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GenNLC

GenNLC - Default Generalized Normal ZDD

By using the relationships of equivalence between the GenHVL and GenNLC models, we make the following simple substitution into the GenHVL model equation to derive the GenNLC model:

a_{0} = Area

a_{1} = Center (as mean of asymmetric peak)

a_{2} = Width (NLC/Giddings kinetic time constant)

a_{3} = HVL/NLC common chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = NLC-indexed asymmetry ( -10 > a_{4} > 10, NLC=0.5 )

Built in model: GenNLC

User-defined peaks and view functions: GenNLC(x,a_{0},a_{1},a_{2},a_{3},a_{4})

Note that the a_{4} value controlling the skew of the GenNLC peak appears as a_{3} in
the nomenclature used in the ZDD
descriptions.

In this plot, only positive a_{4} values are shown for a series of fronted and tailed GenNLC shapes
which vary only in a_{4}. The NLCs (a_{4}=0.5) and HVLs (a_{4}=0) are included.
This range covers that which is routinely seen in analytical peak fits.

GenNLC Considerations

When a_{4}=0, the ZDD becomes a Gaussian and the model reduces to the HVL.

When a_{4}=0.5, the ZDD becomes a Giddings and the model reduces to the NLC.

The GenNLC's a_{4} asymmetry parameter is indexed to the NLC and thus the absolute peak asymmetry
is not independent of the peak's a_{1} location.

Assuming the instrumental distortions have been removed, in a deconvolution step or in the actual fitting,
the GenNLC will successfully model most analytical chromatographic peaks. If you want an analytic peak
model with a kinetic a_{2} width, as opposed to a Gaussian band broadening, this may be the only
model you will ever need.

This a_{4} skew adjustment in the ZDD manages the deviations from the Giddings ideality assumed
in the theoretical infinite dilution NLC. This is an asymmetry parameter index to the NLC at a_{4}=0.5.
For most IC and non-gradient HPLC peaks, you should expect an a_{4} between 1.1 and 2.0 (the deviation
from non-ideality is right skewed or tailed from the Giddings).

In most instances, a_{4} can be assumed constant (shared) across all peaks in the chromatogram.
It is strongly recommended that a_{4} be shared across all peaks and only independently fitted
with each peak if the parameter significance allows and you find such necessary. In our experience, across
a wide range of concentrations, and across peaks ranging from highly fronted to highly tailed, the fitted
a_{4} was very close to constant.

The addition of this single a_{4} parameter to an overall fit can result in orders of magnitude
improvement in the goodness of fit. The impact of just this one additional parameter in a fit of perhaps
many dozens of parameters can be the difference between 5 ppm and 5000 ppm in the unaccounted variance
in the fit.

The a_{4} is also an exacting indicator of the deviation from this ideality. Changes in the a_{4},
in fitting a given standard, may well be indicative of column health. The greater the a_{4} value
varies from 0.5, the greater the deviation from this Giddings ZDD assumption of the NLC.

Note that the a_{4} will be most effectively estimated and fitted when the peaks are skewed with
some measure of fronting or tailing. Higher concentrations are very good for this model, assuming that
one does not enter into a condition of overload that impacts the quality
of the fit.

This model will be least effective in highly dilute samples with a poor S/N ratio since such peaks will generally have much less intrinsic skew.

The GenNLC<irf> composite fits, the model with a convolution integral describing the instrumental distortions, isolate the intrinsic chromatographic distortion from the IRF instrumental distortion only when the data are of a sufficient S/N and quality to realize two independent deconvolutions within the fitting. For very dilute and noisy samples, you will probably have to remove the IRF prior using independent determinations of the IRF parameters.

The GenNLC<ge> model uses the <ge>IRF, consistently the best of the convolution models as
it fits both kinetic and probabilistic instrument distortions. Bear in mind, however, that this fit must
extract the kinetic instrumental distortion, the probabilistic instrumental distortion, the a_{4}
intrinsic skew to the chromatographic distortion, and the primary a_{3} chromatographic distortion
(very possibly for for each peak). It is recommended the IRF parameters be determined by fits of a clean
standard, and the instrumental distortions removed by deconvolving
the known IRF prior to fitting more complex peak data.

Since peaks often slow in kinetic rates with retention time, the a_{2} will probably be varied
(independently fitted) for each peak.

Since peaks often evidence increased tailing with retention time, the a_{3}
will probably be varied (independently fitted) for each peak.

If you are dealing with a small range of time, however, or of you are dealing with overlapping or hidden
peaks in a narrow band, a_{2} and/or a_{3} can be held constant across the peaks in this
band.

If you are addressing gradient peaks, or the overload shapes of preparative chromatography, you will need the Gen2NLC or GenNLC[Y] model where the fourth moment of the peak is also adjusted.

The GenNLC model is part of the unique content in the product covered by its copyright.