Residual Dipolar Broadening and Transverse Relaxation

The standard BWR theory for transverse relaxation anticipates complete motional averaging of all local fields due to dipolar interaction (or by any other spin coupling) on a time scale corresponding to the linewidth in the absence of molecular motions. This time scale is defined by the reciprocal rigid-lattice linewidth, The so-called motional narrowing condition 

The free-induction decay of transverse magnetization has been analyzed in terms of polymer dynamics [23-26]. A solid echo technique was employed for the same purpose [27, 28]. The so-called dipolar correlation effect on the stimulated echo turned out to be a particularly simple and robust tool in this context too [15, 29, 30]. Finally, double-quantum NMR spectroscopy was suggested [31, 32] as a means of probing features of chain dynamics. 

Transverse relaxation under incomplete motional narrowing conditions in multispin systems can be treated with the aid of the Anderson/Weiss approximation [2]. Precession phase shifts caused by spin interactions with many coupling partners is assumed to be subject to the central limit theorem. That is, the distribution of the local fields i-e., the distribution of the corresponding angular frequency offsets and hence the distri- 

The brackets indicate ensemble averages. An analogous formalism for the dipolar correlation effect can be found in Refs. [2, 15, 16]. 

Expressing the autocorrelation function given in Eq. 38 by its Fourier transform, the spectral density I(a ), 

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