# Mitigating Global Methane Emissions Using Metal-Organic Framework Adsorbents
## 3 Results
This results in the hindered rotation of methane molecules in the one-dimensional nanochannel that was observed for a porous coordination polymer [85]. The rotational freedom lost depends on the framework of the porous material. This is because the degree of confinement of the methane molecule is affected by the pore size and pore size distribution of the material. This in turn affects the adsorbed state. Therefore, the degree of rotational freedom lost is important and is related to the pore architecture of the MOF, which allows for the better design of MOFs for this application. In Table 3, the physical characteristics of MOF frameworks are provided. An important parameter which is known as a physical descriptor was used to predict confinement effects. Occupiable volume (V\({}_{\text{occ}}\)) was used as the descriptor. V\({}_{\text{occ}}\) is defined as the number of spheres with a diameter of 2.8 A that can be packed into the framework of the porous material [37]. In Figure 4, the rotational degrees of freedom lost by methane due to confinement was related to V\({}_{\text{occ}}\). F\({}_{\text{rot,conf}}\) or rotational degrees of freedom lost due to confinement approaches zero with larger occupiable volumes. In Figure 5, the entropy change of adsorption was plotted against V\({}_{\text{occ}}\). Figure 4: Calculated rotational degrees of freedom lost upon adsorption with varying occupiable volume (V\({}_{\text{occ}}\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Framework** & \
\begin{tabular}{c} **Largest Cavity** \\ **Diameter (Å)** \\ \end{tabular} &
\begin{tabular}{c} **Void Fraction of Accessible** \\ **Probe-Occupiable Pore Volume** \\ \end{tabular} & **Ref.** \\ \hline HKUST-1 & 13.14982 & 0.67 & [57] \\ DUT-13 & 18.4908 & 0.81 & [85] \\ NU-125 & 19.37323 & 0.73 & [64] \\ PCN-46 & 12.05622 & 0.72 & [87] \\ PCN-61 & 18.70668 & 0.75 & [44] \\ SNU-30 & 14.9209 & 0.83 & [88] \\ UTSA-20 & 9.95246 & 0.57 & [40] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physical characteristics of MOF frameworks [86]. To verify the predictions made using the universal descriptor used to determine methane entropies, a comparison of calculated entropy changes was made with experimental data. Entropies from experimental data were calculated using the Clausius-Clapeyron Equation (12) at constant loading (Figure 6). The calculated methane enthalpy and entropy of adsorption from adsorption experiments are shown in Table 4. The entropy changes of adsorption determined from experimental data were found to be on the same order of magnitude as those determined using the universal descriptor. The relationship between the enthalpy and entropy of adsorption of methane on MOFs was assessed (Figure 7). It was found that entropy and enthalpy of adsorption of methane on MOFs correlate. This was consistent with what was observed for the adsorption of hydrocarbons on zeolites [37]. Increasing enthalpy is associated with increasing entropy. This correlation was described as a compensation associated with an increasingly exothermic adsorption which is countered by decreasing entropy. In case of methane adsorption in zeolites and what is expected for MOFs, the maximum heat of adsorption corresponds to a pore diameter of R = Rc = 2\({}^{1/6}\)\(\sigma\), in which we have the maximum interactions of methane with the spherical shell. With increasing pore diameter from Rc, the heat of adsorption decreases. When decreasing the pore diameter from Rc, the interactions become repulsive and the magnitude of the enthalpy of adsorption quickly decreases until it becomes positive. The entropy loss upon adsorption increases with decreasing pore size. The entropy loss reaches its maximum when the methane molecule is frozen between the wall of the sphere.