Bulk anisotropy

Fig. 23. Easy axis diagram for SmFe2 for four different temperatures and pB Hex/k = 130 K. The dashed lines indicate the transitions due to an additional bulk anisotropy of Kj/k = - 2 K per formula unit, which roughly corresponds to the anisotropy of the iron sublattice.

The bulk anisotropy of liquid crystals depends upon the structures of the mesogens, the molecules that form liquid crystalline phases. Not all molecules can form liquid crystalline phases, and the ones that do tend to have certain shapes. More than in most other fields of chemistry, molecular shape rather than the precise nature of the functionality is a key determinant of liquid crystal behavior. Mesogens most often have a significant elongation in one direction (rod-shaped), leading to the common symbolism of an oval, as in Figure 13.7. 

Farle et al. (1985, 1989) have investigated the uniaxial magnetic anisotropy of monolayers and a 8 nm thick epitaxial Gd layer near the Curie point. For monolayers the magnetization is aligned normal to the surface and is up to 10 times larger than the bulk anisotropy. In zero external field, magnetization lies completely in the surface plane. 

Structure within a sphere of mesophase is modeled in Figure 2.36 where the lamellar polycyclic aromatic mesogens are stacked parallel to each other to create the anisotropy. On coalescence, these structures are maintained when the two adjoining structures merge into each other to create bulk anisotropy. 

Four calculations have been reported in related areas of molecule-field interactions. Evans (1982) has simulated the bulk anisotropy for a collection of molecules, which while dipolar were not polarizable nor based on the properties of a real molecule. The field-induced force was not explicitly defined in terms of a dipole-field interaction, rather a full Lennard-Jones potential was used. Coffey has examined the inertial relaxation of dipolar molecules in intense fields (Coffey et al., 1983). Madden has focused on interaction-induced effects in dielectric absorption (Tildesley and Madden, 1983) and transient nonlinear optical measurements in CS2 (Madden, 1987). Samios and Dorfmuller used a similar local field formalism to ours when they examined far IR absorption and utilized equilibrium fluctations to obtain correlation functions for liquid CS2 (Gburski et al., 1987). More details on these calculations... 

FIGURE 2.1 Demonstration of bulk anisotropy and isotropy. The left and center Images show molecules In an isotropic phase, despite differences in moiecuiar shape. The phase on the right can appear isotropic when viewed from (a) but anisotropic when viewed from (b). 

The concept of bulk anisotropy and molecular orientation is extremely important in the study of liquid crystal materials, and when examining microscopic images of liquid crystals and considering their electrical and optical properties, it is essential to know the molecular orientation (or alignment direction). With some knowledge of the structure of the different liquid crystal phases, it is possible to interpret microscope images and deduce this molecular orientation. These techniques are discussed in the following section. 

In hquid crystal materials, birefringence originates from bulk anisotropy. When a nonpolarized monochromatic light ray passes into a liquid crystal medium, it can be resolved into two components with orthogonal polarization directions. As each of these rays will experience a different refractive index, one will travel faster than the other, creating a phase difference between the two. 

In this section we group techniques that sense the anisotropy in various properties of individual molecules as opposed to those discussed above, which sense bulk anisotropies. It is impossible to measure the anisotropy of a single molecule in a nematic phase rather, these techniques measure the statistical average (both temporal and spatial) of the molecular anisotropy. The averaging process results in the measured anisotropy being proportional to for most of these techniques. For the technique based on Raman scattering measurements, the anisotropy is related to both and . 

Published experimental data for clay minerals and shale demonstrate the strong influence of porosity and compaction and show the high anisotropy of this group of rock craistituents. If clay minerals are aligned, bulk anisotropy results. 

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