Modelling Retention Behavior Over Broad Ranges of Organic Modifier Concentrations in Reversed-Phase Liquid Chromatography Columns

Abstract

The present study aimed to investigate how complex an analytical retention time model needs to be to closely represent the strong curvature in the relation between the logarithm of the retention factor and the fraction of organic modifier $\varphi$ that is often observed when exploring broad ranges of $\varphi$. This is, for example, the case during automated method development. It was found that, when covering wide $\varphi$-ranges, 3-parameter models are essential to capture the curvature of $\ln \left(k\right)$ vs. $\varphi$ relations, with the Neue–Kuss (NK) and hybrid-log (HYL) models outperforming the standard quadratic model. However, moving to 4-parameter models still yielded a statistically significant improvement, as confirmed by the RMSE values (from 0.051 to 0.016 median) and the Akaike Information Criterion (AIC)-values (with ΔAIC > 10), especially for data sets containing compounds that exhibited a retention minimum. Among these, two newly proposed models performed slightly better than the standard cubic model in both global fitting accuracy and high-$k$ extrapolation accuracy. Even so, relatively large performance variance across all methods implied that important exceptions to these general trends exist.