectra were recorded in an Infrared Spectrometer Prestige-21, Shimadzu (Japan) using KBr discs. Thermogravimetric results were obtained using a Netzsch STA 449 F3 Jupiter thermal analyzer. Sample powders (8–10 mg) were crimped in an aluminum pan and heated at a constant rate of 10 °C min⁻¹ over a temperature range of 35 to 700 °C. N₂ was used as purging gas, at a rate of 30 mL min⁻¹.

The point of zero charge (pH_zpc) of the O-CM was determined by the powder addition method described by Ponnusami et al.²¹ 20 mg of O-CM was added to 20 mL 0.1 M sodium chloride (NaCl) solution. The initial solution pH (pH_i) values were adjusted to 2.5, 4.5, 7.4, 9.5 and 11.5, using either 1.0 M hydrochloric acid (HCl) or 1.0 M sodium hydroxide (NaOH). The solutions with O-CM were equilibrated for 24 h at room temperature. After equilibration, the final pH (pH_f) was recorded. A change in pH of the solution (ΔpH = pH_i − pH_f) was recorded for each solution, and ΔpH vs. pH_i was plotted. The pH_i at which ΔpH becomes zero is called pH_zpc.

2.5 Study of pH effect

The effect of pH was determined using 15 mg of adsorbent, 20 mL of RR120 solution 250 mg L⁻¹, and temperature of 25 °C, under continuous agitation and different initial pH values. The initial pH of RR120 solution was adjusted to values in the range of 1.5–11.5 by dropwise addition of 0.1 mol L⁻¹ NaOH or 0.1 mol L⁻¹ HCl solutions. After 60 min of contact time, the concentrations of RR120 left in the supernatant solutions were determined, to study the effect of pH. The magnetic material was then separated using an external magnetic field, and the quantity of dye present in the supernatant was determined based on an analytical curve (adsorbance at 540 nm vs. dye concentration), using a UV-vis spectrophotometer V 630 Jasco (Japan).

The adsorption capacity (q_e) was calculated according to eqn (1):

where C₀ and C_e (mg L⁻¹) are the initial and equilibrium dye concentrations in the liquid phase, respectively, v (L) is the volume of solution, and m (g) is the amount of adsorbent.

2.6 Adsorption kinetics

The adsorption kinetics were performed in the system, thermostated at 25, 35, 45 and 55 °C using 15 mg of adsorbent, 20 mL of RR120 solution 400 mg L⁻¹, under continuous agitation. Aliquots were removed at certain time intervals (5, 15, 30, 45, 60, 90, 105 and 120 min). The magnetic material was then separated using an external magnetic field, and the amount of RR120 adsorbed was calculated, as described above.

2.7 Adsorption isotherms

The adsorption isotherms were obtained using a thermostatic bath with continuous agitation, with 20 mL of dye solution at concentrations of between 300 and 600 mg L⁻¹ containing 20 mg of adsorbent, and agitation time of 60 min. The studies were conducted in saline solution (0.05 M NaCl). To obtain the thermodynamic parameters, the same procedure was performed at solution temperatures of 25, 35, 45 and 55 °C. The amount of RR120 adsorbed was calculated as described above.

2.8 Regeneration and reuse of the adsorbent

For the regeneration, 100 mg of the adsorbent saturated with a RR120 solution was used. The dye was removed with 50 mL of NaOH 0.1 M and acetone 1 : 1 (v/v).²² The dye concentration was determined as described previously. The adsorbent was then washed with HCl 0.01 M and distilled water to neutralize the excess NaOH and recondition the adsorbent. This procedure was repeated five times for each adsorption/regeneration cycle.

2.9 Factorial analysis

The factorial design is useful for studying the joint effect of different factors on a response. The experiments were established based on a Box–Behnken design with three factors and three levels, 3³, was used to evaluate the influence of three parameters (pH, initial concentration (C₀), and temperature) at three levels, here the experimental design included 15. The factorial design matrix and the adsorbed dye in each experiment (q_e, mg g⁻¹) are shown in Table 1. The results were analyzed using the software Statistica version 6.0, and the main interactions between factors were determined.

Table 1 Experimental design matrix's and results for the RR120 adsorption efficiency^a

Experiment	pH	Temperature	Initial concentration	Amount adsorbed (mg g^−1)
a pH: 3.5(+), 6.5(0), 11.5(−); temperature: 55 °C(+), 40 °C(0), 25 °C(−); concentration: 500 mg L^−1(+), 450 mg L^−1(0), 400 mg L^−1(−).
1	0	−	−	373.03
2	0	−	+	419.42
3	0	0	0	429.15
4	−	−	0	364.62
5	0	0	0	429.15
6	−	0	+	391.81
7	+	+	0	444.58
8	−	0	−	368.30
9	+	0	−	369.11
10	0	+	+	473.36
11	0	0	0	429.15
12	+	−	0	406.50
13	0	+	−	389.30

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2.10 Statistic parameters

Non-linear regression was used for all models (kinetic and isotherm) to determine the best-fit model, and three error functions were evaluated: the coefficient of determination (r²), the non-linear chi-square test (χ², eqn (2)), and the residual sum of squares (RSS) (eqn (3)).

