A novel method to measure diffusion coefficients in porous metal-organic frameworks

We present a novel method to determine diffusion constants of small molecules within highly porous metal-organic frameworks (MOFs). The method is based on the recently proposed liquid-phase epitaxy (LPE) process to grow MOF thin films (SURMOFs) on appropriately functionalized substrates, in particular on organic surfaces exposed by thiolate-based self-assembled monolayers (SAMs). By applying the LPE-method to SAM-coated quartz crystals, the time-dependence of the mass-uptake of the MOF when exposing it to a gas is measured by a quartz-crystal microbalance (QCM). The homogenous nature of the SURMOFs together with their well-defined thickness allow to analyze the QCM-data using Fickian diffusion to yield the diffusion constant. We demonstrate the potential of this method for the case of pyridine diffusion within HKUST-1 (Cu₃(BTC) ₂) MOF, for which the diffusion coefficient at room temperature is found to amount to 1.5 × 10^-19 m² s^-1. Assuming a Fickian diffusion and a hopping mechanism, we yield a binding energy of 0.78 eV of the pyridine to the Cu²⁺ sites within the HKUST-1 MOF, a value in good agreement with the results of precise ab initio quantum chemistry calculations.