## 3 Results and Discussion
### KPI: CO\({}_{2}\) Productivity of DAC Systems  
From the previously discussed curves, related to the adsorption and desorption stages, it is possible to find adsorption and desorption times, the full cycle time, and then the CO\({}_{2}\) productivity (amount of CO\({}_{2}\) captured). The adsorption and desorption times are for a 90% approach to equilibrium and are in agreement with data reported in the literature [17; 74].  
The required mass of the sorbent is calculated knowing the volume and porosity of bed and particle density [103]. With all of this information, it is possible to evaluate the  
Figure 8: CO\({}_{2}\) concentration during the desorption step for chemisorbents: (**a**) SI-AEATPMS sorbent and (**b**) APDES-NFC-FD sorbent.  
Figure 7: CO\({}_{2}\) concentration during the desorption step for physisorbents: (**a**) MIL-101, (**b**) MOF-177, and (**c**) MOF-5.  
average single pass recovery, Rc, and the amount of captured CO\({}_{2}\). The average single pass recovery is defined as the ratio between the difference of CO\({}_{2}\) at the inlet and outlet of the bed and CO\({}_{2}\) at the inlet (in terms of mole). The adsorption time can also be calculated as the ratio between the 90% of equilibrium loading and mass sorbent product and the average single pass recovery and CO\({}_{2}\) mole in the feed product [104]. Then, the value of Rc can be obtained by iteration to a self-consistent value.  
The full cycle time (including adsorption and desorption times), average single pass recovery, the mass of the sorbent, and captured CO\({}_{2}\) are evaluated for each sorbent as reported in Table 10.  
Due to a higher adsorption capacity, as discussed above, chemisorbents are able to capture a greater amount of CO\({}_{2}\): 6.43 kgCO\({}_{2}\)/h and 6.66 kgCO\({}_{2}\)/h, respectively, for the silica gel-based sorbent and the cellulose-based sorbent, compared to physisorbents. The MOFs MIL-101, MOF-177, and MOF-5 capture, respectively, 3.96 kg CO\({}_{2}\)/h, 4.5 kgCO\({}_{2}\)/h, and 4 kgCO\({}_{2}\)/h. The best performances of MOF-177 and APDES-NFC-FD among the physisorbents and chemisorbents are due to a lower mass transfer zone, and are underlined by a greater amount of captured CO\({}_{2}\), and then by a higher value of the average single pass recovery, which is 0.89 for the cellulose-based sorbent and 0.59 for MOF-177.  
Adsorption and desorption times are higher for amine-functionalized adsorbents. Additionally, the higher value for the SI-AEATPMS sorbent compared to the other amine-based sorbent is due to the higher amine content of the APDES-NFC-FD sorbent [105]. In fact, results show that a full cycle for the silica gel-based sorbent is 89.2 h (305,500 s for the adsorption time and 16,650 for the desorption time), while only 9.53 h (32,560 s for the adsorption time and 1845 s for the desorption time) are required for the cellulose-based sorbent. For MOFs, full cycle times are lower than 1 h: the lowest value is for MOF-177 for which this parameter is 0.09 h (214 s for the adsorption time and 106 s for the desorption time). For this reason, the number of cycles per day is higher using physisorbent: MOF-177 conducts 271 cycles/day, while 0.3 cycles/day are needed for SI-AEATPMS sorbent.  
Overall, amine-functionalized adsorbents capture 152 kgCO\({}_{2}\)/day (APDES-NFC-FD sorbent) and 147 kgCO\({}_{2}\)/day (SI-AEATPMS), while MIL-101, MOF-177, and MOF-5 capture, respectively, 73 kgCO\({}_{2}\)/day, 72 kgCO\({}_{2}\)/day, and 68 kgCO\({}_{2}\)/day.