Gradient chromatography has been widely applied in analytical and preparative chromatography since it provides better peak shapes and the ability to elute analytes in a shorter time frame. Apart from changes in the composition of a mobile phase also alteration of process temperature can be applied during separation procedures to improve efficiency. However, proper mathematical modeling of the gradient chromatography and further correct prediction of solutes' retention behavior have become a serious challenge as it involves the need to develop computational procedures that accurately account for the time and spatial gradients of crucial parameters. In this work, a computational procedure including the equilibrium-dispersive two-dimensional mass transfer model, the two-dimensional (2D) heat transfer model together with Darcy's law and the continuity equation have been proposed. Additionally, the calculation procedure was simplified by replacing the 2D model with the one-dimensional (1D) mass transfer model in order to speed up the computations. Both proposed solutions were validated employing external experimental data of temperature gradient HPLC [1] as well as with predictions based on the linear elution strength (LES) model available therein. The proposed procedures made it possible to efficiently predict the concentration profiles with average relative errors of calculated retention times not exceeding 3.22%. Moreover, the effect of the axial dispersion coefficient determination method on the obtained peak shapes was examined involving the Gunn, the Wen-Fan, and the Chung-Wen correlations, indicating that the latter produces the most accurate results. Finally, the proposed mathematical procedures were tested under UHPLC conditions, and due to a significant difference in retention times found the 2D model is strongly advised.
Keywords: Concentration profile prediction; HPLC; Mathematical modeling; Temperature gradient; UHPLC.
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