Statistical-Overlap Theory of Column Switching in Gas Chromatography: Applications to Flavor and Fragrance Compounds

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Abstract
First-column gas chromatograms (GCs) of hundreds of flavor and fragrance compounds, and second-column GCs of specific regions of these GCs, are predicted using thermodynamic databases in commercial software. A statistical-overlap theory of column switching with cryogenic focusing then is developed by mimicking the predicted GCs by two kinds of Monte Carlo simulations. In the first kind, a probability distribution is calculated for the number of compounds in a region of the first-column GC, based on the number of observed peaks in the region, the number of observed peaks in the second-column GC, and the retention-time distributions and breadths of single-component peaks in both GCs. In the second kind, criteria are established for the theory's application. The theory is applied to 12 regions of first-column GCs. The theory predicts the number of compounds in all of them and shows that separation rarely is complete in second-column GCs, when 10 or more compounds are transferred between columns. The theory also rationalizes the tedious search required to find good separation conditions by showing that column-switching gas chromatography with cryogenic focusing is inherently statistical. The number of peaks in the second-column GC can be greater than, less than, or equal to the number of peaks in the relevant region of the first-column GC, and the good conditions sought by researchers to substantially improve separation correspond to favorable “rolls of the dice” found only by trial and error.

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