Line width inhomogeneous

If dye molecules are embedded into an amorphous matrix, preferably transparent polymers, greatly and inbornogenously broadened spectral lines are observed. This broadening is caused by the energetic interaction of the dye molecules with the locally different environment in the polymer matrix. The ratio of the homogenous initial line width of the dye molecule T to the inhomogenous line width of the dye in the polymer T ranges from 1 10 to 1 10 . ... 

Fig. 2.7 Dependence of the experimental line width Cexp on the effective absorber thickness t for Lorentzian lines and inhomogenously broadened lines with quasi-Gaussian shape (from [9])...

In the past two decades, 129Xe NMR has been employed as a useful technique for the characterization of the internal void space of nanoporous materials. In particular, the xenon chemical shift has been demonstrated to be very sensitive to the local environment of the nuclei and to depend strongly on the pore size and also on the pressure [4—6], Assuming a macroscopic inhomogeneity resulting from a distribution of adsorption site concentrations, 129Xe NMR spectra of xenon in zeolites have been calculated, and properties such as line widths, shapes as well as their dependence on xenon pressure can be reproduced qualitatively. A fully quantitative analysis, however, remains difficult due to the different contributions to the xenon line shift. (See Chapter 5.3 for a more detailed description of Xe spectroscopy for the characterization of porous media.)... 

Since these terms are proportional to tr, they increase with decreasing temperature.1 There are several line-width contributions, included in oc0, which do not depend on m,-. These include magnetic field inhomogeneity and the spin rotation interaction, the latter increasing with 1/tr and thus with increasing temperature. These and other line-width effects have been studied in some detail and are discussed elsewhere.13... 

There are several other sources of line width in nuclear magnetic resonance. An experimentally caused width occurs when the laboratory static magnetic field inhomogeneity exceeds the true line width. In this case the... 

It should be also noted that the dynamic NMR line width Avayn = is always small (Fig. 11a) as compared to the static glassy line width induced by the inhomogeneous nature of the spectrum. Therefore the nanocluster dynamics can be locally seen only by T2 measurements, and not by ID line shape data which reflect the static glassy nature of the relaxor state characterized by the Edwards-Anderson order parameter. 

Multiple-pulse measurements were performed on both the LP and HP samples at 20° and — 80° C, and when no differences were noted, lower temperature measurements were performed only on the LP sample. Multiple-pulse spectra for the LP sample are illustrated in Figure 4 together with the eight-pulse spectrum of the reference used for the low-temperature measurements, Ca(OH)2. The lineshapes observed are quite broad, and the line center is a function of temperature. The line width was separated into three contributions by performing three related multiple-pulse measurements (I). These indicated that the main contributions to the linewidth came from both relaxation and second-order dipolar effects. The maximum possible field inhomogeneity Hamiltonian is estimated to be less than 16 ppm by this means, which indicates that the com-... 

There are several ways to measure Tx and T2. If Tx is greater than, say, 10 sec, one can place the sample in the B0 field of the spectrometer and immediately make a series of rapid scans of a resonance line, keeping Bx small. The absorption signal is proportional to n, so the approach of n to neq can be followed, and Tx obtained from (8.100). If T2 is less than, say, sec, one can obtain T2 directly from the measured line width. However, if T2 is greater than j sec, then the true line width is quite narrow, and in fact is narrower than the width produced by inhomogeneities in the applied field 0. For Tx and T2 not in the above ranges, one uses various pulse techniques to measure them (Becker, Section 9.7). 

Here <( t ) f(t")> is the autocorrelation function of the electromagnetic field. For the case of excitation by a conventional light source, where the amplitudes and the phases of the field are subject to random fluctuations, the field autocorrelation function differs from zero for time intervals shorter than the reciprocal width of the exciting source. In the limit 8v A, that is when the spectral width, 8v, of the source exceeds the inhomogenously broadened line width, the field autocorrelation function can be represented as a delta function... 

The spin-spin relaxation time can, in principle, be measured from the FID following the 90° pulse (one-pulse experiment Fig. 10a). However, the application of this simple experiment is limited only to very short FIDs, and consequently short T2s, because of the inhomogenities in the laboratory field. The line width in magnetic resonance is proportional to T2, but the observed linewidth,- T, has also a contribution from the magnetic field term ... 

It should be noted that the activation energies for motional processes in the same crosslinked polymer gel calculated from line widths in 13C NMR spectra are higher than those calculated from 1H NMR spectra under the magic angle conditions (residual line width). These findings indicate that 13C line widths (which are of the order of 10 Hz) are probably more affected by sample inhomogeneity and by relatively small residual chemical shift anisotropies 162). 

The observed line width of an NMR signal depends additionally on the field inhomogeneity AB0, whose contribution to Av1/2 arises from eq. (1.8) ... 

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