Assessment of Two-Dimensional Separative Systems Using Nearest-Neighbor Distances Approach. Part 1: Orthogonality Aspects

Abstract

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.

On sample preparation methods for fermented beverage VOCs profiling by GCxGC-TOFMS

“…Used column setup was a polar column followed by a medium polar column, recommended by a previous study (Welke et al 2012 ).Considered independent variables were column flow, temperature program, 2nd oven temperature offset, modulation temperature offset, modulation time, hot pulse time (% of the entire modulation time). The dependent variable was the median value of Nearest Neighbor Distance (NND) (Nowik et al 2013 ), which is calculated only based on the annotated peaks. Modulation time was adjusted to avoid the wrap around phenomena.…”

Review of the role and methodology of high resolution approaches in aroma analysis

“…Due to the lack of flexibility in 'tweaking' the carrier gas phase, approaching the analysis by employing suitable 'orthogonality' of stationary phase dimensions can achieve maximum resolution for aroma analysis. Although various evaluations of stationary phase orthogonality based on the 2D plot results has been reported [98][99][100], but not discussed at length here, progress in the understanding of orthogonality at the level of detailed molecular parameters is still intriguing.…”

Recent applications of chemometrics in one‐ and two‐dimensional chromatography

“…A series of different methods to quantify orthogonality has been developed. Examples include information theory [250], convex-hull strategies [251], bin-counting approaches [252], home-range theory [253], conditional entropy [254], and nearest-neighbour distances [255]. Comparative studies were conducted by Gilar et al [256] and later by Schure and Davis [257].…”

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