Preparative Peak Modeling

Fitting Overload Peaks

PFChrom’s twice-generalized chromatographic models not only fit the compression of HPLC gradient peaks, but they can effectively fit the overload shapes in preparative chromatography.

The following fits use the GenHVL[Yp] model specifically designed for the starting estimates for preparative shapes. Also employed is the <e2> IRF consisting of the sum of two exponentials. Four different concentrations of overload are represented. The white curves are the peaks as eluted from the instrument. The red peaks are those which would exist without the instrumental distortion. The green peaks are the pure HVL chromatographic peaks which would exist if the column had infinite capacity and no overload occurred. Such high concentrations produce close to triangular fronted or tailed HVL shapes.

Unlike the HPLC models, where the fourth moment tail parameter represents a compression (a compactness greater than a Gaussian), a preparative peak represents a dramatic dilation. In the extreme, the zero-distortion density (ZDD) tailing becomes as broad as an exponential decay. We find it significant that a single model can mathematically manage any chromatographic shape, analytic, gradient, or overload.

Specialty Preparative Models

In the above example, the fits vary from 170 to 645 ppm unaccounted variance, the error generally increasing with the measure of overload. This goodness of fit is still respectable, r² from 0.9994 to 0.9998, but nowhere close to the 1-20 ppm that is often observed in fitting peaks where no overload is present. In order to improve upon the fitting of overload shapes, PFChrom offers a model where the ZDD has an independent rise and decay.

The following plots are for the GenHVL[Y2p] model illustrating the adjustments in shape for a given width of overload envelope. By furnishing the zero-distortion density with an independent rise and decay, nuances in the preparative envelope can be modeled.

The GenHVL[Yp2] model makes it possible to estimate the extent to which a column is managing the overload as well the specific parametric components of the overload shape. In a preparative peak, the IRF is especially important.

The following fits use the GenHVL[Y2p] model with the sum of exponentials IRF. Here the Gaussian peaks that would be seen at infinite dilution are also shown in blue.

In this real-world overload data, the GenHVL[Yp2] fits realize from 241 to 94 ppm error, and actually improve with increasing concentration as the relative proportion of IRF diminishes. Every aspect of a preparative peak, including the significant IRF of the instrument, is quantified.

An example of overload modeling can be found in the Fitting Preparative (Overload) Peaks tutorial.