Multiscale simulation of liquid chromatography: Impact of retention on the plate height in packed beds

Through a bottom-up, multiscale simulation approach we studied the impact of the phase-based and zone-based retention factor (k and k", respectively) on the total plate height H and on individual plate height terms, particularly the eddy dispersion term, in reversed-phase liquid chromatography. The studied system comprised the differential retention of six analyte compounds of graded solute polarity by a chromatographic bed of randomly packed, sub-2 µm, mesoporous, endcapped, C₁₈-silica particles at varied elution strength of the mobile phase, realized by employing two mobile-phase compositions (water-acetonitrile and water-methanol) at eight different solvent ratios. 96 density and diffusive mobility distributions specific to a combination of analyte compound and mobile-phase elution strength, obtained from molecular dynamics simulations in a single-mesopore model of the chromatographic interface, were considered in lattice-Boltzmann and Brownian dynamics simulations of advective-diffusive transport in a physically reconstructed model of the macro‒mesoporous bed to derive 96 plate heights over a wide range of retention factors (k = 0.22-504, k" = 1.14-885). Importantly, the velocity fields were rescaled to obtain plate height data under conditions of advection-dominated transport through the bed at a fixed reduced velocity of 10. The simulations revealed a nonmonotonic, oscillating dependence of H from k characterized by three regions. In region 1 (0.22 < k < 1), we observe a small, distinct rise of H with increasing retention. H then decreases in region 2 (k = 1‒10), the range most relevant to chromatographic practice, before increasing again in region 3 (k > 10). Plate height contributions from diffusion along the bed and mass transfer resistance in the stationary zone were subtracted from H to isolate the eddy dispersion term, analyzed subsequently using a model that extends Giddings' coupling theory by embedding analyte retention inside the mesoporous particles. This analysis suggests that with increasing flow velocity, as analyte transport through the bed becomes advection-dominated, the coupling between the short-range interchannel contribution to eddy dispersion (originating in the microscopic disorder of the randomly packed bed) and intraparticle mass transfer produces a local maximum in the H-k relationship at low retention factors, causing the decrease of H with increasing retention factor in region 2.