## 4 Role of Amine Type in CO2 Separation Performance
### Activation Energies for Gas Permeation
As Figure 18 shows, all the membranes with reproduced cases demonstrated comparable and scattered values of \(E_{p}(N_{2})\) at 10-20 kJ/mol, which indicated a similar microstructure regardless of amine type. However, membranes consisting of hindered amines presented an impressive trend of decreases in \(E_{p}(CO_{2})\) compared with membranes that have unhindered amines, which indicated that CO\({}_{2}\) was much more permeable across these membranes with hindered amines. In addition, with respect to membranes with unhindered amines (PA-Si and SA-Si), the PA-Si membranes tended to present a denser microstructure due to somewhat higher levels of \(E_{p}(N_{2})\), but the values for \(E_{p}(CO_{2})\) were comparable. These results suggest that it was the amine type, whether sterically hindered or unhindered, rather than the small differences in basicity and microstructure that played the greater role in CO\({}_{2}\) permeation barriers across these amine-functionalized membranes. Furthermore, the relationships between CO\({}_{2}\) permeation potential and CO\({}_{2}\)/N\({}_{2}\) separation potential via the relationships of \(E_{p}(CO_{2})\) vs. \(E_{p}(CO_{2})-E_{p}(N_{2})\) are also compared in Figure 18, as plotted in previous studies [40; 41]. Lower values are always desired for both \(E_{p}(CO_{2})\) and. \(E_{p}(CO_{2})-E_{p}(N_{2})\) to in order to attain high performance for CO\({}_{2}\)/N\({}_{2}\) separation (the preferred region shown in Figure 19). Obviously, the membranes with hindered amines showed a greater potential to approach the preferred region with both lower \(E_{p}(CO_{2})\) and lower \(E_{p}(CO_{2})-E_{p}(N_{2})\), and thus could probably attain higher separation performance than membranes with unhindered amines. It is worth noting that amine-free silica membranes generally demonstrate scattered results for CO\({}_{2}\)/N\({}_{2}\) separation performance due to the difficulty in precisely controlling pore size, as well as to possible defects induced by a moderate-to-high porous microstructure. The nonporous microstructures of amine-functionalized organosilica membranes, however, lead to a shift in the gas separation mechanism from one that predominantly exerts a molecular sieving effect of microporous SiO\({}_{2}\) membranes to one that relies on a solution-diffusion (or adsorption-diffusion) model. Thus, these membranes demonstrate great potential in improving CO\({}_{2}\)/N\({}_{2}\) separation performance due to the significant increases in CO\({}_{2}\) sorption performance that may highlight differences in the apparent diffusion barriers between CO\({}_{2}\) and N\({}_{2}\) [\(E_{p}(CO_{2})-E_{p}(N_{2})\)]. In addition, as shown in Figure 19, CO\({}_{2}\) separation membranes can sometimes be designed and prepared prior to a rough preselection of materials, regardless of membrane preparation technique, due to the following possible relationships presented in Equation (10). \[E_{p}(CO_{2})-E_{p}(N_{2})\approx E_{d}(CO_{2})-E_{d}(N_{2})+\Delta H_{s}(CO_{ 2})-\Delta H_{s}(N_{2})\equiv\Delta H_{s}(CO_{2})_{\textit{eff}}, \tag{10}\]  
where both \(E_{d}(CO_{2})-E_{d}(N_{2})\) and \(\Delta H_{s}(N_{2})\) can be reasonably ignored sometimes due to the comparable size of CO\({}_{2}\) and N\({}_{2}\), as well as to the negligible adsorption heat of N\({}_{2}\). In such cases, therefore, the values of \(E_{p}(CO_{2})-E_{p}(N_{2})\) can be roughly predicted from the effective adsorption heat of CO\({}_{2}\), \(\Delta H_{s}(CO_{2})_{\textit{eff}}\), which can be fairly measured based on the reversible adsorption/desorption of CO\({}_{2}\) on solid powders, as demonstrated in Figures 10 and 11. Generally, the reversible adsorption amount and heat may vary with the temperature and pressure employed. Therefore, future studies for the systematic and quantitative assessment of \(\Delta H_{s}(CO_{2})_{\textit{eff}}\) are needed. It is worth noting that the membrane microstructure (e.g., pore size or free volume, porosity) also plays an important role in activation energies for gas permeation.