Subject alignment tensor

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 ... 

Whenever a body is subject to an electric field and the body is non-spherical, there exists the possibility of creating a torque. See Figure 4A. Even for spherical bodies, if the polarization is a tensor not parallel to the field there exists the possibility for a torque to arise. For example, early experiments by Griffin and StowelF showed that Euglena (nonspherical) would align parallel to the applied field at low frequencies, or at very high... 

Figure 11 shows that Nitrogen-15 NMR spectrum of NC obtained at 25°C, well below the glass transition. The line shape is typical of the powder pattern expected from aU possible orientations of resonant sites subject to an anisotropic chemical shift interaction. The "divergence" corresponds to those sites where the external magnetic field and the principal axis of the chemical shift tensor are perpendicular the "shoulder" corresponds to parallel alignment of these two directions. The separation between these experimental features is measured to be,... 

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