Orientation Effects in Liquids Liquid Crystals

Study of line shapes in solids often provides valuable information on molecular motion—gross phase changes, overall tumbling of molecules, or internal rotations and other motions. For a limited number of spins the dipolar, CSA, or quadrupo-lar interactions may be simulated and compared with experiment, whereas for multispin systems the line shape is often rather featureless and only the overall shape can be characterized. 

The faithful representation of the shape of lines broadened greatly by dipolar and, especially, quadrupolar interactions often requires special experimental techniques. Because the FID lasts for only a very short time, a significant portion may be distorted as the spectrometer recovers from the short, powerful rf pulse. We saw in Section 2.9 that in liquids a 90°, t, 180° pulse sequence essentially recreates the FID in a spin echo, which is removed by 2r from the pulse. As we saw, such a pulse sequence refocuses the dephasing that results from magnetic field inhomogeneity but it does not refocus dephasing from natural relaxation processes such as dipolar interactions. However, a somewhat different pulse sequence can be used to create an echo in a solid—a dipolar echo or a quadrupolar echo—and this method is widely employed in obtaining solid state line shapes (for example, that in Fig. 7.10).The formation of these echoes cannot readily be explained in terms of the vector picture, but we use the formation of a dipolar echo as an example of the use of the product operator formalism in Section 11.6. 

Molecules that possess magnetic anisotropy experience a slight tendency toward alignment with an imposed magnetic field, but in normal isotropic solvents random thermal motions dominate, and no effects of orientation are usually 

Such order can be described in terms of the preferential alignment of the director, a unit vector that describes the orientation of molecules in a nematic phase. Because the molecules are still subject to random fluctuations, only an average orientation can be described, usually by an ordering matrix S, which can be expressed in terms of any Cartesian coordinate system fixed in the molecule. S is symmetric and traceless and hence has five independent elements, but a suitable choice of the molecular axes may reduce the number. In principle, it is always possible to diagonalize S, and in such a principal axis coordinate system there are only two nonzero elements (as there would be, for example, in a quadrupole coupling tensor). In the absence of symmetry in the molecule, there is no way of specifying the orientation of the principal axes of S, but considerable simplification is obtained for symmetric molecules. If a molecule has a threefold or higher axis of symmetry, its selection as one of the axes of the Cartesian coordinate system leaves only one independent order parameter, with the now familiar form  

When the sample is allowed to equilibrate in a strong static magnetic field, the direction of B0 defines the z axis, and all the anisotropic interactions discussed earlier in this chapter are displayed. Many commercially important materials are liquid crystals, as are biological membranes, and NMR can be used to investigate their structures. In addition, small molecules that would tumble randomly in an isotropic solvent are impeded in a liquid crystal solvent to the extent that they, too, display anisotropic interactions. However, the order parameter for such a small molecule is usually much less than the maximum values of + 1 or — y2. Typically, values of S 0.1 are observed for molecules dissolved in 

---