Comparison of rate models for gradient elution chromatography and experimental evaluation for IEC, HIC, and RPC...

Different rate models are evaluated for their ability to describe the application of solvent gradients in elution chromatography. The analysis is limited to cases where the solute isotherms are linear and a pulse injection is applied. However, as demonstrated in this work by comparison to experimental data, it is still applicable to different practical systems including protein ion exchange chromatography, protein hydrophobic interaction chromatography, and reversed phase high performance liquid chromatography. The four rate models considered are the pore diffusion (PD) model, the linear driving force (LDF) model, and two transport models, one with an adsorbed phase concentration driving force (TRQ), and the other with a mobile phase concentration driving force (TRC). The first three models require numerical solution, while a new analytical solution valid for gradients with arbitrary shape is developed for the latter. The four models can accurately describe the gradient effect on peak sharpening with similar accuracy for relatively shallow gradients. However, significant deviations are observed for the transport models when the gradient is very steep. A common feature of the PD, LDF, and TRC models is the prediction, consistent with experimental observations, of fronting peak shapes for cases where initial adsorption is strong and there is a strong dependence on the modifier concentration. The TRC model with a mobile phase concentration driving force is recommended for practical calculations as compromise of simplicity and accuracy.