*3.7. Kinetic Study*

Kinetic study is very important to explain the adsorption phenomenon. The data obtained from adsorption of BB3 dye were analyzed through Lagergren's pseudo first order, Ho and McKay's pseudo second order, and Weber and Morris's intra particle diffusion models by using Equations (10)–(12).

$$\log(\mathbf{q}\_\mathbf{e} - \mathbf{q}\_\mathbf{t}) = \log \mathbf{q}\_\mathbf{e} - \frac{\mathbf{K}\_1 \mathbf{t}}{2.303} \tag{10}$$

$$\frac{\mathbf{t}}{\mathbf{q}\_{\mathbf{t}}} = \frac{1}{\mathbf{K}\_2 \mathbf{q}\_{\mathbf{t}}^2} + \frac{\mathbf{t}}{\mathbf{q}\_{\mathbf{e}}} \tag{11}$$

$$\mathbf{q}\_{\rm t} = \mathbf{k}\_{\rm d} \mathbf{t}^{1/2} + \mathbf{C} \tag{12}$$

where qe and qt are the amount of dye adsorbed (mg g-1) at equilibrium and at time t, K1, K2, and Kd are rate constant of pseudo first order (min−1), pseudo second order (g mg<sup>−</sup><sup>1</sup> min−1), and intra-particle diffusion models (g mg<sup>−</sup><sup>1</sup> min−1/2), respectively. C (mg g-1) is the constant and t is the time in minutes. Figure 12a–c shows the fitted curves of pseudo first order, pseudo second order, and intra-particle diffusion models for BB3 adsorbed on Fe3O4, PANI, and PANI/Fe3O4 composites, respectively. The kinetics data obtained are shown in Table 4. The correlation factor (R2) indicates that the pseudo second order kinetic model fits more closely to data as compared to the pseudo first order and intra-particle diffusion models. Values of rate constant indicate that as the temperature increases, rate of adsorption decreases [77,78].

**Figure 12.** Kinetics models: (**a**) First order and (**b**) second order kinetics, (**c**) intra-particle diffusion model of adsorption of BB3 dye on Fe3O4, PANI, and PANI/Fe3O4 composite.


**Table 4.** Parameters of Kinetics models of BB3 adsorption onto Fe3O4, PANI, and PANI/Fe3O4 composite.

### *3.8. Mechanism of Adsorption*

Actually, many factors, such as structure and charge on dye, surface of adsorbent, hydrophilic, and hydrophobic properties, electrostatic interaction, and physical forces, such as hydrogen bonding and dipole-dipole interaction, affect the adsorption of BB3 on PANI/Fe3O4 composites. Therefore, different mechanisms can be proposed for the adsorption of BB3 on Fe3O4, PANI, and PANI/ Fe3O4 composites. When BB3 is added to water, it dissociates in a positively-charged complex cation and negatively charged chloride ion as shown below (Scheme 3).

**Scheme 3.** Dissociation of BB3 in a positively-charged complex cation and negatively charged chloride ion into.

There is a possibility of H-bonding between amine and imine groups of PANI/Fe3O4 with nitrogen and oxygen present in the BB3 structure. Similarly, the surface hydroxyl groups of Fe3O4 may also form H-bonds with dye molecules [97].

There may exist Vander Waal's interaction between hydrophobic parts of the dye and hydrophobic parts of the PANI/Fe3O4 composite, because the nonpolar groups have a tendency to associate in aqueous solution. Another possibility is the existence of electrostatic interaction between positively-charged nitrogen present in the dye structure and a lone pair present on the nitrogen of amine and imine group of PANI and PANI/Fe3O4 [98]. The adsorption behavior of BB3 on PANI/Fe3O4 in basic medium is shown as the following (Scheme 4).

5 1+ 2+ 1 2+ 5 12+ 2 +21 + 1+&+ G\H 5 12+ 2 +21 + 1+&+ G\H (OHFWURVWDWLF LQHWHUDFWLRQ

**Scheme 4.** Adsorption behavior of BB3 on PANI/Fe3O4 in basic medium.

Where R represents the non-polar part of the PANI/Fe3O4 with = NH, −NH2 of PANI, and −OH group of Fe3O4.

