Biogas Upgrading by Transition Metal Carbides

The separation of carbon dioxide (CO2) from methane (CH4) is critical in biogas upgrading, requiring materials with high selectivity toward one of the two gas components. Hereby we show, by means of density functional theory based calculations including dispersive forces description, the distinct interaction of CO2 and CH4 with the most stable (001) surfaces of seven transition metal carbides (TMC; TM = Ti, Zr, Hf, V, Nb, Ta, and Mo). Transition state theory derived ad-/desorption rates suggest a very high CO2 uptake and selectivity over CH4 even at ambient temperature and low partial gas pressures.

realistic and therefore useful estimates of selectivity and uptake rates are accessible. 8, 14 We recently applied this computational strategy to assess CO 2 capture on most stable and exhibited (001) surfaces of transition metal carbides (TMCs), with 1:1 TM:C ratio and rocksalt crystal structure under standard and moderate pressures. 15 TiC, ZrC, HfC, NbC, TaC, and δ-MoC were TMCs found to strongly adsorb and even activate CO 2 -a noteworthy case of CO 2 chemisorption. This exceptional behavior can allow for CO 2 capture even at ambient temperatures and low gas partial pressure, with the specific storage power dependent on the TMC composition. 13 The CO 2 capture and activation on TMCs, as predicted by DFT, has been previously directly evidenced by infrared spectroscopy and indirectly by its hydrogenation. 16,17 Such reactivity suggest promising usage of TMCs to catalyze a wide variety of reactions, 13,18 often equaling or surpassing Pt group catalysts performance, 19 with the added benefit of low cost, chemical robustness, and poisoning resistance. 18 Theoretical simulations on CH 4 interaction with TMC surfaces are rather sparse. Only Tominaga et al. predicted CH 4 reforming to ethylene on orthorhombic β-Mo 2 C surfaces, 20 and a recent DFT-D study showed strong CH 4 physisorption on δ-MoC (001), with a predicted possible methane capture at room temperature. 21 Indeed, molybdenum carbides are known to be very reactive TMCs, and CH 4 adsorption is assumed to be weaker on others. That in mind, TMCs could then be suited for CO 2 removal from mixed CH 4 /CO 2 gas streams. To evaluate this possibility, we carried out a thorough DFT-D study of CH 4 attachment to most stable (001) surfaces of seven different TMCs, providing a realistic estimate of initial CO 2 /CH 4 selectivity.
As done in previous works, 13 we restrain our study to experimentally known rocksalt TMCs with 1:1 TM:C ratio, known to be the stable phase under standard and moderate pressure and temperature conditions. 15 Thus structural aspects are circumvented and a meaningful comparison is feasible, while including group 4 (TiC, ZrC, and HfC), group 5 (VC, NbC, and TaC), and group 6 (δ-MoC) TMCs. Note that for MoC rocksalt packing is only present in the high temperature δ-phase.
To assess the CH 4 adsorption on the different TMCs, periodic DFT based calculations were carried out on suitable surface models using the Vienna Ab Initio Simulation Package -VASP code. 22 The Perdew-Burke-Ernzerhof (PBE) 23 exchange-correlation (xc) functional was used to account for xc effects, to which the dispersion (van der Waals) correction D3 as proposed by Grimme (PBE-D3) 24 was added. Further computational details are found in the Supporting Information. For the sake of the oncoming discussion clarity it is necessary to state that favourable adsorption energies, E ads , are defined negative.
