Effect of First-Dimension Undersampling on Effective Peak Capacity in Comprehensive Two-Dimensional Separations

• Published in: Analytical chemistry (Washington) 2008-01, Vol.80 (2), p.461-473
• Main Authors: Davis, Joe M, Stoll, Dwight R, Carr, Peter W
• Format: Article
• Language: English
• Subjects: Algorithms; Analytical chemistry; Chemical reactions; Chemistry; Chromatographic methods and physical methods associated with chromatography; Chromatography - methods; Chromatography, Gas; Chromatography, Liquid; Exact sciences and technology; Gas chromatographic methods; Models, Statistical; Monte Carlo Method; Normal Distribution; Other chromatographic methods; Sampling; Studies
• ISSN: 0003-2700; 1520-6882
• DOI: 10.1021/ac071504j

The objective of this work is to establish a means of correcting the theoretical maximum peak capacity of comprehensive two-dimensional (2D) separations to account for the deleterious effect of undersampling first-dimension peaks. Simulations of comprehensive 2D separations of hundreds of randomly distributed sample constituents were carried out, and 2D statistical overlap theory was used to calculate an effective first-dimension peak width based on the number of observed peaks in the simulated separations. The distinguishing feature of this work is the determination of the effective first-dimension peak width using the number of observed peaks in the entire 2D separation as the defining metric of performance. We find that the ratio of the average effective first-dimension peak width after sampling to its width prior to sampling (defined as ) is a simple function of the ratio of the first-dimension sampling time (t s) to the first-dimension peak standard deviation prior to sampling (1σ):  =This is valid for 2D separations of constituents having either randomly distributed or weakly correlated retention times, over the range of 0.2 ≤ t s/1σ ≤ 16. The dependence of on t s/1σ from this expression is in qualitative agreement with previous work based on the effect of undersampling on the effective width of a single first-dimension peak, but predicts up to 35% more broadening of first-dimension peaks than is predicted by previous models. This simple expression and accurate estimation of the effect of undersampling first-dimension peaks should be very useful in making realistic corrections to theoretical 2D peak capacities, and in guiding the optimization of 2D separations.