*3.2. Isotherms Study*

The most important step in the adsorption study is the fitting of adsorption isotherm models to adsorption data in order to describe how interaction occurs between adsorbent and dye. A number of adsorption isotherms are available and have been successfully applied by the earlier researcher to analyze the adsorption data [71]. In this study, four adsorption isotherms models, namely Freundlich, Tempkin, Langmuir and Dubinin–Radushkevich (D–R) were tested. Adsorption parameters so calculated have been summarized in Table 2. The correlation factor *R*2, indicates that Freundlich adsorption isotherm equation fit more closely to the adsorption data. The linearized form of Freundlich adsorption equation is expressed in Equation (2);

$$\text{llnq}\_{\text{e}} = \text{lnk}\_{\text{f}} + \frac{1}{\text{n}} \text{lnc}\_{\text{e}} \tag{2}$$

where qe (mg g<sup>−</sup>1) and Ce (mg <sup>L</sup>−1) are the solid and liquid phase equilibrium concentration of dye. Kf is constant, and is known as the Freundlich constant and 1/*n* is the slope obtained by plotting lnqe vs. Ce shown in Figure 6A. The values of 1/*n* vary due to heterogeneity of the adsorbing materials. The values of 1/*n* shows favorable (0 < 1/*n* < <sup>1</sup>), unfavorable (1/*n* > 1) or irreversible (1/*n* = 0) adsorption. However, if its value is unity, the system is at equilibrium and will show heterogeneity [72]. In the present work, the values of 1/*n* calculated from Freundlich for Fe3O4, PANI and PANI/Fe3O4 composites are 0.126, 0.504 and 0.723 respectively showing favorable physical adsorption [73].


**Table 2.** Summary of parameters calculated from adsorption isotherms models.

**Figure 6.** The Isotherm plots (**a**) Freundlich, (**b**) Langmuir, (**c**) Separation factor, (**d**) Tempkin and (**e**) D–R of adsorption of AB40 on Fe3O4, PANI and PANI/Fe3O4 composite.

The data were also fitted in the Langmuir adsorption isotherm equation (Equation (3)) as shown below;

$$\frac{\mathbf{c\_e}}{\mathbf{q\_e}} = \frac{1}{\mathbf{q\_{max}}\mathbf{k\_L}} + \frac{1}{\mathbf{q\_{max}}}\mathbf{c\_e} \tag{3}$$

where Ce (mg L −1) and qe (mg g<sup>−</sup>1) indicates the concentration of dye and amount of dye adsorbed per gram of adsorbent at equilibrium, respectively. Similarly, KL (mg <sup>L</sup>−1) represent the Langmuir constant related to adsorption energy and qmax (mg g<sup>−</sup>1) is the maximum adsorption capacity of adsorbing materials which can be calculated from the slope. The maximum adsorption capacity of AB40 onto Fe3O4, PANI and PANI/Fe3O4 composites are 130.5, 264.9 and 216.9 mg g<sup>−</sup>1, respectively, as compared in Table 3A. The dimensionless constant (RL) also called separation factor, expresses essential features of the Langmuir isotherm and is represented by Equation (3a).

$$\mathbf{R\_L} = \frac{1}{(1 + \mathbf{K\_L C\_l})} \tag{3a}$$

where Ci (mg <sup>L</sup>−1) is the initial concentration of AB40. Values of RL indicate that isotherm is either favorable (1 > RL > 0), linear (RL = 1), irreversible (RL = 0) or unfavorable (1 < RL) [74]. In the present study, the values of RL range from 0.00525 to 0.34988 as depicted in Figure 6c, which shows that adsorption of AB40 onto Fe3O4, PANI and PANI/Fe3O4 composites is favorable at low concentration [75].

**Table 3.** Kinetics parameters for adsorption of AB40 on Fe3O4, PANI and PANI/Fe3O4 composite based on pseudo-first-order and pseudo-second-order equations.


The Tempkin isotherm is also an important isotherm model and has been used by researchers to analyze their adsorption data [76,77]. The Tempkin isotherm assumes that due to interactions of the dye with the adsorbent, the adsorption decreases linearly and is characterized by binding energies. It is represented by the following equation (Equation (4));

$$\mathbf{q}\_{\mathbf{e}} = \beta \text{ln}\mathbf{k}\_{\mathbf{T}} + \beta \text{lnc}\_{\mathbf{e}} \tag{4}$$

where Ce (mg <sup>L</sup>−1), qe (mg g<sup>−</sup>1) and KT (L g<sup>−</sup>1) are equilibrium concentration, equilibrium adsorption and binding constant at equilibrium. It is obtained by plotting qe vs. lnCe (Figure 6d). The constant β, considers the interaction between adsorbent and dye (Equation (4a)).

$$
\beta\_- = \frac{\text{RT}}{\text{b}} \tag{4a}
$$

where b is the Tempkin isotherm constant of binding energy (J mol−1K−1). The correlation factors (*R*2) given in Table 2 show that the Tempkin isotherm also fit the adsorption data. The values of KT show that there is strong interaction between AB40 and PANI as compared to Fe3O4 and PANI/Fe3O4 composites (Table 2).

