Characteristic lengths nematic

For the smectic A phase the permeation effect is even more important [16]. In fact, with the layers fixed at the walls of a capillary, a smectic may flow only as a whole, like a plug, without velocity gradients. Fig. 9.10b. The velocity is again given by equation Vp = kpV, where kp is the permeation coefficient depending on the smectic characteristic length given by Eq. (8.46), cmiventional nematic viscosity q and temperature ... 

The director takes on a specified orientation at the boundary. The strength of the nematic effect in flow is determined by a dimensionless Ericksen number E = ( 3 — a2)L Y/K, where L is the characteristic length scale and K is a representative Frank elastic constant. Orientation boundary layers will develop because of competition between the alignment induced by the preferred boundary orientation and the nematic potential in the bulk. 

The factor appearing in the construction of this energy reflects the assumption that the influence of the point defect extends to a depth in the nematic sample having the order of the characteristic length f. 

Here, D stands for the characteristic geometrical length of the system. In the case of spherical particles or strongly anisotropic rod-like particles immersed in a nematic LC phase, D stands for the particle diameter or width, respectively. The strong anchoring regime, in which the surface-imposed tendency is... 

The cholesteric phase is similar to that of the nematic phase on a local scale. As in the nematic phase, the molecules can be described by a director. However, the director in the cholesteric phase is twisted about an axis normal to the molecular orientation, following a helical path (Figure 1.3). The distance over which the molecular director rotates by 2tt along the helix axis is defined as the length of the cholesteric helix pitch, P. The twist is right-handed or left-handed depending on the molecular conformation. Iridescent colors are characteristic of cholesteric phases [1,2]. 

In the X-ray experiments on nematic 8CB, the smectic ordering was observed at the free surface (air-nematic interface). The same phenomenon has also been observed at the solid-nematic interface by the X-ray, an electrooptical technique and molecular force measurements. The principle of the latter is shown in Fig. 10.7. For two mica cylinders submerged in nematic liquid crystal, their interaction force measured with a balance oscillates with a distance between the cylinders and the period of oscillations was found to be equal to molecular length 1. This clearly shows the periodicity in density characteristic of a smectic phase [8]. 

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