Peak overlapping

A spcctruphoLornetric problem in simultaneous analysis (Ewing, 198.2) is taken from the original research of Weissler (194.2), who reaeted hydrogen peroxide with Mo, Ti, and V ions in the same solution to produce corn pounds that absorb light strongly in overlapping peaks with absorbances at. 320. 410. and 460 nrn, respectively as sliown in (Fig, 2-3),... 

The + 1 rule should be amended to read When a proton H is coupled to Hj etc and Jac Jad the original signal for H is split into n + peaks by n protons each of these lines is further split into n + peaks by n pro tons and each of these into n + lines by n Hj protons and so on Bear in mind that because of overlapping peaks the number of lines actually observed can be less than that expected on the basis of the splitting rule... 

It is equivalent, when an ftk spectrometer is used, to re-apodization of the data. Curve fitting is a method of modeling a real absorption band on the assumption that it consists of a series of overlapped peaks having a specific lineshape. Typically the user specifies the number of peaks to attempt to resolve and the type of lineshape. The program then varies the positions, sizes, and widths of the peaks to minimize the difference between the model and the spectmm. The largest difficulty is in knowing the correct number of peaks to resolve. Derivative spectra are often useful in determining the correct number (18,53,54). 

Spectroscopy. Infrared spectroscopy (48) permits stmctural definition, eg, it resolves the 2,2 - from the 2,4 -methylene units in novolak resins. However, the broad bands and severely overlapping peaks present problems. For uncured resins, nmr rather than ir spectroscopy has become the technique of choice for microstmctural information. However, Fourier transform infrared (ftir) gives useful information on curing phenoHcs (49). Nevertheless, ir spectroscopy continues to be used as one of the detectors in the analysis of phenoHcs by gpc. 

A method of resolution that makes a very few a priori assumptions is based on principal components analysis. The various forms of this approach are based on the self-modeling curve resolution developed in 1971 (55). The method requites a data matrix comprised of spectroscopic scans obtained from a two-component system in which the concentrations of the components are varying over the sample set. Such a data matrix could be obtained, for example, from a chromatographic analysis where spectroscopic scans are obtained at several points in time as an overlapped peak elutes from the column. 

ANALYSIS OF OVERLAPPING PEAK-SHAPED ANALYTICAL SIGNALS BY THE TRIANGLE HEIGHT... 

The height of the peak and area of the peak ai e traditionally used for calibration techniques in analytical chemistry. Peak maximum can also be evaluated by the height of a triangle formed by the tangents at the inflection points and the asymptotes to the peak branches. We propose to apply the tangent method for the maximum estimation of the overlapped peaks. 

To sum up, in some instances the proposed tangent method and procedure of systematic error correction allows excluding the necessity of mathematical or chemical resolution of overlapped peak-shaped analytical signals. 

Most EDS systems are controlled by minicomputers or microcomputers and are easy to use for the basic operations of spectrum collection and peak identification, even for the computer illiterate. However, the use of advanced analysis techniques, including deconvolution of overlapped peaks, background subtraction, and quantitative analysis will require some extra training, which usually is provided at installation or available at special schools. 

The minimum detection limit, MDL, of an isolated peak on a uniform background is proportional to the square root of the FWHM. So a 20% reduction in spectrometer resolution will produce about a 10% improvement in MDL. If there is peak overlap, however, then it can be shown that a 20% improvement in resolution can reduce the interference between overlapping peaks by a factor of 3, which gives about a 50% improvement in MDL. 

The spectrum of Figure lb is a fingerprint of the presence of a CO molecule, since it is different in detail from that of any other molecule. UPS can therefore be used to identify molecules, either in the gas phase or present at surfaces, provided a data bank of molecular spectra is available, and provided that the spectral features are sufficiently well resolved to distinguish between molecules. By now the gas phase spectra of most molecules have been recorded and can be found in the literature. Since one is using a pattern of peaks spread over only a few eV for identification purposes, mixtures of molecules present will produce overlapping patterns. How well mixtures can be analyzed depends, obviously, on how well overlapping peaks can be resolved. For molecules with well-resolved fine structure (vibrational) in the spectra (see Figure lb), this can be done much more successfiilly than for the broad. 

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... 

