Quantitative theory of the statistical degree of peak overlapping in chromatography

Abstract

The quantitative theory of the statistical degree of peak overlapping in chromatography is reviewed. Starting from Davis-Giddings' statistical model of overlapping (SMO), the so called pulse-point statistical model of overlapping able to take into account the quantitative aspect of peaks superimposition is described. A 'theoretical chromatogram model' is developed in terms of an interdistance model (IM) to describe the single component (SC) positions and an amplitude model (AM) to characterize the SC relative abundance (SC area/heights statistical distribution). A general solution in Fourier domain is derived, from which a series of useful relationships to characterize multicomponent chromatograms in terms of their statistical attributes are derived. How this model can be used to interpret and to characterize real chromatograms (i.e. to derive all the information 'hidden' therein) is discussed. The starting point is the Chromatographic report, where the peak area/heights together with the retention times are listed. Very simple procedures are described able to obtain the SC number (SC number statistical estimate) and the SC area/heights distribution, starting from the observable peak area/heights mean value. The entropy function and its meaning in describing complex mixtures is discussed. Applications of the described procedures on real samples as well as simulation studies are presented in order to show the validity of the present approach.