Director distortions, nematics

Yokoyama, H., and Van Sprang, H. A. A novel method for determining the anchoring energy function at a nematic liquid crystal-wall interface from director distortions at high fields./. Appl. Phys. 57, 4520 (1985). 

We now consider a twist disclination loop in a twisted nematic. The nematic is supposed to have a planar structure with the director parallel to the xy plane and an imposed twist of q per unit length about the z axis, and the disclination loop of radius R is supposed to be in the xy plane. The director distortions are planar, = cos = sin = 0. On going once round the disclination line at any point on the loop, the director orientation changes by 2tis, the sign of which may be either the same as that of q or opposite. 

In the distorted nematic the director distribution is inhomogeneous, and hence n = n(r) in Eq. (1.46). Taking into account that the length scale of the director variation is much larger than the molecular size we can apply the gradient expansion of the director n(r) with respect to some point Ro inside the molecule ... 

Besides the elastic and the electric torques the so-called flexoelectric (or flexo) torques on the director play an important role as well. Their effect on pattern-forming instabilities in nematics is the main issue of this chapter. Flexotorques originate from the fact that typically (in some loose analogy to piezoelectricity) any director distortion is accompanied by an electric flexopolarization Pa (characterized by the two ffexocoefScients ei, 63). From a microscopic point of view, finite ei and 03 naturally arise when the nematic molecules have a permanent dipole moment. But also for molecules with a quadrupolar moment, finite ei and 63 are possible (see also Chapter 1 in this book ). Flexopolarization has to be incorporated into the free energy P n) for finite E. It is not surprising that this leads to quantitative modifications of phenomena, which exist also for ci = 63 = 0. Though, for example, the Freedericksz threshold field Ep is not modified, the presence of flexoelectricity leads to considerable modifications of the Freedericksz distorted state for E > Ep- ... 

More frequently, instead of the equilibrium pattern sketched so far, one observes electroconvection (EC) patterns in nematics, which present dissipative structmes characterized by director distortions, space charges and material flow. A necessary requirement for their existence is the presence of charge carriers in the nematic. In a distorted nematic, where n is neither parallel nor perpendicular to E, the generation of a non-zero space charge, pei, by charge separation is then inevitable. The resulting Coulomb force in the flow equations (generalized Navier-Stokes equations) drives a... 

The theoretical analysis of ffexodomains in planar nematics, which is briefly reviewed in the following, exploits the balance of torques by minimizing the total free energy E n). If not otherwise stated, an assumption of strong anchoring of the director n at the confining plates is used i.e. the director at the boundaries remains parallel to no x, irrespective of director distortions in the bulk of the nematic layer. 

Nematic liquid crystals are 3D anisotropic fluids, and as such they have no translational order, i.e., they do not support extensional or shear strains. For this reason, the rheology of nematic liquid crystals is similar to conventional organic liquids with similar size of molecules. The main difference is due to the anisotropic nature of the materials the director distortion results in elastic responses, and the magnitude of the viscosity depend on the relative orientation of the director with respect to the velocity gradient. 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

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