Director isotropic

Figure C2.2.2. Isotropic, nematic and chiral nematic phases. Here n denotes tire director. In tire chiral nematic phase, tire director undergoes a helical rotation, as schematically indicated by its reorientation around a cone.

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

Fig. 17. Polymer dispersed Hquid crystal display (PDLC). (a) U < clear state, where U) is the threshold voltage of the ceU. and rij represent the indexes of refraction for light polarized parallel and perpendicular to the director of the Hquid crystal represents the index of refraction of the isotropic...

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

The introduction of a second chiral atom in the system leads to a reduction in the mesogenic properties and only a monotropic chiral nematic transition is observed for compound 23. However, when this compound is cooled down from the isotropic liquid state at a cooling rate of 0.5 °Cmin , very unusual blue phases BP-III, BL-II and BP-I are observed in the range 103-88 °C. Blue phases usually require pitch values below 500 nm. Hence the pitch value of the cholesteric phase for 23 must be very short, suggesting that the packing of two chiral carbons forces a faster helical shift for successive molecules packed along the perpendicular to the director. 

Many other interesting examples of spontaneous reflection symmetry breaking in macroscopic domains, driven by boundary conditions, have been described in LC systems. For example, it is well known that in polymer disperse LCs, where the LC sample is confined in small spherical droplets, chiral director structures are often observed, driven by minimization of surface and bulk elastic free energies.24 We have reported chiral domain structures, and indeed chiral electro-optic behavior, in cylindrical nematic domains surrounded by isotropic liquid (the molecules were achiral).25... 

Most of the results presented in this section, including Eqs. (4.15)—(4.17), are not valid when the equilibrium state of the fluid exhibits global orientational order, for example, a global director. However, they do apply to an isotropic suspension of locally anisotropic objects, such as vesicles or liposomes, which may exhibit a local director, provided that long-range orientational correlations do not extend over a significant fraction of the volume sampled in the experiment. 

Spherical droplet that forms during a transition from an isotropic phase to a nematic mesophase. It has characteristic textures that depend on the droplet size and the director orientation at the nematic-isotropic interface. 

Note 3 A bipolar droplet texture occurs when the director lies in the plane of a nematic-isotropic interface. 

Note 1 The point defect usually forms when the director is normal to the nematic-isotropic interface. 

When a wormlike spherocylinder is in the liquid crystal phase, its tangent vector a at each contour point should align more or less to the preference direction of the phase specified by the director n. This alignment induces the orientational entropy decrease — Sor from the entropy in the isotropic state. Since the orientation of the tangent vector stretches the wormlike spherocylinder, — Sor includes a conformational entropy loss of the spherocylinder. 

FIG. 15.49 Orientation angle 6 between rodlike molecules, described by unit vector u and director n within one nematic domain of a macroscopically isotropic polydomain sample a denotes the size of the domain. From Beekmans, 1997. 

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