## 3 Results  
### CO\({}_{2}\) Capture Capacity of a CO\({}_{2}\) Sorbent  
Table 1 provides information on the surface area, pore volume, and pore size of y-Al\({}_{2}\)O\({}_{3}\), ZrO\({}_{2}\), PZI30 sorbent, and PAI-x sorbents. The bare ZrO\({}_{2}\) had a surface area of 8.05 m\({}^{2}\)/g, a pore volume of 0.02 cm\({}^{3}\)/g, and a pore size of 3.83 nm. The y-Al\({}_{2}\)O\({}_{3}\) had a surface area of 157.65 m\({}^{2}\)/g, a pore volume of 0.31 cm\({}^{3}\)/g, and a pore size of 4.91 nm. Compared with the ZrO\({}_{2}\) support material, the surface area and pore volume of the PZI30 sorbent decreased; it might be expected that the very low surface area and pore volume of PZI30 sorbent results in poor CO\({}_{2}\) capture capacity. When K\({}_{2}\)CO\({}_{3}\) is loaded on the support materials, surface area decreases, whereas a significant change in pore size is not observed regardless of the K\({}_{2}\)CO\({}_{3}\) loading amount. When the K\({}_{2}\)CO\({}_{3}\) loading is 40 wt% (PAI40 sorbent), the surface area is reduced to about 17.3% compared with the Al\({}_{2}\)O\({}_{3}\) support material, and the pore volume is also significantly reduced. The decrease in surface area and pore volume is caused by filling the pores or blocking the pore openings with K\({}_{2}\)CO\({}_{3}\).  
Figure 1 presents the breakthrough curves (a) and the CO\({}_{2}\) capture capacity (b) per 1 g of sorbent for PAI10 to 40 and PZI30 sorbents in the presence of 10 vol% CO\({}_{2}\), 10 vol% H\({}_{2}\)O, N\({}_{2}\) balance at 200 \({}^{\circ}\)C and 20 atm. Figure 1b shows the CO\({}_{2}\) capture capacities of PAI10 to 40 and PZI30 sorbents calculated from the CO\({}_{2}\) sorption breakthrough curves shown in Figure 1a. Under high-pressure conditions (20 atm), PZI30 sorbent was used to investigate the reaction mechanism of alumina-based sorbent. PZI30 and PAI10-40 sorbents had CO\({}_{2}\) capture capacities of 19.7 and 32.3, 63.0, 95.4, and 124.5 mg CO\({}_{2}\)/g sorbent, respectively. CO\({}_{2}\) capture capacities of PAI-x sorbents increased with increasing K\({}_{2}\)CO\({}_{3}\) loading. Compared with the PZI30 sorbent, the PAI30 sorbent showed a higher CO\({}_{2}\) capture capacity.  
Figure 2 shows the amount of CO\({}_{2}\) sorption per 1 g K\({}_{2}\)CO\({}_{3}\) as a function of the K\({}_{2}\)CO\({}_{3}\) loading. The CO\({}_{2}\) sorption per 1 g K\({}_{2}\)CO\({}_{3}\) was calculated from the CO\({}_{2}\) capture capacities of PZI30 and PAI10-40 sorbents, as shown in Figure 1. The CO\({}_{2}\) capture capacities of PAI10-40 sorbents were maintained at approximately 311.2-323.1 mg CO\({}_{2}\)/g K\({}_{2}\)CO\({}_{3}\). These calculated values corresponded to approximately 98-101% of the K\({}_{2}\)CO\({}_{3}\) theoretical value of 318.4 mg CO\({}_{2}\)/g K\({}_{2}\)CO\({}_{3}\). However, the CO\({}_{2}\) capture capacity of PZI30 sorbent was approximately 65.7 mg CO\({}_{2}\)/g K\({}_{2}\)CO\({}_{3}\), which is equivalent to approximately 26% of the K\({}_{2}\)CO\({}_{3}\) theoretical value. The differences in the CO\({}_{2}\) capture capacities of PZI30 and PAI10-40 sorbents mean that the CO\({}_{2}\) sorbents can be absorbed through different reaction mechanisms.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Surface Area** & **Pore Volume** & **Pore Size** \\  & **(m\({}^{2}\)/g)** & **(cm\({}^{3}\)/g)** & **(nm)** \\ \hline y-Al\({}_{2}\)O\({}_{3}\) & 157.65 & 0.31 & 4.91 \\ ZrO\({}_{2}\) & 8.04 & 0.03 & 3.83 \\ PZI30 & 3.92 & 0.02 & 3.82 \\ PAI10 & 134.98 & 0.22 & 4.32 \\ PAI20 & 69.67 & 0.17 & 4.32 \\ PAI30 & 44.26 & 0.17 & 4.32 \\ PAI40 & 27.37 & 0.09 & 4.31 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Textural properties of y-Al\({}_{2}\)O\({}_{3}\), PZI30, and potassium-based alumina sorbents.