Molecular Diffusion and Effective Longitudinal Diffusion under SFC conditions in packed bed columns

The improvement of supercritical fluid chromatography (SFC) instrumentation enhanced its reliability and utility over the past decade. The further development of high speed and high resolution separations is however obstructed by the lack of accurate models for axial dispersion in SFC. This work is a first step to tackle this by developing more reliable methods to measure molecular and longitudinal diffusion in SFC.
The molecular diffusion coefficient (Dmol) affects all aspects of separation efficiency. Dmol drives longitudinal diffusion, enhances mass-transfer in packed bed SFC and counteracts peak dispersion due to packing inhomogeneities. Dmol can be determined using the Taylor-Aris peak broadening method, where the dispersion in an open tubular capillary is measured .The capillary has to be coiled in the lab because the required tube length is impractical. Hence, the flowrate in the capillary must be small, not to cause secondary flow effects that affect radial dispersion and thus the apparent diffusion coefficient. This set-up was further adapted to increase the reliability and reproducibility in SFC conditions. The first modification was the insertion of a column before the capillary to ensure Dmol was measured in the desired mobile phase and not in the initial sample plug. Furthermore, a fraction collection loop was incorporated in the set-up after the column. This second modification avoids the trial-and-error approach to find the optimal column, instrument and mobile phase conditions to achieve symmetric peak shapes, as only a small fraction of an overloaded peak is reinjected into the capillary. A final modification was the addition of a by-pass of the mobile phase flow after the column which made it possible to use higher pump flow rates, improving stability and accuracy of the pump operation and reducing residence time in the column.
Next the effective diffusion coefficient (Deff) was measured using stop-flow experiments where the mobile phase flow rate is stopped when the solute is halfway through the column for a time tpark and then resumed. During this period tpark, longitudinal diffusion (quantified by Deff) is the only source of axial dispersion. This set-up was adapted for SFC as during tpark, pressure drops and supercritical conditions are no longer maintained. In addition, due to the strong compressibility of the mobile phase, restarting the flow rate is accompanied by transient start-up effects that vary flowrate and retention in a non-reproducible way. Therefore a two-column variant of the set-up was developed where two identical columns are coupled in parallel. When the analyte is halfway through the first column, the flow is switched to the second column, parking the peak in the first column (still pressurized) and maintaining the flow and pressure in the SFC system.
This experimental data, together with theoretical models helps us better understand the diffusion process in the packed bed, by modeling longitudinal diffusion and mass transfer contribution to band broadening in SFC. In the future, this will allow us to better investigate, predict and optimize separation performance in SFC, hereby guiding further instrument development (e.g. higher operating pressure, smaller particles, optimal columns dimensions,…).