Optimization of comprehensive two-dimensional separations frequently relies on the assessment of the peak capacity of the system. A correction is required for the fact that many pairs of separation systems are to some degree correlated, and consequently the entire separation space is not chemically accessible to solutes. This correction is essentially a measure of the fraction of separation space area where the solutes may elute. No agreement exists in the literature as to the best form of the spatial coverage factor. In this work, we distinguish between spatial coverage factors that measure the maximum occupiable space, which is characteristic of the separation dimensionality, and the space actually occupied by a particular sample, which is characteristic of the sample dimensionality. It is argued that the former, which we call fcoverage, is important to calculating the peak capacity. We propose five criteria for a good fcoverage metric and use them to evaluate various area determination methods that are used to measure animal home ranges in ecology. We consider minimum convex hulls, convex hull peels, α-hulls, three variations of local hull methods, and a kernel method and compare the results to the intuitively satisfying but subjective Stoll-Gilar method. The most promising methods are evaluated using two experimental LC×LC data sets, one with fixed separation chemistry but variable gradient times, and a second with variable first dimension column chemistry. For the 12 separations in the first data set, in which fcoverage is expected to be constant, the minimum convex hull is the most precise method (fcoverage=0.68±0.04) that gives similar results to the Stoll-Gilar method (fcoverage=0.67±0.06). The minimum convex hull is proposed as the best method for calculating fcoverage, because it has no adjustable parameters, can be scaled to different retention time normalizations, is easily calculated using available software, and represents the expected area of solute occupation based on a proposed linear free energy formalism.
Bibliographical noteFunding Information:
S.C.R. and P.W.C. acknowledge financial support from NSF CHE-0911330 .
- Convex hull peel
- Gaussian kernel
- Local hulls
- Minimum convex hull
- Two-dimensional separations