## 3 Results and Discussion
### Sorption Study
The error capacities for the Freundlich isotherms indicated higher qualities than the Langmuir isotherm type 1, as can be seen in the information recorded in Table 4 for artificially altered chitosan. The Temkin sorption isotherm model (direct and nonlinear), as shown in Table 2, was additionally applied to assess the sorption possibilities of the sorbent. Its capability is communicated by the values that appear in Table 2 for copper, lead, and cadmium, showing a lower biopolymer-metal connection for the lead. If there should be an occurrence of a nonlinear model, these isotherms demonstrated a lower relationship coefficient when contrasted with the straight model for altered items, as shown in Table 5. The chi-square (\(\chi^{2}\)) test was used to confirm the proficiency and adjustment of the models, as reported in earlier studies [38]. The dissemination of error and chi-square test esteems were lower on the off chance that Langmuir isotherm type 1 fit the trial information better. The error elements of the Freundlich and Temkin models likewise were higher than that of the Langmuir model, demonstrating its lowest fit to the outcomes. The amount of cations sorbed has been compared with the pristine chitosan. The amount that the cations were sorbed by the modified chitosan has also been compared with already synthesized material available in the literature, as shown in Table 6. However, it is very difficult to compare our results with the literature due to the differences in the chitosan source as well as differences in the degree of deacetylation and the molecular weight of the polymeric chain. This is because the extent of sorption depends on its source, its degree of deacetylation, molecular weight, the nature of the cations, and the pH of the solution [39]. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Material** & **Isotherm** & **Constant** & **Type I** & **Type II** & **Type III** & **Type IV** \\ \hline \multirow{8}{*}{CH-ANP} & \multirow{8}{*}{Cu\({}^{2+}\)} & N/ & 2.82 & 2.82 & 2.82 & 2.82 \\  & & Ns & \(2.94\pm 0.01\) & \(2.93\pm 0.01\) & \(2.95\pm 0.02\) & \(2.95\pm 0.14\) \\  & & b & \(2.63\pm 0.01\) & \(2.62\pm 0.01\) & \(2.59\pm 0.01\) & \(2.57\pm 0.06\) \\  & & R\({}^{2}\) & 0.999 & 0.996 & 0.993 & 0.993 \\  & & SE & 0.034 & 0.034 & 0.031 & 0.031 \\  & & \(\chi^{2}\) & 0.007 & 0.007 & 0.006 & 0.006 \\ \hline \multirow{8}{*}{CH-ANP} & \multirow{8}{*}{Pb\({}^{2+}\)} & N/ & 1.60 & 1.60 & 1.60 & 1.60 \\  & & Ns & \(1.85\pm 0.03\) & \(1.89\pm 0.01\) & \(1.88\pm 0.01\) & \(1.88\pm 0.01\) \\  & & b & \(0.61\pm 0.01\) & \(0.57\pm 0.01\) & \(0.58\pm 0.05\) & \(0.58\pm 0.08\) \\  & & R\({}^{2}\) & 0.998 & 0.998 & 0.995 & 0.995 \\  & & SE & 0.016 & 0.016 & 0.016 & 0.016 \\  & & \(\chi^{2}\) & 0.002 & 0.001 & 0.001 & 0.001 \\ \hline \multirow{8}{*}{Cd\({}^{2+}\)} & N/ & 1.96 & 1.96 & 1.96 & 1.96 \\  & & Ns & \(2.48\pm 0.03\) & \(2.51\pm 0.01\) & \(2.51\pm 0.02\) & \(2.52\pm 0.01\) \\ \cline{1-1}  & & b & \(0.45\pm 0.01\) & \(0.43\pm 0.01\) & \(0.43\pm 0.01\) & \(0.43\pm 0.01\) \\ \cline{1-1}  & & R\({}^{2}\) & 0.998 & 0.999 & 0.993 & 0.993 \\ \cline{1-1}  & & SE & 0.025 & 0.025 & 0.025 & 0.026 \\ \cline{1-1}  & & \(\chi^{2}\) & 0.0026 & 0.003 & 0.003 & 0.003 \\ \hline \end{tabular}
\end{table} 
Table 3: Isotherm results of tested divalent metal ions for their interaction with the chemically modified CH-ANP material. Four different linear types (type I to type IV) of Langmuir were employed under standard conditions. (Abbreviations: N/–number of sorbed moles (mmol g\({}^{-1}\)), Ns (mmol g\({}^{-1}\)), and b (g mmol\({}^{-1}\))–Langmuir parameters, r–correlation coefficients, and SE–standard errors).