## 3 Results and Discussion
### Adsorption Isotherm  
An adsorption study mainly depends upon the interaction between adsorbents and pollutants. These interactions can be clearly understood by considering the adsorption isotherms. Various types of isotherms like Dubinin-Radushkevitch (D-R), Langmuir, Freundlich, and Tempkin isotherm models have been successfully applied by earlier researchers [60; 61; 62]. In the present study, the data were fitted into Langmuir, Freundlich, Tempkin, Dubinin-Radushkevitch (D-R), and Elovich isotherm models shown in Figure 5. Various adsorption parameters were calculated from these models shown in Table 1.  
The Freundlich isotherm is the most common adsorption model and describes the formation of multilayers by the molecules of pollutants on the surface of adsorbent materials. It also explains heterogeneity of adsorption due to different interactions between pollutants and adsorbents. A linearized form of Freundlich adsorption isotherm equation has been expressed by the following Equation (2). \[\text{lnq}_{\text{e}}=\text{lnK}_{\text{f}}+\frac{1}{\text{n}}\text{lnC}_{\text {e}} \tag{2}\]  
where K\({}_{\text{f}}\) is constant known as the Freundlich constant, 1/n is the slope referring to the adsorbent intensity, C\({}_{\text{e}}\) (mg\(\cdot\)L\({}^{-1}\)) is the remaining concentration of heavy metals at equilibrium, and q\({}_{\text{e}}\) (mg\(\cdot\)g\({}^{-1}\)) shows adsorption of heavy metals by one gram of adsorbent at equilibrium. Figure 5a shows the Freundlich isotherm graph obtained by plotting lnq\({}_{\text{e}}\) vs. lnC\({}_{\text{e}}\). From the intercept and slope of this graph the constants K\({}_{\text{F}}\) and 1/n were calculated, which relate respectively to the adsorption capacity \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Isotherms**} & \multirow{2}{*}{**Parameters**} & \multicolumn{6}{c}{**Adsorbents and Heavy Metals Adsorbed**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Fe\({}_{3}\)O\({}_{4}\)**} & \multicolumn{2}{c}{**PANI**} & \multicolumn{2}{c}{**PANI/Fe\({}_{3}\)O\({}_{4}\)**} \\ \cline{3-8}  & & **Ni+2** & **Cr+6** & **Ni+2** & **Cr+6** & **Ni+2** & **Cr+6** \\ \hline \multirow{2}{*}{**Freundlich**} & **1/n** & 0.2987 & 0.3688 & 0.3545 & 0.4716 & 0.2139 & 0.3905 \\ \cline{2-8}  & **Kf** & 6.9559 & 35.026 & 39.244 & 26.119 & 55.523 & 53.801 \\ \cline{2-8}  & **R\({}^{2}\)** & 0.9366 & 0.9472 & 0.9232 & 0.9890 & 0.9307 & 0.9684 \\ \hline \multirow{2}{*}{**Langmuir**} & **q\({}_{\text{max}}\)** & 13.209 & 64.339 & 51.379 & 82.284 & 134.88 & 174.09 \\ \cline{2-8}  & **k\({}_{\text{L}}\)** & 20.554 & 25.877 & 111.59 & 66.374 & 900.52 & 1564.2 \\ \cline{2-8}  & **R\({}_{\text{L}}\)** & 0.0242 & 0.0198 & 0.0448 & 0.0753 & 0.0555 & 0.0324 \\ \cline{2-8}  & **R\({}^{2}\)** & 0.8136 & 0.9325 & 0.9068 & 0.9246 & 0.9184 & 0.8615 \\ \hline \multirow{2}{*}{**Tempkin**} & **B** & 2.799 & 7.488 & 18.989 & 09.041 & 8.7281 & 24.414 \\ \cline{2-8}  & **kT** & 1.302 & 19.96 & 114.13 & 102.217 & 90.838 & 95.693 \\ \cline{2-8}  & **R\({}^{2}\)** & 0.811 & 0.912 & 0.952 & 0.897 & 0.798 & 0.902 \\ \hline \multirow{2}{*}{**D–R**} & **q\({}_{\text{a}}\)** & 39.056 & 37.412 & 45.695 & 43.243 & 62.053 & 62.427 \\ \cline{2-8}  & **E\({}_{\text{ads}}\)** & 22.499 & 26.982 & 33.298 & 32.653 & 34.742 & 37.981 \\ \cline{2-8}  & **R\({}^{2}\)** & 0.9025 & 0.8979 & 0.9316 & 0.7748 & 0.7995 & 0.8277 \\ \hline \multirow{2}{*}{**[PERSON]**} & **q\({}_{\text{e}}\)** & 73.874 & 13.879 & 14.592 & 13.766 & 12.048 & 26.285 \\ \cline{2-8}  & **k\({}_{\text{E}}\)** & 0.08683 & 44.688 & 51.886 & 31.199 & 782.8354 & 21.519 \\ \cline{2-8}  & **R\({}^{2}\)** & 0.5588 & 0.8235 & 0.8197 & 0.8749 & 0.7998 & 0.8767 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Isotherm parameters calculated for Cr(VI) and Ni(II) adsorbed on Fe\({}_{3}\)O\({}_{4}\), PANI, and Fe\({}_{3}\)O\({}_{4}\)/PANI composites. and the adsorption intensity.