Reducing Effect of Gradient Deformation For LC Retention Modelling

Tijmen Bos and other CAST members collaborated with Agilent Technologies to investigate means to minimize the effect of gradient deformation to retention modelling in LC.
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Retention modelling is a useful technique which can be used to substantially reduce the method-development process for LC separations. One approach utilizes so-called scanning (or ‘scouting’) experiments using isocratic or gradient elution [1]. Here, a number of pre-defined methods are employed to record retention times to which empirical models are fitted. 

Isocratic experiments will generally yield reliable solid datasets that are very suitable for retention modelling. Using isocratic elution is, however, not always very practical. Indeed, scouting experiments can take rather long for the slower experiments. Moreover, some manual fine-tuning and experience with the analytes in question are needed to identify the appropriate modifier concentrations.

In contrast, gradient elution allows rather quick and easy scanning experiments at the significant cost of the usefulness of the resulting data. Where isocratic experiments directly measure the retention factor at a certain modifier (φ) fraction, the retention time in gradient elution depends on the gradient experienced by the analyte.


Figure 1. Schematic illustrating a programmed linear gradient and the experienced gradients for two different systems.

However, as the programmed change in composition produced by the pump migrates through the chromatographic system, its shape is altered. In Figure 1, above, we can see how this leads to the familiar difference between the programmed (dark blue) and effective (purple, light blue) gradients for two different systems.

This deviation is the product of an array of effects, such as the morphology and inefficiencies in the pump components, chromatographic system volumes and the accuracy of pumped mobile-phase composition (A vs. B). The latter can rather easy deviate if the pump does not take into account the change in density as φ increases.

Figure 2. Response functions of systems 1 and 2. The shape essentially represents the differences between the programmed and effective gradients shown in Figure 1.

The overall effect can be represented by response functions. These functions essentially describe the difference between the programmed and measured gradient. Two examples for two different systems are shown above in Figure 2. Indeed, depending on the pump characteristics, dramatic changes can be observed.

The problem is only complicated further as the recorded dwell curve may also in itself represent an inaccurate depiction. Depending on the detector, solvatochromic effects and  the presence of other mobile-phase components can severely convolute the true depicted of the experienced gradient.

For modelling, deformation is a problem because

As part of a larger collaboration with Agilent Technologies in the “DAS PRETSEL” project, Tijmen Bos, with assistance of other CAST members Mimi den Uijl, Leon Niezen and Stef Molenaar, developed an algorithm to reduce partially the effects of gradient deformation.

In their work, Bos et al. showed that the impact of the gradient deformation significantly impacts retention parameters. By modelling so-called Stable distribution functions to the measured dwell curves, the authors were able to significantly reduce the prediction errors for water-water systems (Figure 3). Conveniently, the Stable parameters turned out to be related to physical parameters of the chromatographic system.

Figure 3. Relative errors (%) in the predicted retention times of the test compounds on Instruments 2 (top) and 3 (bottom) obtained when using retention parameters determined for the test compounds on Instrument 1 at different flow rates. Please see the publication for details about the instruments. Reproduced with permission from [2].

This work is part of a larger project. In this first stage, we mainly targeted the geometric-influences. Now, we shift our focus to more complicated solvent systems and also the effect on larger molecular systems.

The work was recently published open-access in Journal of Chromatography A and can be downloaded for free here. An accompanying video pitch can be viewed below. Readers interested in learning more about retention modelling and its application areas are referred elsewhere


[1] Recent applications of retention modelling in liquid chromatography, M.J. den Uijl,  P.J. Schoenmakers,  B.W.J. Pirok, and  M.R. van Bommel, J. Sep. Sci.2020, DOI: 10.1002/jssc.202000905.

[2] Reducing the influence of geometry-induced gradient deformation in liquid chromatographic retention modelling, T.S. Bos, L.E. Niezen, M.J. den Uijl, S.R.A. Molenaar, S. Lege, P.J. Schoenmakers, G.W. Somsen, B.W.J. Pirok, J. Chromatogr. A, 2021, 1635, 461714, DOI: 10.1016/j.chroma.2020.461714.

The Authors

Tijmen Bos

Mimi den Uijl

Leon Niezen

Stef Molenaar

Researchers Bos, Niezen and Molenaar are part of the UNMATCHED project, which is supported by BASF, DSM and Nouryon, and receives funding from the Netherlands Organization for Scientific Research (NWO). Den Uijl is part of the TooCOLD project, which is supported by Unilever and and NWO. You can read more about them and find their contact info on the Team page.


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