Multiscale simulation of liquid chromatography: How the mobile-phase flow velocity modulates the plate height-retention factor relationship in random and ordered beds of porous particles.

Because the separation efficiency is classically analyzed as total plate height H vs. the average mobile-phase flow velocity at selected retention factors, the complementary analysis of H vs. the retention factor at distinctly different velocities is rare. As a consequence, the impact of retention on eddy dispersion in chromatographic beds remains underinvestigated. Here, we illuminate the plate height-retention factor relationship in a randomly packed bed of sub-2 µm, mesoporous particles through our established multiscale simulation approach by beginning with a low flow velocity, for which analyte transport in the bed is diffusion-limited, and increasing the velocity well into the advection-dominated transport regime. This reveals that in the range of phase-based retention factors (k) most relevant to chromatographic practice (k = 1-10), the actually set mobile-phase flow velocity determines the basic H-k relationship, i.e., if H increases or decreases with k or remains relatively unaffected by k. At low velocity, band broadening is dominated by longitudinal diffusion and H increases with k; at intermediate velocity, H becomes independent of k; and at high velocity, when eddy dispersion gets most important, H decreases with k. In particular, the coupling between eddy dispersion and intraparticle analyte transport leads to a maximum in the H-k relationship between k = 0.5 and 1, which emerges gradually with increasing velocity as a result of two effects: (i) The interplay of mobile-zone and stationary-zone transport via short-range interchannel eddy dispersion makes the lateral exchange of analyte molecules between adjacent interparticle pores of the bed by diffusion through the particles increasingly unfavorable as k increases (because the effective intraparticle diffusion coefficient decreases with increasing k), causing H to increase. (ii) The uptake of analyte molecules by porous particles and their subsequent, random release at a different location is a simple, efficient, and general mechanism interrupting the velocity-memory imprint of the analyte molecules by the interparticle flow paths. In turn, the decay of velocity memory is accelerated with increasing k, which ultimately causes H to decrease between k = 1 and 10. The downward slope of the H-k plot at high velocity reflects the degree of eddy dispersion, thus, the degree of heterogeneity of the packed bed, as we could illustrate by simulations in an ordered packing, for which microstructural heterogeneity (as in the random packing) and the resulting pore-to-pore variation in the velocity distribution and associated short-range interchannel eddy dispersion are absent.