Evaluation of three temperature- and mobile phase-dependent retention models for reversed-phase liquid chromatographic retention and apparent retention enthalpy

Predicting retention and enthalpy allows for the simulation and optimization of advanced chromatographic techniques including gradient separations, temperature-assisted solute focusing, multidimensional liquid chromatography, and solvent focusing. In this paper we explore the fits of three expressions for retention as a function of mobile phase composition and temperature to retention data of 101 small molecules in reversed phase liquid chromatography. The three retention equations investigated are those by Neue and Kuss (NK) and two different equations by Pappa-Louisi et al., one based on a partition model (PL-P) and one based on an adsorption model (PL-A). More than 25 000 retention factors were determined for 101 small molecules under various mobile phase and temperature conditions. The pure experimental uncertainty is very small, approximately 0.22% uncertainty in retention factors measured on the same day (2.1% when performed on different days). Each of the three equations for ln(k) was fit to the experimental data based on a least-squares approach and the results were analyzed using lack-of-fit residuals. The PL-A model, while complex, gives the best overall fits. In addition to examining the equations' adequacy for retention, we also examined their use for apparent retention enthalpy. This enthalpy can be predicted by taking the derivative of these expressions with respect to the inverse of absolute temperature. The numerical values of the fitted parameters based on retention data can then be used to predict retention enthalpy. These enthalpy predictions were compared to those obtained from a modified van 't Hoff equation that included a quadratic term in inverse temperature. Based on analysis of 1 211 van 't Hoff plots (solute-mobile phase-day combinations), ninety-eight percent showed a significantly better fit when using the modified van 't Hoff expression, justifying its use to provide apparent enthalpies as a function of mobile phase composition and temperature. The foregoing apparent enthalpies were compared to the apparent enthalpies predicted by the three models. The PL-A model, which contains a temperature dependent enthalpy, provided the best enthalpy prediction. However, there is virtually no correlation between the overall lack of fit to experimental ln(k) for each model and the corresponding lack of fit of the linear (in 1/T) van 't Hoff expression. Thus, the temperature-dependent enthalpy is apparently not the cause of a model's ability to fit ln(k) as a function of mobile phase composition and temperature. The value in these expressions is their ability to predict chromatograms, allowing for optimization of an advanced chromatographic technique. The two simpler models NK and PL-P, which do not contain a temperature dependent enthalpy, have their merits in modelling retention (NK being the better of the two) and enthalpy (PL-P being the better of the two) if a simpler expression is required for a given application.