Thickness Biased Capture of CO2 on Carbide MXenes

where S0 is the initial sticking coefficient, the CO2 partial pressure, A stands for the area of an CO2 adsorption site, and m corresponds to the mass of the CO2 molecule. Commonly, when unknown, initial sticking coefficients are set to unity, assuming a mobile physiosorbed precursor rate.1 However, reported initial sticking coefficients were found to be in the range of 0.43–0.73 for CO2 on clean metal surfaces,3 which seem more realistic. Here we used the conservative value of S0 = 0.40 as used in the past.4 Equal adsorption probabilities of all sites were assumed, and A was therefore calculated by dividing the unit cell area of each surface by the total number of sites in it. Three representative operative conditions of CO2 partial pressure ( ) are highlighted, including the atmospheric partial pressure of CO2 (air), = 40 Pa;5 CO2 CO2 a partial pressure which is a reference value for post-combustion exhaust gases (exhaust), = 15·103 Pa;6 CO2 and a reference value for pure CO2 stream generation from a CCS system (desorption), = 105 Pa.7 CO2


S1. Reaction Rate Estimates
A procedure to evaluate the Carbon Capture and Storage (CCS) capabilities of MXenes is to evaluate the CO 2 rates of adsorption (r ads ) and desorption (r des ), easily obtained from Transition State Theory (TST), 1,2 (1), where k B T is the product of Boltzmann constant, k B , and temperature, T. E would be the energy barrier for the i th described transition process. In Eq. (1) is the prefactor term obtained from TST with h being the Planck constant, whereas and stand for the partition function of the transition and initial states, respectively.
The r ads for a non-activated adsorption depends on the impingement of adsorbates on the surface and defines, where S 0 is the initial sticking coefficient, the CO 2 partial pressure, A stands for the area of an 2 adsorption site, and m corresponds to the mass of the CO 2 molecule. Commonly, when unknown, initial sticking coefficients are set to unity, assuming a mobile physiosorbed precursor rate. 1 However, reported initial sticking coefficients were found to be in the range of 0.43-0.73 for CO 2 on clean metal surfaces, 3 which seem more realistic. Here we used the conservative value of S 0 = 0.40 as used in the past. 4 Equal adsorption probabilities of all sites were assumed, and A was therefore calculated by dividing the unit cell area of each surface by the total number of sites in it. Three representative operative conditions of CO 2 partial pressure ( ) are highlighted, including the atmospheric partial pressure of CO 2 (air), = 40 Pa; 5 2 2 a partial pressure which is a reference value for post-combustion exhaust gases (exhaust), = 15·10 3 Pa; 6 2 and a reference value for pure CO 2 stream generation from a CCS system (desorption), = 10 5 Pa. 7

S1
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The r des is obtained from the adsorption energy (E ads ) values, Zero Point Energy (ZPE) corrected. It is worth pointing out that E ads = -E des . Thus, E ads is considered in Eq. (3), where the prefactor for desorption, , contains the partition function of the molecule in an early 2D transition state in the numerator. This partition function is given by the product , in which where is the vibrational frequency of each normal mode as obtained from our DFT calculations, either for CO 2 in vacuum or adsorbed. Note that Eq. 5 corresponds to the situation for which the adsorption energy is ZPE corrected. is the product of the rotational temperature for CO 2 and its symmetry number 2. From ·2 the literature the value is taken as 0.561 K. 8 The T-dependent adsorption/desorption rates see Fig. S1, lead to identify the range of temperatures at which the adsorption prevails and, consequently, the CO 2 gets stored on the studied substrate. The crossing point between r ads and r des , shown in Fig. S1, takes place at a certain temperature labelled as T 1 . Below such temperature the adsorption is favorable (r ads > r des ) and, therefore, the CO 2 is stored. On the other hand, the region located at temperatures above T 1 correspond to a process of favorable desorption (r ads < r des ). One step further consists in the design of the kinetic phase diagram based on the equilibrium region where both rates are equal (r ads = r des ) at a certain temperature, T 1 . Note that r ads depends on Eq. 2 and, therefore, we can represent different r ads corresponding to different -see the right panel of Fig. S2. By doing this, we can 2 analyze several equilibrium regions that are characterized by different value of T and . Such set of 2

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values allow us constructing the kinetic phase diagram depicted in the right panel of Fig. S2. The solid line depicted in the kinetic phase diagram stands for the CCS-to-non-CCS crossover and, hence, the region located in the left side corresponds to the T and conditions at which the CCS is kinetically favorable, 2 and the left side from the line indicates the non-CCS. It is worth to point out that can be estimated as a 2 function of temperature under the r ads = r des condition by, .
Following the abovementioned strategy, we were able to build kinetic phase diagrams for all MXene and metal carbide surfaces investigated in this study, as depicted in Fig. S3.

Fig. S1
General scheme of calculated rates for adsorption (r ads ) and desorption (r des ) of CO 2 on a given substrate.