Resolution contour plots

Figure 7.22 shows the H NMR chromatogram (contour plot) of the separation of a 10% phthalate mixture in CH2CI2. The spectrum is almost free from interferences the NMR resolution is excellent, and it is possible to identify all plasticisers even at concentrations as low as 2%, which corresponds to 60 xg per component. In contrast, in on-line HPLC- H NMR separation the regions between 3.9-3.3 and 1.9-1.7 ppm are completely obscured by solvent signals. 

Fig. 2.54 presents a two-dimensional carbon-proton shift correlation of D-lactose after mutarotational equilibration (40% a-, 60% / -D-lactose in deuterium oxide), demonstrating the good resolution of overlapping proton resonances between 3.6 and 4 ppm by means of the larger frequency dispersion of carbon-13 shifts in the second dimension. The assignment known for one nucleus - carbon-13 in this case - can be used to analyze the crowded resonances of the other nucleus. This is the significance of the two-dimensional CH shift correlation, in addition to the identification of CH bonds. For practical evaluation, the contour plot shown in Fig. 2.54(b) proves to be more useful than the stacked representation (Fig. 2.54(a)). In the case of D-lactose, selective proton decoupling between 3.6 and 4 ppm would not afford results of similiar quality. 

Figure 5.2 (a) Pseudo-isometric three-dimensional response and (b) iso-response contour plot for a two-parameter optimization problem. Parameters (in triangular representation) quaternary mobile phase composition. Criterion normalized resolution product (see section 4.3.2). O, is the location of the optimum. For further details see section 5.5.2. Figure taken from ref. [502]. Reprinted with permission. 

The simulated double-quantum coherence 2D INADEQUATE spectrum of 2-chlorobutane is shown in Figure 13.18. The normal 13C spectrum is plotted along the top. Only the cross peaks appear in the contour plot, and each cross peak appears as a doublet (a pair of dots) at this level of resolution. The separation between these dots, about 35 Hz in this case, is /Cc- Each pair of correlated (by one-bond coupling) cross peaks is indicated by a separate dotted horizontal line, with the midpoint of each line on the diagonal. The F axis is the double-quantum frequency, essentially the sum of the 8v values of the two coupled nuclei. 

Fig. 6.20. A simple response surface describing resolution as a function of two variables.. i and. v > (adapted from 127)) and the corresponding i.soresponsc contour plot.

As stated earlier the model should be obtained for responses such as k (or log< ). These are also the responses that should be predicted from the models and only then responses such as or the global responses of Section 6.2 should be obtained. The optimum is typically derived by first obtaining isorespon.se contour plots from the response surfaces such as those of Fig. 6.20 or directly on the response surface and then visually deciding where the optimum is to be found. For the measured responses, the surfaces are often relatively simple (Fig. 6.21), but for the global responses they can be very complex (Fig. 6.22). If a threshold criterion is applied, then overlapping resolution maps can be obtained similar to those of Fig. 6.4. 

Homonuclear contour plots are symmetric with respect to both spectral widths, and data point resolutions are almost always identical. Linear prediction can help greatly in making DRi equal to DR2 by keeping the data accumulation time within acceptable limits. 

The elution order of the enantiomers was the same for all experiments. Thus, a modeling of the resolution is meaningful. The 2D contour plot and the 3D response surface plot for this response Rs are shown in Figure 2.18. 

Figure 5.22. Contour plots of (a) the phase-twist lineshape, (b) the same following magnitude calculation, and (c) the same following resolution enhancement with an unshifted sine-bell window and magnitude calculation.

Fig. 20.13. Contour plot from the HPLC/FT-ICR-MS coupling of a pyrrole amide compound collection (R2 = C6Hs, R3 = H) This method allows to prove the identity of isomers. The isotope resolution of the molecule ion peaks is recognizable.

Finally, a comparison of the experimental and theoretical velocity contour plots for the reaction D+(HD, H)D2 is given in Fig. 7. It will be noted that exact detailed agreement of such plots can not be expected because of instrumental beam spread and energy resolution. To within such limitations the agreement in Fig. 7 is good. It will be noted that the large barycentric... 

Early visualization in chemical three-way analysis was used in curve resolution methods, and especially GRAM. The extraction and visualization of unknown spectra (curve resolution) was considered very important. Tucker and PARAFAC analysis were used much in the exploratory sense and PARAFAC also for curve resolution. The first publication of Ho et al. [1978] has figures of eigenvalues expressed as a function of a parameter /S, see Figure 8.1. The second publication of Ho et al. [1980] also contains contour plots for the excitation-emission spectra of polyaromatic compounds (see Figures 8.2 and 8.3). They also show excitation and emission spectra as line plots (see Figures 8.4 and 8.5). The plots are only used to show the raw data and show no results after analysis. An early publication of de Ligny et al. [1984] has all the results shown as numbers in tables. 

Fig. 19 PVP film patterned as TU Dresden logo by electron beam lithography. The contour plot demonstrates the influence of the proximity effect on the spatial resolution. Reprinted from Burkert et al. (2007b), p. 537. Copyright Wiley. Reproduced with permission...

Figure 5.16 Diagrammatic representation of presentation of data from FT 3D NMR correlation experiments. In this representation, frequency domain (spectral) information, Jnmr (fi, p2, F ) is plotted as a stack or cube of 2D NMR Jnmr(F i, fa) contour plots, each plot resolved at a different value of fa- Frequency resolution is done to aid resolution of individual resonance signals in order to achieve unique and unambiguous assignment of resonance signals to resonating nuclei.

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