Orientation-dependent modulation depth

While ENDOR lines correspond fairly well to powder patterns and exhibit clear line shape singularities, this is not the case for ESEEM lines. The reason can be seen in Eq. 16 modulation depth depends on orientation and vanishes at the 9=90° singularity of a powder pattern as well as at the 0 = 0° outer edge (cf. Eig. 2a). Furthermore, ESEEM spectra usually cannot be properly phased and have to be displayed as magnitude spectra rather than absorption spectra. The combination of these problems makes line shapes in ID ESEEM spectra unreliable and hard to simulate. Line shape analysis in ID ESEEM spectra is therefore strongly discouraged. One-dimensional ESEEM spectra are useful for well-defined coordination environments in transition metal complexes, in particular, if single crystals are available. This situation is, however, unusual in polymer applications. 

If ID ESEEM data are dominated by contributions from a single element, time-domain analysis can provide estimates for the distance of closest approach of nuclei of this element and of the average number of such nuclei. This technique relies on the distance dependence of the modulation depth (Eq. 16) and on the fact that the total ESEEM signal caused by several nuclei is the product of contributions from the single nuclei. The modulation depth ko at time zero (Fig. 13) depends on both distance and number of the nuclei. The decay of the modulation is due to the frequency dispersion, which to first order depends only on the distance. By analyzing depth and decay of the modulation, the two parameters can thus be separated. A popular way of doing this is ratio analysis. In this approach, the ESEEM data are reduced to the ratio / exp between the upper and lower envelope of the echo decay (Fig. 13). For N nuclei at the same distance in the absence of orientational correlations. 

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