Evaluation of spectra

Present data illustrate the technique for an in situ determination of surface areas. Related methods had been applied primarily to the study of site distributions in clay minerals, particularly by Russian workers (66), and they were used by Bergmann and O Konski in a detailed investigation of the methylene blue-montmorillonite system (3). In fact, changes in electronic spectra arising from surface interactions received sufficient attention in the past to warrant their review by A. Terenin (65). Most of these investigations involved transmittance spectra but new techniques in reflection spectrophotometry and applications of the Kubelka-Munk relation have facilitated the quantitative evaluation of spectra in highly turbid media (35, 69, 77). Thus, in agreement with the work of Kortiim on powders and anhydrous dispersions (31, 32, 33), our results demonstrate the applicability of the Kubelka-Munk function... 

Part of the incident beam is reflected at each optical boundary (air-sample boundary in the case of a free-standing thin sample or air-window/window-sample boundaries in the case of a liquid cell), even at normal incidence. Of particular importance is that part of the radiation which undergoes multiple reflections at the two opposite surfaces of a plane-parallel sample. The double-reflected beam can interfere with the original beam, which results in sinusoidal type periodical features in the background of the spectrum (Fig. 6.5). Such features usually cause difficulties during evaluation of spectra. On the other hand, the interference provides access to the effective thickness of the sample as well as the optical quality of its boundaries (deviations from plane-parallelity cause reduced amplitudes of the interference fringes). The effective sample thickness can be calculated according to ... 

The evaluation of spectra will be discussed separately for qualitative and quantitative analysis. Particular emphasis will be laid (i) on state-of-the-art methods for searching spectra in spectral libraries or searching for spectroscopic information in data banks and on (ii) procedures for multivariate data analysis. 

Two of the basic operations mentioned in Tab. 22.1 are of particular importance for the evaluation of spectra, centering and standardization. They will be considered first. 

Contemporary spectrometers are able to produce huge amounts of data within a very short time. This development continues due to the introduction of array detectors for spectral imaging. The utilization of as much as possible of the enclosed spectral information can only be achieved by chemometric procedures for data analysis. The most commonly used procedures for evaluation of spectra are systematically arranged in Fig. 22.2 with the main emphasis on application, i.e. the variety of procedures was divided into methods for qualitative and quantitative analysis. Another distinctive feature refers to the mathematical algorithms on which the procedures are based. The dominance of multivariate over univariate methods is clearly discernible from Fig. 22.2. 

In the case of quantitative analysis, the amount of, or the exact relation between, the constituents of a compound or a mixture have to be estabhshed. The direct relation between the properties of a specimen and the concentration of its constituents could also be the aim of the quantitative investigation. In the latter case so-called calibration models have to be established, the corresponding model parameters have to be estimated, and they have to be confirmed by statistical methods. Calibration models estabhshed this way may then be used to determine, on a statistically verified basis, the concentration of constituents of an analyte within the calibrated range. AU multivariate methods for quantitative analysis mentioned in Fig. 22.2 are employed for the evaluation of spectra. 

With respect to the applied mathematical algorithms, quantitative evaluation of spectra can be subdivided into univariate and multivariate methods (cf. Fig. 22.2). The independent variables x and respectively, are denoted regressors, whereas the dependent variables y and y , respectively, are denoted regressands. The basic sequence of a quantitative evaluation is always the same ... 

Chapters 10 and 11 form the most exciting and important part of this book and deal with all aspects of manipulation and evaluation of spectra. 

OPUS QUANT is a package for the quantitative evaluation of spectra. 

It is beyond the scope of the present work to discuss the different options for the analytical methods. We only present one example here, showing what can be achieved with modern instrumental analysis. Fig. 4.15 shows a NMR-spectrum of a formaldehyde + water + methanol mixture taken with an online technique with a 400 MHz NMR spectrometer. Signals from a large number of different species can be resolved. Obviously, the band assignment is non-trivial for such complex mixtures and special techniques, such as two dimensional NMR, have to be applied. One of the most attractive features of NMR spectroscopy compared with other spectroscopic methods is that the quantitative evaluation of spectra such as that shown in Fig. 4.15 can be achieved without calibration, as the area below the peaks is directly proportional to the number of the different nudei in the solution if the NMR experiment is carried out properly. 

The correlations presented here cannot of course be considered quantitative since the reaction processes are quite different. Reactions in solution depend on such factors as solvation and equilibria, whereas mass spectral reactions are strictly unimolecular decompositions of activated molecular ions. However, as a qualitative approach, these comparisons can be useful in the evaluation of spectra of related compounds. Differences in the intensities of various fragment peaks have been used to distinguish between numerous sets of isomeric compounds. 

The Mossbauer parameters are derived from the peak parameters (base line parameters, peak position, peak width, and peak area/height) via the fitting process by computer evaluation of spectra in the case of the so-called model-dependent evaluation. In this case, an exact a priori knowledge about the spectrum decomposition (peak-shape function, number, and type of subspectra corresponding to the interactions assumed for each microenvironment in the model) is inevitably necessary. (Incorrectly chosen number of peaks renders the analysis itself incorrect.)... 

This method offers the evaluation of spectra showing strong background noise and only low spectral variation and the prediction of the relative carotenoid concentration by using only a single reference spectrum. In addition, this reference compound does not need to be structurally identical to the target compound, as demonstrated for the predicted versus measured target spectrum for carotenoids [162]. 

Like the resonance lines, the X-ray lines are always accompanied by satellites with intensities of up to 10% of that of the main line. This must be considered in the evaluation of spectra. For example, the small sUiictures seen at the low binding energy side of the photoelectron lines in Figs, la, 10c, and 14 are due to the satellites of the exciting radiation. In addition to the satellites, there is always a bremsstrahlung continuum underlying the characteristic X-ray lines. This continuum can be reduced by inserting a thin metal foil (the nature of which depends on the anode material) between the X-ray source and the collision chamber. The foil must be sufficiently thin and cannot be used to maintain a reasonable pressure difference between the source and the chamber. 

---