Modeling hydrogen diffusion in hybrid activated carbon-MIL-101(Cr) considering temperature variations and surface loading changes

MIL-101(Cr) and activated carbon (AC) doped MIL-101(Cr) materials were synthesized under mild conditions, avoiding the use of hydrofluoric acid, and characterized by X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and physisorption. It was shown that the AC doping induced enhancements of the specific surface area and increase in the pore volume of the adsorbent. Hydrogen adsorption isotherms and kinetics were measured at 77 K up to 50 bar by using a volumetric method. A hydrogen uptake of 9.3 wt.% was measured for the hybrid material, which was significantly higher than that for pristine MIL-101(Cr) which reached an uptake of 6.2 wt.% under the same conditions of temperature and pressure. Effective diffusion coefficients were besides attempted to be extracted from experimental kinetic curves, by using the Linear Driving Force (LDF) model in a first approach. However, this model failed to describe correctly the experimental kinetic data as it does not explicitly consider the external mass transfer resistance, neither the temperature nor the surface loading effects on the intra-crystalline diffusion process. To overcome these limitations, a more detailed model was proposed, based on the evaluation of both an external mass transfer coefficient and of an internal surface diffusivity in the adsorbed phase that accounts for the effects of temperature and adsorbent surface coverage. This model was proved to predict well the hydrogen adsorption rates in both the MOF and hybrid AC-MOF material at 77 K, in the pressure range up to 20 bar.