## 3 Results and Discussion
### Adsorption Performance
#### 3.2.3 Adsorption Isotherms  
To evaluate the equilibrium characteristics of m-cresol adsorption onto the XDA-1G resin, isotherm experiments were conducted and fitted using the Langmuir, Freundlich, and Temkin models. The results are illustrated in Figure 9, and the corresponding parameters are summarized in Table 3. The Langmuir isotherm provided the best fit to the experimental data, with the highest correlation coefficient (R\({}^{2}\) = 0.9953), indicating that the adsorption process was dominated by monolayer adsorption on a homogeneous surface. The maximum adsorption capacity was calculated to be 833.3 mg g\({}^{-1}\), and the Langmuir constant was 0.3077 L mg\({}^{-1}\), suggesting likely strong binding affinity between m-cresol and the XDA-1G resin surface. The Freundlich isotherm, which accounts for heterogeneous surface adsorption, also produced a strong fit (R\({}^{2}\) = 0.9501), with a Freundlich constant of 9.636 (mg g\({}^{-1}\))(L mg\({}^{-1}\))\({}^{-1/n}\) and a heterogeneity factor of 0.5607. The value of 1/n less than 1 indicates favorable adsorption and moderate surface heterogeneity. The Temkin model, which incorporates adsorbate-adsorbent interactions, also demonstrated good agreement with the data (R\({}^{2}\) = 0.9753), yielding a Temkin binding constant of 3.523 and a heat of sorption constant of 173.8 mg g\({}^{-1}\). These values suggest moderate interaction energies and the presence of energetic heterogeneity during adsorption. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**[PERSON]**} & \multicolumn{4}{c}{**[PERSON]**} & \multicolumn{4}{c}{**[PERSON]**} \\ \hline
**qmax** & **b** & **R\({}^{2}\)** & **K\({}_{\text{F}}\)** & **1/n** & **R\({}^{2}\)** & **k\({}_{\text{1}}\)** & **k\({}_{\text{2}}\)** & **k\({}^{2}\)** \\
**(mg g\({}^{-1}\))** & **(L mg\({}^{-1}\))** & **R\({}^{2}\)** & **(mg g\({}^{-1}\))** & **(L mg\({}^{-1}\))** & **1/n** & **R\({}^{2}\)** & **(mg g\({}^{-1}\))** & **(L mg\({}^{-1}\))** & **R\({}^{2}\)** \\ \hline
833.3 & 0.3077 & 0.9953 & 9.636 & 0.5607 & 0.9501 & 173.8 & 3.523 & 0.9753 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Adsorption isotherm parameters of m-cresol adsorption on resin based on linear fit. Figure 9: Isotherm modeling of m-cresol adsorption onto the XDA-1G resin. (**a**) [PERSON], (**b**) [PERSON], and (**c**) Temkin isotherm fits with linear fit showing the relationship between equilibrium concentration and adsorption capacity, demonstrating the applicability of different adsorption models to describe m-cresol uptake behavior. In addition to the linear fitting results, non-linear isotherm modeling was also performed to further validate the adsorption behavior with the corresponding fits illustrated in Figure S2 and fitting parameters summarized in Table S5. The non-linear Langmuir model yielded a \(\mathrm{q_{max}}\) of 843.1 mg g\({}^{-1}\) (R\({}^{2}\) = 0.9714), comparable to the linear result, confirming the consistency of model trends. Similarly, non-linear Freundlich and Temkin models produced R\({}^{2}\) values of 0.9679 and 0.9753, respectively, with parameter values supporting moderate heterogeneity and interaction energy. These results align with the linear fits and further reinforce that Langmuir model best represent the adsorption behavior of m-cresol onto XDA-1G. The excellent fit of the Langmuir model is consistent with the XDA-1G resin's well-developed structural features. As confirmed through BET analysis, the XDA-1G resin exhibited a high specific surface area of 1439 m\({}^{2}\) g\({}^{-1}\), with a hierarchical porous architecture composed of micropores and mesopores, as evidenced by nitrogen adsorption-desorption data. This structure enables efficient diffusion and access to uniformly distributed adsorption sites. To better contextualize the adsorption performance of XDA-1G, we compared our results with those reported for various resins and adsorbent materials used in cresol or phenol removal. For example, [PERSON] et al.