*3.2. Equilibrium Study*

An equilibrium study is very valuable for understanding the interaction of BB3 with Fe3O4, PANI, and PANI/Fe3O4 composites. The adsorption data are shown in Table 2, which shows that the adsorption capacity of the dye on these materials increases as the concentration of dye increases. BB3 is a cationic dye and gets adsorbed on Fe3O4, PANI, and PANI/Fe3O4 composites from aqueous solution due to interactions with negative sites on the surface of the adsorbent. In the literature it has been explained that these binding sites are present (electron pair) on oxygen of Fe3O4 and nitrogen of amine and imine PANI and PANI/Fe3O4, which are capable of interacting with oppositely charged ions present in the dye [76]. The data obtained from the equilibrium study were fitted into Freundlich, Langmuir, Tempkin, and D-R adsorption isotherms for estimation of various adsorption parameters.


**Table 2.** Parameters calculated from adsorption isotherm models applied for adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composites.

Freundlich adsorption equation is expressed by the following equation.

$$
\ln \text{ q}\_{\text{e}} = \ln \text{K}\_{\text{f}} + \frac{1}{\text{n}} \ln \text{ C}\_{\text{e}} \tag{2}
$$

where qe (mg/g) is the amount of dye adsorbed per gram of adsorbent, Ce (mg/L) is the concentration of dye at equilibrium, Kf is Freundlich isotherm constant, and n is the intensity of adsorbent. A plot of lnqe vs. lnCe is shown in Figure 7a.

**Figure 7.** Adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4. (**a**) Freundlich, (**b**) Langmuir, (**c**) Tempkin, and (**d**) D-R adsorption isotherms.

From the value of the slope obtained from the Freundlich adsorption isotherm, it can be demonstrated whether adsorption is favorable or unfavorable, reversible or irreversible. It also explains whether the system is heterogeneous or not [77]. If 1/n > 1, adsorption is unfavorable at low concentration but favorable at high concentration; if 1/n < 1, adsorption is favorable over the entire range of concentrations and the system is heterogeneous. However, if 1/n = 1, then the system is homogenous [78]. The values of 1/n obtained from the Freundlich adsorption isotherm in the present study are 0.9593, 0.8673, and 0.9112 for adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composites, respectively, as shown in Table 2. These values are in close resemblance with the literature showing that adsorption is favorable and heterogeneous. R<sup>2</sup> values show that the Freundlich adsorption isotherm fits to the adsorption data for Fe3O4, PANI, and PANI/Fe3O4 composites.

The adsorption data were also analyzed through the Langmuir adsorption isotherm, which is expressed in the following equation.

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

where qmax is the max adsorption capacity (mg/g), qe is the amount of dye adsorbed at equilibrium (mg/g), Ce is the equilibrium adsorption concentration (mg/L), and KL is the constant related to energy (Langmuir constant). From the Langmuir isotherm, RL (dimensionless separating factor) is calculated by the following equation.

$$\mathbf{R\_L} = \frac{1}{(1 + \mathbf{K\_L C\_i})} \tag{4}$$

From RL value it can be demonstrated whether adsorption is favorable, unfavorable, reversible, or irreversible. If RL value is less than one but more than zero (0 < RL < 1) adsorption is favorable, but if 1 < RL adsorption is unfavorable. If RL = 0 adsorption is irreversible and RL = 1 indicates that adsorption is reversible [79]. The adsorption data obtained through the Langmuir isotherm are given in Table 2, which show that the maximum adsorption capacities (qmax) are 7.474, 47.977, and 78.13 mg/g for Fe3O4, PANI and PANI/Fe3O4 composites, respectively. The values of Langmuir constant (KL) and dimensionless separating constant (RL) for all the three types of adsorbents shows that adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composites is monolayer and favorable. R<sup>2</sup> values show that the Langmuir adsorption isotherm fits more closely to the adsorption data than the other isotherms.

Tempkin adsorption isotherm, shown in the Equation (5), was also applied to explain the adsorption data.

$$\mathbf{q}\_{\text{e}} = \beta \ln \mathbf{K}\_{\text{T}} + \beta \ln \mathbf{C}\_{\text{e}} \tag{5}$$

R<sup>2</sup> values show that Tempkin isotherm does not fit very well to adsorption data as compared to Freundlich and Langmuir isotherms, but is still helpful in explaining the binding forces between adsorbents and adsorbate. KT is the binding constant at equilibrium and corresponds to maximum binding energy [80]. Its values calculated from the intercept of plot qe vs. lnCe (Figure 7c) are 8.565, 22.26, and 33.04 <sup>L</sup>/g for Fe3O4, PANI, and PANI/Fe3O4 composites, respectively. These results show that there are strong binding forces between BB3 and PANI/Fe3O4 as compared to binding forces of dye with Fe3O4 and PANI, respectively. The value of constant β is related to the heat of adsorption in Equation (6)

$$
\beta\_- = \frac{\text{RT}}{\text{b}} \tag{6}
$$

where b is Tempkin isotherm constant of binding energy (J/mol K). The negative sign of β values for all the three adsorbents shows that adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composites is exothermic.

