Understanding the Loading Dependence of Adsorbate Diffusivities in Hierarchical Metal–Organic Frameworks

Using atomistic simulations, we studied the diffusion of n-hexane in a series of isoreticular hierarchical metal–organic frameworks (MOFs) NU-100x. Nonmonotonic diffusivity–loading relationships that depend on the pore sizes were observed, which can be explained by the spatial distribution of adsorbates at different loadings. For one of the MOFs in the series, NU-1000-M, the diffusivity–loading relationship is almost identical to the previously reported results of n-hexane diffusion in the hierarchical self-pillared pentasil (SPP) zeolite. Detailed analysis revealed that the similarity results from their similar micropore and window sizes, which was confirmed by free-energy mapping. The effects of temperature and adsorbate chain length on the diffusion were also studied, which supported our conclusion that the diffusivity in hierarchical nanoporous materials is primarily controlled by the sizes of the micropores and the connecting windows, particularly at relatively low loadings.