3 Results

3.1 Characterization

The crystal structure of O-CM was investigated by the X-ray diffraction method with Fe Kα radiation. The pattern obtained is shown in Fig. 1. The sharp line pattern observed is consistent with the one reported for the spinel structure of magnetite and maghemite. Thus, the accurate phase of particles in the sample studied cannot be distinguished as in other granular Fe-oxide materials.²³ The amorphous halo observed for 2θ between ∼20 and ∼30 can be attributed to the chitosan matrix.²⁴

Fig. 1 X-ray diffraction pattern of the magnetic O-CMCh nanocomposite.

Mössbauer spectroscopy was used to gain a better insight into the nanoparticle structure. This is a local method that enables us to distinguish between different iron oxides. The spectrum obtained at 77 K (Fig. 2) presents a magnetically split component, with the average values of the hyperfine field 〈B_hf〉 ≈ 51.2 T, quadrupolar splitting around zero, and isomer shift 〈δ〉 ≈ 0.46 mm s⁻¹. Although the value of the hyperfine field is typical of both magnetite and maghemite, but considering the mean value of the isomer shift, which is highly sensitive to the electron density, i.e. valency state of Fe ions, it can be concluded that the nanoparticles mainly consist of maghemite.²⁵ The Mössbauer spectrum exhibits broad and asymmetric lines which can be attributed to Fe ions located in both tetrahedral and octahedral sites, but the estimation of their respective ratios would require the application of an external magnetic field. The broadening of magnetic lines may also originate from different local environments of Fe cations resulting from the particular nonstoichiometry of maghemite nanoparticles, as well as surface disorder.

Fig. 2 Mössbauer spectrum of the magnetic O-CMCh/Gl nanocomposite at 77 K.

The morphology of O-CM has been studied by transmission electron microscopy. An exemplary micrograph, obtained by deposition of the O-CM on a carbon film, is shown in Fig. 3a and indicates that magnetic nanoparticles are dispersed in the O-C uniformly, but also that the distribution of particle sizes is very broad. A high resolution image is presented in Fig. 3b and confirms that even small nanoparticles are well-crystallized, as regular fringes are clearly observed, with spacings typical of the interplanar distances of cubic maghemite. Detailed image processing reveals the bimodal distribution of the created maghemite nanoparticles, and the appropriate histograms are shown in Fig. 3(c and d). Both histograms were fitted with log-normal particle size distributions. For small particles the calculated average particle diameter is 〈D_s〉 ≈ 8.7 nm, with a standard deviation of σ_s ≈ 1.8 nm (Fig. 3c) whereas for big nanoparticles, the diameter is 〈D_b〉 ≈ 85 nm, with a standard deviation of σ_b ≈ 21.6 nm (Fig. 3d).

Fig. 3 Synthesized O-CM: large area TEM micrograph (a), high resolution image (b), size distribution of small (c) and big (d) maghemite nanoparticles.

Magnetic characterization of O-CM was performed by measuring temperature and field dependences of the magnetization using a vibrating sample magnetometer. Fig. 4 shows the hysteresis loop of the sample at 300 K in the field range ±1.5 kOe. At room temperature the observed coercivity is around 50 Oe, and on cooling, coercivity increases to ∼320 Oe at 2 K. The room temperature saturation magnetization, estimated from the approach to saturation of the high field portion of the magnetization curve measured in the field up to 50 kOe, is 21 emu g⁻¹. Considering that the saturation magnetization of maghemite nanoparticles is in the range of 60–80 emu g⁻¹,²⁵ the weight fraction of γ-Fe₂O₃ particles in the sample studied is around 30%. The variation in magnetization with temperature, measured in the so-called zero-field-cooled and field-cooled (ZFC-FC) regime at an applied field of 50 Oe is shown in the inset to Fig. 4. These results indicate a wide distribution of the energy barrier for magnetic nanoparticle systems; the difference between the ZFC and FC curves gradually disappears with increasing temperature, but the two curves do not overlap over the entire temperature range (2–300 K), and at room temperature, non-zero coercivity is observed. This behavior clearly shows that the O-CM is far from a superparamagnetic state. It is related, first of all, to the very broad distribution of nanoparticle sizes (4–160 nm – see Fig. 3(c and d)), with the significant amount of big nanoparticles, and secondly, it is partly related to magnetic interparticle interactions. In addition, the increase in ZFC magnetization with temperature is not monotonic, and evidences two abrupt increases (for T > ∼15 and ∼250 K), which can be attributed to the bimodal size distribution of the γ-Fe₂O₃ particles.

Fig. 4 Magnetization curve of the O-CM at the room temperature. Inset – temperature dependences of ZFC-FC magnetization measured at 50 Oe.

The FT-IR spectrum of O-C crosslinked (1) and O-CM (2) (Fig. 5) shows a broad band at 3500 cm⁻¹ which corresponds to the stretching vibrations of N–H and O–H groups. Peaks appearing at 2900 and 2800 cm⁻¹ are characteristic of C–H stretching vibrations. The sorption bands around 1100 and 1027 cm⁻¹ display the stretching vibrations of the C–O bonds. The bands at 1400 and 1640 cm⁻¹ are assigned to the stretching vibration of COO⁻ (symmetric) and COO⁻ (asymmetric). The spectrum of O-CM, 2, show a peak at 594 cm⁻¹ corresponds to the stretching vibration of the Fe–O groups of the magnetic nanoparticles.