Figure 4.8 The GC X GC experiment can be considered to be a series of fast second clno-matograms conducted about five times faster than the widths of the peaks on the first dimension. The ID elution time is the total chromatograpliic run time, wliile the 2D time is the modulation period (e.g. 4-5 s). This figure shows two overlapping peaks A and B, with the zones of each peak collected together. When these slices are pulsed to the second column, they are resolved. Here, we show peak B eluting later on column 1, but earlier on column 2, with the 2D peak maxima nacing out a shape essentially the same as the original peak on 1D.

In the case of citrus essential oils, LC pre-fractionation can be used to obtain more homogeneous chemical classes of compounds for analysis by GC without any problems of overlapping peaks. 

The measurement of individual peak areas can be difficult when the chromatogram contains overlapping peaks. However, this problem can be often overcome by the use of derivative facilities which give first- or second-derivative chromatograms (see Section 17.12, for the analogous derivative procedures used in spectroanalytical methods). 

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). 

Foley, J. R, Systematic Errors in the Measurement of Peak Area and Peak Height for Overlapping Peaks, Journal of Chromatography 384, 1987, 301-313. 

An increasing intensity of the diffraction peaks of hematite is observed when comparing the dried and calcined catalyst as shown in Fig. 2(a), indicating that hematite forms at M er temperatures. No obvious diffraction peaks to lithium such as lithium iron oxide (LiFcsOg) could probably be ascribed to the small fraction of lithium or overlapped peaks betwem hematite and lithium iron oxide. The diffraction peak intensity of magnetite in tested catalysts increases significantly. 

The accuracy and precision of carotenoid quantification by HPLC depend on the standard purity and measurement of the peak areas thus quantification of overlapping peaks can cause high variation of peak areas. In addition, preparation and dilution of standard and sample solutions are among the main causes of error in quantitative analysis. For example, the absorbance levels at of lutein in concentrations up to 10 mM have a linear relationship between concentration and absorbance in hexane and MeOH on the other hand, the absorbance of P-carotene in hexane increased linearly with increasing concentration, whereas in MeOH, its absorbance increased linearly up to 5 mM but non-linearly at increasingly higher concentrations. In other words, when a stock solution of carotenoids is prepared, care should be taken to ensure that the compounds are fuUy soluble at the desired concentrations in a particular solvent. 

NMR with the C3 proton used as an internal standard. Determination of hydrogen content at C4 was not possible on the 200 MHz instrument due to overlapping peaks. 

The Rietveld analysis is mainly used for refining the structures of crystalline phases and to perform quantitative analysis of multiphase samples. The quantitative analysis is possible since the Rietveld method can easily deal with diffraction patterns with strongly overlapped peaks, while preferred orientation can be quantitatively treated. 

It is important to note that expression (23) can be applied to the crystalline phase intensities only if we include, in the first integral, its own smooth diffuse background and not just the intensity belonging to the crystalline peaks. In fact, a pure crystalline sample also has a smooth background due to the incoherent inelastic scattering (i.e. Compton scattering), the TDS, disorder scattering and, very often, unresolved tails of overlapped peaks. 

Let us illustrate the method with a LC-UV-visible data set of three overlapping peaks (Fig. 34.10). The TFA results obtained with six candidate spectra, including the pure spectra are given in Fig. 34.11. The assignment of the right spectra by an evaluation of the correlation coefficients between input and output target is obvious. 

Fig. 40.33. Restoration of two overlapping peaks by deconvolution. Dashed line measured data. Solid line after restoration. Dotted line difference between true and restored signals.

J. Chen and S.C. Rutan, Identification and quantification of overlapped peaks in liquid chromatography with UV diode array detection using an adaptive Kalman filter. Anal. Chim. Acta, 335(1996) 1-10. 

MS detection does not necessarily require as highly resolved GC separations as in the case of selective detectors because the likelihood of an overlapping mass spectral peak among pesticides with the same retention time is less than the likelihood of an overlapping peak from the same element. Unfortunately, this advantage cannot always be optimized because SIM and current gas chromatography/tandem mass spectrometry (GC/MS/MS) methods, it is difficult to devise sequential SIM or MS/MS retention time windows to achieve fast GC separations for approximately > 50 analytes in a single method. 

Rather than the separation function, resolution between individual peak pairs is used in most automated optimization procedures because it is easier to calculate, although non-Gaussian pe2dcs and overlapping peaks can present problems due to the difficulty of estimating peak widths. A simple objective function would be to consider only the separation between the worst separated peak pair, ignoring all others. If a set of... 

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