## 1 Introduction
[PERSON] and [PERSON] [43] considered a mixture of tetraethylenedamine (TEPA) and PEI, obtaining a CO\({}_{2}\) uptake of 2.5 molCO\({}_{2}\)/kg, using temperature swing adsorption for regeneration. Other amines which have been investigated are: poly(propyleneimine) (PPI) [33,44] and poly(allylamine) (PAA) [45]. For amine-based sorbents of class II, CO\({}_{2}\) uptakes of up to 2.13 molCO\({}_{2}\)/kg and 3.89 molCO\({}_{2}\)/kg have been obtained, respectively for 3-aminopropyldiethylchooxysilane (APDES) grafted onto nanofibrilated cellulose (NFC) [46] and hydrazine (H\({}_{2}\)N\({}_{4}\)) onto Mg\({}_{2}\)(dobpdc) [47]. Good adsorption capacities are also reported in the work of [PERSON] et al. [30], [PERSON] et al. [48], and [PERSON] et al. [40], respectively of 1.4 molCO\({}_{2}\)/kg for triaminesilane (TRI) onto MCM-41, 1.39 molCO\({}_{2}\)/kg for N-(2-aminoethyl)-3-aminopropylmethyldimethoxysilane (AEAPDMS) onto NFC and 1.5 for ethylenediamine (ED) grafted onto Mg/DOBDC. Lower CO\({}_{2}\) uptakes are measured for amine-functionalized sorbents of class III. In total, 1.78 molCO\({}_{2}\)/kg and 1.68 molCO\({}_{2}\)/kg are shown in the work of [PERSON] et al. [49] and [PERSON] et al. [36]. In the first case, aziridine is considered with silica support, while in the second case, 3-aminopropyl triethoxysilane (APTMS) is evaluated in hybrid silica material. Similar experimental analyses have been carried out for MOFs, showing adsorption capacities to be lower compared to those of amine-based sorbents, as in Table 2. Capacities of 0.18 molCO\({}_{2}\)/kg for SIFSIX-3-Ni [50], 0.05 molCO\({}_{2}\)/kg for HKUST-1 [39], and 0.14 for Mg-MOF-74 [51] have been measured. These experimental analyses are complemented by mathematical models, which are able to replicate the process cycles, explore operating conditions not investigated in experimental work, and save time and cost for screening, development, and optimization [52]. More importantly, modeling can carry out economic and energetic analysis to evaluate costs and energy consumption, including the thermal energy required for the desorption stage and the electrical energy for fans blowing air through the air sorbent contactor. Moreover, other key performance indicators (KPIs) can also be evaluated by using mathematical models, with the aim to compare, screen, and select the best scenarios. Estimates of costs and energy consumptions for main DAC technologies, and in particular for adsorption systems are reported by [PERSON] et al. [53]. Here, electricity requirements can range between 150 and 300 kWh\({}_{\text{el}}\)/tonneCO\({}_{2}\) for amine-based sorbents, and up to 1420 kWh\({}_{\text{el}}\)/tonneCO\({}_{2}\) for MOFs. On the other hand, thermal energy of between 1170 and 2000 kWh\({}_{\text{th}}\)/tonneCO\({}_{2}\) is required. Regarding costs for adsorption, as reported in Table 3, [PERSON] et al. [53] suggest a value between 63 and 86 USD/tonneCO\({}_{2}\) obtainable by 2040. The expected cost for the technology in the future is lower than those evaluated by others in the literature for the present day. [PERSON] and [PERSON] [54] report a cost of CO\({}_{2}\) capture of 43-494 USD/tonneCO\({}_{2}\), while [PERSON] et al. [18] suggest a cost between 91 and 227 USD/tonneCO\({}_{2}\) (not including capital costs for equipment). [PERSON] et al. [55] estimate a cost of capture of 60-190 USD/tonneCO\({}_{2}\) (without discounting cash flows, and assuming a self-contained sorbent). However, these analyses reported in the literature are conducted with different assumptions for energy inputs, different output conditions (pressure and CO\({}_{2}\) purity), and without transparency [53]. Estimates provided by companies are also present in the literature. Generally, these companies suggest a low cost, but such estimates need to be considered in the context that the companies are in the process of commercializing the technology [2].