Liquid crystal director definition

Thennotropic liquid crystal phases are fonned by rodlike or disclike molecules. However, in the following we consider orientational ordering of rodlike molecules for definiteness, although the same parameters can be used for discotics. In a liquid crystal phase, the anisotropic molecules tend to point along the same direction. This is known as the director, which is a unit vector denoted n. 

The surface polarization can be measured by different means. The most straightforward one is based on the pyroelectric technique [15]. To measure P one has to deal only with one surface of a cell with uniform director alignment, either planar or homeotropic at both interfaces. The main idea is to use a spatially dependent temperature increment in order to separate the contributions to the pyroelectric response coming only from the surface under study and not from the opposite one. By definition, the pyroelectric coefficient is y = dPIdT where P is macroscopic polarization of a liquid crystal and T is temperature. If we are interested only in the polarization originated from the orientational order we can subtract the isotropic contribution to y and calculate P in the nematic or SmA phases by integrating the pyroelectric coefficient, starting from a certain temperature T, in the isotropic phase ... 

Figure 2.1 shows three situations in which the director of the liquid crystal points along different directions. It is not difficult to imagine that the force necessary to move the top plate at a specified velocity is different for each situatioa If two assumptions are made, namely that the flow is laminar and that the velocity of the fluid next to each plate moves with the same velocity as the plate, then the general definition of viscosity as the shearing stress divided by the velocity gradient becomes... 

A perhaps more significant example of a lyotropic liquid crystal is the cell membrane. The phospholipid bilayers of all cells behave as liquid crystals, maintaining a definite director and displaying only limited fluidity. Interestingly, most membranes are not pure phospholipids, but contain additives whose function is presumably to tune the structural and dynamic properties of the membrane. In animals, the most common additive is cholesterol, while plants use a similar steroid. As such, cell membranes can truly be thought of as cholesteric liquid crystalline phases. 

The microstructure of an ER system definitely determines how this system behaves under an electric field. Figure 22 shows the shear stress of oclylcynaobiphenyl vs. the electric field at shear rate 329.5 s " and various temperatures. As indicated in the literature [70-73], Oclylcynaobiphenyl is a liquid crystal material, and has a phase transition from the smectic to the nematic phase at 306.72 K and from the nematic to the isotropic phase at 313.95 K. With the increase of temperature from 306.6 K to 312.8 K, oclylcynaobiphenyl may have the different structures marked as a to b [73]. The ER property of oclylcynaobiphenyl should depend on how the director is orientated in the fields, fhe shear stress passes through a maximum value when the liquid crystal material is in the smectic phase state. Once the material is in tlie nematic phase state, the ER effect becomes weak and saturates at the electric field strength above 0.7 kV/mm. 

Nematic liquid crystals have anisotropic molecules, and they are arranged in space in more or less in one direction called director, but there is no regularity in their positions like liquids. They are only more viscous than ordinary liquids and like liquids they do not possess definite shape. It is the most type of liquid crystal phase [5,6]. 

In the SmC liquid crystals, the primary order parameter is the director tilt and not the spontaneous polarization. The polarization, therefore, is often called secondary-order parameter, and the SmC materials are called improper ferroelectrics. The main reason for this is the weakness of the dipole-dipole interactions in the molecules. The polar order can be estimated by the ratio of the actual spontaneous polarization and which is the value that would appear when complete polar order is assumed. From its definition, the polarization is the density of the molecular dipoles. Assuming molecular dipoles of 3 Debye ( 10 Cm) and typical molecular weight of 300 g, density of about 1 g/cm = 10 kg/m, we get that in 1 m we have 6 10 molecules, which would give Po 2 W C/m = 2000nC/cm. For a SmC with Pg <100 nC/cnP, this means that less than 5% of the dipoles are ordered in one direction. For this reason, in the first approximation the polarization is proportional to the tilt angle. This relation, indeed, is found to be true for materials with moderate or low polarization. However, for materials with large polarization, like Pg 500 nC/cm, the dipole-dipole interaction becomes considerable, and the proportionality is not true. The deviation is more pronounced at lower temperatures, when the dipole-dipole... 

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