Slow motional limit

At temperatures around 50-60°C the three-site jump model is not a good approximation to the multi-site jump model, because the motion is not sufficiently rapid to be in the fast motion limit. However, the calculated spectra are fairly fitted with the observed ones. This is because the calculated spectrum is a superposition of constituent spectra whose rates are spread over several orders, so that the resultant spectrum is governed by the constituent spectra in the fast and slow motion limits having greater intensity than that in the intermediate exchange regime. 

Fig. 7.10. Maximal intensity of the ROE as a function of (A) magnetic field for x, = 10 ns and (B) tr at a field of 800 MHz, for two hydrogen nuclei at 1.8 A distance. Curves (a), (b) and (c) refer to a field-independent R pM (Eq. (3.21)) of 0, 50 and 200 s-1, respectively. For R pM 0, the fast motion limit is the same as that of transient ROE the slow motion limit is positive and equal to 0.675.

Based on random fields, relaxation theory R2 decreases as molecular tumbling gets faster and more effectively averages the residual dipolar broadening. Both in the fast and slow motion limits, R2 is proportional to tc. ... 

Similar to fluorescence depolarization and NMR, two limiting cases exist in which the molecular motion becomes too slow or too fast to further effect the ESR lineshape (Fig. 8) (35). At the fast motion limit, one can observe a narrow triplet centered around the average g value igxx + gyy + giz with a distance between lines of aiso = Axx- -Ayy- -A2,z)l3, where gu and Ajj are principal values of the g-tensor and the hyperflne splitting tensor A, respectively. At the slow motion limit, which is also referred to as the rigid limit, the spectrum (shown in Fig. 8) is a simple superposition of spectra for all possible spatial orientations of the nitroxide with no evidence of any motional effects. Between these limits, the analysis of the ESR lineshape and spectral simulations, which are based on the Stochastic Liouville Equation, provide ample information on lipid/protein dynamics and ordering in the membrane (36). 

Thus, M2XC is the relaxation rate 1/ T2, which has been calculated in (3.5.6) by the BPP theory in the fast motion limit. In the slow motion limit of (3.5.6) only the spectral density (3.5.8a) at frequency zero needs to be considered, and... 

NMR is ideally suited to explore molecular motions in the polymer. Different types of motion can be discriminated on behalf of their timescale and geometry of exchange. One-dimensional quadrupole echo lineshapes (see Section 6.2.7.1) are particularly sensitive to segmental dynamics [1-6, 9-12], when there is either fast exchange between discrete geometries (with Tc <1/Avq) or when the motion occurs on the intermediate timescale (tc= 1/Aj q). Dynamic processes in the intermediate to slow motional limit (tc > l/Ar Q) are addressed by 2D exchange spectroscopy (see Section... 

It turns out that the secular part depends on the spectral density at zero frequency, 7(0). We can see that this makes sense as this part of transverse relaxation requires no transitions, just a field to cause a local variation in the magnetic field. Looking at the result from section 8.5.2 we see that 7(0) = 2tc, and so as the correlation time gets longer and longer, so too does the relaxation rate constant. Thus large molecules in the slow motion limit are characterised by very rapid transverse relaxation this is in contrast to longitudinal relaxation is most rapid for a particular value of the correlation time. 

It is worth noting that the linewidth of this resonance decreases with increasing Tc This behavior is in sharp contrast to the situation described by Eq. (2) and to the dipolar relaxation process, where the linewidth increases with increasing VqTc. From the field dependence of the chemical shift and linewidth described in Eqs. (3) and (4), the values of 7 and for spin 5/2 nuclei in the slow motion limit can be obtained. As the parameter % provides a measure of the coupling between the nuclear quadrupole and the electric field gradient at the nucleus, it reflects the symmetry of the local environment of the nucleus and thus can give information on the nature of the colloidal species, ic is a measure of the mobility of the species involved and, in principle, can provide information on the magnitude of the particle size when Eq. (1) is used. 

Spin-labeling Studies of Complex Systems Intennediate and Slow Motion. - HF EPR spectra in the slow motion limit are especially informative because of the superior angular resolution resulted from the dominance of... 

NOESY spectra are preferred in the slow-motion limit but never near the transition from positive to negative NOEs cr 0) because the... 

Then, in the slow motion limit, where Jq Jp J2, the dynamic shift undergone by the narrow +1/2 -1/2 line is... 

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