Dielectric torque

C.4. "Thin" dielectric cylinders, parallel and at all angles, interaxial separation z << radius R Lifshitz form retardation, magnetic, and ionic-fluctuation terms not included C.4.a. Parallel, interaxial separation z C.4.b.l. At an angle 0, minimal interaxial separation z C.4.b.2. Torque r(z, 0)... 

The application of an electric field above the threshold value results in a reorientation of the nematic liquid crystal mixture, if the nematic phase is of negative dielectric anisotropy. The optically active dopant then applies a torque to the nematic phase and causes a helical structure to be formed in the plane of the display. The guest dye molecules are also reoriented and, therefore, the display appears coloured in the activated pixels. Thus, a positive contrast display is produced of coloured information against a white background. The threshold voltage is dependent upon the elastic constants, the magnitude of the dielectric anisotropy, and the ratio of the cell gap to the chiral nematic pitch ... 

The ion-dipole interaction exerts a torque on the dipole, which reduces the activation energy of the rotation. For randomly oriented molecules, the average torque U exerted on a molecule with dipole moment by a singly charged ion at a distance r through a medium of dielectric constant is roughly... 

Physical origin of dielectric loss The foregoing conclusions correspond to a static description or cases for which the polarization can perfectly follow the oscillation of the electric field. Indeed, the electric field orientation depends on time with a frequency equal to 2.45 GHz (the electric field vector switches its orientation approximately every 10 s). The torque exercised by the electric field induces rotation of polar molecules, but they cannot always orient at this rate. The motion of the particles will not be sufficiently rapid to build up a time-dependent polarization P(t) that is in equilibrium with the electric field at any moment. This delay between electromagnetic stimulation and molecular response is the physical origin of the dielectric loss. 

One can easily identify the effect of various terms in Eq. (7) with the increase of the orientational elasticity the dielectric torques... 

Case C homeotropic alignment, Ca < 0 0. In this combination of the material parameters, the linear stability analysis of the basic state does not predict a direct transition to EC since the resulting expression for U q) in Eq. (8) is negative for all q 0 (except for e in the immediate vicinity of zero, see below). The reason is that the two terms in the denominator act differently compared to the case B ca > 0, aa < 0) described in the previous subsection. The Carr-Helfrich torque is now stabilizing while the dielectric torque (oc is destabilizing. At q = qp = 0, this term dominates and describes, at the threshold Ups (see Eig. 7a), the continuous bifurcation to the Freedericksz distorted state of homogeneous (along the x direction) bend (see Fig. 8a). 

The elastic, dielectric and magnetic torques can be evaluated from the functional derivative... 

In this chapter, we will be describing different electro-optic techniques that have been developed specifically for measurement of the flexocoeffi-cients. In these techniques, an electric field is applied to a nematic liquid crystal in a cell with well-defined boundary treatments. The net torque on the medium, which involves dielectric, elastic and flexoelectric components, is set to zero both in the bulk and at the two surfaces in order to And the equilibrium director configuration if a DC field is applied. In AC techniques, the above torques are balanced with the viscous torque. The optical properties of the medium are in turn calculated for the distorted profiles and compared with experimental measurements. The flexoelectric, and in some... 

Any spatial distortion of n leads to elastic restoring torques, which are determined in the standard continuum description of nematics (exclusively used in this review) by three elastic constants Ki (splay), K2 (twist) and Ks (bend). In addition, the electric field E gives rise to an electric torque on the director. The balance of these torques, reflected in the resulting equilibrium director configuration, corresponds to the minimum of the orientational free energy J- n). For positive dielectric anisotropy (ca = — x) the dielectric torque (oc is destabihzing in the pla-... 

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