Assessment of two-dimensional separative systems using the nearest neighbor distances approach. Part 2: separation quality aspects.

In this paper we propose a method for the evaluation of real separation quality in multidimensional separations based on the nearest neighbor distances (NND). This approach allows us to overcome the principal drawback of the orthogonality measurement which does not evaluate how good the real separation obtained with one system is, especially when compared to another one. Separation quality evaluation takes into account the distances (di(s)) between peaks in whole separation space. The distances between nearest neighbors were calculated in resolution scaled analysis space to overcome statistically different peak widths in each dimension. The obtained separation quality is ranked by harmonic mean (H̅(s)) of the distances di(s). The extent of peak spreading, described by arithmetic mean (A̅(s)), gives an appreciation of the effective analysis space of 2D separation. The classifications of systems obtained with the same retention data using separation quality and orthogonality approaches show important differences in ranking orders depending on two different targets of these evaluations: the separation potential of a 2D system and the divergence of selectivity between both separation directions. This study shows separation quality and orthogonality merit to be evaluated in parallel for the same systems. The other new threshold descriptor, minimal limit distance (dilim) derived from resolution dependent peak capacity scale, was used to predict the separation quality as a function of desired resolution. We also introduce here a composed descriptor for 2D systems: the optimality coefficient (Oc), which may be useful in the 2D separation optimization process. It takes into account the maximization of homogeneity of peak spreading (H̅(s)/A̅(s)) and the minimization of effective analysis space (or compactness, dilim/A̅(s)) terms.

Assessment of two-dimensional separative systems using nearest-neighbor distances approach. Part 1: orthogonality aspects.

We propose here a new approach to the evaluation of two-dimensional and, more generally, multidimensional separations based on topological methods. We consider the apex plot as a graph, which could further be treated using a topological tool: the measure of distances between the nearest neighbors (NND). Orthogonality can be thus defined as the quality of peak dispersion in normalized separation space, which is characterized by two factors describing the population of distances between nearest neighbors: the lengths (di(o)) of distances and the degree of similarity of all lengths. Orthogonality grows with the increase of both factors. The NND values were used to calculate a number of new descriptors. They inform about the extent of peak distribution, like the arithmetic mean (A̅(o)) of NNDs, as well as about the homogeneity of peak distribution, like the geometric mean (G̅(o)) and the harmonic mean (H̅(o)). Our new, NND-based approach was compared with another recently published method of orthogonality evaluation: the fractal dimensionality (DF). The comparison shows that the geometric mean (G̅(o)) is the descriptor behaving in the most similar way to dimensionality (DF) and the harmonic mean (H̅(o)) displays superior sensitivity to the shortest, critical distances between peaks. The latter descriptor (H̅(o)) can be considered as sufficient to describe the degree of orthogonality based on NND. The method developed is precise, simple, easy to implement, and possible to use for the description of separations in a true or virtual system of any number of dimensions.