A stochastic view on column efficiency

Abstract

A stochastic model of transcolumn eddy dispersion along packed beds was derived. It was based on the calculation of the mean travel time of a single analyte molecule from one radial position to another. The exchange mechanism between two radial positions was governed by the transverse dispersion of the analyte across the column. The radial velocity distribution was obtained by flow simulations in a focused-ion-beam scanning electron microscopy (FIB-SEM) based 3D reconstruction from a 2.1 mm × 50 mm column packed with 2 μm BEH-C18 particles. Accordingly, the packed bed was divided into three coaxial and uniform zones: (1) a 1.4 particle diameter wide, ordered, and loose packing at the column wall (velocity uw), (2) an intermediate 130 μm wide, random, and dense packing (velocity ui), and (3) the bulk packing in the center of the column (velocity uc).First, the validity of this proposed stochastic model was tested by adjusting the predicted to the observed reduced van Deemter plots of a 2.1 mm × 50 mm column packed with 2 μm BEH-C18 fully porous particles (FPPs). An excellent agreement was found for ui = 0.93uc, a result fully consistent with the FIB-SEM observation (ui = 0.95uc). Next, the model was used to measure ui = 0.94uc for 2.1 mm × 100 mm column packed with 1.6 μm Cortecs-C18 superficially porous particles (SPPs). The relative velocity bias across columns packed with SPPs is then barely smaller than that observed in columns packed with FPPs (+6% versus + 7%). uw=1.8ui is measured for a 75 μm × 1 m capillary column packed with 2 μm BEH-C18 particles. Despite this large wall-to-center velocity bias (+80%), the presence of the thin and ordered wall packing layer has no negative impact on the kinetic performance of capillary columns. Finally, the stochastic model of long-range eddy dispersion explains why analytical (2.1–4.6 mm i.d.) and capillary (<400 μm i.d.) columns can all be packed efficiently (1 <hmin< 2) with particles of size larger than 2 μm. In contrast, the model predicts that 0.4–1.2 mm i.d. columns and 2.1 mm i.d. columns cannot be packed well (hmin>3) with sub-2 μm particles and with 1 μm particles, respectively.