Overlapping chromatograms

The program Ma in ALS, m forms the backbone of the ALS algorithm. It reads in the data set Data Chrom2a (p.251) which simulates an overlapping chromatogram of three components. It is the data set we used previously in Chapter 5.3.3 to demonstrate the concepts of iterative and explicit computation of the concentration profiles, based on the window information from EFA. 

Chromatogram D is not acceptable, because peaks 4 and 5 overlap. Chromatogram E is terrible because peaks 1 and 3 overlap and peaks 4, 5, and 6 overlap. But (hurrah ) chromatogram F is what we have been looking for All peaks are separated and the first... 

O Spreadsheet Summary Chapter 15 of Applications of Microsoft si Excel in Analytical Chemistry begins with an exercise treating the resolution of overlapped Gaussian peaks. The overlapped chromatogram, the response, is modeled as the sum of Gaussian curves. Initial estimates are made for the model parameters. Excel calculates the residuals, the difference between the response and the model, and the sum of the squares of the residuals. Excel s Solver is then used to minimize the sum of the squares of the residuals, while displaying the results of each iteration. 

Fig. 19. A Overlapped chromatograms of four PI obtained at three different temperatures near the critical condition of PI. Column three RP columns (Nucleosil C18 100 A, 300 A, and 500 A 250x4.6 mm), eluent 1,4-dioxane. Amplitudes of the elution peaks are rescaled for visual aid. B Chromatograms of the PS precursor (M =12.0 kg/mol) and two PS-I /ocfc-PI with fixed PS block length at 12.0 kg/mol (M (PI)=6.0 and 21.4 kg/mol for SI-1 and SI-2, respectively) at the same temperatures as in A. Reproduced from [47] with permission...

The general elution problem in chromatography. Improving the resolution of the overlapping bands in chromatogram (a) results in a longer analysis time for chromatogram (b). 

Further, peak overlap results in nonlinear detector response vs concentration. Therefore, some other detection method must be used in conjunction with either of these types of detection. Nevertheless, as can be seen from Figure Ilf, chiroptical detection can be advantageous if there is considerable overlap of the two peaks. In this case, chiroptical detection may reveal that the lea ding and tailing edges of the peak are enantiomerically enriched which may not be apparent from the chromatogram obtained with nonchiroptical detection (Fig. He). 

Each of the four columns was packed with CPG00120C d = 13.0 nm). The column dimensions and experimental conditions are listed in Table 23.1. The flow rates (solution and solvent) were set to be proportional to the cross section of the column, whenever possible. The number of drops collected in each test tube was almost proportional to the cross section, especially for the initial fractions that might show a shift in M. Figure 23.9 shows chromatograms for some the fractions separated using 2.1-, 3.9-, and 7.8-mm i.d. columns. The result with the 7.8-mm i.d. column is a reproduction of Fig. 23.2 (3). Chromatograms of the fractions obtained from the 1.0-mm i.d. column overlapped with the chromatogram of the injected polymer sample (not shown). 

Figure 14.19 Typical GC chromatogram of the separated di-aromatics fraction of a middle distillate sample Peak identification is as follows 1, naphthalene 2, 2-methylnaphthalene 3, 1-methylnaphthalene 4, biphenyl 5, C2-naphthalenes 6, C3-naphthalenes 7, C4-naph-thalenes 8, C5+-naphthalenes 9, benzothiophene 10, methylbenzothiophenes 11, C2-ben-zotliiopIrenes. Note the clean baseline between naphthalene and the methylnaphthalenes, which means that no overlap with the previous (mono-aromatics) fraction has occuned.

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). 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

Nelson, T. J., Deconvolution method for accurate determination of overlapping peak areas in chromatograms, /. Chromatogr., 587, 129, 1991. 

Certainly two-dimensional techniques have far greater peak capacity than onedimensional techniques. However, the two-dimensional techniques don t utilize the separation space as efficiently as one-dimensional techniques do. These theories and simulations utilized circles as the basis function for a two-dimensional zone. This was later relaxed to an elliptical zone shape for a more realistic zone shape (Davis, 2005) with better understanding of the surrounding boundary effects. In addition, Oros and Davis (1992) showed how to use the two-dimensional statistical theory of spot overlap to estimate the number of component zones in a complex two-dimensional chromatogram. 

Davis, J.M., Giddings, J.C. (1983). Statistical theory of component overlap in multicomponent chromatograms. Anal. Chem. 55, 418-424. 

Consequently, several hidden quantities can be estimated on the basis of the SMO approach. The procedure based on Equation 4.13 can be simply extended even to 2D separations as described in Fig. 4.7. In practice, the 2D pattern, in terms of spot positions and abundances, is divided into several strips. Each strip is transformed into a ID line chromatogram and the procedure described in Fig. 4.7 is then applied. Equation 4.13 is employed to calculate the m value of each strip from which the total m value is obtained. Applications to this procedure will be reported in Section 4.5. At this point, the reader s attention is drawn to the fact that the procedure of transforming 2D strips into ID chromatograms (see Fig. 4.7) once more corresponds to the overlapping mechanisms described in Fig. 4.2 and has been evocated in comparing Fig. 4.4 with Fig. 4.3. In this way, if random structures (e.g., such as those marked in Fig. 4.1b) are present, their memory is lost and the 2D pattern is reduced to a Poissonian ID one. Therefore, the number of SCs can be correctly estimated, even if the 2D pattern was not Poissonian. 

Equations 4.22 1.24 are the 2D equivalents of Equations 4.17 1.20. The comparison of the two sets of equations shows a surprising consequence. If the peak capacities of the 1D and 2D separation systems were identical, the 2D separation would lead to more severe overlap. In order to have the same number of components isolated as singlets with a 1D and a 2D separation system, the peak capacity of the 2D system ( 2d) should be double of that of the ID system (nw). Ideally, in an orthogonal system 112D = n j D, but part of the gain in peak capacity is lost due to the increased probability of peak overlap provided the 2D chromatogram is disordered. 

---