Peak cluster

Similar experiments exist to correlate the resonances of different types of nucleus, e.g. C with H, provided that some suitable couplings are present, such as It is necessary to apply pulses at both the relevant frequencies and it is also desirable to be able to detect either nucleus, to resolve different peak clusters. Detection tlirough the nucleus with the higher frequency is usually called reverse-mode detection and generally gives better sensitivity. The spectrum will have the two different chemical shift scales along its axes... 

In pharmaceutical analysis the detection of impurities under a chromatographic peak is a major issue. An important step forward in the assessment of peak purity was the introduction of hyphenated techniques. When selecting a method to perform a purity check, one has the choice between a global method which considers a whole peak cluster (from the start to the end of the peak), and evolutionary methods, which consider a window of the peak cluster, which is... 

Although the decomposition of a data table yields the elution profiles of the individual compounds, a calibration step is still required to transform peak areas into concentrations. Essentially we can follow two approaches. The first one is to start with a decomposition of the peak cluster by one of the techniques described before, followed by the integration of the peak of the analyte. By comparing the peak area with those obtained for a number of standards we obtain the amount. One should realize that the decomposition step is necessary because the interfering compound is unknown. The second approach is to directly calibrate the method by RAFA, RBL or GRAFA or to decompose the three-way table by Parafac. A serious problem with these methods is that the data sets measured for the sample and for the standard solution should be perfectly synchronized. 

K. The gain in resolution is particularly clearly visible for the Q49/Q62 peak cluster. 

A typical application can be found in chromatography. A group of components elute in a strongly overlapping peak cluster. We suspect that a particular chemical, for which we know the spectrum, might be in the unknown mixture, but due to overlap, its spectrum does not appear pure in the matrix Y. 

The racemate of 1,3,2-benzodithiazole 1-oxide 42 was separated by supercritical fluid chromatography on the (A j )-Whelk-( )l column with supercritical carbon dioxide containing 20% methanol as a mobile phase. Peak areas of enantiomers prior to and after the separation, used for the calculation of the enantiomerization barrier, were detected by computer-assisted peak deconvolution of peak clusters registered on chromatograms using computer software <2002CH1334>. 

The chromatogram was sampled every 1 s, and a 40 s portion of each chromatogram was selected to contain the peak cluster, and aligned to the major peak maximum. Fifty-one wavelengths between 230 and 350 nm (sampled at 2.4 nm intervals) were recorded. Hence a dataset of dimensions 14 X 40 X 51 was obtained, the aim being to use multimode calibration to determine the concentration of the minor component. Further experimental details are reported elsewhere.4... 

Eqn.(5.27) shows that the total absorption is the result of the contributions of a series of factors which depend either exclusively on the wavelength (a. factors = spectra) or on the time (Cj factors = elution profiles). The individual factors may be obtained with PCA, but an unambiguous solution for the mathematical problem may only be obtained in a small part of the chromatogram ( peak cluster ), in which three or fewer components contribute to the absorption [592]. 

Figure 5.38 An example of the application of principal component analysis to obtain the individual spectra and elution profiles of ill-resolved proteins, (a) Illustration of the chromatogram obtained at a low wavelength (e.g. 200 nm) (b), (c) and (d) Spectra of the three pure components identified in the peak cluster by PCA (drawn lines) and true pure component spectra (dashed lines) (e) pure component elution profiles from PCA (drawn lines) and estimated pure component profiles (dashed lines). Figure adapted from ref. [592]. Reprinted with permission.

This method can be extended to fairly complex peak clusters, as presented in Figure 6.26 for die data in Table 6.2. Ignoring die noise at die beginning, it is fairly clear diat there are three components in die data. Note diat die central component eluting approximately between times 10 and 15 does not have a true composition 1 region because die correlation coefficient only reaches approximately 0.9, whereas the odier two compounds have well established selective areas. It is possible to determine the purest point for each component in die mixture successively by extending the approach illustrated above. 

Whereas some datasets can be very complicated, it is normal to divide die data into small regions where diere are signals from only a few components. Even in die spectroscopy of mixtures, in many cases such as MIR or NMR it is normally easy to find regions of the spectra where only two or three compounds at the most absorb, so this process of finding windows rather dian analysing an entire dataset in one go is normal. Hence we will limit die discussion to three peak clusters in this section. Naturally the methods in Section 6.3 would usually first be applied to die entire dataset to identify diese regions. We will illustrate the discussion below primarily in the context of coupled chromatography. 

The table on page 402 represents the intensity of 49 masses in LC-MS of a peak cluster recorded at 25 points in time. The aim of this exercise is to look at variable selection and the influence on PC plots. The data have been transposed to fit on a page, with the first column representing the mass numbers. Some preprocessing has already been performed with the original masses reduced slightly and the ion current at each mass set to a minimum of 0. You will probably wish to transpose the matrix so that the columns represent different masses. 

The amplitudes of the individual components and constituent peaks create a departure from theoretical predictions in these highly saturated simulations when the peak number is visually interpreted. Consider a peak cluster composed of at least two overlapping components. The coordinates of the centers of gravity of the first and last components in the cluster are, respectively, Xi and X2. Therefore, the beginning of the first component in the cluster occurs along coordinate x at xj-Xq/2, and the end of the final component in the cluster has coordinate X2+Xq/2. The peak width is then postulated to be X2 Xj+Xq in our model. 

Figure 8.17 Peak cluster analysis by valley to valley baseline correction.

For overlapping peaks the data matrix contains linear combinations of the pure spectra of the overlapping components in its rows, and combinations of the pure elution profiles in its columns. Multivariate analysis of the data matrix may allow extraction of useful information from either the rows or columns of the matrix, or an edited form of the data matrix [107,116-118]. Factor analysis approaches or partial least-squares analysis can provide information on whether a given spectrum (known compound) or several known compounds are present in a peak. Principal component analysis and factor analysis can be used to estimate the maximum number of probable (unknown) components in a peak cluster. Deconvolution or iterative target factor analysis can then be used to estimate the relative concentration of each component with known spectra in a peak cluster. 

The molecular ion cluster and the peak cluster caused by loss of one chlorine atom from the molecular ion (M-Cl) were masked in the sample spectrum by the spectra of interfering components. 

The method is subject to some errors if peaks appear frequently (for instance, as peak clusters) in areas far from the diagonal of the separation space, and does not take into account the operation in the programmed temperature mode. 

Fig. 8. GC-MS key ion plots for the thio-PAHs in the pyrolyzed samples 2-7. Sum of m/z 184, 234, 284 temperatures are indicated 1, dibenzothiophene 2, benz[T ]naphtho[l,2-d]thiophene 3, benzo[b]-naphtho[2,l-d]thiophene 4, benzo[b]naphtho[2,3-d]thiophene peak cluster at scans 1300-1420, dinaphthothiophenes.

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