# Mitigating Global Methane Emissions Using Metal-Organic Framework Adsorbents
## 3 Results
Adsorption entropies were calculated to determine the equilibrium adsorption, maximum uptake of methane at process conditions, and rate constants for the methane adsorption process. Important characteristics of MOFs including open metal-sites allow for methane adsorption from the gas phase. The entropy of methane gas at 298 K is 188.66 J mol\({}^{-1}\) K\({}^{-1}\). The Sackur-Tetrode equation was used to estimate the entropy of translation of methane at 298 K to be 143.420 J mol\({}^{-1}\) K\({}^{-1}\) (Figure 2). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**MOF** & **V\({}_{\text{P}}\)** & **BET Surface** & **Lang. Surface** & **T (K)** & **P (bar)** & **Methane Uptake** & **Q\({}_{\text{dt}}\) (d) mol\({}^{-1}\)** & **Ref.** \\ \hline Carbonaceous materials & & & & & & & \\ MW-CNTs/bt/DC32-2 & - & 146 & 0.75  & 298 & 1 & - & [84] \\ KUA1701 & 0.92 & 2123 & 1.32  & 298 & 1 & - & [84] \\ FELT 1 & 0.81 & 1741 & 1.34  & 298 & 1 & - & [84] \\ LIC30 & 0.41 & 930 & 1.22  & 303 & 1 & 20.1 & [55] \\ NaX & - & 473 & 0.65  & 303 & 1 & 29.0 & [55] \\ _Polymers_ & & & & & & & \\ _p_-Dichloroxyhene & & & & & & & \\ _p_-DCMO & 0.36 & 1307 & 0.73  & 298 & 1 & - & [54] \\ \hline \hline \end{tabular} a
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[FOOTNOTE:a]Footnote a
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\end{table} 
Table 2: Pore volume, surface area, \(Q_{\text{dt}}\), and methane uptake of selected carbons, zeolites, and porous organic polymers. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**MOF** & **V\({}_{\text{P}}\)** & **BET Surface** & **Lang. Surface** & **Methane** & **T (K)** & **P (bar)** & **Q\({}_{\text{dt}}\) (d) mol\({}^{-1}\)** & **Ref.** \\ \hline Carbonaceous materials & & & & & & & \\ MW-CNTs/bt/DC32-2 & - & 146 & 0.75  & 298 & 1 & - & [84] \\ KUA1701 & 0.92 & 2123 & 1.32  & 298 & 1 & - & [84] \\ FELT 1 & 0.81 & 1741 & 1.34  & 298 & 1 & - & [84] \\ LIC30 & 0.41 & 930 & 1.22  & 303 & 1 & 20.1 & [55] \\ NaX & - & 473 & 0.65  & 303 & 1 & 29.0 & [55] \\ _Polymers_ & & & & & & & \\ _p_-Dichloroxyhene & & & & & & & \\ _p_-DCMO & 0.36 & 1307 & 0.73  & 298 & 1 & - & [54] \\ \hline \hline \end{tabular} a
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[FOOTNOTE:a]Footnote a
[ENDFOOTNOTE] \(V_{\text{P}}\): pore volume.  
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[FOOTNOTE:a]Footnote a
[ENDFOOTNOTE]  
\end{table} 
Table 1: _Cont._The rotational entropy of methane gas at 298 K is 40.74 J mol\({}^{-1}\) K\({}^{-1}\). For one-dimensional translation, the entropy of methane at 298 K is 47.81 J mol\({}^{-1}\) K\({}^{-1}\). The calculated methane entropy change of adsorption on a slab based was determined using Campbell and Sellers estimate to be \(-\)84.0342 J mol\({}^{-1}\) K\({}^{-1}\)[38]. This value provides an estimate of what degree of interaction is required for an enthalpic energy change for an effective adsorbent for methane for global methane emissions abatement. In Figure 3, the entropy of methane gas is compared to the entropy of adsorbed methane obtained by using the equation provided by [PERSON] and Sellers (Equation (1)) and compared to some experimental data [38]. Figure 3: Entropy of adsorbed methane on MgO (100), Mg (100), PdO (101), Pt (111), and C (0001) surfaces from temperature programmed desorption (TPD) data analysis and adsorption data plotted against the entropy of methane gas represented by black data points. Orange point represent data determined from experiments associated with C\({}_{2}\)-C\({}_{10}\) alkane adsorption on slabs [38]. Figure 2: Methane translational entropy as a function of temperature determined using the Sackur Tetrode equation. To further get insight into how to design MOFs for methane emission mitigation, the translation and rotational components of the gas phase entropy that were lost upon methane adsorption were estimated. Two degrees of translational freedom are preserved, which are associated with methane travelling through the porous network. On the other hand, rotational freedom is more restricted particularly in the case where the pore diameter shrinks.