Chromatographic Peak Shape Analysis and Modeling.

Various aspects of chromatographic peak quantitation and shape characterization are investigated in detail for single and overlapping chromatographic peaks. From the viewpoint of providing better quantitation of real chromatographic data while minimizing computational complexity, the results presented should be easily incorporated into existing routine chromatographic data analysis regimes. Three topics applicable to modern chromatographic data analysis are considered. First, progress in the application of the exponentially modified Gaussian (EMG) function to chromatography is reviewed. The review covers the following areas: (1) equations derived from the model, (2) studies of inherent errors in the quantitation of chromatographic peaks via use of the EMG model, (3) chromatographic applications since 1983, and (4) applications to flow injection analysis. The information discussed and the references included in this review should provide a valuable resource for those researchers considering or already using the EMG model in their studies. Second, improved empirical equations based on the EMG model are presented. The equations utilize measurements of the graphical parameters peak height (hp), width (W), and asymmetry for the calculation of the following chromatographic figures of merit (CFOMs): $\tau$, $\sigma$, area, variance, third and fourth statistical moments, excess, and skew. The equations are shown to be more accurate than traditional numerical methods when applied to single and overlapped chromatographic peaks that fit the EMG model. Application to simulated and real chromatographic peaks is discussed. Finally, a computationally simple, normalized data transformation that can be used for peak shape analysis and comparison is introduced. Compared to slope analysis, moment analysis, and the distribution function, the Q transformation performs much better over a wide range of experimental conditions, including signal to noise (S/N) ratios of less than 100 in which the other methods often fail. This method is shown to be computationally simple, easy to automate, and very intuitive in nature. Application of the Q transformation for impure chromatographic peak detection using single-channel channel data is discussed. Its advantages over the skew, excess, slope analysis and distribution function methods are reported using both simulated and real data