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.

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.

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