True anisotropic state

However, at a low content of a solvent in the system, the viscosity becomes so high that it is difficult to distinguish between the true (thermodynamically stable) anisotropic state of the system and the artificially created (thermodynamically unstable) oriented state which appears upon mechanical deformation of such systems and which very slowly relaxed owing to a high viscosity of the system. 

In almost all cases the admixture of excited states is anisotropic that is, the observed g value varies according to the orientation of the paramagnetic species in relation to the applied magnetic field (orientation-dependent). The g-factor anisotropy is characterized by three principal g values, namely, gxx, gyy, and g--. When these three values are different, the symmetry is defined as rhombic and in the case of axial symmetry, gxx = gyy gzz. In the orientation-independent (isotropic) situation the g factor is represented by a single value. This is also true if the species paramagnetic is in a solution of low viscosity (water) where the molecular tumbling causes all the g factor anisotropy to be averaged out (Knowles et al., 1976 Campbell and Dwek, 1984). 

As discussed in previous paragraphs, the spectral absorption of the chromophores of vision is much more comphcated than that described by Beer s Law for true solutions of low molarity. The absorption of the chromophores of vision is a function of the environment, the chemical state, the spatial relationship, and the orientation of the molecules. They actually exhibit additional, and generally dominant, absorption spectra in the liquid crystalline state that are not found for the same material in low molarity solution. These additional spectra are highly anisotropic. They also exhibit a high absorption coefficient along the preferred axis. Because of these properties, it is extremely difficult to make a comparison of the properties of the chromophores when they are in-vivo with their properties when in-vitro. Because the chromophores are not in solution, when in-vivo, it is not appropriate to use Lambert-Beer s Law to evaluate them (See Section 5.3.5.3), The results of using this law are generally spurious. 

Although not explicitly stated, the discussion so far is only strictly true for isotropic, e.g., cubic, polycrystalline materials. Crystals that are noncubic and consequently are anisotropic in their thermal expansion coefficients behave quite differently. In some cases, a crystal can actually shrink in one direction as it expands in another. When a polycrystal is made up of such crystals, the average thermal expansion can be very small, indeed. Cordierite and lithium-aluminosilicate (LAS) (see Fig. 4.4) are good examples of this class of materials. As discussed in greater detail in Chap. 13, this anisotropy in thermal expansion, which has been exploited to fabricate very low-a materials, can result in the buildup of large thermal residual stresses that can be quite detrimental to the strength and integrity of ceramic parts. 

Although liquids are usually isotropic, some 200 cases are known of substances that exhibit anisotropy in the liquid state at temperatures just above their melting point. These liquids bear the unfortunate, but popular, name liquid crystals the term is inapt because the word crystal implies the existence of a precise space lattice. Lattice formation is not possible in the liquid state, but some form of molecular orientation can occur with certain types of molecules under certain conditions. Accordingly, the name anisotropic liquid is preferred to liquid crystal . The name mesomorphic state is used to indicate that anisotropic liquids are intermediate between the true liquid and crystalline solid states. 

Liquid crystal polymers (LCPs) were introduced over the last three decades. In the liquid state, either as a solution (lyotropic) or a melt (thermotropic), they lie between the boundaries of solid crystals and isotropic liquids. This polymeric state is also referred to as a mesomorphic structure, or a mesophase, a combined term adopted from the Greek language (mesos = intermediate morphe = form). This state does not meet all the criteria of a true solid or a true liquid, but it has characteristics similar to both a solid and a liquid. For instance, the anisotropic optical properties of LC polymeric fluids are like those of crystalline solids, but their molecules are free to move as in liquids. 

It is still true that choosing molecules with reduced anisotropy in the molecule-fixed frame is beneficial. After all, if there is no anisotropy in the molecule-fixed frame, the helium interaction in the lab frame is spherical for all rotational states. It is therefore desirable to seek molecules with short bond lengths, which should reduce the anisotropy of the electron charge cloud in the molecule frame for a fixed helium approach distance. There is potential for the Zeeman relaxation of superficially anisotropic molecules to be suppressed by spatially large, roughly spherical electron wavefunctions, much like was found with the submerged-shell rare earth elements. 

Generally speaking, when light is propagating in a uniform anisotropic medium, the direction of the electric field, and therefore the polarization state, will vary in space. Only when the electric field is in some special directions, known as the eigenmode, will its direction remain invariant in space, which will be proved to be true in this section. In the eigenmode, the electric field has the form... 

The mesomorphic state refers to anisotropic liquids (LCs) that are intermediate between a true liquid and a pure crystalline phase. More explicitly, it refers to the degree of molecular order that lies in-between the ideal three-dimensional, long-range positional and orientational order found in crystals and the random arrangement found in isotropic liquids, gases, and amorphous phases. Anisotropic liquids that exhibit the mesomorphic state are usually elongated, aromatic organic molecules. The mesomorphic state can be divided into the smectic and the nematic states. 

When a polycrystalline solid is under stress, the anisotropic character of many physical properties will be manifested, often quite strongly. This is obviously true in crystalline or cross-linked polymer systems. (It is also true of an amorphous polymer above its Tg, when in a nonequilibrium state of deformation.) As... 

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