Extension of statistical overlap theory to poorly resolved separations

A general theory of statistical overlap is developed that enables prediction of the number of observable peaks in separations, even when the peak capacity is much less than the number of single-component peaks requiring separation. The theory is applicable to any separation in which the distribution of intervals between adjacent single-component peaks is governed by homogeneous statistics. The theory shows that the average resolution required to separate single-component peaks varies with saturation, This variation occurs because multicomponent peaks, and not single-component peaks, overlap as separation efficiency decreases. Previously reported equations relating the average number of observable peaks to the average number of single-component peaks are shown to be good even when the former is only 10-15% or so of the latter, as long as this variation is addressed. The theory is verified further by its application to experimental gas chromatograms, This paper consequently represents a significant advance in the ability to describe overlap in separations by statistical means.