Frederiks external fields

Here, the first term describes the nematic-like elastic energy in raie crmstant approximation (K in 9). This term allows a discussion of distortions below the AF-F threshold (a kind of the Frederiks transition as in nematics in a sample of a finite size). In fact, the most important specific properties of the antiferroelectric are taken into account by the interaction potential W between molecules in neighbour layers the second term in the equation corresponds to interaction of only the nearest layers (/) and (/ + 1). Let count layers from the top of our sketch (a) then for odd layers i, i + 2, etc. the director azimuth is 0, and for even layers / + 1, / + 3, etc. the director azimuth is n. The third term describes interactimi of the external field with the layer polarization Pq of the layer / as in the case of ferroelectric cells. Although for substances with high Pq the dielectric anisotropy can be neglected, the quadratic-in-field effects are implicitly accounted for by the highest order terms proportiOTial to P. ... 

The isotropic phase of nematogens differs from conventional isotropic liquids in two aspects. First, the pretransitional phenomena in the vicinity of the clearing point dramatically change the bulk properties (in particular, the Kerr constant) of the isotropic phase due to the short-range nematiclike order. Second, quasi-nematic surface layers form at the interface with a solid substrate. Due to their dielectric (and optical) anisotropy they can contribute to the electrooptical properties of cells filled with the isotropic phase. For example, they can be reoriented by an external field (an analogy with the Frederiks transition). We will discuss briefly both phenomena. 

We now turn to the changes that occur in the macroscopic structure of a liquid crystal due to a destabilization and reorientation of the director under direct action of an electric or magnetic field. The external field might be coupled either to the dielectric (diamagnetic) anisotropy (magnetically or electrically driven uniform Frederiks transition and periodic pattern formation) or to the macroscopic polarization (flexoelectric effect and ferroelectric switching) of the substance. The fluid is considered to be nonconductive. 

Figure 11. The geometry of the bend Frederiks transition (a) and the profile of the director deviation, induced by an external field (b).

The Frederiks transition in linear-chain and comb-like polymers may be treated in an analogous way as low-molecular-weight compounds, with some precautions [13], because, in general, the electric and viscoelastic properties of liquid crystal polymers are field dependent and the response of the materials to an external field is essentially nonlinear. Unfortunately, in the major part of electro-optical experiments this nonlinearity is not taken into account and results are interpreted in terms of conventional nema-todynamics and constant material parameters. In addition, in only a few papers (e.g. 

The anchoring transition considered above is driven by repulsive interactions as controlled by the grafting density. Related transitions may be driven by geometrical confinementwhich can induce a tilting transition. The transition is reminiscent of the Frederiks transition in single component nematics, but is driven by the elasticity of the LCP rather than by an external field. 

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