Fig. 5 FTIR spectra of O-C crosslinked (1) and O-CM (2).

As shown in Fig. 6, the TG curve for O-CM exhibits three steps of weight loss; the first is of 18% at 100 °C, which may be due to the loss of adsorbed water in the sample. The second step of weight loss is in the range of 240–600 °C, and corresponds to the loss of organic polymer. The final amount of mass remainder was 38%, which represents the amount of inorganic material (magnetic particles) contained in the material.

Fig. 6 TG curve of O-CM.

The pH reaction is a widely used control for most dye sorption from aqueous solution. This is because the pH dictates the adsorbent surface properties (e.g., pH_pzc), and the ionic state of functional groups. Surface charge, and therefore electrostatic attraction are a function of pH. The pH with which the net total surface charge is zero is called the point of zero charge (pH_pzc). Below pH_pzc, the surface of the adsorbent is positively charged, otherwise it is negatively charged. In this work, the O-CM displays a zero surface charge at pH_pzc 5.92, (Fig. 7).

Fig. 7 The point of zero charge (pH_zpc) of the O-CM.

3.2 Effect of initial solution pH

The pH value of the adsorption medium is one of the most important parameters influencing the adsorption property of an adsorbent. The effects of initial solution pH on RR120 adsorption on O-CM were studied within the pH range of 1.5 to 11.5 at room temperature, as shown in Fig. 8. The adsorption capacities of RR120 present a decreasing trend from 350 to 19 mg g⁻¹, with the increase of pH values in the range of 1.5 to 11.5.

Fig. 8 The effect of initial pH of dye solution on adsorption of the RR120 onto O-CM experimental conditions: RR120 concentration 400 mg L⁻¹, T = 25 °C, amount adsorbent 0.02 g.

Adsorption is affected by changes in the pH of the solution, because this parameter affects the degree of ionization of the dye and the surface properties of the sorbents. Generally, pH values lower than pH_pzc (5.92) result in increase in the number of positively charged sites of the O-CM, which enhances the adsorption of anionic dyes.

The underlying mechanism is likely to be the ionic electrostatic interactions between the anionic dye and the –R₂N– groups of the polymer. In aqueous solution, the RR120 can be ionized and converted to anionic dye ions with sulfonate groups –SO₃⁻. In acidic solution pH < 4.0, the –R₂N– of crosslinked O-carboxymethylchitosan can be protonated by hydrogen ions (–R₂N–⁺). The removal of RR120 by O-CM, at acidic pH, occurs mainly due to the electrostatic interaction between the (–R₂N–⁺) on polymer and the SO₃⁻ groups of the anionic dye structure.²⁶ However, there is still a small amount of dye adsorption capacity at pH above 8 because in addition to the electrostatic adsorption, there is also physical adsorption and aggregation.^18,27

In solution with pH 1.5 occurred a decrease in the dye adsorption capacity, Fig. 8, this behavior can be attributed to degradation of adsorbent, observed by swelling and separation of magnetic material from the polymer.

The effect of the type of absorbent was evaluated at pH 2.5 and 7.5 (EIS 3) and the results are shown Table ESI1.† Fe₃O₄ alone has small adsorption capacity of the dye RR120 in both pH, these results are in agreement with literature.²⁸ Crosslinked O-carboxymethylchitosan alone has great day adsorption capacity, Table ESI1,† these results are in agreement with literature.²⁹ At pH 2.5 the adsorption capacity of the O-C is very close to that observed for the O-CM. Moreover, the magnetic nanoadsorbents are economical and can be easily separated from the solution by applying a magnetic field. Therefore, the developed O-CM in this study facilitated a higher adsorption capacity and offer a more efficient adsorption of textile dyes compared with crosslinked O-carboxymethylchitosan adsorbents.

3.3 Kinetic adsorption

To investigate the controlling mechanisms of the adsorption process, such as chemical reaction, diffusion control and mass transfer, kinetics models were used to test the experimental data. The pseudo-first-order, pseudo-second-order and intraparticle were used, Fig. 9a.

Fig. 9 (a) Pseudo-first-order kinetics, pseudo-second-order kinetics and (b) intraparticle diffusion model for adsorption of the RR120 onto O-CM; RR120 concentration 400 mg L⁻¹, T = 25 °C, amount adsorbent 0.02 g.

The pseudo-first-order model³⁰ is represented by (eqn (4)):

q_e − q_t = q_e − k₁t (4)

where, k₁ (min⁻¹) is the constant of the first order adsorption, q_e (mg g⁻¹) is the amount of dye adsorbed at equilibrium, and q_t (mg g⁻¹) is the amount of dye adsorbed at time t (min).

