Computational study of the band broadening in two-dimensional etched packed bed columns for on-chip high-performance liquid chromatography

The chromatographic performance of several straightforward two-dimensional etched packed bed column lay-outs (equilaterally staggered arrays of, respectively, circular, hexagonal, and diamond-like pillars) has been compared using commercial computational fluid dynamics software. In all cases, the bed porosity was kept at ε=0.4 and a retained component with zone capacity ratio k″=2 was considered. Exploring the use of six different possible characteristic dimensions to bring the Van Deemter plots of the three different considered particle shapes into agreement, none of them yielded a perfect agreement. Using the pillar volume-based equivalent cylinder diameter (deq) as the characteristic dimension, the diamond-like pillars yielded a significantly smaller hmin value than the cylinders and the hexagons (hmin≅0.74 for the former versus hmin≅0.83 for the two latter). Including the flow resistance into the analysis, it was found that the “hydrodynamic” shape of the particles has an important influence on the separation impedance E. The more axially elongated diamond pillars yielded an Emin number as small Emin=180 (for a retained component with k″=2), i.e. about 40% smaller than the cylinders and the hexagons (Emin=300–330). The obtained hmin and Emin values are also significantly smaller than the values often cited for the best possible packed bed HPLC columns. We believe this is a consequence of the assumed perfect homogeneity of the etched structures, and hence hints at the potential benefits of perfectly ordered chromatographic columns, as was already inferred by Knox [J. Chromatogr. A 831 (1999) 3; 960 (2002) 7] and He et al. [Anal. Chem. 70 (1998) 3790].