MIL-53(Cr), and its isostructural form MIL-47(V), are built up from infinite chains of corner-sharing Cr3+O4(OH)2 or V4+O6 octahedra interconnected by 1,4-ben — zenedicarboxylate groups (Fig. 2.5). These three dimensional MOFs contain one-dimensional diamond-shaped channels with pores of nm dimensions. One may note that MIL-53(Cr) exhibits hydroxyl groups located at the metal-oxygen-metal links (u2-OH groups) which open up the possibility of additional preferential adsorption sites and thus different adsorption or diffusion mechanisms to that of MIL-47(V) where these specific groups are absent.

The self-diffusion of H2 in these two structures was studied by QENS combined with molecular dynamics (MD) simulations [2, 22]. For the QENS measurements, the frameworks and the ^2-OH groups in MIL-53(Cr) were deuterated to reduce the signal from the MOF. To illustrate the possibility to obtain information on diffusion anisotropy, one and three dimensional diffusion models are compared with exper­imental spectra in Figs. 2.6 and 2.7. When the diffusion is isotropic (three­dimensional), the theoretical dynamic structure-factor, S(Q, rn), corresponding to a translational motion has a Lorentzian profile in energy, but the line shape is more elongated in the case of diffusion in one-dimensional channels, because a powder average has to be made [22].

In MIL-53(Cr), profiles corresponding to three-dimensional diffusion and con­voluted with the instrumental resolution do not fit perfectly through the experi­mental points (Fig. 2.6a and Ref. [22] for spectra obtained at other Q values). A normal one-dimensional diffusion model, with a more waisted shape, fits better the experimental data (Fig. 2.6b and Ref. [22]). This is due to the interaction between H2 and the ^2-OD groups, leading to a one-dimensional diffusion along the tunnels via a jump sequence involving these hydroxyl groups. Normal one­dimensional diffusion means that the molecules can cross each other in the tunnels of MIL-53. When the molecules cannot pass each other, the diffusion is called single file [23].

In MIL-47(V), the reverse is found: The three-dimensional diffusion model reproduces better the QENS spectra than one-dimensional diffusion (Fig. 2.7 and Ref. [22]). The motions of H2 in this MOF are random because there are no specific adsorption sites for hydrogen.

The Ds values of H2 in both solids are reported in Fig. 2.8 as a function of loading. Contrary to the concentration dependence obtained in NaX (Fig. 2.4), Ds decreases in both MILs when the H2 loading increases, this is due to steric reasons in these one-dimensional systems, and to the absence of strong adsorption sites. Experiment and simulation find higher diffusivities in MIL-47(V) than in MIL-53 (Cr), whatever the loading. This can be explained by the presence of the ^2-OD groups in MIL-53(Cr) which act as attractive sites and steric barriers for H2, leading thus to a slower diffusion process. Further, a high H2 mobility is observed in both MILs, at low loading, the Ds values are about two orders of magnitude higher than in zeolites (Fig. 2.4 and Ref. [15]). Extrapolating Ds to zero loading in Fig. 2.8 leads to a value of the order of 10-6 m2s-1 in MIL-47(V). This is comparable to the supermobility predicted in single-walled carbon nanotubes [24].

Fig. 2.8 Self-diffusivities of H2 at 77 K as a function of loading in MIL-47(V) (rounds) and MIL-53(Cr) (squares): QENS (full symbols) and MD (empty symbols), where u. c. = unit cell