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 In k and Phi. In this work we show that this assumption is true only in narrow range of mobile phase strength. The In k versus Phi 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 In k versus Phi is measured in narrow range of mobile phase strength (Delta Phi similar to 0.1-0.2) both linear and nonlinear models provide comparable retention prediction results. We propose that the linear trend of In k versus Phi 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 In k versus Phi 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 In k versus Phi 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). (C) 2019 Elsevier B.V. All rights reserved.