The pseudo-second-order model,³¹ is represented by (eqn (5)).

where, k₂ (min⁻¹) is the constant of the second order adsorption, q_e (mg g⁻¹) is the amount of dye adsorbed at equilibrium, and q_t (mg g⁻¹) is the amount of dye adsorbed at time t (min).

Based on the correlation coefficients obtained (Table 2), the pseudo-second-order equation kinetic was the best kinetic model to explain the adsorption process, indicating a chemisorption process. Based on the results obtained, it was evident that as the temperature increased from 25 to 55 °C, the amount of RR120 dye adsorption increased. This may be due to an increase in the mobility of RR120 ions with temperature. As a result, the adsorption capacity increased with a rise in temperature. The r², RSS and χ² for the pseudo-second-order model was the lowest for all the experimental conditions, as shown in Table 2.

Table 2 Kinetic parameters for adsorption of RR120 on the O-CM

	25 °C	35 °C	45 °C	55 °C
Pseudo-first order
qe (mg g^−1)	228	240	485.6	511.7
k1 (min^−1)	7.2 × 10^−2	2.7 × 10^−2	1.8 × 10^−2	2.3 × 10^−2
r^2	0.9960	0.9871	0.9944	0.9935
χ^2	28	118	156	228
RSS	171	472	935	1370
Pseudo-second-order
qe (mg g^−1)	251.67	315	697	697.17
k2 (mg g^−1 min^−1)	4.5 × 10^−4	8.1 × 10^−5	2.0 × 10^−5	2.8 × 10^−5
r^2	0.999	0.98164	0.99214	0.9892
χ^2	7	16	22	38
RSS	41	67	132	228

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Intraparticle diffusion
	25 °C		35 °C		45 °C		55 °C
	Step 1	Step 2	Step 1	Step 2	Step 1	Step 2	Step 1	Step 2
C	94.00	208.97	−87.09	263.65	126.62	110.55	−126.2	323.70
ki (mg g^−1 min^−0.5)	17.34	2.11	38.48	4.79	59.75	29.17	68.05	13.75
r^2	0.9632	0.4101	0.9739	0.7182	0.9750	0.8321	0.9539	0.0814

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To test the diffusion mechanism between the RR120 molecule and O-CM, an intra-particle diffusion model proposed by Weber and Morris has been (eqn (6)).³²

q_t = k_it^0.5 + C (6)

where, k_i (mg g⁻¹ min^0.5) is the intraparticle diffusion rate constant, C is a constant related to the extent of the boundary layer effect, and q_t (mg g⁻¹) is the amount of dye adsorbed at time t (min).

The plot of q_t vs. t^0.5 exhibits multi-linear plots, so two steps influence the sorption process (Fig. 9b). The first sharp phase represents boundary layer diffusion due to the mass transfer from the dye solution to the external surface of the nanoparticle. The second part shows a gradual adsorption step, corresponding to intra-particle diffusion of dye molecules throughout the pores of the nanoparticle. The presence of multilinearity and boundary layer thickness suggests that in combination with the intraparticle diffusion model, some other mechanism may also be contributing to the significant role in the adsorption process. Therefore, it is believed that surface adsorption and intraparticle diffusion occur simultaneously.³³

The diffusion rate constants (k_i) for each temperature follow the order of: step 1 > step 2 (Table 2). The first diffusion stage is the fastest, which might be attributed to the existence of fresh active sites on the O-CM surface.³⁴

The activation energy can be described as the minimum kinetic energy necessary for a reaction to occur, and gives an estimated energy barrier that the adsorbate must overcome prior to biosorption. The activation energy can be obtained by fitting the kinetic constant from the pseudo-second-order model at different temperatures to the Arrhenius equation (eqn (7)). The pseudo-second-order rate constant shown in Table 2 was used to obtain the activation energy of RR120 adsorption on O-CM.

where k₂ is the rate constant of the pseudo-second-order (mg g⁻¹ min⁻¹), k₀ is the Arrhenius factor, which is the temperature independent factor, R is the gas constant (8.314 J mol⁻¹ K⁻¹), T is the absolute temperature (K) of the solution, and E_a is the activation energy (J mol⁻¹).

The plot of ln k₂ vs. 1/T, shown in Fig. S1,† for adsorption of RR120 onto O-CM, was applied to obtain the E_a from the slope, which was found to be 71.73 kJ mol⁻¹, which a R² = 0.8219. The E_a value is used to identify the predominant type of adsorption, suggesting the adsorption of the anionic dye is related to chemisorption in this case.³⁵

The adsorption process is classified as film-diffusion controlled when E_a is below 16 kJ mol⁻¹, particle-diffusion controlled when E_a is 16–40 kJ mol⁻¹, and chemical-reaction controlled when E_a is greater than 40 kJ mol⁻¹.³⁶

3.4 Equilibrium isotherms

Three models were applied to the data (Langmuir, Freundlich, and Langmuir–Freundlich). The Langmuir isotherm assumes monolayer adsorption, which means that the adsorption process can occur at a fixed number of sites, in thickness of the adsorbed layer of only one molecule as the adsorbed layer.³⁷ The Langmuir isotherm is represented by eqn (8):where C_s is the amount of dye adsorbed at equilibrium (mg g⁻¹), C_e is the dye concentration at equilibrium (mg L⁻¹), K_L is the Langmuir adsorption constant (L mg⁻¹), related to adsorption energy, and q_m is the maximum adsorption capacity (mg g⁻¹).

