Overlapped bands

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). 

Figure 6.25 The 3q, infrared band of HCN and two weaker, overlapping bands. (Reproduced,...

The UV spectrum of a complex conjugated molecule is usually observed to consist of a few broad band systems, often with fine structure, which may be sharpened up in non-polar solvents. Such a spectrum can often be shown to be more complex than it superficially appears, by investigation of the magnetic circular dichroism (MCD) spectrum, or by introduction of dissymmetry and running the optical rotatory dispersion (ORD) or circular dichroism (CD) spectrum. These techniques will frequently separate and distinguish overlapping bands of different symmetry properties <71PMH(3)397). 

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). 

The basic methods of the identification and study of matrix-isolated intermediates are infrared (IR), ultraviolet-visible (UV-vis), Raman and electron spin resonance (esr) spectroscopy. The most widely used is IR spectroscopy, which has some significant advantages. One of them is its high information content, and the other lies in the absence of overlapping bands in matrix IR spectra because the peaks are very narrow (about 1 cm ), due to the low temperature and the absence of rotation and interaction between molecules in the matrix. This fact allows the identification of practically all the compounds present, even in multicomponent reaetion mixtures, and the determination of vibrational frequencies of molecules with high accuracy (up to 0.01 cm when Fourier transform infrared spectrometers are used). 

Spectra of s.o. samples differed markedly from those of a.p. samples and were unaffected by a subsequent evacuation up to 673 K (Fig. 4, a). Spectra consisted of a composite envelope of heavily overlapping bands at 980-1070 cm-, with two weak bands at 874 and 894 cm-. Irrespective of the preparation method, the integrated area (cm- ) of the composite band at 980-1070 cm- was proportional to the V-content up to 3 atoms nm-2. An analysis of spectra by the curve-fitting procedure showed the presence of several V=0 modes. The relative intensity of the various peaks contributing to the composite band depended only on the V-content and did not depend on the method used for preparing the catalysts. Samples with V > 3 atoms nm-2 R-spectra features similar to those of pure V2O5 (spectrum 8 in Fig. 4, a). 

The amount of information, which can be extracted from a spectrum, depends essentially on the attainable spectral or time resolution and on the detection sensitivity that can be achieved. Derivative spectra can be used to enhance differences among spectra, to resolve overlapping bands in qualitative analysis and, most importantly, to reduce the effects of interference from scattering, matrix, or other absorbing compounds in quantitative analysis. Chemometric techniques make powerful tools for processing the vast amounts of information produced by spectroscopic techniques, as a result of which the performance is significantly... 

For a metal such as sodium, there are overlapping bands formed from the 2p and 3s atomic orbitals. In a general way, we can consider that a band is formed from each type of atomic orbitals that is occupied. However, there are energy gaps between the bands. If we again consider the case of sodium, there will be bands from the Is, 2s, 2p, 3s, and 3p (although the 3p orbitals are unoccupied) that can be shown as in Figure 11.2. Each band can hold 2(21 + 1)N electrons, where N is the number of atoms. 

The PE spectra of some cyclic triamines with the nitrogen atoms in 1,3-positions like hexahydro-l,3,5-triazines (59) and tetracyclic derivatives such as 60 and 61 have been studied and interpreted with regard to their conformational properties110. The n ionizations lead to two strongly overlapping bands between 7.5 and 9.5 eV which are consistent with diequatorial-monoaxial nitrogen substituent orientations at the hexahydro-... 

Figure 19.7. Cyclic batch elution chromatography obtaining high product purity and high throughput by using incomplete resolution (overlapping bands) and recycling the mixed fraction (mf) to the feedstock (a) Control of band separation and cut points determines fractional impurities t mij mr and Ami /mr2-<4l)> (b) Chromatogram for separation of pure ds- and trans- 1,3-pentadiene. Components 1, isoprene 2, trans- 1,3-pentadiene 3, cis-l,3-pentadiene 4, cyclo-pentadiene. Component 1 is eluted at almost the same time as component 4 of the...

Their increased application in light food and drink products has given a new impetus to develop fast and accurate method for their determination. Among computer-controlled instruments multivariate calibration methods and derivative techniques are playing very important role in the multicomponent analysis of mixtures by UV-VIS molecular absorption spectrophotometry [2]. Both approaches ate useful in the resolution of overlapping band in quantitative analysis [3, 4]. 

Even if these problems with overlapping bands can be avoided, at high enough pressures the gas phase absorption will be so strong that the sensitivity will be detector noise limited. This problem can only be handled by keeping the optical path length in the pressure cell as small as possible. 

The challenges in this work concerned the fundamental limits of NIR spectroscopy. Eirst, would NIR, with its typically broad and highly overlapped bands, have enough spectral resolution to distinguish the ortho, meta, and para isomers from each other and from the extractant Second, would NIR, with its typically weak overtone and combination bands, have enough sensitivity to quantify the minor components of the stream, especially the ortho isomer, typically present at only 1% ... 

So far we have assumed that the electronic structure of the crystal consists of one band derived, in our approximation, from a single atomic state. In general, this will not be a realistic picture. The metals, for example, have a complicated system of overlapping bands derived, in our approximation, from several atomic states. This means that more than one atomic orbital has to be associated with each crystal atom. When this is done, it turns out that even the equations for the one-dimensional crystal cannot be solved directly. However, the mathematical technique developed by Baldock (2) and Koster and Slater (S) can be applied (8) and a formal solution obtained. Even so, the question of the existence of otherwise of surface states in real crystals is diflBcult to answer from theoretical considerations. For the simplest metals, i.e., the alkali metals, for which a one-band model is a fair approximation, the problem is still difficult. The nature of the difficulty can be seen within the framework of our simple model. In the first place, the effective one-electron Hamiltonian operator is really different for each electron. If we overlook this complication and use some sort of mean value for this operator, the operator still contains terms representing the interaction of the considered electron with all other electrons in the crystal. The Coulomb part of this interaction acts in such a way as to reduce the effect of the perturbation introduced by the existence of a free surface. A self-consistent calculation is therefore essential, and the various parameters in our theory would have to be chosen in conformity with the results of such a calculation. 

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