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Anal. Chem. 1985, 57, 2178-2182
Statistical Method for Estimation of Number of Components from Single Complex Chromatograms: Application to Experimental Chromatograms Joe M. Davis and J. Calvin Giddings* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
A procedure developed In a prevlous paper for deducing statlsticai parameters from single complex chromatograms has been Implemented In this paper. The procedure, based on our statistical model of overlap (SMO), was applied to three experimental chromatograms havlng considerable overlap. The number of components present In selected regions of these chromatograms was estlmated. Calculations have also yleided values for the stand-alone probability, a key parameter expressing the Ilkellhoodthat any glven component Is adequately isolated from Its neighbors. Despite the hlgh resolution exhiblted by the chromatograms, the calculations indicate that there are roughly 50% to 100% more components than there are chromatographic maxima. The standalone probabliltles are found to be discouragingly low, ranglng from 0.04 to 0.19 for the reglons investigated.
In a previous paper ( I ) , a procedure for the evaluation of the number of detectable components from a single complex chromatogram was developed using the statistical model of overlap (SMO). This procedure was then tested by using various forms of computer-generated chromatograms. In this paper, we apply the procedure to estimate the number of components (expressed as single-component peaks or SCPs) in portions of three experimental complex chromatograms. These chromatograms were given to us by two research groups working in high-resolution chromatography and were generated in the course of their research from mixtures containing principally neutral polynuclear aromatic hydrocarbons, oxygenated and nitrogenated polynuclear aromatic compounds, and aliphatic hydrocarbons. The apparent applicability of the model to significant portions of each chromatogram strengthens the hypothesis that the distribution of components (SCPs) and overlap in most complex chromatograms are largely statistical. The acquisition of statistical parameters for complex chromatograms has other uses beyond estimating component numbers. For example, we can calculate the stand-alone probability, which is the probability that any given component will be resolved from other components. If this probability is too low, we can determine the increase in column efficiency needed to reach acceptable levels. The basis of this approach is more fully discussed in our original work on the statistical basis of chromatography (2). We shall use the symbols and conventions adopted in the first paper ( I ) . Any "sets" described herein refer to specific examples of computer-generated chromatograms and data derived from them, as described in Table I of the first paper (1). EXPERIMENTAL DATA Chromatogram I was provided by Milton Lee and COworkers of Brigham Young University (3). The chromatogram was produced from solubles in a river sediment which was
air-dried and extracted with a methylene chloride/benzenelethanol azeotrope. The extract was concentrated and fractionated on a classical alumina liquid chromatography column which was first eluted with n-hexane and then with benzene to obtain the neutral polynuclear aromatic hydrocarbons (PAHs). The concentrated benzene fraction was injected in a splitless mode onto a 20 m x 0.3 mm i.d. capillary column coated with a 0.25-pm film of SE-54 (cross-linkedwith azo-t-butane) and incorporated into an H P 5880A gas chromatograph equipped with a flame ionization detector (FID). Chromatographic conditions were as follows: injector port, 265 "C; FID temperature, 285 "C; carrier gas and linear velocity, hydrogen at -90 cm/s; temperature sequence, isothermal operation at 40 "C for 2 min followed by a linear temperature ramp at 4 "C/min to 265 "C and then by isothermal operation at 265 "C for 10 min. Chromatograms I1 and I11 were provided by Francis W. Karasek and co-workers of the University of Waterloo ( 4 , 5 ) . Both chromatograms were derived from fly ash which was grab-sampled from the electrostatic precipitator of a municipal incinerator. The fly ash was extracted with benzene and the extract was concentrated by rotary evaporation and evaporation under purified nitrogen. The extract was injected onto a 250 X 9.4 mm semipreparative HPLC column packed with 10-pm Spherisorb silica (Terochem, Toronto, Canada) and incorporated into a Spectra-Physics SP-8000 liquid chromatograph equipped with an SP-8400 UV-vis detector operated at 254 nm. Fractions containing principally aliphatic hydrocarbons, nonpolar PAHs, and polar polynuclear aromatic compounds (PACs) were eluted with n-hexane, an n-hexane/methylene chloride gradient, and methylene chloride, respectively. The components in the final and first fractions were further separated by gas chromatography to produce chromatograms I1 and 111, respectively. The extracts were concentrated and injected onto a 30 m x 0.32 mm i.d. fused silica capillary coated with a 0.25-pm film of DB-5 (J and W Scientific, Inc., Ranch Cordova, CA) and incorporated into an HP-5880A gas chromatograph equipped with an FID and a cool on-column injector. Chromatographic conditions were as follows: injector port,
