Computational study of the mass transfer effects in metal–organic framework columns for liquid chromatography

We present an in-depth theoretical study of the band broadening processes originating from the specific shape and intra-particle diffusion characteristics of metal–organic framework (MOF) particles used in high- performance liquid chromatography (HPLC). Studying perfectly ordered packings, the complex nature of the eddy-dispersion process is filtered out, leaving the pure particle contributions. Using a recently developed modification of Brenner’s dispersion formalism to make it applicable to chromatographic systems, highly accurate and comprehensive data sets could be produced. The Dpart/Dm dependence (Dpart: intra-particle diffusion coefficient, Dm: bulk molecular diffusion coefficient) of plate height curves confirmed that the plate height values in the C-term dominated regime obtained with significantly low Dpart/Dm (=0.004), which can be observed in MOF particles, can be up to approx. 50 times higher (at Pe ≅100 (Pe: dimensionless interstitial velocity)) than those with larger Dpart/Dm (=0.3) which is typically observed in silica particles used in reversed-phase HPLC. Comprehensive investigation employing typical cuboidal MOF particles revealed that high plate heights which can be observed in MOF-based LC column are almost exclusively due to the inherently slow intra-particle diffusion rates, because the other attributes (non- spherical shape, anisotropic intra-particle diffusion) only showed a minor effect on the produced band broadening. In fact, the non-spherical shape is even advantageous when only considering the pure intra-particle contribution to the plate height. Next to the very small pore diameter compared to the molecular size of typical analyte molecules, another main reason for the low intra-particle diffusion in MOF particles is pointed out to be the fact that the diffusion in the perpendicular direction is strongly suppressed compared to the main diffusion direction (channel direction) in MOFs with anisotropic channel structures (e.g., one-dimensional (1D) or pseudo-1D channel). In the presently considered example, where the diffusion in the two perpendicular directions was reduced to 1/4 of the diffusion in the main diffusion direction, this led to an overall suppression of the intra-particle diffusion with a factor of 2.49.