Validation of theory of n-column separations with gas chromatograms predicted by commercial software.

A probability theory for the average number of compounds resolved by the partial separation of complex mixtures on n columns was tested using commercial-software predictions of gas chromatograms. Such n-column separations are traditional means for addressing peak overlap, in which one chooses additional columns of different selectivity to separate compounds that cannot be separated by a single column. Gas chromatograms of five types of complex mixtures containing from 99 to 283 compounds were predicted for eight stationary phases using both optimized and other temperature programs. The number n of columns for different mixtures varied from 2 to 5. The numbers of compounds separated as singlet peaks at different resolution thresholds were compared to predictions, as evaluated with point-process statistical-overlap theory based on a Poisson distribution. A good agreement between theory and results was found in all cases corresponding to low saturation. Both good and poor agreements were found for cases corresponding to high saturation. A good agreement also was found for results based on resolving complex mixtures by a single column subject to two temperature programs. The moments and distribution of the number of resolved compounds were computed by Monte Carlo simulation, thus gauging the significance of departures between results and theory. The potential of such simulations to explore the limitations of theory was briefly investigated.