Influence of theoretical and semi-empirical peak models on the efficiency calculation in chiral chromatography

Abstract

Height equivalent to theoretical plate (H) equations, such as the van Deemter or Knox-Saleem equations, and other efficiency vs. linear velocity equations (u), provide kinetic insights into chromatographic separations phenomena and column performance. In enantioselective separations, the peak shape of the two enantiomers can differ significantly and are often asymmetric. The peak efficiency calculations heavily impact these efficiency-flow profiles, leading to erroneous estimations of eddy diffusion, longitudinal diffusion, and mass transfer terms. In this work, new asymmetric peak functions are employed for modeling enantiomer peaks based on the Haarhoff-Van der Linde function, its generalized variant (GHVL), once Generalized Asymmetric Gaussian (AGN), and Twice Generalized Gaussian (TGN). The new models (AGN, TGN, and GHVL) incorporate higher statistical moments besides the zeroth, first, and second moments to account for two-sided asymmetry (fronting or tailing). The fit results are compared with the traditional efficiency calculation methods endorsed by official pharmacopeia and numerical estimation of moments from the raw data. Enantiomeric separations of ibuprofen and dl-homophenylalanine were chosen as probe molecules. The results demonstrate that non-linear least squares fitted functions provide better estimations of peak efficiency data even in the presence of high noise. In particular, the generalized models consistently offered the best quality fits for various peak shapes in chiral separations. Conversely, the half-height Gaussian method greatly overpredicted skewed peak efficiencies. This investigation reveals that the commonly held assumptions of peak shape and numerical integration of raw data are highly insufficient for chiral chromatography. The impact of asymmetry on plate height should not be overlooked when accurate data from efficiency-flow rate curves is derived. We advocate for the broader adoption of these new generalized peak (AGN, TGN, GHVL) models because they provide robustness at various SNRs that account for right or left asymmetry while accurately representing peak geometry.