Journal
JOURNAL OF CHROMATOGRAPHY A
Volume 1218, Issue 2, Pages 293-302Publisher
ELSEVIER
DOI: 10.1016/j.chroma.2010.11.016
Keywords
Liquid chromatography; Gas chromatography; Fractal measure; Peak distribution; Peak spacing; Chromatographic quality; Multidimensional separations; Selectivity; Optimization; Statistical overlap theory; Power law distributions; Orthogonality; Orthogonal separations
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The box-counting or capacity dimension algorithm, known from the fractal mathematics literature, is used to measure the dimensionality D of chromatographic separation techniques for any number of dimensions. It is shown that D has limit properties that match Giddings' sample dimensionality s. D values are shown to be sensitive to the uniformity of peak spacing. A number of examples are given where D is calculated for various limits in one- and two-dimensional separations and for heart-cutting separations. The use of D as a quantitative measure of multidimensional orthogonality is suggested as D, due to the scale-free nature, is not dependent on the effective separation area. The connection to statistical peak overlap theory is discussed. (C) 2010 Elsevier B.V. All rights reserved.
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