Concentration Dependence of the Pitch

Theoretical considerations are rare for the concentration dependence of LC cellulos-ic/solvent systems and the same is true for experimental studies. In many instances it is difficult to keep a constant concentration over a longer time during which experiments are carried out. If a functionality P=kc is assumed k a constant, c concentration, m a variable that might depend on the stiffness of the molecules as well as on the solvent, the temperature, and the molecular mass), the value of m is 2 for somewhat stiff LC poly-y-benzyl-L-glutamate in dioxane and 3 for semi-flexible LC HPC in water. A detailed study of LC CTC/MAA [17] led to a value of m=2.4 for lower concentrations between 38 and 44 wt%, independent of the temperature. At a higher concentration of 44-50 wt%, a value of m = 1.1 at 20 °C was determined, which increases 

Generally, a decrease in the pitch with increasing concentration occurs for most lyotropic LC cellulosics. However, in some cases, such as CTC/ketone systems or CTC in some glycols, an increase in pitch is observed (see Fig. 14b), and in rare cases a sharp change has been detected in the concentration gradient of the pitch, quite similar to the temperature gradient. 

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Since the microscopic structure of nematics and cholesterics is similar, these two phases are mixed like two nematics. Thus the thermodynamic behavior of nemato-cholesteric mixtures needs no special discussion (see Section 1.2.1). What is of interest, especially for liquid crystalline materials for technological applications, is the concentration dependence of the helical pitch and the physical parameters relevant to this dependence. 

FIGURE 6.3. Dependence of the pitch of a cholesteric hehx on the concentration of cholesteryl oleylcarbonate in a nematic mixture with Ae = 7.6 at a temperature of 25 °C. 

Fig. 73. Dependence of the pitch of the cholesteric helix on the concentration of solutions of PBG-L in dioxane (1) and hydroxypropylcellulose in H2O (2) [2, 15].

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 inverse of the pitch which corresponds to the helical twist of the lamellas against each other, is plotted in Fig. 5.35 for different concentrations of formamide. The values shown in the upper part of Fig. 5.35 were determined with the Cano method, while the bottom part shows the results obtained by the direct method. The two plots in Fig. 5.35 basically show the same behavior. In both plots no clear temperature dependence of the helical twist can be found. Right after the phase transition into the lyotropic SmC analog phase, the helical structure is... 

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.)...

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]. 

The structures shown in Fig. 4-1 are for B-form DNA, the usual form of the molecule in solution. Different double-helical DNA structures can be formed by rotating various bonds that connect the structure. These are termed different conformations. The A and B conformations are both right-handed helices that differ in pitch (how much the helix rises per turn) and other molecular properties. Z-DNA is a left-handed helical form of DNA in which the phosphate backbones of the two antiparallel DNA strands are still arranged in a helix but with a more irregular appearance. The conformation of DNA (A, B, or Z) depends on the temperature and salt concentration as well as the base composition of the DNA. Z-DNA appears to be favored in certain regions of DNA in which the sequence is rich in G and C base pairs. 

Optical Exposure. Multicomponent LB films were prepared from solutions of novolac/PAC varying in concentration from 5-50 wt% PAC, and transferred at 2.5 -10 dyn/cm. The films were composed of 15 - 20 monolayers, with an average film thickness of 30 nm, as measured by ellipsometry. Exposures were performed with a Canon FP-141 4 1 stepper (primarily g-line exposure) at an exposure setting of 5.2 and with a fine line test reticle that contains line/space patterns from 20 to 1 pm (40 to 2 pm pitch). They then were then developed in 0.1 - 0.2 M KOH, depending on the PAC content The wafers received a 20 min 120°C post development bake to improve adhesion to the Cr. Finally, the Cr was etched in Cyantek CR-14 chromium etchant, and the resist and Cr images were examined by SEM. 

When the time dependence takes the form of a periodic perturbation of some parameter, we speak of this as periodic forcing.19 The response will obviously not be a steady state, but can be periodic, quasi-periodic, or chaotic. If the response is periodic, it may be with a period that is a multiple of the period of forcing. It is quasi-periodic if the response winds itself onto the cylinder in a helix whose pitch is an irrational multiple of the forcing period, so that it is never quite truly periodic. An example20 of a forced system is the Gray-Scott autocatalator with the feed concentration sinusoidally perturbed ... 

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