Effective Saturation: A More Informative Metric for Comparing Peak Separation in One- and Two-Dimensional Separations

Abstract

A theoretical comparison is made of the numbers of observed peaks in one-dimensional (1D) and two-dimensional (2D) separations having the same peak capacity, as calculated from the traditional metric of resolution. The shortcoming of the average minimum resolution of statistical overlap theory (SOT) for this comparison is described. A new metric called the "effective saturation" is introduced to ameliorate the shortcoming. Unlike the "saturation", which is the usual metric of peak crowding in SOT, the effective saturation is independent of the average minimum resolution and can be determined using traditional values of resolution and peak capacity. Our most important finding is that, under a wide range of practical conditions, 1D and 2D separations of the same mixture produce almost equal numbers of observed peaks when the traditional peak capacities of the separations are the same, provided that the effective saturation and not the usual saturation is used as the measure of crowding. This is the case when peak distributions are random and when edge effects are minor. The numerical results supporting this finding can be described by empirical functions of the effective saturation, including one for the traditional peak capacity needed to separate a given fraction of mixture constituents as observed peaks. The near equality of the number of observed peaks in 1D and 2D separations based on the effective saturation is confirmed by simulations. However, this equality is compromised in 2D separations when edge effects are large. The new finding does not contradict previous predictions by SOT of differences between 1D and 2D separations at equal saturation. Indeed, the simulations reaffirm their validity. Rather, the usual metric, i.e., the saturation, is just not as simple a metric for comparing 1D and 2D separations as is the new metric, i.e., the effective saturation. We strongly recommend use of the new metric for its great simplifying effect.