Separation of Overlapping Peaks

The second method is to integrate the intensities under the whole arcshaped reflections. The separation of overlapping peaks can be done automatically, once the peak shape has been parameterized from a few well-separated peaks. Occasionally there is a possibility of full overlapping when two or more reflections have the same or almost (within given precision) the same geometrical properties, like dm and Dm values (see equations (8) and (11)). Only then the overlapping reflections cannot be separated. 

Resolution a measure of the separation of two adjacent peaks (A and B), in the chromatogram. Resolution may be assessed by the valley between the peaks hy or by peak width Wb in quantitative analyses a baseline separation should be obtained. The separation of overlapping peaks may be measured as follows ... 

A variety of chromatography data software, which also includes well-known names, still do not use deconvolution. In the example as well as in other studies [5] it has already been shown that the use of deconvolution results is a clear optimization for the separation of overlapped peaks. The area and height and retention time determinations are clearly more accurate. Even at the deconvolution the made error depends on the resolution. The lower the resolution, the larger the error. 

Figure 6 Area separation of overlapping peaks by means of a perpendicular line...

This present chapter will not focus on the statistical theory of overlapping peaks and the deconvolution of complex mixtures, as this is treated in more detail in Chapter 1. It is worth remembering, however, that of all the separation techniques, it is gas chromatography which is generally applied to the analysis of the most complex mixtures that are encountered. Individual columns in gas chromatography can, of course, have extremely high individual peak capacities, for example, over 1000 with a 10 theoretical plates column (3), but even when columns such as these are... 

The infra-red measurements were of two types, normal-film measurements with the sample sandwiched between KBr plates, and tilted-film experiments with the sample sandwiched between 45° prisms of KBr, in each case with layers of Nujol to provide optical matching. Whereas the 1616 cm 1 Raman line occurs in a region well clear of other lines so that it was satisfactory to measure peak intensities, the infra-red spectrum of PET shows many overlapping bands. Accurate assessment of absorption intensities therefore requires the computer separation of the spectrum into a set of overlapping peaks (shown to be Lorentzian in profile) and a linear background. The procedures adopted and the band assignments are discussed in detail by Hutchinson et al. 6). 

The ion exclusion interference can be eliminated for ultraviolet active anions by placing the ultraviolet detector between the separator and suppressor columns (position 1). In addition, the problem of overlapping peaks can sometimes be resolved spectrophotometrically by proper choice of wavelength. 

An obvious criterion by which to judge the extent of separation of chromatographic peaks, especially for the optimization of a quantitative analysis, is the fraction of the peak that is free of overlap from adjacent peaks. The definition for this so-called fractional overlap criterion is illustrated in figure 4.3. An equation to describe the fractional overlap is... 

In terms of organization, the text has two main parts. The first six chapters constitute generic background material applicable to a wide range of separation methods. This part includes the theoretical foundations of separations, which are rooted in transport, flow, and equilibrium phenomena. It incorporates concepts that are broadly relevant to separations diffusion, capillary and packed bed flow, viscous phenomena, Gaussian zone formation, random walk processes, criteria of band broadening and resolution, steady-state zones, the statistics of overlapping peaks, two-dimensional separations, and so on. 

The widths of the amide I bands which are associated with the different structures are large compared to the separation of their peak maxima, which is why the amide I absorption of a complex protein consists of several overlapping bands. Deconvolution and derivative techniques have been employed to detect the individual components (Kaup-pinen et al., 1981 Susi and Byler, 1983 Mantsch et al., 1986). Quantitative estimates for different conformations have been obtained by ulterior curve fitting procedures (Byler... 

In an ideal chromatographic analysis the sample molecules will be completely separated, and detection of components will result in a series of discrete individual peaks corresponding to each type of molecule. However, to minimize the possibility of overlapping peaks, or of peaks composed of more than one substance, it is important to maximize the separation efficiency of the technique, which depends on ... 

Figure 2.5 shows that relative concentration (or for analytical separations chromatographic response) must also be taken into account when considering resolution. In particular it should be noted that the position of the valley between the peaks is shifted to longer times as the relative concentration of the second peak is decreased. When the peak separation is 3.2ct, then = 0.8 and no valley is detected if the ratio of the concentrations of the two peaks is 10 1. When the separation of the peak maxima is equal to 6a, then Rg = 1.5, and the degree of peak overlap is less than 1%. 

The AB part of the ABX spectrum is made up of two overlapping quartets (Figure A4-3). The doublet separation between the first and second and between the third and fourth peaks in both quartets gives four independent measurements of 7ab- (No absolute or relative information about the sign is obtained.) The separation of alternate peaks (first and third or second and fourth) provides redundant determinations of D+ and D. The separation of the midpoints of the two quartets gives an additional measurement of 2 (Ax Ax) of these spacings are illustrated in the figure. 

A reproducible base-line drawing procedure and a kind of peak deconvolution procedure is necessary to determine the area of this rubber loss maximum and that of the original PP relaxation maxima. A computerised deconvolution program for the separation of overlapping DMA loss maxima was described by... 

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