Random jump cone

SRPAC spectra of Fig. 9.33a with a model that allows random, single-activated jumps of the EFG on a cone (Fig. 9.33b) was possible over the entire temperature range. This random jump cone model follows an Arrhenius law with activation energy a = (20.1 0.8) kJ moP and frequency factor A = (5.5 1.6) 10 s and it yields a cone opening angle of about 47° above 380 K [81]. 

Fig. 9.33 (a) SRPAC time spectra of FC in SSZ-24 at different temperatures. For comparison the spectra at low temperatures are multiplied as indicated, (b) Model, which allows random jumps of the EFG on a cone. (Taken from [35])... 

C-2H bond performs rotational random jumps on the surface of a cone with a full opening angle X = 6° (from Ref. 93). (b) Experimental 2H NMR spectra of chlorobenzene-ds in a mixture with cis-decalin at various temperatures T < Tg and at a long solid-echo delay tp [429]. 

Fig. 14. Effects of small-amplitude reorientation on 2H NMR experiments, as calculated by means of RW simulations. In the model, C-2H bonds (<5 = 2n 125 kHz, rj = 0) perform rotational random jumps on the surface of a cone with a full opening angle % = 6°. (a) 2H NMR spectra for various solid-echo delays tp (tj = t = 30 pis), and (b) 2H NMR correlation functions Fcos(tm) for various evolution times tp (tj = t = 10ms). (Adapted from Ref. 76.)...

In this model,110 it was assumed that all C 2H bonds perform thermally activated rotational jumps within energy landscapes on the surface of a cone. Specifically, six basins were supposed to be separated by six energy barriers at positions 0, 60,..., 300° around the axis of the cone. For each cone, the barriers were drawn anew from the distribution of activation energies determined for TOL in DS.12,19 Further, it was assumed that all positions on the surface of the cone, except for the barriers, have the same energy, i.e., a random-barrier model was considered. The thermally activated jumps lead to a random new position in one of the two neighboring basins. This means that several back-and-forth jumps occur over relatively low energy barriers until relatively high barriers are crossed. In other words, many... 

The Dejean-Laupretre-Monnerie (DLM) orientation autocorrelation function is based on the above description. It takes into account independent damped conformational jumps, described by the Hall-Helfand autocorrelation function, and librations of the internuclear vectors represented, as proposed by Howarth [17] (see chapter 4) by a random anisotropic fast reorientation of the CH vector inside a cone of half-angle and axis the rest position of the internuclear vector. The resulting orientation autocorrelation function can be written as... 

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