Effect of first-dimension undersampling on effective peak capacity in comprehensive two-dimensional separations

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 〈β〉) 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): 〈β〉 = √1+0.21(t_s/¹σ)² 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 〈β〉 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.