A new metric for relating macroscopic chromatograms to microscopic surface dynamics: the distribution function ratio (DFR)

Abstract

Heterogeneous stationary phase chemistry causes chromatographic tailing that lowers separation efficiency and complicates optimizing mobile phase conditions. Model-free metrics are attractive for assessing optimal separation conditions due to the low quantity of information required, but often do not reveal underlying mechanisms that cause tailing, for example, heterogeneous retention modes. We report a new metric, which we call the Distribution Function Ratio (DFR), based on a graphical comparison between the chromatogram and Gaussian cumulative distribution functions, achieving correspondence to ground truth surface dynamics with a single chromatogram. Using a Monte Carlo framework, we show that the DFR can predict the prevalence of heterogeneous retention modes with high precision when the relative desorption rate between modes is known, as in during surface dynamics experiments. Ground truth comparisons reveal that the DFR outperforms both the asymmetry factor and skewness by yielding a one-to-one correspondence with heterogeneous retention mode prevalence over a broad range of experimentally realistic values. Perhaps of more value, we illustrate that the DFR, when combined with the asymmetry factor and skewness, can estimate microscopic surface dynamics, providing valuable insights into surface chemistry using existing chromatographic instrumentation. Connecting ensemble results to microscopic quantities through the lens of simulation establishes a new chemistry-driven route to measuring and advancing separations.