Spontaneous macroscopic polarization

The advantages of SSFLC devices derive to a large extent from the spontaneous macroscopic polarization P of the phase. For example the electrooptic rise time of a prototypical SSFLC light valve is inversely proportional to the magnitude of the polarization. In order to design new FLC materials with large P in a directed way, we... 

Liquid crystals can be composed both of polar and apolar molecules. An important fact in connection with polar substances is that in uniaxial phases there is no polar ordering of the molecules. In average the dipole moments aligned in a given direction are compensated by those aligned in the opposite direction. As a consequence no spontaneous macroscopic polarization develops. More generally one can state that rotation of the director by n does not affect the physical state of the liquid crystal. In biaxial phases built of chiral molecules, such as the chiral smectic C phase, the situation is different. In these systems the compensation of the dipole moments is not perfect, a macroscopic polarization appears in the direction perpendicular both to the layer normal and the director. These phases are therefore ferroelectric. Ferroelectric liquid crystals are currently perhaps the... 

In the middle diagram of Fig. 5 we have also traced the response for the modification of an antiferroelectric, which we get in the case where the two sublattices have a different polarization size. This phase is designated ferrielectric. Because we have, in this case, a macroscopic polarization, ferrielectrics are a subclass of ferroelectrics. It also has two stable states as it should, although the spontaneous macroscopic polarization is only a fraction of that which can be induced. If the polarization values of the sublattices are F, and P2saturation polarization after sublattice reversal is (F + P2). 

Figure 14. Idealized presentation of the orientation process, which leads to piezoelectricity in chiral smectic C elastomers (only the mesogens are shown) [28], P macroscopic polarization). The deformed states with a partially unwound helix (left and right) are prepared from the ground state with a helical superstructure (middle) by mechanical forces. 0 and direction of the spontaneous polarization in and out of the plane of drawing, respectively.

It is known that the crystal symmetry defines point symmetry group of any macroscopic physical property, and this symmetry cannot be lower than corresponding point symmetry of a whole crystal. The simplest example is the spontaneous electric polarization that cannot exist in centrosymmetric lattice as the symmetry elements of polarization vector have no operation of inversion. We remind that inversion operation means that a system remains intact when coordinates x, y, z are substituted by —x, —y, —z. If the inversion center is lost under the phase transition in a ferroic at T < 7), Tc is the temperature of ferroelectric phase transition or, equivalently, the Curie temperature), the appearance of spontaneous electrical polarization is allowed. Spontaneous polarization P named order parameter appears smoothly... 

Figure 15. The helical configuration of the director-polarization couple is unwound by a sufficiently strong electric field E. The increasing field induces a macroscopic polarization (which is thus not spontaneous) and finally polarizes the medium to saturation (all dipolar contributions lined up parallel to the field), as shown to the right.

Owing to the coherence, we need to consider the macroscopic evolution of the field in a medium that shows a macroscopic polarization induced by the field-matter interaction. This will be done in three steps. First, the polarization induced by an arbitrary field will be calculated and expanded in power series in the field, the coefficients of the expansion being the material susceptibilities (frequency domain) or response function (time domain) of wth-order. Nonlinear Raman effects appear at third order in this expansion. Second, the perturbation theory derivation of the third-order nonlinear susceptibility in terms of molecular eigenstates and transition moments will be outlined, leading to a connection with the spontaneous Raman scattering tensor components. Last, the interaction of the initial field distribution with the created polarization will be evaluated and the signal expression obtained for the relevant techniques of Table 1. 

Figure 12 Helical superstructure of the ferroelectric Sc phase and unwinding toward a macroscopic polar structure by the application of an electrical field. The spontaneous polarization is opposite to the applied electrical field.

The starting system is achiral (plates at 90° with isotropic fluid between), but leads to the formation of a chiral TN structure when the fluid becomes nematic. In this case, enantiomeric domains must be formed with equal likelihood and this is precisely what happens. The size of these domains is determined by the geometry and physics of the system, but they are macroscopic. Though the output polarization is identical for a pair of heterochiral domains, domain walls between them can be easily observed by polarized light microscopy. This system represents a type of spontaneous reflection symmetry breaking, leading to formation of a conglomerate of chiral domains. 

Figure 8.20 Structure and phase sequence of prototypical bent-core mesogen NOBOW (8) are given, along with space-filling model showing one of many conformational minima obtained using MOPAC with AMI force field. With observation by Tokyo Tech group of polar EO switching for B2 smectic phases formed by mesogens of this type, banana LC field was bom. Achiral, polar C2v layer structure, with formation of macroscopic spontaneous helix in polarization field (and concomitant chiral symmetry breaking), was proposed to account for observed EO behavior.

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