Dubinin–Radushkevich (D–R) as expressed in Equation (5) was also fitted to the adsorption data.

$$\text{Inq}\_{\text{c}} = \text{Inq}\_{\text{s}} - \beta \,\varepsilon^2 \tag{5}$$

where qe is the amount of dye in mg adsorbed per gram of adsorbent (mg g<sup>−</sup>1), β (mol<sup>2</sup> <sup>K</sup>−1J−2) is the activity coefficient useful in obtaining the mean adsorption energy Ead (kJ mol−1), qs is the adsorption maximum, and ε is Polanyi potential. ε and Ead are expressed by Equations (5a) and (5b) respectively.

$$
\varepsilon = \text{RTln}(1 + \frac{1}{\mathbf{c}\_{\mathbf{e}}}) \tag{5a}
$$

$$E\_{\rm ad} = \frac{1}{\sqrt{1 - 2\beta}}\tag{5b}$$

where R is the gas constant which has a value of 8.314 (J mol−<sup>1</sup> <sup>K</sup>−1) and T is the kelvin temperature.

D–R adsorption model is a unique model used to di fferentiate between the chemical and physical adsorption on the basis of adsorption energy. In early research, it has been demonstrated that if the value of adsorption energy is less than 40 kJ mol−1, the adsorption is physical [78]. In the present work, the values of Ead, calculated by the Equation (5b) are less than 40 kJ mol−<sup>1</sup> for adsorption of AB40 and PANI as compared to Fe3O4 and PANI/Fe3O4 composites showing physical adsorption as shown in Table 2.

### *3.3. E*ff*ect of Contact Time and Temperature on Adsorption*

The contact time between adsorbent and dye is of grea<sup>t</sup> interest in the adsorption process. The optimum time of equilibrium was determined by adding 0.0340 ± 0.0001 g of each Fe3O4, PANI and PANI/Fe3O4 composite to 20 mL of AB40 (50 mg <sup>L</sup>−1) in a series of experiments and was shacked at 150 rpm at 30 ◦C. The adsorption data so obtained was plotted as a function of time (Figure 7a). The graph shows that adsorption is very fast in the initial 10–15 min. The initial fast adsorption is due to a strong interaction between active sites of adsorbents and dye molecules. After 40–50 min, adsorption rate of dye become constant due to filling of active sites on the surface of adsorbents. This time period is defined as the dynamic equilibrium time. At the equilibrium time, rate of adsorption and desorption occurs simultaneously with the same speed [79]. Maximum adsorption of AB40 on Fe3O4, PANI and PANI/Fe3O4 composite is observed at 30 ◦C indicating exothermic nature (Figure 7b).

**Figure 7.** Effect of (**a**) time and (**b**) temperature on adsorption of AB40 onto Fe3O4, PANI and PANI/Fe3O4 composite.

### *3.4. E*ff*ect of pH on Adsorption*

The pH of the dye solution plays a unique role in adsorption process. In the present work, the e ffect of pH on adsorption was investigated between 2–12. Results so obtained are plotted as adsorption versus pH (Figure 8). The plot indicates that adsorption of AB40 is high in acidic medium on all three adsorbents. When at a low pH, the backbone of adsorbents is positively charged and the active sites like Fe–O and –C=N are protonated. These positively charged sites have a strong interaction with the negatively charged sites of AB40 dye and hence enhance the adsorption. On the other hand, in a basic medium, the deprotonation of Fe–O–H and –C–N–H will create a negative charge in these groups which will repel the negatively charged sites of dye electrostatically, thus adsorption reduces [80].

**Figure 8.** The effect of solution pH on adsorption of AB40 on PANI, Fe3O4 and PANI/Fe3O4 composite.

### *3.5. E*ff*ect of Ionic Strength on Adsorption*

The effluent of industrial water also contains several ions. Therefore, the presence of these ions will also affect the adsorption process. In the present study, ionic strength effect of sodium sulfate and calcium chloride on adsorption has been studied in the pH between 5–6. The adsorption data so obtained are plotted against ionic strength (Figure 9). The plots (Figure 9a,b) show that adsorption of AB40 on PANI, Fe3O4 and PANI/Fe3O4 composite increases with an increase in ionic strength. This can be attributed to the fact that when both dye and adsorbent have similar charges, an increase in ionic strength will increase adsorption. This effect is more prominent in the adsorption of AB40 on PANI/Fe3O4 composite as compared to pristine PANI, because PANI/Fe3O4 composite contains a greater number of sites with a lone pair of electrons which behave as negatively charged groups [81]. Moreover, the significant increase in the adsorption of AB40 by increasing the ionic strength can be attributed to the dimerization of dye. A number of intermolecular forces like dipole-dipole, ion-dipole and Van der Waals forces have been suggested as the cause of the dimerization. Alberghina and co-workers have observed such type of dimerization while studying salts and temperature effect on adsorption of reactive dyes onto activated carbon [51].

**Figure 9.** The effect of ionic strength of (**a**) Na2SO4.7H2O and (**b**) CaCl2.2H2O on adsorption of AB40 onto Fe3O4, PANI and PANI/Fe3O4 composite.

### *3.6. E*ff*ect of Adsorbent Dosage on Adsorption*

To investigate the effect of adsorbent dosage on adsorption, 0.034, 0.045, 0.075 and 0.1 g of each Fe3O4, PANI and PANI/Fe3O4 composite were added to 100 mg L−<sup>1</sup> of AB40 separately and shook at 150 rpm at 30 ◦C and the amount adsorbed was noted (Figure 10). An increase in the adsorption of dye was observed by increasing the adsorbent dose. Initially the rate of adsorption is fast due to greater number of active site and splitting effect of the flux between adsorbents and dye [82].

**Figure 10.** Effect of adsorbent dosage on adsorption of AB40 onto Fe3O4, PANI and PANI/Fe3O4 composite.
