*3.8. Adsorption Mechanism*

Two routes can be proposed for the adsorption of AB40 on the surface of PANI salt and PANI/Fe3O4 composite. In the first one, electrostatic interaction may occur between the molecules of AB40 and PANI. The second one involves the formation of an H-bond between the dye and –NH group of PANI. H-bond formation is also possible between AB40 and –OH group present on the surface of Fe3O4.

The electrostatic interactions are based on the fact that when dye is dissolved in water it splits into positively and negatively charged ions (Dye-SO3 −). These negatively charged anions (Dye-SO3 −) interact with positively charged sites (–+NH–) on PANI surface. The enhancement of dye adsorption in acidic medium is good evidence of electrostatic interaction expressed in Section 3.4. Existence of physical forces (H-bond) is also supported by FTIR spectra shown in Figure 4B. After adsorption of AB40, all peaks in the spectra of PANI and PANI/Fe3O4 composite are shifted towards low-frequency values. Moreover, appearance of peak at 2356.7 cm<sup>−</sup><sup>1</sup> shows existence of AB40 adheres to the surface of PANI and PANI/Fe3O4 composites [72].

### *3.9. Thermodynamics of Adsorption*

The nature of adsorption can be described well with thermodynamic parameters like Gibbs free energy, change in enthalpy and change in entropy. Values of Gibbs free energy were calculated by the equation shown below (Equation (10));

$$
\Delta \mathbf{G} = -\mathbf{R} \mathbf{T} \ln \mathbf{K}\_{\mathbf{e}} \tag{10}
$$

where Ke is the equilibrium constant, R is the gas constant having the value of 8.314 J K−<sup>1</sup> mol−<sup>1</sup> and T represents the Kelvin temperature. The negative sign of ΔG values shows that the adsorption of AB40 onto Fe3O4, PANI and PANI/ Fe3O4 composites are spontaneous (Table 5). The values of Δ G which range from −20 to zero kJ mol−<sup>1</sup> show physical adsorption [47]. The values of ΔH and ΔS were calculated from the slope and intercept of van't Ho ff equation respectively by plotting lnke vs. 1/T (Figure 12b). The van't Ho ff equation is expressed as below;

$$
\Delta \mathbf{K}\_{\mathbf{e}} = -\frac{\Delta \mathbf{H}}{\mathbf{R} \mathbf{T}} + \frac{\Delta \mathbf{S}}{\mathbf{R}} \tag{11}
$$

$$\mathbf{K\_{e}} = \frac{\mathbf{q\_{e}}}{\mathbf{c\_{e}}} \tag{11a}$$

where qe (mg g<sup>−</sup>1) is the adsorption maximum and Ce (mg <sup>L</sup>−1) is the concentration of dye at equilibrium. The negative values of ΔH and ΔS shown in Table 4 show that adsorption is exothermic and correlate to the e ffect of temperature on adsorption expressed in Section 3.3. Activation energy also expresses the nature of adsorption. Its values are calculated from the slope of Arrhenius equation by plotting lnK vs. 1/T shown in Figure 12b. The Arrhenius equation is expressed as below;

$$\text{lnk} = \text{lnA} - \frac{\text{Ea}}{\text{RT}} \tag{12}$$

where K is the rate constant, A is Arrhenius constant, Ea is the activation energy, R is the general gas constant and T is kelvin temperature. The activation energy of adsorption of AB40 onto Fe3O4, PANI and PANI/Fe3O4 composites are 30.12, 22.09 and 26.13 kJ mol−<sup>1</sup> showing physical adsorption. Ozcan and co-workers have demonstrated that physical adsorption is characterized by the activation energy values range from 5 to 40 kJ mol−<sup>1</sup> and its higher values (40–800) kJ mol−<sup>1</sup> express chemical adsorption [85].

**Table 5.** Activation energy and thermodynamic parameters of AB40 adsorption.


**Figure 12.** (**a**) Arrhenius plot and (**b**) van't Hoff plot for calculation of activation energy and thermodynamic parameters.
