Intermediate modulation regime

Consider the calculation of T2 pertinent to experiments in the fast and intermediate modulation regimes (t < Tj). The instantaneous frequency co(t) of the oscillator is given classically from the Hamiltonian H [Eq. (1)] by... 

Refinements of the Kubo expression, to which we alluded above, involving nonexponential decay of the modulation correlation function have been made. These refinements (in particular that of Rothschild et al. ) would appiear to be limited to spiecific applications in view of actual experimental precision as in fact exponential decay describes rather well a large body of data in ordinary liquids. The presence of two or more modulation mechanisms—in the intermediate modulation regime—will be equally difficult to demonstrate experimentally. 

In this work, it has been demonstrated that periodic modulation of the Hamiltonian describing a dynamic process introduces spectral effects that depend upon the nature of the modulations. For both MAS and QCPMG experiments, sidebands are broadened in the intermediate dynamic regime and a significant narrowing of the sideband manifold is observed for higher order jump processes due to averaging of the anisotropic part of the quadrupolar tensor. 

Given the beat-modulated decays and phase-shift behavior, it is apparent that the intermediate-energy regime we have defined for S, t-stilbene is one in which restricted IVR is prevalent. Nevertheless, it is also apparent that IVR in f-stilbene does not fit as cleanly into the theory of vibrational coherence as anthracene does. This point will be addressed in subsection d. 

In the fast modulation limit [Equation (8)], the loss of information is fundamental. The lifetime of the frequency perturbations is short compared to their magnitude, and the uncertainty principle precludes a full characterization of w(t) by any experimental technique. However, in the slow modulation limit and in the intermediate regimes, the loss of information in the FID is not fundamental. The next section shows that the Raman echo contains additional information about the rate of the frequency fluctuations that is not present in the FID. By using a combination of Raman echo and... 

Rotational motion of a nitroxide modulates the anisotropic electron-nuclear magnetic dipolar interaction, giving rise to electron relaxation that affects the EPR spectral line shape. At X-band frequency, the spectra are sensitive to motions with correlation times in the range of 10-11 < rc < 10-7, but also reflect the anisotropy of the motion. Figure 5B shows simulated EPR spectra for isotropic motion in the fast, intermediate, and slow motional regimes and illustrates the high sensitivity of the line shape to motional rate. 

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