Liquid crystals ordering

The transitions of the coil-globule type were considered not only in the usual space, but also in the space of monomeric units orientation, where such transition is equivalent to the nematic liquid crystal ordering [60,61]. Such an approach using the formalism developed by I.M. Lifshitz has led to the creation of the theory of liquid crystal ordering in the solutions of semi-flexible macromolecules [62,63]. 

For the synthesis of side chain liquid crystal polyphosphazenes, the most important examples in Figure 2 are the alkoxy- and aryloxy-polymers. Mesophase behavior has been noted with simple side chains, such as trifluoroethoxy and aryloxy side chains (9). This mesophase behavior is not conventional liquid crystal order, but polymers which exist in a conformationally disordered state (10). 

Als-Nielsen J, Litster J D, Birgeneau R J, Kaplan M and Safinya C R 1980 Lower marginal dimensionality. X-ray scattering from the smectic-A phase of liquid crystals Ordering in Strongly Fluctuating Condensed Matter Systems ed T Riste (New York Plenum)... 

Zhang Q, Bazuin CG, Barrett CJ. 2008. Simple spacer free dye polyelectrolyte ionic complex side chain liquid crystal order with high and stable photoinduced birefrin gence. Chem Mater 20 29 31. 

Liquid Crystal Order in Polymer / Ed. A. Blumshtein. Moscow. 

The counter-ion concentrations around the polyelectrolyte chain may fluctuate, which induces an attractive interaction between the chains sharing the same clouds of counter-ions (Golestanian et al. 1999). Parallel stacking of polyelectrolyte chains favors such kind of attractions, as demonstrated in Fig. 4.11. This effect will result in the spontaneous liquid crystal ordering in polyelectrolyte solutions (Potemkin et al. 2002 Potemkin and Khokhlov 2004). Such a tendency of liquid crystal ordering acmally stabilizes the parallel rolling of DNA long chains, and squeezes them into the very limited space of cell nucleus. 

Fig. 4.11 Illustration of parallel stacking of polyelectrolyte chains dark gray rods with negative charges) favoring the sharing of counter-ion clouds light gray positive charges) and hence forming liquid-crystal-ordering structure...

Liquid crystal order in polymer, Blumshtein, A. Ed. Moscow. 

W. G. Miller, Liquid Crystals Ordered Fluids, Vol. 11, Plenum Press, New York, 1974, p. 243. 

Fig. 3.4.2 The temperature dependence of the magnitude of the liquid crystal order parameter on grooved surfaces with various pitches (4). Solid lines show the cases using grating surfaces with pitches of 0.5, 0.75, 1, and 2 pm. The broken line shows the case for the surface made by SiO oblique evaporation. The lines, (a) and (b), show the values in the bulk for the LC cells using grating surfaces with pitches of 0.5 and 2 pm, respectively.

According to the phase diagram schematically shown in Fig. 4.7, two types of liquid crystal ordering with different preparation methods can be categorized. One is the lyotropic liquid crystal approached by changing the concentration in solutions. The other is the thermotropic liquid crystal approached by changing the... 

The straight short lines represent the molecules. In terms of the two characteristic properties of liquid crystals, order and mobility, the two extremes among the four phases are the crystal phase and the liquid phase. The crystal phase is the one that is well ordered and the liquid phase is the one that is disordered. The two liquid-crystal phases, also known as mesophases, are ranked between the two extremes. The smectic phase is more ordered than the nematic phase. By contrast, increasing mobility runs in the opposite direction. A crystal has no mobility whereas a liquid has high mobility. Both mesophases are mobile, with nematic more so than smectic. Figure 6.1 also illustrates that crystal and liquid phases are isotropic, meaning that no direction is involved in the order and mobility. The two mesophases are anisotropic that is, both have direction. This is particularly true in the nematic phase. The properties of the nematic phase are very sensitive to direction. 

Polymers may exhibit the behavior of liquid-crystal order either in melt (thermotropic liquid crystals) or in solution (lyotropic liquid crystals). In thermotropic liquid crystals, the phases of the liquid crystals may be observed to change as temperature is increased. In lyotropic liquid crystals, the ordered crystalline state is... 

Similary the global liquid crystal order parameter <5lc> can be written as... 

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