The Freundlich model describes a non-ideal and reversible adsorption, assuming heterogeneous surface energies. It is given by eqn (9):

C_s = K_FC_e^(1/c) (9)

where K_F is the Freundlich adsorption constant (L g⁻¹) related to adsorption capacity, and c is the heterogeneity factor. The term 1/c is related to the adsorption intensity or surface heterogeneity. Values of 1/c below one indicate the Langmuir model, while values higher than one indicate cooperative adsorption. Values closer to zero are indicative of more heterogeneous systems.³⁸

The Langmuir–Freundlich isotherm is a combination of the Langmuir and Freundlich models. It is represented by eqn (10):

where K_LF is the Langmuir–Freundlich adsorption constant (L mg⁻¹). When the c values are less than one, this represents a heterogeneous adsorbent.³⁹

Fig. 10 shows the adsorption isotherms of RR-120 dye onto O-CM at 25 °C. The Langmuir, Freundlich and Langmuir–Freundlich models indicate that the maximum adsorption capacity of RR120 (Table 3) increases as the temperature increases.

Fig. 10 Langmuir, Freundlich and Langmuir–Freundlich adsorption isotherm of the RR120 onto O-CM; pH 7.5, T = 25 °C, amount adsorbent 0.02 g.

Table 3 Isotherm parameters for adsorption of RR120 on the O-CM

Langmuir
	KL (L g^−1)	qe (mg g^−1)	r^2	χ^2	RSS
25 °C	0.13	461	0.9063	2337	9349
35 °C	0.045	503	0.9954	34	69
45 °C	1.7	476	0.9315	553	1660
55 °C	0.87	531	0.8912	980	2941

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Freundlich
	KF (L g^−1)	C	r^2	χ^2	RSS
25 °C	138	0.23	0.7769	5564	2227
35 °C	132	0.24	0.9353	471	943
45 °C	329	0.098	0.9396	487	1463
55 °C	330	0.12	0.7063	2646	7939

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Langmuir–Freundlich
	KLF (L g^−1)	qe (mg g^−1)	c	r^2	χ^2	RSS
25 °C	0.058	433	1.51	0.9264	2447	7343
35 °C	0.024	477	1.21	0.9984	24	52
45 °C	1.46	498	2.1	0.9681	431	836
55 °C	2.14	541	0.43	0.9849	191	383

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As shown in Table 3, the R² of the Langmuir–Freundlich isotherm model was greater than that of the Freundlich and Langmuir isotherm for the adsorption of RR120. The parameters of error (χ² and RSS) are also given in Table 3. Although the Langmuir–Freundlich and Langmuir models had similar high correlation coefficients, the results of the error functions indicated that the Langmuir–Freundlich model was more appropriate to describe the adsorption of RR120, which is usually adopted for heterogeneous adsorption.

The adsorption capacity of O-CM for RR120 at 25 °C, estimated by the Langmuir–Freundlich model (433 mg g⁻¹), was higher than for other reported adsorbents such as chitosan (51.2 mg g⁻¹),⁴ Jatropha curcas shells (13.29 mg g⁻¹),²² Fe₃O₄ magnetic nanoparticles/ionic liquid as modifier (166.67 mg g⁻¹),⁴⁰ chitosan–Fe(III)-crosslinked (270.90 mg g⁻¹),⁴¹ nano alumina (65.23 mg g⁻¹),⁴² Hydrilla verticillata (250 mg g⁻¹),⁴³ and Spirulina platensis microalgae (390 mg g⁻¹).⁴⁴

3.5 Thermodynamic adsorption parameters

Thermodynamic parameters, such as change in Gibbs free energy (ΔG°, kJ mol⁻¹), enthalpy (ΔH°, kJ mol⁻¹), and entropy (ΔS°, J mol⁻¹ K⁻¹), were determined using the eqn (11)–(13);

ΔG° = −RT ln K_D (12)

where K_D is the equilibrium constant, C_s is the amount of dye adsorbed (mg g⁻¹), C_e is the equilibrium concentration (mg L⁻¹), R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), and T is absolute temperature (K). By plotting a graph of ln K_D versus 1/T, the ΔH° and ΔS° values can be determined from the slopes and the intercept, respectively.⁴⁵

The negative values of ΔG° (−2.39, −2.90, −4.39 and −6.99 kJ mol⁻¹ at 298, 308, 318 and 328 K, respectively) confirm the spontaneous nature and the feasibility of the adsorption. Also, the decrease in negative value of ΔG°, with an increase in temperature, suggests the adsorption is more favorable at higher temperatures.

