## 3 Results and Discussions
### Kinetic Models for the Absorption of Heavy Metals  
The kinetic analysis of the adsorption processes for different metal-resin systems allowed for the identification of characteristic models underlying the interactions between metal cations and the functional groups of the resins investigated (Table 1). The use of pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic models helped explain the main mechanisms and specific kinetic features of each system. For many metal-resin combinations, the PSO model showed a strong fit to the experimental data, with determination coefficients (R\({}^{2}\)) ranging from 98% to 100%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metal–Resin** & **Best Model** & **R\({}^{2}\) (\%) (PFO)** & **R\({}^{2}\) (\%) (PSO)** & **K1 (min\({}^{-1}\))** & **K2 (g/mg\({}^{*}\)min)** \\ \hline Cu\({}^{2+}\)–PS—DVB & PSO & — & 99.9 & — & 0.002 \\ Cu\({}^{2+}\)–PA—DVB & PSO & — & 98.6 & — & 0.00033 \\ Cu\({}^{2+}\)–TFSA & PFO & 98.0 & — & 0.0704 & — \\ Cu\({}^{2+}\)—OGL & — & — & — & — & — \\ \hline Pb\({}^{2+}\)–PS—DVB & PSO & — & 99.5 & — & 0.00021 \\ Pb\({}^{2+}\)–PA—DVB & PFO & 98.3 & — & 0.0377 & — \\ Pb\({}^{2+}\)–TFSA & PSO & — & 99.5 & — & 0.0008 \\ Pb\({}^{2+}\)–OGL & — & — & — & — & — \\ \hline Co\({}^{2+}\)–PS—DVB & PSO & — & 99.7 & — & 0.000576 \\ Co\({}^{2+}\)–PA—DVB & PFO & 97.8 & — & 0.127 & — \\ Co\({}^{2+}\)–TFSA & PSO & — & 99.8 & — & 0.0605 \\ Co\({}^{2+}\)–OGL & — & — & — & — & — \\ \hline Ni\({}^{2+}\)–PS—DVB & PSO & — & 98.3 & — & 0.00079 \\ Ni\({}^{2+}\)–PA—DVB & PFO & 97.8 & — & 0.126 & — \\ Ni\({}^{2+}\)–TFSA & — & — & — & — & — \\ Ni\({}^{2+}\)–OGL & — & — & — & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the kinetic model fitting results for various metal–resin pairs. For each combination, the best-fitting kinetic model (PSO or PFO) is indicated, along with the corresponding correlation coefficients R\({}^{2}\) for the PFO and PSO models, and kinetic constants \(K1\) for PFO (in min\({}^{-1}\)) and K2 for PSO (in g/(mg\({}^{*}\)min)). The table highlights the adsorption behavior and model accuracy for each metal–resin pair, showing which kinetic model best describes the ion exchange process. Blank entries indicate cases where data were not available or where the model did not adequately describe the adsorption process. The PS--DVB resin proved to be very versatile and particularly efficient in the adsorption of various metal cations, predominantly following the second-order kinetic model (PSO). This suggests that the adsorption process involves specific chemical interactions between the active sites of the resin and the metal ions. For Cu\({}^{2+}\), it showed a PSO R\({}^{2}\)- value of 99.9%, suggesting very good fit and chemical adsorption, despite \(K2\) being relatively low (0.002 g/(mg*min)). This suggests moderate kinetics for copper on PS--DVB. For Pb\({}^{2+}\), PS--DVB fit the PSO model well (R\({}^{2}\) = 99.5%), but the \(K2\) was relatively low (0.00021 g/(mg*min)), indicating slow adsorption kinetics for this metal. For Co\({}^{2+}\), the PS--DVB resin showed a good fit to the PSO model (R\({}^{2}\) = 99.7%), with a \(K2\) constant of 0.000576 g/(mg*min), indicating moderate adsorption kinetics. Finally, for nickel (Ni\({}^{2+}\)), the PSO model also fit well (R\({}^{2}\) = 98.3%), although the \(K2\) constant was lower (0.00079 g/(mg*min)), indicating a slow adsorption rate. We can, therefore, conclude that PS--DVB proved to be an effective resin for the removal of the tested metals. The PA--DVB resin exhibited a different behavior, fitting both the second-order (PSO) and first-order (PFO) models depending on the target metal, suggesting the possibility of mixed adsorption mechanisms. For Cu\({}^{2+}\), PA--DVB fit the PSO model better (R\({}^{2}\) = 98.6%), with a \(K2\) constant of 0.00033 g/(mg*min), indicating slower adsorption kinetics than the PS--DVB resin for this metal.