## 4 Role of Amine Type in CO2 Separation Performance
### Gas Permeation Properties  
As discussed above, the amine-functionalized organosilica xerogel powders developed in our previous studies showed comparable microstructures but different reaction activities with acidic molecules with impressively different CO\({}_{2}\) adsorption/desorption properties. Gas permeation performance for these relevant membranes was then collected to investigate of the roles of amine type in CO\({}_{2}\) transport behaviors. Figure 13 shows the kinetic diameter dependence of gas permeance for amine-functionalized organosilica membranes. All the synthesized membranes demonstrated sufficiently high qualities with He/SF\({}_{6}\) selectivities of 3000-40,000. In addition, these membranes displayed comparable gas permeation performance (actual or normalized permeance) in terms of kinetic diameter dependence, probably due to their similar chemical structures or ratios of organic/silica. Note that both the sufficiently high qualities and comparable structures could to some extent enable investigation into the effect of amine type on CO\({}_{2}\) transport performance. Figure 14 compares the temperature dependence of gas permeance for amine-functionalized organosilica membranes. Generally, the temperature dependence of gas permeance values with a wide spectrum that was enabled by the superior thermal stability of organosilica membranes, could offer important information on gas-transport mechanisms. As shown in Figure 14, all the gases considered led to a linear relationship for gas permeance in the logarithmic coordinates vs. _1000/T_, which can be accurately represented by _Arrhenius_-type equations. Universally, gaseous transport through microporous or dense membranes requires sorption (adsorption onto the pore walls and/or dissolution into a nonporous phase) of gas molecules prior to the subsequent diffusion process and demonstrates several types of temperature dependence. Therefore, the gas permeance (\(P\)) that is a product of the diffusivity (\(D\)) and solubility (\(S\)) coefficients (\(Pl=DS\), where \(l\) is the membrane thickness), as well as the diffusivity coefficient (\(D\)), could also be represented using _Arrhenius_-type equations. Meanwhile, the solubility coefficient (\(S\)) is usually described via _Van't Hoff_ expression [39; 40; 41; 42]. \[P =P_{0}\exp{(\frac{-E_{p}}{RT})}, \tag{5}\] \[D =D_{0}\exp{(\frac{-E_{d}}{RT})}, \tag{6}\]  
Figure 12: Time course of normalized CO\({}_{2}\) adsorption amount for the 1 st cycle of a CO\({}_{2}\) adsorption/desorption process for amine-functionalized organosilica xerogel powders performed on TG/DTA equipment. A 60 vol% of CO\({}_{2}\) in a CO\({}_{2}\)-Ar mixture with a flow rate of 50 cm\({}^{3}\)/min and a total pressure of 100 kPa was adopted for the CO\({}_{2}\) adsorption process, while pure Ar with the same flow rate and pressure was used for CO\({}_{2}\) desorption process. The samples were activated by heating at 200 \({}^{\circ}\)C for 12 h, followed by cooling to 35 \({}^{\circ}\)C under a pure Ar atmosphere. Results were reorganized from refs. [21; 22]. \[S=S_{0}\exp{(\frac{-\Delta H_{s}}{RT})}, \tag{7}\]  
In Equations (5)-(7), \(P_{0}\), \(D_{0}\), and \(S_{0}\) are the pre-exponential factors, \(E_{p}\) and \(E_{d}\) are the apparent activation energies for permeation and diffusion, respectively, \(\Delta H_{s}\) is the effective sorption enthalpy, \(R\) is the universal gas constant, and \(T\) is the operation temperature. A relationship among \(E_{p}\), \(E_{d}\) and \(\Delta H_{s}\) can then be obtained after the combination of Equations (5)-(7) when \(Pl=DS\), as shown in Equation (8). \[E_{p}=E_{d}+\Delta H_{s}, \tag{8}\]  
The gas permeance of all the gases, except that of CO\({}_{2}\), was decreased with a decrease in the permeation temperature, indicating an activated transport mechanism (\(E_{p}>0\)).