Molecular directivity

Liquid crystals (LCs) are organic liquids with long-range ordered structures. They have anisotropic optical and physical behaviors and are similar to crystal in electric field. They can be characterized by the long-range order of their molecular orientation. According to the shape and molecular direction, LCs can be sorted as four types nematic LC, smectic LC, cholesteric LC, and discotic LC, and their ideal models are shown in Fig. 23 [52,55]. 

Multiayer L-B films can be prepared in both methods, by repeated deposition of monolayer on the substrate, with the molecular direction changing alternatively after each deposition (Y-type), or keeping the same molecule direction in all monolayers (X-type or Z-type). 

A convenient way to handle Eq. (1.20) is that of defining a tensor g which couples the magnetic moment S with the external magnetic field. Such a tensor defines the coupling between S and Bo for all molecular directions. We can represent the tensor as a solid ellipsoid (Fig. 1.15) with three principal directions defining the axes of the ellipsoid and of the molecule. In any kk direction we have a value of gkk such that... 

Once the Ax values and the molecular directions are obtained, the metal centered pseudocontact shifts can be calculated of nuclei which experience also contact and ligand centered pseudocontact shifts. With this procedure the contact plus ligand centered pseudocontact shift (which is small [100]) have been calculated for several systems. In Table 2.11 the data relative to the low spin iron(III) containing heme in cytochrome b are reported [101]. 

FIGURE 1.10 Panel (a) shows the effect of ZFS (left side) and application of a magnetic field in three molecular directions on the spin states giving rise to the observed saturation magnetization behavior (VTVH MCD) plotted in panel (b) for a S = 5/2, D> 0, and EID = 1/3 Kramers ion. 

Figure 11. Definition of angles describing the relative orientations of the magnetic field (HI the instantaneous molecular direction m, and the average molecular direction (a) in a dynamically disoriented system. In amorphous PTFE represents the instantaneous chain direction and d the local director.

From the direction cosines associated with each coupling, comparisons can be made with specific molecular directions known from the x-ray crystal structure, in particular enabling the identification of the major sites of unpaired spin density. Examples of studies to obtain free radical assignments are included. 

The structure at temperatures above the transition temperature (phase II), is illustrated in the schematic drawing in Figure 19b. Both the side chains and the backbone are conformationally disordered, but the side chains remain organized preferentially on planes perpendicular to the polymer chain axis. Furthermore, significant runs of trans conformations remain in the backbone (26) in such a manner that the original molecular direction is preserved as the chains pack in cylinders in a hexagonal array. The resulting... 

Therefore, for each weighting scheme w, 11 molecular directional WHIM descriptors (i 3 is excluded) are obtained ... 

The intensity of a Bragg reflection depends on the size of the anisotropic displacement parameters of those atoms that contribute to the reflection [6] and so individual parameters can be extracted from crystallographic data. As extracted they are referred to the crystallographic axes and are not necessarily simply oriented with respect to significant molecular directions. These parameters are of some interest in the study of molecular vibrations with neutrons because of the dynamical contribution to their value (but not the disorder contribution). The dynamic contribution plays an important role in determining the observed transition intensities, through the Debye-Waller factor ( 2.5.1.2). 

Liquid crystals are materials which exhibit characteristics of both liquids and crystalline solids. From a continuum mechanical point of view, they possess a local unit vector n, the director, corresponding to the molecular direction. Liquid crystals generally exist in nature in three forms (a) nematics, in which the microstructure is oriented by direction, but not by position (b) cholesterics, in which the orientation is helical and (c) smectics, in which the microstructure is oriented by position, i.e. in layers. The smectic case is further divided into cases A,C, and others. We are concerned here with the smectic A case, in which the director is oriented normal to the layers. 

We have noted that the smectic A layers are flexible and easily distorted, but tend to preserve the interlayer spacing (fig. 5.3.1). Moreover, as the layers can slide over one another, the structure adjusts itself readily to surface conditions. For example, when there is a centre of attachment at the glass surface the molecules adopt a radiating or a fan-like arrangement and the layers form a family of equi-spaced surfaces normal to the molecular directions. Under a polarizing mica-oscope such distortions give... 

In the phase, on the other hand, the molecules are tilted, and their rotation about their long axes is biased. The symmetry plane of the ordinary structure (fig. S.8.1) is now absent because the molecules are chiral. The only symmetry element that remains is a twofold axis parallel to the layers and normal to the long molecular direction. This allows the existence of a permanent dipole moment parallel to this axis. (Of course, these arguments apply to the S,. phase as well.)... 

Thirdly, it would appear that we need to maximize the degree of molecular alignment represent by the average molecular direction cosines. For a typical... 

Now, we try to take the average of Eq. (1.77) over orientations, fixing the distance between two sites. However, it is obviously impossible to take the average analytically. The essential approximation of the RISM theory consists of representing the molecular direct correlation function, c(12), by a sum of the site-site direct correlation functions, Cay rai —... 

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