Diffusion as a function of guest molecule length and functionalization in flexible metal–organic frameworks†
Understanding guest diffusion in nanoporous host–guest systems is crucial in the efficient design of metal–organic frameworks (MOFs) for chemical separation and drug delivery applications. In this work, we investigated the effect of molecule length on the diffusion rate in the zeolitic imidazolate framework 8 (ZIF-8), trying to find a simple and straightforward variable to characterize the complicated guest diffusion. We found that, counter-intuitively, long guest molecules can diffuse as quickly as short molecules; the diffusion coefficient of ethyl acetate for example is of the same order of magnitude as ethane and ethanol, as excludes the existence of a simple relationship between molecule length and diffusion rate. This phenomenon is explained by a study of the contributions of intra- and inter-cage movement to overall transport. Steric confinement limits the degrees of freedom of long guest molecules, shortening their residence time and increasing the efficiency of radial diffusion. In contrast, shorter molecules meander within MOF cages, reducing transport. Furthermore, the energy barrier of inter-cage transport also does not exhibit a simple dependence on a guest molecule length, attributing to the effect of the type of functional group on diffusion. Guests over varying lengths were investigated by using theoretical methods, revealing that the guest diffusion in ZIF-8 depends on the number of contiguous carbon atoms in a molecule, rather than its overall length. Thus, we proposed simple criteria to predict arbitrary guest molecule diffusivity in ZIF-8 without time-consuming experimentation.