Linear peak capacity of a comprehensive multi‐dimensional separation

Abstract

In order to resolve (quantifiably and identifiably separate) the same number of peaks in the analysis of the same mixture yielding statistically uniform peak distribution, a comprehensive 2-D separation needs a two times larger peak capacity than a 1-D separation does. Each additional dimension further reduces the utilization of the peak capacity of comprehensive multi-dimensional (MD) separation by a factor of two per dimension. As a result, the same peak capacity means different things for separations with different dimensionalities. This complicates the use of the peak capacity for comparison of the potential separation performance of the separations with different dimensionalities. To facilitate the comparison, a concept of a linear peak capacity has been proposed. The linear peak capacity of an MD separation is the peak capacity of a 1-D separation that, in the analysis of the same mixture, is statistically expected to resolve the same number of peaks as the MD separation is. There are other factors that differently affect the performance of the separations that have different dimensionalities. Peak capacity of a 2-D separation with a rectangular separation space is 27% larger than the product of the peak capacities of its first and second dimension. This advantage of a 2-D separation is essentially nullified by the fact that the peak capacity of the first dimension of an optimized 2-D separation cannot be higher than 80% of the peak capacity of its first dimension standing alone. All in all, the incremental peak capacity gained from addition of a second dimension will not exceed 50% of the peak capacity of the added second dimension. All results are valid for arbitrarily shaped (not necessarily Gaussian) peaks.