Residual linewidth

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

Implementation of Equation 9.18 in spectral simulators requires some extra precautions (Hagen 1981 Hagen et al. 1985d) (A) The increased periodicity now requires one half of the unit sphere to be scanned. (B) The fact that the term within the absolute-value bars in Equation 9.18 can change sign as a function of molecular orientation implies the possibility that for specific orientations the linewidth becomes equal to zero. To avoid a program crash due to a zero divide, e.g., in the expression for the lineshape in Equation 4.8, a residual linewidth W0 has to be introduced ... 

In order to check further the correctness of this procedure, we used the deduced values for the distribution parameters and the residual linewidth to simulate the experimental spectra at X-band and S-band, using an expression which specifically includes the linewidths dependence on the distribution parameters. An orientation dependent linewidth was used, eq. 5, with Hj,= H. ... 

The study of isopropyl benzene can be sumnarized as follows. The width of the UPS line corresponding to removal of the lowest binding energy ir-electron is temperature dependent. This temperature dependence contributes significantly to the UPS line-width at elevated temperatures. The fact that the width is temperature dependent indicates that the mechanism involves vibrations. Although experimentally, intramolecular and inter-molecular effects could not be separated, theoretical models predict that of the effect is mostly intermolecular. The small residual linewidth observed is due to sample inhomogeneities. Presumably, an ideal single crystal thin film would exhibit the same A(T) but have a smaller A. ... 

Although the AHT is powerful in predicting which terms in the Magnus expansion are zero, it is rather weak in estimating what residual linewidths... 

When finite pulsewidths are taken into account, second-order dipolar terms do not drop out completely for the BR-24 sequence and we learn from the tp = t data in Fig. 6 that such terms dominate the residual linewidth. The resolution obtained with the MREV sequence for = r is inferior by a factor of 2.4 compared to that for tp => 0, irrespective of the pulse spacing r. By contrast, the gap between the tp = t and tp 0 data widens for BR-24 when r becomes smaller. 

Dependence of Residual Linewidth on Errors of Individual Pulses, Power Droop, and Offset... 

It has been established that the mobility of protons can be estimated by the detailed analysis of NMR lineshape. Brunner described theoretical model for the lineshape of H MAS NMR as a function of correlation time when proton mobility is a decisive factor for the residual linewidth. ... 

The large mean squared displacement can by the way explain the small residual linewidth of the triplet ESR lines in a natural way (for small A - B spacing) this was also observed for the triplet excitons in naphthalene crystals (Eig. 7.21). It is due to the complete averaging-out of the hyperfine structure, because the number N of molecules over which the average is carried out is not 2, as for the mini-excitons, but rather is very large (N 1). The second moment is then not reduced by the factor V2, as for the mini-excitons, but instead by the factor 1/N. The exciton ESR linewidth is therefore narrowed in relation to the linewidths of the isolated... 

Figure Ic shows the corresponding Cl NMR linewidth measurements as a function of slow ageing. Clearly, the linewidth enhancements generated with ageing time correlate well with the Mn(II) formation, both in the presence and absence of added chloride ions. Upon addition of 20 fiK EDTA to mask the paramagnetic effects of the Mn(II) ions, the residual linewidth enhancement, which would reflect chloride binding and/or viscosity effects, is the same in completely aged samples as in fresh samples. This result indicates that the ageing response does not lead to the exposure of new NMR-detectable chloride interaction sites.

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