The plot of ln K_D vs. 1/T (K), shown in Fig. S2,† results in a R² = 0.8464. The positive ΔS° value 18.11 J mol⁻¹ K⁻¹ indicates the increased degree of freedom of the system, suggesting randomness at the solid/liquid interface. The value of ΔH° 5.16 kJ mol⁻¹ indicates that RR120 adsorption onto O-CM is a physisorption process and that the adsorption reaction is endothermic, which is consistent with the effect of temperatures. The negative values of ΔG°, demonstrate that the dye adsorption is spontaneous and that the system does not gain energy from any external source.⁴⁶

3.6 Regeneration and reuse of the adsorbent

A considerable characteristic for an adsorbent, for a practical application, is the reuse by a longer period, leading to a significant reduction in the cost of the treatment. As shown in Fig. 11, the recycling of O-CM led to a decrease in efficiency, from 280 to 240 mg g⁻¹ after the first desorption step, remaining high (220 mg g⁻¹) even after five consecutive adsorption/desorption cycles. This slight decrease in efficiency is probably due to loss of adsorbent during washing.

Fig. 11 Recycles of O-CM for adsorption of RR120.

3.7 Factorial analysis

In order to identify the parameters that have a significant influence on the adsorption process, and to find the setting values of the principal parameters for setting the results of the process at the desired values, a factorial design was performed.

The matrix codes used for the factorial design, and the results, are shown in Table 1. The effects, standard error, t value, p value, errors of coefficients and regression coefficient are shown in Table 4.

Table 4 Effect estimated coefficients for the adsorption of the dye RR120^a

Factor	Effect	Std. Err.	t value	p value	Coeff.	Std. Err.
a A = temperature; B = pH; C = concentration. R^2 = 0.9981; R^2 adjusted 0.9937.
Mean/Interc.	406.3393	0.871676	466.1587	0.000000	406.3393	0.871676
A	32.0238	1.900777	16.8477	0.000073	16.0119	0.950389
A^2	11.2768	1.642642	6.8650	0.002358	5.6384	0.821321
B	−50.9643	2.982971	−17.0851	0.000069	−25.4821	1.491486
B^2	19.7887	1.552879	12.7432	0.000218	9.8943	0.776439
C	64.1131	2.307560	27.7839	0.000010	32.0565	1.153780
C^2	5.3006	1.848897	2.8669	0.045611	2.6503	0.924449
A × B	−8.4524	2.880977	−2.9339	0.042649	−4.2262	1.440488
A × C	18.1369	2.416088	7.5067	0.001685	9.0685	1.208044
B × C	−41.8393	3.953054	−10.5840	0.000451	−20.9196	1.976527

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A quadratic model was used for the initial calculation of the eqn (14):

Q_e = β₀ + β₁x_A + β₂x_B + β₃x_C + β₄x_A² + β₅x_B² + β₆x_C² + β₅x_Ax_B + β₆x_Ax_C + β₇x_Bx_C (14)

where, β₀ is the global media, representing the linear and quadratic regression coefficients related to interactions, and A, B and C represent the temperature, pH and initial concentration, respectively.

Substituting the coefficients β_i for their respectively values, (Table 4), it was possible to derive an equation model relating the parameters with the adsorption of the dye RR120.

Q_e = 406.33 + 32.02A + 11.28A² − 50.96B + 19.79B² + 64.11C + 5.30C² − 8.45AB + 18.14AC − 41.84CB (15)

Regression analysis and Pareto analysis of variance (ANOVA) were used to test the adequacy and fitness of the models. The results in indicate that the equation adequately represented the relationship between the input parameters and the responses. ANOVA followed by Fisher's statistical test (F-test) was conducted to analyze the significance of each independent variable. The results of ANOVA, given in Table 5, show the Fisher F-value for adsorption as 283.84, which suggests that the model is highly significant. The high Fisher value means that the variation in responses can be explained by the regression equation. The associated p value estimates whether the F value is high enough to show statistical significance. p values lower than 0.05 indicate that the model and the associated terms are statistically significant.

Table 5 ANOVA for RR120 adsorption (mg g⁻¹)^a

Factor	SS	df	MS	F	p
a A = temperature; B = pH; C = concentration.
A	1746.16	1	1746.163	283.8465	0.000073
A^2	289.93	1	289.925	47.1286	0.002358
B	1795.70	1	1795.705	291.8997	0.000069
B^2	998.99	1	998.988	162.3899	0.000218
C	4748.85	1	4748.851	771.9468	0.000010
C^2	50.56	1	50.562	8.2191	0.045611
A × B	52.95	1	52.952	8.6075	0.042649
A × C	346.66	1	346.659	56.3509	0.001685
B × C	689.13	1	689.135	112.0219	0.000451
Error	24.61	4	6.152
Total SS	12 739.71	13

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The data obtained by ANOVA, and the main effects, were visualized in the form of a Pareto chart, as shown in Fig. 12. To indicate the minimum statistically significant effect for p = 0.05, a vertical line was drawn. The linear factor initial concentration (C) is the most significant, followed by linear factors pH (B) and temperature (A). Quadratic factor pH (BB), interaction effects between pH and initial concentration (BC) and between temperature and initial concentration (AC), and quadratic factor temperature (AA), were also significant.

Fig. 12 Standardized main effect Pareto chart.

