## 4 Role of Amine Type in CO2 Separation Performance
### Activation Energies for Gas Permeation  
To further compare the influence of amine type on the CO\({}_{2}\) transport behaviors of these amine-functionalized organosilica membranes, the activation energies for the permeation (\(E_{p}\)) of CO\({}_{2}\) and  
Figure 16: Comparison of CO\({}_{2}\) separation performance for amine-functionalized organosilica membranes at 35 \({}^{\circ}\)C. The Robeson upper bound was plotted by assuming a membrane thickness of 500 nm. Results were reorganized from refs. [21; 22; 23]. Figure 17: Comparison of CO\({}_{2}\) transport mechanisms across strong-affinity (APTES) and mild-affinity (BTPP) membranes. Reproduced from ref. [21] with permission. Copyright (2017), _Elsevier_. \(\mathrm{N_{2}}\) in Equation (5) together with the relevant CO\({}_{2}\) separation performance are summarized in Table 4. As mentioned above, \(E_{p}\) represents the sum of the activation energy for diffusion and the apparent adsorption enthalpy (\(E_{p}=E_{d}+\Delta H_{s}>0\)), which reflects the total energy barriers for the permeation of gases. A higher \(E_{p}\) for a gas equates to a greater difficulty in permeation. Diffusivity depends on the kinetic diameter of the permeating gases and could be the rate-determining process for gas-permeation flux. On the other hand, CO\({}_{2}\) allowed strong interactions with the amine groups and exhibited significant sorption performance onto/into the rigid-pore surface and the organic nonporous phase, thereby allowing the effective solubility coefficient reflected by the negative value of sorption enthalpy (\(\Delta H_{s}\)) to play a more critical role in the CO\({}_{2}\) permeation performance. The relatively higher negative value of \(\Delta H_{s}(CO_{2})\) led to a low total activation energy for permeation in the case of CO\({}_{2}\) [\(E_{p}(CO_{2})\)]. Indeed, for all the membranes listed in Table 5. lower values for \(E_{p}(CO_{2})\) were always observed compared with that of \(E_{p}(N_{2})\), despite the comparable size between CO\({}_{2}\) (3.3 A) and N\({}_{2}\) (3.64 A). In addition, the gas permselectivity, \(\alpha_{ij}\), could be quantitatively linked with the difference in the values for the activation energy of permeation, \(E_{pi}-E_{pj}\), by considering \(\alpha_{ij}=P_{i}/P_{j}\). As shown in Equation (9), \(\alpha_{ij}\) could be expressed by an Arrhenius-type equation, similar to that of gas permeance and diffusivity. \[\alpha_{ij}=\frac{P_{i0}}{P_{j0}}\exp\left(-\frac{E_{pi}-E_{pj}}{RT}\right) \propto\exp\left(-\frac{E_{pi}-E_{pj}}{RT}\right), \tag{9}\]  
where \(P_{i0}\) and \(P_{j0}\) are pre-exponential factors for components \(i\) and \(j\), respectively. Considering the possible differences in pre-exponential factors that may depend on the membrane and the penetrant, the negative values for the difference in \(E_{p}\) between a smaller/sorptive component, \(i\), and a larger component, \(j\) (\(E_{pi}-E_{pj}\)), could to some extent reflect the potential in gas permselectivity for this gas pair (\(\alpha_{ij}\)). Under a given system, higher negative values for \(E_{pi}-E_{pj}\), would likely offer higher values for \(\alpha_{ij}\), and this trend might increase with a decrease in the operational temperature. As listed in Table 4, such a trend can be evident regardless of amine type. Most importantly and specifically, the relationships between \(E_{p}(CO_{2})\) and \(E_{p}(N_{2})\), which could predict the CO\({}_{2}\)/N\({}_{2}\) separation performance, are compared in Figure 18. Owing to a non-reactivity feature and to a kinetic size that approximates the membrane pore size, \(E_{p}(N_{2})\) has greater advantages to reflect the microstructure of these amine-functionalized organosilica membranes. Generally, higher values for \(E_{p}(N_{2})\) reflect the denser microstructure of silica-based membranes, and vice-versa. In a similar manner, the lower values for \(E_{p}(CO_{2})\) reflect the greater permeation potential for CO\({}_{2}\) when the relevant values of \(E_{p}(N_{2})\) are comparable.