During the adsorption process the amount of energy released compensates for the entropy change of adsorbed molecules and depends upon the forces between adsorbent and adsorbate molecules; the stronger the force, the more energy will be released. The energy released during the adsorption process for H-bond is (2–40 kJ/mol), dipole-dipole interaction is (2–29 kJ/mol), Vander Waals forces is (4–10 kJ/mol), and is about 5 kJ/mol for hydrophobic forces, and more than 60 kJ/mol for electrostatic interaction [99]. In the present study the enthalpy change are −32.84, −62.93, and −74.26 kJ/mol when BB3 adsorbs on Fe3O4, PANI, and PANI/Fe3O4, respectively.

### *3.9. Calculation of Thermodynamic Parameters*

Thermodynamic parameters, such as activation energy, Gibb's free energy change, enthalpy change, and entropy change, are helpful to explain the nature of adsorption. Activation energy is calculated by Arrhenius equation, shown below.

$$\mathbf{k} = \mathbf{A}\mathbf{e}\mathbf{x}\mathbf{p}^{(-\text{Ea/RT})}\tag{13}$$

where Ea is the activation energy, T is the absolute temperature, A is the Arrhenius constant, and k is the rate constant. Gibb's Free energy change is calculated by the following equation.

$$
\Delta \mathbf{G} = -\mathbb{R} \text{Tln} \frac{\mathbf{q}\_{\text{c}}}{\mathbf{C}\_{\text{c}}} \tag{14}
$$

Enthalpy change and entropy change are calculated by Van't Hoff equation by plotting the lnqe/Ce vs. 1/T, as given below.

$$
\ln \frac{\mathbf{q}\_{\text{e}}}{\mathbf{C}\_{\text{e}}} = \frac{\Delta \mathbf{S}}{\mathbf{R}} - \frac{\Delta \mathbf{H}}{\mathbf{R} \mathbf{T}} \tag{15}
$$

where ΔH is the enthalpy change and ΔS is the change in entropy, and T is the absolute temperature. Figure 13a shows the Arrhenius plot, obtained by plotting lnK2 vs. 1/T after adsorption of BB3. From the slope the activation energy values of adsorption of BB3 were to found to be 11.14, 11.97, and 09.94 kJ/mol, respectively, which indicate that adsorption is physical and is a diffusion control process (Table 5) [100]. The value of enthalpy change is also helpful in explaining the adsorption phenomenon. It was reported that enthalpy change in the range of 84–420 kJ/mol suggests chemical interaction between dye and adsorbent (chemisorption), while its value below 84 kJ/mol indicates physical adsorption [95]. The values of enthalpy change in the present work, as shown in Table 5, are −32.84, −62.93, and −74.26 kJ/mol for the adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composite, respectively, thereby confirming the physical process. The negative sign of ΔH indicates that adsorption is exothermic. The ΔG value is also helpful in explaining the adsorption phenomenon, it explains the spontaneity and non-spontaneity of adsorption. The negative sign for ΔG shown in Table 5 indicates that adsorption is exothermic and spontaneous. The ΔG values in the range of −20 to 0 kJ/mol show physiosorption, and from −400 to −80 kJ/mol show chemisorption [101,102]. The ΔG values for Fe3O4, PANI, and PANI/Fe3O4 composite used as adsorbents are −04.05, −07.78, and −10.63 kJ/mol, respectively, which sugges<sup>t</sup> that adsorption of BB3 dye on all the three adsorbents is physical, exothermic, and spontaneous [103]. These observations strongly correlate with the data presented in Section 3.5 for temperature effect on the absorption phenomenon.

**Figure 13.** (**a**) Arrhenius plot for calculation of activation energy. (**b**) The van't Hoff plot for calculation of enthalpy and entropy.


**Table 5.** Thermodynamic parameters of adsorption of BB3 on Fe3O4, PANI, and PANI/Fe3O4 composite.