First, the surface exposed sites that most strongly interact with CH 4 have been identified by a computational screening at PBE-D3 level: Four non-equivalent sites were tested for each TMC (001) model, namely bridge Mo-C (b), hollow (h), top C (t C ) and top metal (t M ). Interaction at each site was evaluated with two different CH 4 orientations, with either two or three H pointing towards the surface, denoted H 2 and H 3 , respectively. 21 Notice that orientations with a sole H pointing towards the TMC surface were neglected as previously found to be overall less favourable. 21 Table 1. PBE-D3 adsorption energies, E ads , of CH 4 on TMC (001) surfaces. Previously reported values for adsorbed CO 2 are also included. 13 All values are given in eV. Methane adsorption is almost exclusively due to dispersive forces, as revealed by comparing to PBE values, see Table S1 in the Supporting Information, where adsorption energies range +0.03 to -0.02 eV, suggesting that the electronic interaction in between CH 4 and TMC surfaces is almost negligible. Given the weak interaction neither significant distortion of CH 4 nor of surface atoms is found. CH 4 is adsorbed ranging 3.06 to 3.39 Å away from the surface, distance measured by the vertical distance between methane carbon and highest surface carbon, see Fig. 1 and distances in Further better-grounded evaluation of CO 2 selectivity over CH 4 is provided for the temperature range 50-1000 K as based on the estimation of adsorption and desorption rates from harmonic transition state theory (TST) using present DFT-D results, as fully explained in the Supporting Information. Notice that such theoretical approach has been successfully used to explain the experimental biogas upgrading in PMOs. 8 In short, adsorption rates !"# !" ! and !"# !" ! for CO 2 and CH 4 depend on the impingement of molecules on the surfaces and therefore on their partial pressures. Here we evaluate these at two partial pressures, (i) 0.01 bar, for capture from dilute streams, e.g. coal mine ventilation air with CO 2 and CH 4 contents of 1 v/v % each, 7 and (ii) 1.0 bar, to assess gas enrichment at higher pressure, e.g. useful for pressure swing adsorption.
We refrained the evaluation at higher partial pressures, as model validity could become compromised, see below.
Desorption rates differ for each of the identified sites given in Table 1, but a macroscopic rate is likely superimposed from all contributions, justifying the use of average desorption rates !"# !" ! and !"# !" ! . For their calculation, two different models for entropy losses upon adsorption were devised, accounting for upper and lower limits, 26 which help to rationalize such an effect.
In the hindered model all translations and rotations are impeded upon adsorption and effectively converted to frustrated vibrations; in the free model gas-phase rotational and translational degrees are preserved, the latter in two dimensions above the surface, with the adsorbate fixed only in height. We initially evaluated both models for physisorbed species, namely for CH 4 on all TMCs and CO 2 on VC, though for strongly chemisorbed CO 2 on the other TMCs only the hindered model is considered, being the most likely situation.
To clarify these models, their estimated ad/desorption rates are given in Fig. 2a   For completeness, T 5 = 360 K and T 6 = 435 K mark temperatures below which CO 2 accumulates on TiC at 0.01 and 1.0 bar, respectively, considerably high values that lead us to suggest these materials for CO 2 capture. 13 In combination with fringe CH 4 temperatures T 2 and T 4 , lower and higher temperature ends are marked where capture of high amounts of CO 2 with good selectivity over CH 4 are thus predicted. These ranges are graphically depicted in Fig. 2b  Further estimates of low coverage CO 2 selectivity over CH 4 , S CO 2 /CH 4 are obtained for equal CO 2 and CH 4 partial pressures. Selectivity is defined through adsorption/desorption equilibrium constants K !" ! and K !" ! more conservative free model. Among all studied TMCs, CO 2 selectivity is rather high for TiC, NbC, and TaC and very high for ZrC and HfC, with a wider working temperature range.
According to this, selectivity values of 10 5 or higher are predicted even for very low partial pressures of 0.01 bar, which, in theory, ensure a biogas CH 4 enrichment above 99.9%. In contrast, a rather low selectivity is expected for VC and δ-MoC, but the latter does capture both CH 4 and CO 2 , interesting for possible use in methane dry reforming at moderate temperatures.
Note that present estimations are given for initial adsorption stages, 8  In summary, periodic DFT PBE-D3 calculations on the interaction of CH 4 with most stable (001) surfaces of seven transition metal carbides (TMCs) predict a weak CH 4 attachment for groups 4 and 5 TMCs (TM=Ti, Zr, Hf, V, Nb, Ta) with adsorption energies of ~-0.2 eV, almost exclusively dominated by dispersion. In contrast δ-MoC (group 6) displays a strong interaction with CH 4 of ~-0.8 eV. Comparison to earlier results of strong CO 2 interaction on these materials suggest a highly preferred CO 2 adsorption over CH 4 when TMCs (TM=Ti, Zr, Hf, Nb, Ta, Mo) are exposed to CO 2 /CH 4 mixtures. Adsorption and desorption rate estimates mark temperature ranges around ambient conditions (TiC and NbC) or even up to elevated temperatures (ZrC, HfC, and TaC) at which CO 2 capture selectivities above 99.9% are expected even at very low partial pressures, highlighting the usage of such TMCs for CO 2 separation from CH 4 in biogas upgrading.