The coefficient of determination (R²) and adjusted-R² were calculated, to determine the sufficiency and fitness of the model. The R² value was calculated to be 0.998, which indicates that 95% of experimental data was a good fit. The high value of adjusted-R² 0.9937 supports a high correlation between the experimental and the predicted values. The high coefficient of determination and the very low p-value (<0.05) demonstrate that the quadratic polynomial model is significant and adequate to characterize the actual relationship between the response and the input.

The good agreement and high correlation coefficient of the plot of experimental versus predicted values for the amount of dye adsorbed suggest high efficiency of the abovementioned equation to evaluate and explain the experimental data, as shown in Fig. 13. The data points on this plot are positioned close to the straight line, and signify that there is sufficient agreement between the actual data and the model data.

Fig. 13 The predicted versus observed values.

Three-dimensional (3D) response surface and contour plots were constructed, based on model eqn (15). This response surface methodology is an empirical modeling technique used to evaluate the relationship between the experimental and the predicted results. In the present study, the Box–Behnken design was used to obtain a proper model for the optimization of the RR120 adsorption process, with three process variables (temperature, pH and dye concentration), at three levels (Fig. 14(a–c)).

Fig. 14 Surface response to RR120 amount adsorbed (mg g⁻¹): pH × temperature (a), temperature × initial concentration (b) and initial concentration × pH (c).

Fig. 14a shows the 3D response surface plots for RR120 removal by the O-CM as a function of solution pH and temperature with an amount of the O-CM (20 mg). The removal efficiency of O-CM increased with increasing temperature, and decreased with the increase in initial pH values of the solution, within their respective experimental ranges.

The interactive effect of temperature and dye concentration on RR120 adsorption in aqueous solution by O-CM at constant pH (7.5) is shown in Fig. 14b. It is evident that the dye adsorption removal efficiency of O-CM showed an increase with dye concentration and temperature, within the experimental ranges.

The response surface for the combined effect of the solution pH and dye concentration (Fig. 14c) suggests that the RR120 adsorbed by the O-CM increased with increasing dye concentration and decreased with increasing pH of the solution. The maximum RR120 adsorbed (500 mg g⁻¹) was observed at the lowest pH and the highest concentration.

4 Conclusions

The adsorption process of RR20 dye onto O-MC fitted well with pseudo-second-order model. The adsorption data in the present study also fitted well with the Langmuir–Freundlich isotherm compared with the Freundlich and Langmuir isotherms. In thermodynamics study, the value of ΔG° falls within the range −20 kJ mol⁻¹ and 0 kJ mol⁻¹. This indicated the occurrence of chemisorption. The adsorption was endothermic and spontaneous, based on positive ΔH° value, and negative ΔG° values. In addition, the influence of pH, initial dye concentration and temperature on adsorption efficiency was designed using a 3³ Box–Behnken factorial design and analyzed using analysis of variance (ANOVA), t-test, and the F-test. According to the Pareto chart, normal probability plot, main effects, and interaction plots in variance analysis, the most significant factors in adsorption efficiency were found to be pH and temperature. The results showed that O-CM is effective for adsorption of RR120 dye, and can be used in the dye adsorption process.

Acknowledgements

We gratefully acknowledge the financial support received from CNPq, Universidade do Vale do Itajaí, and the Government of the State of Santa Catarina.