The Dubinin-Radushkevitch (D-R) adsorption equation has also been successfully applied to the data obtained by plotting lnqe vs. ε2, and is shown in Figure 7d. A linearized form of D.R adsorption equation is given below

$$
\ln \mathbf{q}\_{\mathbf{e}} = \ln \mathbf{q}\_{\mathbf{e}} - \mathbf{B} \boldsymbol{\varepsilon}^2 \tag{7}
$$

where qs is the theoretical monolayer saturation capacity (mg/g), B is the constant, called D-R model constant, and ε2 is the Polanyi potential, which is calculated by the Equation (8)

$$
\varepsilon = \text{RTlog}(1 + \frac{1}{\text{C.e}}) \tag{8}
$$

where R is the general gas constant and T is the absolute temperature. From the D-R model, energy of adsorption was calculated by Equation (9)

$$\mathcal{E}\_{\text{ads}} = \frac{1}{\sqrt{(1 - 2\mathcal{B})}} \tag{9}$$

In the literature it has been explained that for physical adsorption, the value of adsorption energy should be less than 40 kJ/mol [81]. Its value also tells about the route of adsorption through ion exchange process. In the early literature it has been explained that for ion exchange process the value of adsorption energy should be in the range of 8–16 kJ/mol. The values of qs calculated from the linear plot of D-R isotherm are 0.888, 9.183, and 20.54 mg/g for Fe3O4, PANI, and PANI/Fe3O4 composites, respectively, showing that adsorption is physical. Similarly, values of (Eads), shown in Table 2, demonstrate that adsorption does not follow ion exchange process [82]. A comparison of the adsorption efficiency of the synthesized materials with those reported earlier is also provided in Table 3.

**Table 3.** Comparative adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 with other adsorbents.


### *3.3. E*ff*ect of Ionic Strength*

Electrostatic interactions, such as ionic strength, greatly affect the surface properties of the adsorbent [91]. The effect of ionic strength on adsorption of BB3 (dye concentration 80 mg/<sup>L</sup> in 20 mL volume) on Fe3O4, PANI, and PANI/Fe3O4 was observed by adding sodium sulphate solution in the range of 0.01–0.3 mol dm−3. The obtained results (Figure 8) show that the adsorption capacities of Fe3O4, PANI, and PANI/Fe3O4 composites decrease as the concentration of salt (ionic strength) increases. The minimum dye adsorption on Fe3O4, PANI, and PANI/Fe3O4 was observed at 0.25, 0.21, and 0.25 ionic strengths, respectively. The competition of Na<sup>+</sup> or SO4<sup>2</sup>− ions with BB3 dye for active sites present on the surface of Fe3O4, PANI, and PANI/Fe3O4 might be a reason for the decrease in adsorption capability [71,92]. This competition is related to the interactions between hydrated ions and active sites of the adsorbent. Cations with a smaller hydrated radius occupy more active sites on the adsorbent, leading to stronger interaction with the adsorbent [93].

**Figure 8.** Effect of ionic strength on adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composites.

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

The pH of the solution plays a major role in the removal of adsorbates from aqueous solutions. Figure 9 shows the effect of pH on the adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4. As BB3 is a cationic dye, at low pH the H<sup>+</sup> ions compete with dye for active sites present on the surface of the adsorbent and protonate them. These active sites are Fe–O and –C–N groups. Similarly, the nitrogen and oxygen in the dye are also protonated. This causes electrostatic repulsion between dye and adsorbent, hence reducing adsorption [94]. As the pH of dye solutions increases, the adsorption increases and reaches a maximum for Fe3O4, PANI, and PANI/Fe3O4 composites when the pH of the dye solution is 12, 8, and 10, respectively. At high pH de-protonation of Fe–OH and –C–N–H groups occurs, resulting in negatively charged sites, such as Fe–O− and –C–N<sup>−</sup>, which have stronger interactions with dye. Figure 9 also indicates that after optimum pH, adsorption once again decreases. This may be due to hydroxylation of active sites of adsorbents [95].

**Figure 9.** Effect of pH on adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composite.

### *3.5. E*ff*ect of Contact Time and Temperature*

Contact time and temperature are also important parameters for explaining the adsorption phenomenon. The adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composites as a function of time is shown in Figure 10a, which shows that the adsorption increases with the passage of time. This figure also shows that initially adsorption is fast and contributes significantly to the equilibrium, but as the time passes, the adsorption slows down and its contribution to equilibrium decreases. This is due to filling of active sites on the surface of the adsorbent by the molecules of dye, and gradually adsorption becomes less effective. At this time, a dynamic equilibrium is established between the amount of dye adsorbed and desorbed from the adsorbent. This time is termed "equilibrium time" and the dye adsorbed at the equilibrium time is referred to as the maximum adsorption capacity of the adsorbent. It is evident from Figure 10a that the equilibrium time of adsorption is reached for Fe3O4, PANI, and PANI/Fe3O4 composites within 50 to 60 min [96]. Figure 10b shows that adsorption of BB3 on PANI and PANI/Fe3O4 composites is maximal at 30 ◦C and decreases beyond this temperature, indicating exothermic behavior.

**Figure 10.** Adsorption of BB3 at (**a**) different time intervals and (**b**) temperature on Fe3O4, PANI, and PANI/Fe3O4 composites.

### *3.6. E*ff*ect of Adsorbent Dose*

The effect of adsorbent dose on adsorption of BB3 (50 mg/L) is studied with different amounts (0.02 g, 0.06 g, and 0.1 g) of Fe3O4, PANI, and PANI/Fe3O4 composites, respectively. The results are shown in the Figure 11, which shows that amount of adsorption of BB3 increases as the amount of adsorbent increases. This shows that as the amount of adsorbent increases, more active sites are available for the adsorption of dye, which results in more interactions between dye and adsorbent. The figure shows that the adsorption capacity of PANI/Fe3O4 composites is more than Fe3O4 and PANI.

**Figure 11.** Effect of adsorbent dose for (**a**) Fe3O4, (**b**) PANI, and (**c**) PANI/ Fe3O4 composite on adsorption of BB3.
