HPLC Gradient Peak Modeling

Modeling HPLC gradient peaks can be challenging. We invested a significant measure of R&D to realize effective techniques for modeling gradient peaks. The methods PFChrom offers are uniquely its own.

Directly Fitting Twice-Generalized Closed-Form Models

The first of the HPLC gradient methods, the simplest and easiest to implement, involves fitting a twice-generalized model, such as the Gen2HVL or Gen2NLC directly to the data. Although these models appear to be far from simple, these are closed-form (non-integral) models that can usually be fitted to the data in seconds.

In this type of gradient fit, the IRF is assumed to be largely canceled by the gradient and the fourth moment’s tail compression is used as an estimate of the gradient strength.

The twice-generalized HVL and NLC models adjust both the third and fourth moments of the underlying zero-distortion density. It is this fourth moment adjustment that makes it possible to fit HPLC gradient peak data directly and realize an estimate for the strength or compression of the gradient. This approach is extensively discussed in the HPLC Gradient Peaks – Direct Closed Form Fits tutorial.

Directly Modeling the Gradient using Deconvolution Fitting

In this approach to Gradient HPLC modeling, the actual gradient is estimated in a deconvolution fit. In most instances, a single width half-Gaussian was found to accurately model a well-designed HPLC gradient. The fit is identical to that of an isocratic model with an IRF, except a deconvolution occurs in the Fourier domain instead of a convolution.

In directly fitting the gradient, a deconvolution model (as opposed to a convolution model) is fitted. Here the white peak is the data from the instrument, the red peak is the estimated isocratic peak that would exist if there were no gradient present, the green peak is the pure HVL absent all ZDD third-moment adjustments for multiple adsoprtion sites and other deviations from the theoretical expectation, and the blue curve is the Gaussian that would exist with infinite dilution, again if no gradient was present in the separation. Note the accuracy of the fit, <1 ppm unaccounted variance.

This method is explored in the HPLC Gradient Peaks – Fits Which Model the Gradient tutorial. Although this procedure is most useful for a one-step estimation of the gradient parameter(s) when fitting a single peak standard, it can be cautiously used to fit production data with multiple baseline-resolved peaks. An example is given in the HPLC Gradient Peaks – Fitting Unwound Data tutorial.

Fitting the Unwound Data

In this third approach, a known estimate of the gradient from either a deconvolution fit or from a genetic algorithm using Fourier methods, is used to ‘unwind’ the gradient. This removes the compression of the gradient allowing isocratic peak models to be fit, often to an exceptional accuracy.

This is the same data which was fit directly to a twice-generalized model. In this instance, the fit is to unwound data. Because much of the IRF is canceled by the gradient, it is often possible to fit the unwound data to the once-generalized closed-form models. In this example, the fit is improved from 20 ppm to 8ppm.

This method is extensively discussed in the HPLC Gradient Peaks – Fitting Unwound Data tutorial.