Chromatographic Peak Modeling

Unparalleled Fitting Accuracy

When modeling chromatographic data, it is all about the quality of the fitting. There are statisticians who will assert that a goodness of fit <10 ppm unaccounted variance (r²>0.99999) is impossible with real world laboratory data without severe overfitting (generating over-specified fits where the significance fails on one or more of the parameters).

For most real-world chromatographic data, PF Chrom will generate fits of this exceptional accuracy, or higher, while maintaining full statistical significance on all model parameters. What may be deemed impossible by many in the modeling field you will prove as not only possible but routinely achieved with your own data!

This is a fit of a fronted peak with an IRF tailing that produces an ambiguous shape; one of the hardest to fit of real-world baseline-resolved analytic peaks. By using one of PF Chrom’s primary chromatographic models, the data are fitted to less than 4 ppm least-squares error. The lower plot displays the various deconvolutions realized by the fitting. The white peak is the peak as registered by the instrument. The red peak is absent the instrumental distortion. The green peak is the pure NLC kinetic model. The blue peak is the infinite dilution Giddings, the peak with all concentration-dependent chromatographic distortion removed.

Fitted Parameters with Physical Meaning

Historically, the fitting of chromatographic peaks has yielded either ad-hoc or empirical parameters, as was typically the case for the EMG model, or unsatisfactory theoretical parameters, as in the case of the HVL and NLC models.

With the advent of PF Chrom’s generalized HVL and generalized NLC chromatographic models, ALL of the parameters have intrinsic physical meaning useful for characterizing every aspect of the separation, column health, and instrumental effects.

With PF Chrom, you can concentrate directly on these parameters. For example, consider the single peak in the above fit. The main chromatographic model parameters, a0-a3, are the pure chromatographic peak model parameters absent instrumental distortions and theoretical non-ideality:

a0 – the fitted area of the peak

a1 – the fitted center of mass of the pure zero-distortion peak, with or without the a4 multiple-adsorption site non-ideality, and absent the a3 chromatographic distortion and its concentration dependency.

a2 – either a statistical width as a standard deviation, or a kinetic width as a time constant, of the pure zero distortion peak, absent the a3 chromatographic distortion and its concentration dependency

a3 – the chromatographic distortion, the fronting or tailing, in the pure chromatographic peak

The additional chromatographic model parameters, a4-a7, are the parameters which adjust for non-ideality and instrumental distortions:

a4 – the non-ideality associated with the zero-distortion density, that which likely addresses multiple-site adsorptions, usually treated as common across all peaks

a5 – the narrow width instrumental distortion, in LC likely addressing axial dispersion and interphase mass-transfer resistances, again treated as common across all peaks

a6 – the larger width instrumental distortion likely associated with first order exponential delays in the detection and flow path, and usually close to a constant across all peaks

a7 – the area fraction of the narrow IRF relative to the total instrumental distortion, also very close to constant across all peaks

True R&D Peak Modeling Capabilities

PF Chrom was developed with over one-hundred exploratory instrument response functions and as many experimental zero distortion densities in the chromatographic models. Although the once and twice-generalized HVL and NLC models will probably manage most isocratic peaks, there are many types of chromatography, and HPLC gradient peaks and peaks with overload will require special models. If we found a model in any manner useful, we have included it in the product for R&D peak modeling. PF Chrom also offers an extensive set of statistical and spectroscopic models.

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