## 3 Results and Discussion
### Adsorption Performance
#### 3.2.4 Kinetic Analysis  
To elucidate the adsorption mechanism and rate-controlling steps in the removal of m-cresol using 0.15 g of functionalized resin, kinetic studies were performed at four temperatures (30, 40, 50, and 60 \({}^{\circ}\)C). The experimental data were analyzed using three kinetic models: PFO, PSO, and IPD, with the corresponding fits illustrated in Figure 10a-c and fitting parameters summarized in Table 4.  
The PFO model yielded moderate correlation coefficients (R\({}^{2}\) ranging from 0.9558 to 0.9718), with calculated equilibrium adsorption capacities significantly lower than the experimental values. This discrepancy suggests that physical adsorption alone does not adequately capture the adsorption behavior of m-cresol on the XDA-1G resin. In contrast, the PSO model provided an excellent fit across all temperature conditions, with R\({}^{2}\) values exceeding 0.9915. Moreover, the predicted qe values (500-555.6 mg g\({}^{-1}\)) closely matched the experimental data, implying that the adsorption process was indicative of chemisorption involving valence forces and electron-sharing mechanisms supported by thermodynamic parameters, surface functional group characteristics, and molecular interactions [40]. The PSO rate constants showed a decreasing trend with increasing temperature (from 5.27 \(\times\) 10\({}^{-5}\) to 4.03 \(\times\) 10\({}^{-5}\) g mg\({}^{-1}\) min\({}^{-1}\)), likely due to changes in the XDA-1G resin-adsorbate interaction dynamics under thermal conditions. Consistent with the linear analysis, the non-linear second-order model again demonstrated superior agreement with the experimental data, and providing adsorption capacities closely aligned with the measured values. In contrast, the non-linear first-order model yielded underestimated qe. The consistency between linear and non-linear results highlights the robustness of the second-order model in describing m-cresol uptake kinetics on XDA-1G. The IPD model revealed a two-stage adsorption mechanism, as evidenced by multi-linear plots. The initial steep segment corresponds to rapid surface adsorption, while the subsequent linear phase reflects slower intra-particle diffusion within the XDA-1G resin pores. Although the correlation coefficients (R\({}^{2}\): 0.9216-0.9274) were reasonably high, the linear plots did not pass through the origin, indicating that intra-particle diffusion was not \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Category** & **Parameter** & **Unit** & **30 °C** & **40 °C** & **50 °C** & **60 °C** \\ \hline PFO & k\({}_{1}\) & min\({}^{-1}\) & 0.0036 & 0.0036 & 0.0037 & 0.0037 \\  & qe & mg g\({}^{-1}\) & 267.1 & 284.9 & 306.5 & 307.6 \\  & R\({}^{2}\) & & 0.9718 & 0.9633 & 0.9627 & 0.9558 \\ \hline PSO & k\({}_{2}\) & g mg\({}^{-1}\) min\({}^{-1}\) & 5.270 \(\times\) 10\({}^{-5}\) & 4.769 \(\times\) 10\({}^{-5}\) & 4.027 \(\times\) 10\({}^{-5}\) & 4.583 \(\times\) 10\({}^{-5}\) \\  & qe & mg g\({}^{-1}\) & 500 & 526.3 & 454.5 & 555.6 \\  & R\({}^{2}\) & & 0.9963 & 0.9957 & 0.9915 & 0.9948 \\ \hline IPD & k\({}_{\rm p}\) & g mg\({}^{-1}\) & 7.551 & 7.883 & 8.255 & 8.187 \\  & C & mg g\({}^{-1}\) & 242.5 & 248.6 & 170.6 & 277.9 \\  & R\({}^{2}\) & & 0.9223 & 0.9216 & 0.9257 & 0.9274 \\ \hline \end{tabular}
\end{table} 
Table 4: The linear fitted parameters of kinetic models for m-cresol adsorption on 0.15 g resin. Figure 10: Kinetic and thermodynamic modeling of m-cresol adsorption onto the XDA-1G resin. (**a**) Pseudo-first-order, (**b**) pseudo-second-order, and (**c**) intra-particle diffusion kinetic model fits with linear fit. the sole rate-limiting step. The increasing intercept values (C) with temperature suggest a thicker boundary layer at elevated temperatures, which may hinder external mass transfer. Overall, the kinetic behavior of m-cresol adsorption onto the XDA-1G resin is best described by the pseudo-second-order model, indicative of chemisorption.