Analysis of line-shapes

Dynamic motion of the alkyl stationary phases can also be obtained from NMR studies through an analysis of line shapes, comparisons between single-pulse (SP) and CP-MAS spectra, and various relaxation time constants. Zeigler and Maciel... 

The simplest theoretical approach to exchange is via the Bloch equations, to which terms are added to reflect the rate phenomena. The spectra shown in Fig. 2.14 are obtained from such a treatment. It is apparent that the line shapes depend on the ratio R/ vA — vB), where the exchange rate R = 1/t. Thus fast and slow are measured with respect to differences in the nuclear precession frequencies in the two sites. Exchange rates can be measured by analysis of line shapes and by certain pulse experiments, as described in later chapters. 

A treatment of the analysis of line-shapes to extract particle size, shape and strain information is discussed in detail in Chapter 13. Here we present an overview. 

More detailed information about strain in networks can be gained from analysis of line-shapes, in particular the second moment M2- When interchain couplings are neglected, M2 is related to the elongation ratio A according to [War2]... 

Expression 120 is sufficient for analysis of line shapes seen at the detector. 

This type of fluxional behaviour is exhibited by several organometaUic compounds and is readily detected by the analysis of line shape in NMR [3], The major hmitation of this method is that it is useful only in the free energy change in the range of 40—801 /mol. Microwave and infrared spectroscopy are also sometimes usefijl in studying the fluxional behaviour of organometaUic compounds. 

NMR spectroscopy can provide valuable information on the structure of mesophases. The most commonly used method for this is the analysis of line shapes in spectra of various nuclei, and, in particular, of H. For a large number of mesophases, NMR spectra are motionally averaged and the spectral line shape reflects the phase symmetry. Line shape analysis of NMR spectra has been employed successfully to investigate the molecular organization and tilt angle of smectic C phases, as well as the structure of columnar discotic phases and it has been shown to be more sensitive than optical techniques to some aspect of biaxial ordering. Moreover, this technique has been shown to be extremely helpful in the discrimination of lyotropic phase symmetry. As examples, NMR spectra of some lyotropic phases are reported in Figure 4. 

A Simple Example of Line Shape Analysis Spin-State Relaxation in the Nitrosyl... 

The analysis of a full tilt series of 2H NMR spectra not only allows the determination of the unique bond angle for a deuteriated methyl group, but also provides an internal check for the consistency of the spectral interpretation. In particular, simulations provide a means for the analysis of line-broadening effects, which arise from the sample mosaic spread as well as the intrinsic line width of the nuclear transition and instrumental factors. When line shapes are fitted to a full tilt series of spectra in a concerted manner and are also compared with the powder spectrum of an unoriented sample, the different contributions can be discerned. In that way an intrinsic line width of around 2 kHz is found for the spectra shown here, together with a mosaic spread between 8° and 10° for the three samples. 

Although this equation only applies when the coalescence point is reached, rate constants for the exchange between two or more exchanging sites are accessible by analysis of line widths at half height, Avip, and shift differences, Ar, in Hz. The comparison between the experimental spectrum and the spectrum calculated by use of a simulation package for line shapes provides the mechanism for determining the rate constant of exchange [161, 162]. 

Proton-hydride exchanges similar to those in Scheme 10.9 are manifested in the H NMR spectra as broadenings and coalescences of the hydride and HX resonances upon heating and can be characterized quantitatively with the help of line-shape analysis or saturation transfer experiments. As in the case of proton... 

Applications to Biological Samples. - Methods of distance measurements were compared for four doubly spin-labelled derivatives of human carbonic anhydrase.53 The distances between the spin labels were obtained from continuous wave spectra by analysis of the relative intensity of the half-field transition, Fourier deconvolution of the line-shape broadening, and computer simulation of line-shape changes. For variants with interspin distances greater than 18 A, the DEER method also was used. For each variant, at least two methods were applicable and reasonable agreement between distances obtained by different methods was obtained. The useful distance ranges for the techniques employed at X-band with natural isotope abundance spin labels were estimated to be half-field transition (5-10 A), line-shape simulation (up to 15 A), Fourier deconvolution (8 - 20 A), and four-pulse DEER (> 18 A).53... 

Here, we shall not go any further into the analysis of this sort. Instead, we show a few examples of line shape functions calculated by Eq. (72) for the Gaussian models, which are characterized by the operator T given by Eq. (52). The Gaussian models are not very adequate for the electric field in a plasma, as is seen by the fact that the Holtzmark distribution is far from Gaussian. Still, it may serve to give one an understanding of the... 

Table 4.2. Empirical induced dipole moments of systems involving molecules m and Is stand for moment analysis and line shape analysis, respectively.

The analysis of the shape of the EPR line of the Fs+ -centres in MgO [71] has shown that, at 77 K with increasing depth of Fs+ -centre decay to 40-50%, the intensity in the wings of their EPR line decreases markedly and the line... 

Relatively large differences were observed on the 31P spectra of the investigated compounds (see Figure 37). On the basis of line shape analysis, it was possible to distinguish among the various PO4 units (PjB, P3B, PgB, P2BandP3B) represented differently from different types of phosphorus tetrahedra. In... 

Investigating molecular dynamics using NMR, in contrast to DS and LS, involves the application of several conceptually quite different techniques. For example, in spin-lattice relaxation studies one is concerned with familiar time correlation functions that are probed as spectral density point by point (Section II.D.2). In the case of line-shape analysis, usually a two-pulse echo sequence is applied, and the... 

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