Utility of linear and nonlinear models for retention prediction in liquid chromatography

Linear solvation strength model in reversed-phase liquid chromatography assumes linear relationship between ln k and Φ. In this work we show that this assumption is true only in narrow range of mobile phase strength. The ln k versus Φ relationship could be more accurately described by three-parametric non-linear model in a wide range of eluent strength. We investigated the consequences of non-linearity on retention prediction accuracy and analyte retention behavior in reversed-phase chromatography. When the ln k versus Φ is measured in narrow range of mobile phase strength (ΔΦ ~ 0.1-0.2) both linear and nonlinear models provide comparable retention prediction results. We propose that the linear trend of ln k versus Φ relationship is obtained in the range flanking the elution factor k_e (value of retention factor at the column end). We calculated and plotted changes of retention factor of analytes along the column. The visualization illustrates the ranges of retention factor values participating in separation during gradient. For typical gradient slopes employed in liquid chromatography practice and small molecules the elution factor k_e value is between 2 and 8. As a simplified generalization for typical gradient slopes we propose using linear ln k versus Φ trend in the k range between 1 and 30. The spreadsheet was utilized to compare the retention prediction accuracy of linear and non-linear retention models. When fitting ln k versus Φ trend in k range 1-30 the simple linear model is in good agreement with nonlinear model with retention time prediction error 0.3-4.7% (for gradient slope 0.013-0.260).