Determination of the correct migration time and other parameters of the Haarhoff–van der Linde function from the peak geometry characteristics

Abstract

For Gaussian peaks, the migration time of the analyte results as the position of the top of the peak and the zone variance is proportional to the peak width. Similar relations have not yet been derived for the Haarhoff-van der Linde (HVL) function, which appears as a fundamental peak-shape function in electrophoresis. We derive the relations between the geometrical measures of the HVL-shaped peak, that is the position of its maximum, its width and a measure of its asymmetry, and the respective parameters a1, a2, and a3, of the corresponding HVL function. Under the condition of the HVL-shaped peak, the a1 parameter reflects the true migration time of the analyte, which may differ from the peak top position significantly. Our procedure allows us to express the parameters without the need of any external data processing (nonlinear regression). We demonstrate our approach on simulated peaks and on experimental data integrated by the ChemStation software (delivered with the CE instrumentation by Agilent Technologies). A significant improvement is achieved reading the migration time of the experimental and simulated peaks, which draws the error of the HVL-shaped peak migration time evaluation down to the resolution of the data sampling rate.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: Part I. Theory

“…The correct (i.e. dispersion unaffected) effective mobility can be determined by a nonlinear regression or approximate solution [33]. Although the same effect can be expected for weak analytes and multiple selectors, the appropriate mathematical theory that would substantiate this expectation has not been formulated yet.…”

Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Theory and software PeakMaster 6—Next Generation

“…This enabled the model to predict not only the positions of all peaks but also their shapes. Although the practice of fitting distorted peaks by electromigration dispersion (EMD) with the Haarhoff–van der Linde (HVL) function was already recommended , the NLTEM model provided mathematical bases for such an approach. In addition, this practice demonstrated the time dependence of the fitted parameters that should be considered when analyzing peaks naturally detected in the time domain.…”

The dynamics of band (peak) shape development in capillary zone electrophoresis in light of the linear theory of electromigration

“…The HVL function can be expressed in either of two parameterizations . The matter is further complicated by the fact that Erny et al arbitrarily interchanged the spatial and the temporal ( x and t ) variables in the HVL function , while the original Haarhoff and Van der Linde solution applies to the spatial domain only.…”

“…The HVL function can be expressed in either of two parameterizations . The matter is further complicated by the fact that Erny et al arbitrarily interchanged the spatial and the temporal ( x and t ) variables in the HVL function , while the original Haarhoff and Van der Linde solution applies to the spatial domain only. While using one or the other parameterization as well as switching from the spatial to the temporal domain does not introduce severe practical consequences, the move makes any theoretical discussion unnecessarily difficult.…”