Chemical shift anisotropies local molecular motions

A second important mechanism for fluorine spin-lattice and spin-spin relaxation is produced by the chemical shielding anisotropy (CSA) [13, 14, 21, 71]. The magnetic field experienced by a nuclear spin depends on both the electronic structure of the molecule and how easily the electrons can move in the molecular orientations. In addition, the CSA depends on how the molecule is oriented in the magnetic field. Like spin-spin and dipole-dipole interactions, the CSA of small, rapidly tumbling molecules will be an averaged value (the chemical shift). However, these tumbling motions cause fluctuations of the local magnetic field that lead to relaxation. Also slower reorientation, or an environment that restricts the molecular motion, will result in broader lines due to CSA. 

The chemical shift of a nuclear spin is a tensorial quantity. Its value depends on the orientation of the electronic distribution about the nucleus with respect to the external magnetic field. In a liquid, due to the rapid molecular motions, this interaction is averaged to zero and the observed chemical shift is the trace of the tensor. In contrast, in a powder, in the absence of motions, all the orientations have the same probability and the signal obtained for each carbon is the sum of the elementary chemical shifts corresponding to the different orientations. When local motions occur in the bulk below 7g, they usually induce a partial averaging of the chemical shift anisotropy. 

Hq, Hd, Hcs and Hj describe the quadrupolar, dipolar, chemical shift and indirect electron coupled interactions, respectively, and are listed according to their typical magnitude. The Zeeman term was given by equ. (1) and is not influenced by the local environment. Quadrupolar interactions occur for nuclei with I> A only and are described in the next chapter for the case of 2H with 1=1, thus the dominant interaction for IH and 13C is given by Ho and Hcs. The dipole-dipole interaction between spins is a strongly anisotropic interaction. Similarly, the chemical shift depends on the orientation of the molecule with respect to Bq, this part is the so-called chemical shift anisotropy (CSA). In a static sample without any molecular motions... 

Generally, sharp peaks can be observed and microstructure in solution can be discussed because the local magnetic field and chemical shift anisotropy diminishes as a time-averaged quantity due to the fast, isotropic molecular motion. The polymer chains in a gel are much more restricted in comparison to those in solution or a very broad peak, in an extreme case. 

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