# Metal-Organic Frameworks Characterization via Inverse Pulse Gas Chromatography
## 3 Applications of IGC for the Characterization of MOFs
### MIL-Based MOFs
Furthermore, the amino groups exposed in the pores of amino-MIL-53 enhance the electrostatic contribution of molecules with double bonds. Although double bonds contribute to total interactions, van der Waals interactions were found to be the dominant element for the adsorption interactions of molecules. Using a simple model, [PERSON] et al. predicted that hydrogen atoms and double bonds contributed to these adsorption properties. The determined confinement factor Z pointed to an increased degree of confinement in amino-MIL-53(Al) compared to MIL-53 and MIL-47. Amino-MIL-53(Al) also exhibited a smaller pore aperture, which is due to either the presence of amino groups or to the framework shrinking as a result of the interaction between amino functional groups and hydroxyl groups. [PERSON] et al. demonstrated that the enhanced adsorption activities of CO\({}_{2}\) over CH\({}_{4}\)[63] and CH\({}_{4}\) over N\({}_{2}\)[64] over Al-BDC MOFs due to larger pore size. Their XRD patterns were different from those of MIL-53(Al). There was a slight difference compared with the  
Figure 10: Relationship between mean molecular polarizability and adsorption enthalpy at zero coverage. Reprinted with permission from [61]. Copyright (2012) American Chemical Society. standard MIL-53(Al), which may be as a result of the presence of some free H\({}_{2}\)BDC linkers within the pores and the metastable phase of BDC and Al\({}^{3+}\) as a result of the different conditions of crystal growth. The pore size of Al-BDC MOFs increased from 0.86 (AlBDC\({}_{\text{Micro}}\)) to 2.58 nm (AlBDC\({}_{\text{Meso}}\)) via a simple washing and drying process. Subsequently, an analysis of the adsorption equilibrium and thermodynamics of the different gases, CH\({}_{4}\), CO\({}_{2}\), and N\({}_{2}\), was done via volumetric\(-\)chromatographic and IGC methods [62]. The initial adsorption heat was estimated to be 11.5 kJ mol\({}^{-1}\) for CH\({}_{4}\) and 25.2 for CO\({}_{2}\) on AlBDC\({}_{\text{Meso}}\) MOF, which is approximately 25% less than on AlBDC\({}_{\text{Micro}}\) MOF. These data indicated that enlarged pore size not only increased the CO\({}_{2}\) adsorption selectivity over that of CH\({}_{4}\), but also decreased the value of \(\Delta H_{ads}\), suggesting that it should be the preferred method for selecting a satisfactory absorbent for CO\({}_{2}\)/CH\({}_{4}\) separation [63]. The heats of adsorption of CH\({}_{4}\), N\({}_{2}\), and CO\({}_{2}\) were calculated as 15.3, 11.5, and 32.2 kJ mol\({}^{-1}\), respectively, which is aligned with the gravimetric study [64]. MIL-101(Cr) with the formula (Cr\({}_{3}\)O(H\({}_{2}\)O)\({}_{2}\)F(BDC)\({}_{3}\)) has a very large surface area and cubic cell volume with two kinds of cages: smaller 29 A cages with pentagonal faces and larger 34 A cages with both pentagonal and hexagonal faces [100]. The adsorption behavior of MIL-101(Cr) towards p-xylene was investigated using IGC [65]. These data showed that the specific component of the free energy of adsorption (\(\Delta G_{spec}\)) values of the polar probes were negative, suggesting spontaneous adsorption. The adsorption specific component of the free energy \(\Delta G_{spec}\) for polar molecules on MIL-101(Cr) were found to be in the order p-xylene > toluene > acetone. The \(\Delta G_{spec}\) for polar probes was inversely proportional to their dipole moment, although the authors have not provided an explanation for this phenomenon [65].