## 3 Results and Discussion
### Mathematical Modeling
The calculated parameters are listed in Table 3. The results indicate that the [PERSON] model offers a better fit for the experimental breakthrough data compared to the [PERSON] model. Furthermore, the adsorption capacity estimated by the [PERSON] model (\(q_{T}\)) was closer to the values calculated from the experimental data (Table 4). Figure 8a-c shows the simulated breakthrough curves resulted from the fitting of experimental data in the [PERSON] and [PERSON] models. The statistical parameters and the estimated adsorption capacity of the modeling are represented in Tables 5 and 6, respectively. Results of mathematical modeling revealed that the breakthrough curves of the toluene adsorption at all tested RH fit very well with the [PERSON] model. The [PERSON] model, however, predicts the breakthrough curves at RH of 40% and 60% are more accurate compared to those of RH of 80%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Adsorption** & **As-Synthesize** & **ZIF-8/Air/300 \({}^{\circ}\)C** & **ZIF-8/N\({}_{2}\)/300 \({}^{\circ}\)C** & **ZIF-8/N\({}_{2}\)/400 \({}^{\circ}\)C** \\
**Capacity** & **(mg:g\({}^{-1}\))** & **(mg:g\({}^{-1}\))** & **(mg:g\({}^{-1}\))** & **(mg:g\({}^{-1}\))** \\ \hline \(qT\) ([PERSON]) & 102.3 & 578.2 & 114.4 & 268.3 \\ \(q\)/([PERSON]) & 78.1 & 540.8 & 95.72 & 204 \\ \(q\) (Experimental) & 131.43 & 562.17 & 155.31 & 260.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimated adsorption capacity of ZIF-8 (activated in the different conditions) by the [PERSON] and [PERSON] models and comparison with the experimental data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistical Parameters** & **As-Synthesized** & **ZIF-8/Air/300 \({}^{\circ}\)C** & **ZIF-8/N\({}_{2}\)/300 \({}^{\circ}\)C** & **ZIF-8/N\({}_{2}\)/400 \({}^{\circ}\)C** \\ \hline \multirow{4}{*}{[PERSON]} & K\({}_{T}\) & 3.26 & 1.98 & 2.75 & 3.33 \\  & R\({}^{2}\) & 0.97 & 0.98 & 0.99 & 0.98 \\  & R\({}^{2}\)\({}_{\text{adi}}\) & 0.97 & 0.98 & 0.99 & 0.98 \\  & RMSE & 0.034 & 0.043 & 0.022 & 0.038 \\  & SSE & 0.026 & 0.88 & 0.012 & 0.04 \\ \hline \multirow{4}{*}{[PERSON]} & A\({}_{y}\) & 1.11 & 2.37 & 1.17 & 2.1 \\  & R\({}^{2}\) & 0.84 & 0.98 & 0.89 & 0.93 \\ \cline{1-1}  & R\({}^{2}\)\({}_{\text{adi}}\) & 0.84 & 0.98 & 0.89 & 0.93 \\ \cline{1-1}  & RMSE & 0.086 & 0.044 & 0.071 & 0.077 \\ \cline{1-1}  & SSE & 0.16 & 0.095 & 0.13 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical parameters obtained from the fitting of toluene breakthrough curves of ZIF-8 (activated in the different conditions) using the Yan and Thomas models. RMSE: root mean square error; SSE: sum square error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistical Parameters** & **As-Synthesized** & **ZIF-8/Air/300 \({}^{\circ}\)C** & **ZIF-8/N\({}_{2}\)/300 \({}^{\circ}\)C** & **ZIF-8/N\({}_{2}\)/400 \({}^{\circ}\)C** \\ \hline \multirow{4}{*}{Thomas} & K\({}_{T}\) & 3.26 & 1.98 & 2.75 & 3.33 \\  & R\({}^{2}\) & 0.97 & 0.98 & 0.99 & 0.98 \\  & R\({}^{2}\)\({}_{\text{adi}}\) & 0.97 & 0.98 & 0.99 & 0.98 \\  & RMSE & 0.034 & 0.043 & 0.022 & 0.038 \\  & SSE & 0.026 & 0.88 & 0.012 & 0.04 \\ \hline \multirow{4}{*}{Yan} & A\({}_{y}\) & 1.11 & 2.37 & 1.17 & 2.1 \\  & R\({}^{2}\) & 0.84 & 0.98 & 0.89 & 0.93 \\ \cline{1-1}  & R\({}^{2}\)\({}_{\text{adi}}\) & 0.84 & 0.98 & 0.89 & 0.93 \\ \cline{1-1}  & R\({}^{2}\)\({}_{\text{adi}}\) & 0.84 & 0.98 & 0.89 & 0.93 \\ \cline{1-1}  & RMSE & 0.086 & 0.044 & 0.071 & 0.077 \\ \cline{1-1}  & SSE & 0.16 & 0.095 & 0.13 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical parameters obtained from the fitting of toluene breakthrough curves of ZIF-8 (activated in the different conditions) using the [PERSON] and [PERSON] models. RMSE: root mean square error; SSE: sum square error. By looking at the breakthrough curves (Figures 6-8) and the statistical parameters (Tables 3-6) it can be concluded that the Yan equation (compared to the Thomas equation) is more suitable for accurate simulation of breakthrough curves with sigmoidal or tilted S shapes.