## 3 Results and Discussion
### Adsorption Isotherm
Table 1 shows that 1/n values for adsorption of Ni(II) were 0.2987, 0.3545, and 0.2139 while for adsorption of Cr(VI) these values were 0.3688, 0.4716, and 0.3905 respectively, on Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/Fe\({}_{3}\)O\({}_{4}\) composites. These results showed high favorability of adsorption over the entire range of concentrations and closely resembled already published research works [58]. Moreover, by comparing the values of 1/n after adsorption of Cr(VI) and Ni(II) ions over all three adsorbents (Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/ Fe\({}_{3}\)O\({}_{4}\) composites), one can deduce that Cr(VI) shows more heterogeneity as compared to Ni(II). [PERSON] et al. has reported that when the value of 1/n is smaller than one but more than zero (1 \(>\) 1/n \(>\) 0) the adsorption is highly favorable and heterogeneous, but when its values are more than unity (1 \(<\) 1/n) adsorption is unfavorable. However, if 1/n = 0, adsorption is irreversible. Similarly, when the value of 1/n is unity then system is at equilibrium and homogeneous [43]. Figure 5: Adsorption isotherms (**a**) [PERSON], (**b**) Langmuir, (**c**) Tempkin, (**d**) Dubinin–Radushkevich (D–R), and (**e**) Elovich models of Cr(VI) and Ni(II) adsorbed on Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/ Fe\({}_{3}\)O\({}_{4}\) composites. The Langmuir adsorption isotherm is another important model which expresses that adsorption of heavy metals occurs homogeneously resulting in the formation of a monolayer without interaction between the absorbed materials. It is expressed by the following Equation (3):  
\[\frac{\mathrm{C_{e}}}{\mathrm{q_{e}}}=\frac{1}{\mathrm{q_{max}K_{L}}}+\frac{1}{ \mathrm{q_{max}C_{e}}} \tag{3}\]  
where K\({}_{L}\) is constant called the Langmuir constant, qmax (mg\(\cdot\)g\({}^{-1}\)) refers to maximum adsorption, q\({}_{e}\) (mg\(\cdot\)g\({}^{-1}\)) is the amount of heavy metals adsorbed at equilibrium, and C\({}_{e}\) (mg\(\cdot\)L\({}^{-1}\)) is the remaining concentration of heavy metals when equilibrium is established. Figure 5b shows a Langmuir isotherm plot between C\({}_{e}\)/q\({}_{e}\) and C\({}_{e}\). The adsorption maximum of Cr(VI) as well as Ni(II) on Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/Fe\({}_{3}\)O\({}_{4}\) composites were obtained from the slope of Figure 5b. These values are 13.209, 51.379, and 134.88 mg\(\cdot\)g\({}^{-1}\) for adsorption of Ni(II) onto Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/Fe\({}_{3}\)O\({}_{4}\) composites, while for Cr(VI) these value were respectively 64.339, 82.284, and 174.09 mg\(\cdot\)g\({}^{-1}\) onto Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/Fe\({}_{3}\)O\({}_{4}\) composites (Table 1). The results show enhancement in the adsorption of Cr(VI) as well as Ni(II) on composite materials as compared to pristine PANI and Fe\({}_{3}\)O\({}_{4}\). Moreover, high values of qmax for Cr(VI) indicated strong interactions of Cr(VI) with adsorbent materials as compared to Ni(II). High adsorption of Cr(VI) was attributed to its existence as oxyanions (CrO\({}_{4}\)\({}^{2-}\), Cr\({}_{2}\)O\({}^{7-2}\), and HCrO\({}_{4}\)\({}^{-}\)) in aqueous environments which may cause greater interactions with positively charged sites present on the surface of adsorbents. Similar results were shown in the already published work [63]. A dimensionless constant, also called separation factors (R\({}_{L}\)), can be calculated by using the initial concentrations of pollutants (C\({}_{0}\)) and constant K\({}_{L}\) according to Equation (4) shown below:  
\[\mathrm{R_{L}}=\frac{1}{(1+K_{L}C_{0})} \tag{4}\]  
Table 1 shows R\({}_{L}\) values for Cr(VI) and Ni(II) adsorbed on Fe\({}_{3}\)O\({}_{4}\), PANI, and PANI/Fe\({}_{3}\)O\({}_{4}\) composites. The results closely resembled previously published reports which demonstrated that adsorption was favorable if the R\({}_{L}\) value was more than zero but less than unity (1 \(>\) R\({}_{L}\) \(>\) 0), unfavorable (1 \(<\) R\({}_{L}\)), irreversible (R\({}_{L}\) = 0), and linear (R\({}_{L}\) = 1) [64]. adsorption and estimation of the energy of adsorption.