Statistical study of peak overlapping in multicomponent chromatograms: importance of the retention pattern

A general method is reported for evaluating the statistical degree of overlapping (SDO) in a multicomponent chromatogram, whose retention pattern is known and described by the frequency function of interdistances between subsequent single component peaks (interdistance model, IM). The content of SDO is the expected numbers of singlet, doublet, triplet, etc., peaks, as a function of the number of components, the separation performance and the IM. The proposed method is exploited in practice for three cases of IMs: gamma, normal and uniform, which are known to represent a wide variety of cases. Two different approaches are presented and discussed: analytical expression and simulation computation, according to whether the IM can be analytically integrated or not. The advantages and differences of the two approaches are considered, even in the case of negative interdistances (normal case). A real case of chromatographic separation of a multicomponent mixture, composed of polychlorinated biphenyls, is also exploited. The separation requirements for obtaining a given separation goal are investigated and the relevance of the IM type in determining the overlapping pattern is proved. The basic underlying hypothesis of the present treatment is the stationarity of the component distribution along the chromatogram. Means to check this hypothesis are also reported.