Cholesteric pitch dependence

Analytical approaches to understanding the effect of molecular flexibility on orientational order have concentrated on both the isotropic-nematic and the nematic-smectic transition [61, 62] and mean field theory has shown that cholesteric pitch appears not to depend on the flexibility of the molecule [63]. 

Another technique widely used to measure the cholesteric pitch is based on the Bragg scattering of monochromatic light (obtained by a helium-neon laser) from fingerprint or planar textures of the cholesteric32 Its angular dependence is strictly related to the cholesteric pitch. 

The temperature dependence of the cholesteric pitch in the polypeptide liquid crystals has been investigated in various solvents. The pitch P is related to the twisting angle (p between neighboring molecules separated by a distance d along the axis of torsion as follows. 

Fig. 26a and b. Temperature dependence of CD spectra of a colored PBLG film a cholesteric pitch bands around 500 nm b LCICD of the side-chain phenyl groups... 

Recently Blumstein and coworkers reported on the thermotropic properties of a series of main chain copolyesters with different azoxybenzene mesogenic units and flexible spacers consisting of varying ratios of (-I-) 3-methyl adipic acid and 1,12-dodecanedioic acid. Melting temperature of the copolyesters showed minimum values for either the 50/50 compositions or the 25/75 combination of the two spacer components, depending on the nature of the mesogenic units. However, Tj tended to decrease linearly with the content of the 1,12-dodecanedioic acid unit, except in one case. They also observed that the cholesteric pitch of the copolyesters seemed to increase as the concentration of the achiral unit, dodecanedioic acid, increased. Similar observations were reported earlier by Strzelecki s group... 

Dependence of cholesteric pitch on temperature and external field... 

In main chain cholesteric liquid crystalline polymers, the mesogenic groups and flexible spacers are linked alternatively. The flexible units contain asymmetrical carbon atoms which enable the polymers to possess chirality and thus form cholesteric liquid crystals. By varying the ratio of chiral to non-chiral parts, the cholesteric temperature range and pitch can be changed. The cholesteric range depends on the mol fraction of the polymers. A typical main chain cholesteric liquid crystalline polymer is shown in Figure 6.27. 

For an external field pardlel to tlK helicoidal axis, the cholesteric pitch varies depending on the relative magnitudes of 22 and 33 (the bending elastic constant ) 53). 

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. 

In addition to the electromechanical observations described so far, which have been confirmed [73], the dependence on the cholesteric pitch, p, has been studied [73]. It is found that the electromechanical response coefficient is directly proportional to l/p and vanishes for a racemic sample. 

LCs were the earliest studied structures, in which polypeptide homopolymer rods pack in an ordered manner to form smectic, nematic, and cholesteric phases. The smectic LCs are mainly formed by polypeptide homopolymers with identical polymer length. The cholesteric phase can be prepared by synthetic polypeptides with polydisperse chain length. The nematic phase can be regarded as a special example of the cholesteric phase with an infinite cholesteric pitch. The cholesteric pitch and chirahty in the polypeptide LCs are dependent on many factors, such as temperature, polymer concentration, solvent nature, and polypeptide cOTiformation. Deep understanding of such phenomena is necessary for preparation of ordered polypeptide assembles with delicate stmctures. The addition of denaturing solvent to polypeptide solution can lead to an anisotropic-isotropic reentrant transition at low temperatures where the intramolecular helix-coil transformation occurs. However, the helical structure is more stable in LC phase than in dilute solution due to the conformational ordering effect. 

Watanabe J, Nagase T (1988) Thermotropic polypeptides. 5. Temperature dependence of cholesteric pitches exhibiting a cholesteric sense inversion. Macromolecules 21 171-175... 

Recently, there are several reportsA.) discussing the twist mode of the binary system of the thermotropic liquid crystals composed of a nematic solvent and a cholesteric solute. Another interest is in attempting to pursue the structural similarity between thermotropic liquid crystals and lyotropic one, especially for the dependence of cholesteric pitch on the temperature. 

One of the best measures of twist is thought to be the cholesteric pitch. The temperature dependence of cholesteric pitch is then measured for poly-y-benzyl-L-, and poly-y-benzyl-D-glutamates ( PBLG, and PBDG ) and poly-y-alky1-L-glutamates, in various sol-ven-t systems. The temperature dependence of some physical properties were also measured. 

Recently DuPre et al reported that, S increases linearly with temperature rise. Qualitatively, their results are consistent with ours. However, the time required to reach the equilibrium pitch, varied with temperature, the concentration of polymer, and also the thermal history. For PBLG solution in dichloro-ethane (EDC), which concentration is 0.12 vol/vol, the variation of pitch with time was measured at a constant temperature by T-jump method. Fig. 1 shows the time dependence of cholesteric pitch by the T-jump method from -2°C to +30°C, 40°C and 50°C respectively. It is clear that the time required to arrive at the equilibrium pitch is shorter at higher temperature but is still over several hours. Therefore, the equilibrium pitch must be measured after prolonged aging at each measuring temperature. It was found that the... 

The extrapolated line of log S-log C crossed each other at a critical concentration Cq at which S stays constant and independent of temperature. These results suggest that the temperature dependence of the cholesteric pitch would inflect at the concentration higher than Cq This is analogous to the behavior of thermotropic liquid crystals composed of cholesteric solute and nematic solvent, where the sign of dS/dT reverses at a critical concentration. It is understood that the behavior of both thermotropic and lyotropic liquid crystals is comparable provided that the nematic substances of the former are substituted with the solvents of the latter. The critical concentration Cq is about 0.41 vol/vol and this value is very close to the concentration at which the side chains on neighboring molecules of the polymer come to contact each other ( refer to fig.5 ). From these results, it is expected that the origin or mechanism of twist would change at this concentration Cq. The... 

The slope B depends on the concentration, and it increases with concentration. If the cholesteric pitch was measured at constant concentration, the following equation holds ... 

Although instances of lyotropic PLCs predate studies of thermotropic PLCs, as they involved solutions of comparatively esoteric species — virus particles and helical polypeptides — studies of these liquid crystals were isolated to a few laboratories. Nevertheless, observations on these lyotropic PLCs did stimulate the first convincing theoretical rationalizations of spontaneously ordered fluid phases (see below). Much of the early experimental work was devoted to characterizing the texture of polypeptide solutions. (23) The chiral polypeptides (helical rods) generate a cholesteric structure in the solution the cholesteric pitch is strongly dependent on polymer concentration, dielectric properties of the solvent, and polymer molecular weight. Variable pitch (<1 - 100 pm) may be stabilized and locked into the solid state by (for example) evaporating the solvent in the presence of a nonvolatile plasticizer.(24)... 

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. 

Both magnitudes depend on the cholesteric pitch despite the unwound state of the helix. The sign and the amplitude of the angle of the field-induced domain rotation (at threshold) depends on handedness and the pitch of the helix... 

Figure 4 Changes in the cholesteric pitch of poly(y-p-alkylbenzyl-a,L-glutamate)s concentrated solutions (a) dependence of the half-pitch on polymer concentration (b) polarizing optical micrographs (1 octyl, 2 dodecyl, 3 hexadecyl, 4 docosyl). (Adapted from E.l. lizuka, K. Abe, K. Hanabusa, and H. Shirai. In R.M. Ottenbrite, Ed. Current Topics in Poiymer Science, Munich Carl Hanser, 1987, p. 235. With permission.)...

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