Pitch-dependent

In Section 3.4.6 it was noted that chiral mesophases behave as chiral perturbation moieties for achiral molecules inserted to the mesophases. Here, only relations between the observed signs in LCICD and the pitch-dependent CD in liquid crystalline systems, and the helical sense of the liquid crystalline phases are described. 

Figure 12.14 Pitch-dependent fill factor of conveying elements...

The theory predicts that the handedness of cellulosic liquid crystalline solutions, designated by the sign of the pitch, depends not only on temperature (T) and on steric repulsion of the chain X), but also on an attractive interaction parameter, %, which depends on the nature of the solvent. The chiral forces are balanced when (x XkT) = 0. In this compensated condition, the pitch of the mesophase should become infinite, and the mesophase resembles a normal nematic phase. 

The RELACS technique offers many advantages over a thermal shrink approach. For example, it reduces iso-dense bias when compared to thermal shrink techniques, has very low pitch dependence, reduces LER and line width roughness (LWR), and improves etch resistance. 

The local order in a cholesteric may be expected to be very weakly biaxial. The director fluctuations in a plane containing the helical axis are necessarily different from those in an orthogonal plane and result in a phase biaxiality . Further, there will be a contribution due to the molecular biaxiality as well. It turns out that the phase biaxiality plays a significant role in determining the temperature dependence of the pitch. Goossens has developed a general model taking this into account. The theory now involves four order parameters the pitch depends on all four of them and is temperature dependent. However, a comparison of the theory with experiment is possible only if the order parameters can be measured. 

The round conductor is twisted around the central axis at a convenient pitch, depending on the size of the magnet and the size of the conductor, in order to force equal current in the various sectors of the conductor. It can also be supported discretely and periodically to form a magnet. Discrete support allows the conductor to be cooled along most of its length, resulting in high current densities in the stabilizer. 

The condition of the yeast on pitching depends on its previous history. It has been shown that lack of contact between yeast and oxygen over successive fermentations has a cumulative and deleterious effect. Thus in a... 

The composition of the final pitch depends on the initial source of the tar and the nature of the subsequent treatment processes and typical properties are given in Table 4.11. Coal tar pitches have been investigated as precursors for carbon fibers [192]. 

Barillaro G, Strambini LM (2010) Controlling macropore formation in patterned n-t3/pe silicon existence of a pitch-dependent etching current density lower bound. Electrochem Commun 12 1314-1317... 

FIGURE 6.12. The planar Grandjean texture in an a.c. electric field [25] (cholesteric mixture with Pq = 30 /mi and Ae = +0.74, directors at opposite boundaries are parallel to the ridge of the wedge), (a) Pitch dependence on reduced cell thickness d — 2djPo (b) director distribution in different Grandjean zones and (c) thickness dependence of the dielectric instability just at the threshold voltage. 

Variable pitch (depends on volume coverage, usually <1)... 

As the intermolecular dispersion forces that maintain the molecules in the cholesteric structure are relatively small, a low additional amount of energy suffices to change the helix pitch. The pitch depends particularly on temperature. In some cases the dependence is so pronounced that typically a temperature rise of less than 3°C is adequate to change the color of reflected light from red over the entire visible spectrum to blue. The use of cholesteric liquid crystals in thermographic applications is based on this property (see also first part of this book). 

It is also of interest to note that compounds 131 and 132 are reported to show anomalous pitch dependency in their chiral nematic phase the pitches are both reported to increase from 1.1 to 1.6 im with increasing temperature. 

The flow properties of cholesteric liquid crystals are surprisingly different from those of the nematics. The most important difference is that, in some directions (along the helical axis), the viscosity measured in Poiseuille flow geometries (see Appendix B) is about six orders of magnitude larger than in the isotropic phase, or in the cholesteric phase when the flow direction is perpendicular to the helix axis. In this latter case, the viscosity is similar to that of nematics, although the behavior is somewhat non-Newtonian above a pitch-dependent threshold shear rate. It was found that the shear rate above which the fluid becomes non-Newtonian is inversely proportional to the square of the pitch. The apparent viscosities as the function of shear rate of materials with different pitch values are shown in Figure 4.6. 

Although experimentally the pitch dependence is difficult to measure, the temperature dependence of the apparent viscosity indeed was foimd to show oscillating behavior, which is due to the temperature dependence of the pitch. Details of the Leslie and other theories and of the relevant experiments are discussed in the book of Chandrasekhar. ... 

Laivins et al. proposed a possible explanation of the pitch dependence of the molar mass in which the segment density and hence the chiral forces could be somewhat diluted for a low molar mass polymer. 

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