References

1. K. Hunger, Industrial dyes – chemistry, properties, application, Wiley, Frankfurt, 2003.
2. K. B. Tan, M. Vakili, B. A. Horri, P. E. Poh, A. Z. Abdullah and B. Salamatinia, Sep. Purif. Technol., 2015, 150, 229–242.
3. O. Ozdemir, M. Turan, A. Z. Turan, A. Faki and A. B. Engin, J. Hazard. Mater., 2009, 166, 647–654.
4. M. Malakootian, H. J. Mansoorian, A. Hosseini and N. Khanjani, Process Saf. Environ. Prot., 2015, 96, 125–137.
5. H. Gao, S. Zhao, X. Cheng, X. Wang and L. Zheng, Chem. Eng. J., 2013, 223, 84–90.
6. A. Ahmad, S. H. Mohd-Setapar, C. S. Chuong, A. Khatoon, W. A. Wani, R. Kumar and M. Rafatullah, RSC Adv., 2015, 5, 30801–30818.
7. P. Sharma, H. Kaur, M. Sharma and V. Sahore, Environ. Monit. Assess., 2011, 183, 151–195.
8. G. Z. Kyzas and D. N. Bikiaris, Mar. Drugs, 2015, 13, 312–337.
9. X. G. Chen and H. J. Park, Carbohydr. Polym., 2003, 53, 355–359.
10. L. Fan, Y. Zhang, C. Luo, F. Lu, H. Qiu and M. Sun, Int. J. Biol. Macromol., 2012, 50, 444–450.
11. S. An, X. Liu, L. Yang and L. Zhang, Chem. Eng. Res. Des., 2015, 94, 726–735.
12. O. V. Kharissova, H. V. R. Dias and B. I. Kharisov, RSC Adv., 2015, 5, 6695–6719.
13. G. A. Sayğıl, H. Sayğıl, F. Koyuncu and F. Güzel, Process Saf. Environ. Prot., 2015, 94, 441–451.
14. A. Debrassi, T. Baccarin, C. A. Demarchi, N. Nedelko, A. Slawska-Waniewska, K. Sobczak, P. Dłuzewski, M. Bilska and C. A. Rodrigues, Environ. Sci. Res., 2012, 19, 1594–1604.
15. A. Debrassi, A. F. Corrêa, T. Baccarin, N. Nedelko, A. Slawska-Waniewska, K. Sobczak, P. Dłuzewski, J. M. Greneche and C. A. Rodrigues, Chem. Eng. J., 2013, 183, 284–293.
16. Y. Han, H. Li, H. Yang, A. Li and R. Cheng, Chem. Eng. J., 2013, 223, 402–411.
17. H. Y. Zhu, Y. Q. Fu, R. Jiang, J. Yao, L. Xiao and G. M. Zeng, Bioresour. Technol., 2012, 105, 24–30.
18. Z. Zhou, S. Lin, T. Y. Yue and T. C. Lee, J. Food Eng., 2014, 126, 133–141.
19. D. W. Cho, B. H. Jeon, C. M. Chon, F. W. Schwartz, Y. Jeong and H. Song, J. Ind. Eng. Chem., 2015, 28, 60–66.
20. P. Wang, Q. Ma, D. Hu and L. Wang, React. Funct. Polym., 2015, 91–92, 43–50.
21. V. Ponnusami, V. Gunasekar and S. N. Srivastava, J. Hazard. Mater., 2009, 169, 119–127.
22. L. D. T. Prola, E. Acayanka, E. C. Lima, C. S. Umpierres, J. C. P. Vaghetti, W. O. Santos, S. Laminsi and P. T. Djifon, Ind. Crops Prod., 2013, 46, 328–340.
23. B. D. Cullity and S. R. Stock, Elements of x-ray diffraction, Prentice Hall, New Jersey, 2001.
24. Y. Wang, B. Li, Y. Zhou and D. Jia, Polym. Adv. Technol., 2008, 19, 1256–1261.
25. R. M. Cornell and U. Schwertmann, The iron oxides: structure, properties, reactions, occurrence and uses, Wiley, Weinheim, 2004.
26. S. Rosa, M. C. Laranjeira, H. G. Riela and V. T. Fávere, J. Hazard. Mater., 2008, 155, 253–260.
27. L. Cui, Z. Xiong, Y. Guo, Y. Liu, J. Zhao, C. Zhang and P. Zhu, Carbohydr. Polym., 2015, 132, 330–337.
28. C. C. Lin, Y. S. Lin and J. M. Ho, J. Alloys Compd., 2016, 666, 153–158.
29. L. Wang and A. Wang, Bioresour. Technol., 2008, 88, 1403–1408.
30. Y. Liu and Y. J. Liu, Sep. Purif. Technol., 2008, 61, 229–242.
31. Y. S. Ho and G. Mckay, Process Biochem., 1999, 34, 451–465.
32. W. J. Weber and J. C. Moris, J. Sanit. Eng. Div., 1963, 89, 31–60.
33. C. A. Demarchi, A. Debrassi, F. C. Buzzi, N. Nedelko, A. Slawska-Waniewska, P. Dluzewski, J. Dal Magro, J. Scapinello and C. A. Rodrigues, Arabian J. Chem., 2015 DOI:10.1016/j.arabjc.2015.08.028.
34. B. Tanhaei, A. Ayati, M. Lahtinen and M. Sillanpaa, Chem. Eng. J., 2015, 259, 1–10.
35. M. A. Ahmad and R. Alrozi, Chem. Eng. J., 2011, 171, 510–516.
36. I. A. W. Tan, A. L. Ahmad and B. H. Hameed, J. Hazard. Mater., 2009, 164, 473–482.
37. I. Langmuir, J. Am. Chem. Soc., 1916, 38, 2221–2295.
38. H. M. F. Freundlich, J. Phys. Chem., 1906, 57, 385–471.
39. K. Y. Foo and B. H. Hameed, Chem. Eng. J., 2010, 156, 2–10.
40. G. Absalan, M. Asadia, S. Kamrana, L. Sheikhiana and M. Goltzb, J. Hazard. Mater., 2011, 192, 476–484.
41. C. A. Demarchi, M. Campos and C. A. Rodrigues, J. Environ. Chem. Eng., 2013, 1, 1350–1358.
42. K. Nadafi, M. Vosoughi, A. Asadi, M. O. Borna and M. Shirmardi, J. Water Chem. Tech., 2014, 36, 125–133.
43. N. Naveen, P. Saravanan, G. Baskar and S. Renganathan, J. Taiwan Inst. Chem. Eng., 2011, 42, 463–469.
44. N. F. Cardoso, E. C. Lima, B. Royer, M. V. Bach, G. L. Dotto, L. A. A. Pinto and T. Calvete, J. Hazard. Mater., 2012, 241–242, 146–153.
45. S. Chatterjee, S. Chatterjee, B. P. Chatterjee, A. R. Das and A. K. Guha, J. Colloid Interface Sci., 2005, 288, 30–35.
46. N. M. Mahmoodi, B. Hayati, M. Arami and C. Lan, Desalination, 2011, 268, 117–125.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra04249j

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