# Zinc-Decorated and Nitrogen-Functionalized Hierarchical Porous Carbons for Carbon Dioxide Capture
## 3 Results and Discussion
### CO\({}_{2}\) Adsorption
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **Temperature (K)** & \(K_{\text{F}}\) **(mmol/g/kPa\({}^{1/n}\))** & \(n\) & \(\Delta G\) **(kJ/mol)** & \(\Delta H\) **(kJ/mol)** & \(\Delta S\) **(kJ/mol/K)** \\ \hline \multirow{3}{*}{ZIF-8} & 298 & 0.0035 & 0.84 & \(-\)5.64 & & \\ \cline{2-7}  & 313 & 0.0020 & 0.80 & \(-\)3.69 & \(-\)44.27 & \(-\)0.130 \\ \cline{2-7}  & 328 & 0.0006 & 0.69 & \(-\)1.75 & & \\ \hline \multirow{3}{*}{Z8-650} & 298 & 0.2202 & 1.79 & \(-\)16.79 & & \\ \cline{2-7}  & 313 & 0.2294 & 1.96 & \(-\)16.08 & \(-\)31.03 & \(-\)0.048 \\ \cline{2-7}  & 328 & 0.1153 & 1.62 & \(-\)15.36 & & \\ \hline \multirow{3}{*}{Z8-750} & 298 & 0.3085 & 1.93 & \(-\)16.49 & & \\ \cline{2-7}  & 313 & 0.1982 & 1.82 & \(-\)15.85 & \(-\)29.20 & \(-\)0.043 \\ \cline{2-7}  & 328 & 0.1000 & 1.51 & \(-\)15.21 & & \\ \hline \multirow{3}{*}{Z8-850} & 298 & 0.2393 & 1.66 & \(-\)15.66 & & \\ \cline{2-7}  & 313 & 0.1458 & 1.54 & \(-\)15.09 & \(-\)26.88 & \(-\)0.038 \\ \cline{2-7}  & 328 & 0.0935 & 1.46 & \(-\)14.53 & & \\ \hline \multirow{3}{*}{Z8-950} & 298 & 0.1580 & 1.53 & \(-\)14.79 & & \\ \cline{2-7}  & 313 & 0.0978 & 1.42 & \(-\)14.43 & \(-\)21.95 & \(-\)0.024 \\ \cline{1-1} \cline{2-7}  & 328 & 0.0639 & 1.36 & \(-\)14.07 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fitted parameters for the Freundlich equation for CO\({}_{2}\) adsorption isotherms and the thermodynamic properties at zero loading of CO\({}_{2}\) adsorption on the samples. Figure 10: Adsorption performance of CO\({}_{2}\) on samples at (a) 298 K\({}_{\text{F}}\) (b) 313 K\({}_{\text{F}}\) (c) 328 K\({}_{\text{F}}\) (d) 101.3 kPa; (e) 15 kPa. (f) Isosteric heat of adsorption of CO\({}_{2}\). The values of \(\Delta H\) for CO\({}_{2}\) adsorption for all the samples were negative, which confirmed that the adsorption process is exothermic. The magnitude of \(\Delta H\) also provides insights into the adsorption mechanism. The absolute values were 21.95 to 31.03 kJ/mol for the ZDCs and 44.27 kJ/mol for ZIF-8, implying that the adsorption of CO\({}_{2}\) on the ZDC samples involved physisorption, while combined (both physical and chemical) CO\({}_{2}\) adsorption occurred on ZIF-8 [45]. The negative values of \(\Delta S\) suggested a decrease in the disorder and randomness of the adsorption system during the CO\({}_{2}\) adsorption process. This could be attributed to the decrease in the degrees of freedom of CO\({}_{2}\) molecule movement because the CO\({}_{2}\) molecules were adsorbed on the surface of the adsorbents, making the system more ordered. As shown in Figure 10f, the Q\({}_{\rm st}\) values decreased logarithmically with the CO\({}_{2}\) loading from 0.01 to 1.2 mmol/g, indicating that the adsorption active sites on the material surface were energetically heterogeneous for CO\({}_{2}\) capture [60]. The Qst values on specific CO\({}_{2}\) loadings were ranked as follows: Z8-650 > Z8-750 > Z8-850 > Z8-950 > ZIF-8. This indicates that the interactions between CO\({}_{2}\) and the ZDCs were enhanced compared with ZIF-8 and that the N=C and C=O/O=C-N groups, which are abundant in ZIF-8, might have an insignificant role in CO\({}_{2}\) adsorption. However, the presence of nitrogen and zinc species on carbonized ZIF-8 actually promoted the interactions between CO\({}_{2}\) and the adsorbents. This may be due to the dissociation of ZIF-8 during pyrolysis, which produced more active sites, exposing nitrogen and zinc atoms, and converting them into more active functional groups. Although physical adsorption might be predominant adsorption behavior in this study, under low CO\({}_{2}\) loading, some chemosorption may have occurred on Z8-650 and Z8-750. In order to evaluate the potential applications of the ZDCs for CO\({}_{2}\) capture from flue gas, the adsorption selectivity for CO\({}_{2}\) over N\({}_{2}\) was investigated. Since the molecular sizes of CO\({}_{2}\) and N\({}_{2}\) are very close, it is relatively difficult to separate them based on kinetics.