title: The dimensionality of chromatographic separations.
abstract: 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.
authors.affiliation: Theoretical Separation Science Laboratory, The Dow Chemical Company, 727 Norristown Road, Box 0904, Spring House, PA 19477-0904, USA. MSchure@Dow.com
authors.forename: Mark R
authors.initials: MR
authors.lastname: Schure
mesh_terms: D000438:Alcohols / Q000737:chemistry; D000465:Algorithms; D002849:Chromatography, Gas / Q000379:methods*; D002853:Chromatography, Liquid / Q000379:methods*; D016018:Least-Squares Analysis; D008956:Models, Chemical; D010446:Peptide Fragments / Q000737:chemistry
chemical_list: D000438:Alcohols; D010446:Peptide Fragments