# Mitigating Global Methane Emissions Using Metal-Organic Framework Adsorbents
## 3 Results
According to [PERSON] and [PERSON], high gas adsorption could be achieved at ambient temperatures if the isosteric heat of adsorption could be increased for MOFs with large free volumes, but the negative impact for this theory was finding strategies for increasing the Q\({}_{\text{st}}\) without losses in free volume [90]. [PERSON] and [PERSON] reported increasing the isosteric heat of adsorption helps to increase methane uptake [36]. By using the same theory, the optimal Q\({}_{\text{st}}\) in case of methane adsorption can be estimated. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Framework** & \(-\Delta\)**H\({}_{\text{ads}}\) (kJ/mol)** & \(-\Delta\)**S\({}_{\text{ads}}\) (J/mol K)** & **Ref.** \\ \hline MOF-905-Naph & 10.87 & 36.7 & [61] \\ MOF-905-NO\({}_{2}\) & 9.86 & 33.2 & [61] \\ MFM-300 (In) & 16.49 & 55.66 & [89] \\ ATC-Cu & 23.6 & 90.2 & [35] \\ MOF-520 & 14.0 & 47.1 & [65] \\ Al-soc-MOF-1 & 15.3 & 51.2 & [59] \\ MOF-519 & 14.1 & 47.2 & [65] \\ ZIF-68 & 16.7 & 61.2 & [74] \\ ZIF-69 & 18.4 & 61.8 & [74] \\ Cu-**to**-MOF-5 & 21.6 & 71.8 & [68] \\ NJU-Bai-19 & 14.7 & 49.4 & [67] \\ NJU-Bai-42 & 12.8 & 46.9 & [60] \\ NJU-Bai-41 & 14.4 & 48.3 & [60] \\ MOF-950 & 11.3 & 38.1 & [61] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 7: Relationship between \(\Delta\)H\({}_{\text{ads}}\) and \(\Delta\)S\({}_{\text{ads}}\) of methane for various MOFs from experiments. Each point represents a MOF whose enthalpy and entropy of adsorption was determined from experimental data at 1 bar. It was noticed when the Qst\({}_{0}\) increased the storage capacity of MOFs which gives an idea of possibility for all MOFs structures to attain the capture target, assuming Qst\({}_{0}\) is increased enough without the loss in free volume. Each MOF structure has an optimal Qst\({}_{0}\) which gives the maximum deliverable capacity. The optimal Qst was calculated as a function of entropy change relative to the standard pressure P\({}_{0}\) (1 bar) (Figure 8). With increasing entropy change relative to the standard pressure P\({}_{0}\) (1 bar), Qst decreased. Finally, it was concluded that materials creating with large surface area (\(>\)4800 m\({}^{2}\)/g) and large Qst values (around 20 kJ/mol) is potentially advantageous. While keeping the other variables the same, the Qst values increased. In case of real materials, the Qst value can be increased by adding some heavy atoms to the structure or by reducing the free volume which reduced the gravimetric or volumetric capacities to some degree but increased the challenge of attaining this design target. In addition to the uptake capacity of the MOF for methane, the rate of desorption is important for this process in practice. The pre-exponential factor for the desorption of methane from porous materials was calculated. As shown in Equations (11) and (12) the pre-exponential factor depends on the rotational entropy and the 1-dimensional translational entropy. Because the translational entropy is a term, confinement effects. Therefore, the occupiable volume and pore diameter of the MOF effect the rate of methane desorption. The rate of methane desorption is important in this process because it indicates how long it will take to remove adsorbed methane after adsorption. This is important for the process to be cyclable. For methane desorption from a flat surface, the pre-exponential was calculated to be \(6.2\times 10^{12}\) s\({}^{-1}\). The logarithm of the pre-exponential factor is shown in Figure 9 for methane desorption. The rate of desorption depends on the molecular size as well as the degrees of rotational freedom lost upon adsorption. As shown in Figure 4, the rotational degrees of freedom lost upon adsorption depends on the occupiable volume and therefore the pore structure of the MOF. Figure 8: Optimal Qst as a function of the entropy change relative to the standard pressure P\({}_{0}\) (1 bar). Figure 9: A plot of the logarithm of the pre-exponential factor of methane desorption against the degrees of rotational freedom lost upon adsorption.