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GenNLC[Z] - [Z] ZDD
By using the relationships of equivalence between the GenHVL and GenNLC models, we make the basic substitution into the GenHVL[Z] model equation:
To convert the GenHVL[Z] to the GenNLC[Z], the a2 is converted to a Giddings kinetic time constant, the a4 is converted to a Gidding's indexed asymmetry.
a0 = Area
a1 = Center (as mean of generalized normal ZDD)
a2 = Kinetic Width (Giddings time constant of ZDD)
a3 = NLC/HVL Chromatographic distortion ( -1 > a3 > 1 )
a4 = NLC indexed asymmetry ( -10 > a4 > 10 ) a4=0.5 NLC (Giddings)
Built in model: GenNLC[Z]
User-defined peaks and view functions: GenNLC[Z](x,a0,a1,a2,a3,a4)
The GenNLC[Z] model is identical to the default GenNLC with the exception of the parameterization of a1 which is the median of the asymmetric generalized normal ZDD instead of the mean.
In this plot, only positive a4 values are shown for a series of fronted and tailed GenNLC[Z] shapes which vary only in a4. The NLCs (a4=0.5) and HVLs (a4=0) are included. This range covers that which is routinely seen in analytical peak fits.
When a4=0, the ZDD becomes a Gaussian and the model reduces to the HVL.
When a4=0.5, the ZDD becomes a Giddings and the model reduces to the NLC.
The GenNLC[Z]'s a4 asymmetry parameter is indexed to the NLC and thus the absolute peak asymmetry is not independent of the peak's a1 location.
This a4 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 a4=0.5. For most IC and non-gradient HPLC peaks, you should expect an a4 between 1.1 and 2.0 (the deviation from non-ideality is right skewed or tailed from the Giddings).
In most instances, a4 can be assumed constant (shared) across all peaks in the chromatogram. It is strongly recommended that a4 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 a4 was very close to constant.
The addition of this single a4 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 a4 is also an exacting indicator of the deviation from this ideality. Changes in the a4, in fitting a given standard, may well be indicative of column health. The greater the a4 value varies from 0.5, the greater the deviation from this Giddings ZDD assumption of the NLC.
Note that the a4 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[Z]<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[Z]<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 a4 intrinsic skew to the chromatographic distortion, and the primary a3 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 a2 will probably be varied (independently fitted) for each peak.
Since peaks often evidence increased tailing with retention time, the a3 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, a2 and/or a3 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 GenNLC[Y] model where the fourth moment of the peak is also adjusted.
The GenNLC[Z] model is part of the unique content in the product covered by its copyright.