Nonpolarity, ferroelectrics

Using this method, the M6R8/PM6R8 blend showed precisely the behavior expected for the achiral SmAPA structure. Specifically, the optical properties of the films were consistent with a biaxial smectic structure (i.e., two different refractive indices in the layer plane). The thickness of the films was quantized in units of one bilayer. Upon application of an electric field, it was seen that films with an even number of bilayers behaved in a nonpolar way, while films with an odd number of bilayers responded strongly to the field, showing that they must possess net spontaneous polarization. Note that the electric fields in this experiment are not strong enough to switch an antiferroelectric to a ferroelectric state. Reorientation of the polarization field (and director structure) of the polar film in the presence of a field can easily be seen, however. 

From this discussion the clear similarity between the SmAPA and SmCsPA structures is easily seen. In addition, the suggestion of Brand et al.29 that a bilayer smectic with all anticlinic layer interfaces (the SmAPF) would produce an achiral ferroelectric smectic follows directly. The unanticipated tilt of the director in the tilt plane, leading to a chiral layer structure, seems to be a general response of the bent-core mesogens to the spontaneous nonpolar symmetry breaking occurring in these rigid dimer structures. 

In Eq. (20) the three terms are related to the Maxwell stress (first), piezoelectric effect (second) and electrostriction (third). In order to obtain information about ferroelectricity via piezoresponse measurements, we need a link between the spontaneous polarisation and the piezoelectric constant. According to Furukawa and Damjanovic, piezoelectricity in ferroelectrics can be explained as electrostriction biased by the spontaneous polarisation if their paraelectric phase is nonpolar and centrosymmetric [461, 495, 496]. Therefore the d33 constant depends on the spontaneous polarisation P5 ... 

PVDF film, as produced from the melt, is largely in the nonpolar a-form, the fS phase only being obtained after subsequent processing operations, as described above. If however, vinylidene fluoride is copolymerized with as little as 7% by weight of trifluoroethylene, a copolymer is formed with crystallites completely in the / -form. This obviates the need for stretching after synthesis and the copolymer can be processed byway conventional routes, such as injection molding. Moreover, unlike PVDF, copolymers of vinylidene fluoride and trifluoroethylene have been shown to demonstrate the ferroelectric to paraelectric transition. For a copolymer with a composition of 55% vinylidene fluoride and 45% trifluoroethylene, a phase transition is observed near 70°C, and with 90% vinylidene difluoride, a phase transition at 130°C. 

The temperature at which a - ferroelectric material undergoes a first-order polar-nonpolar transition. It is not the same as the Curie-Weiss temperature. 

The temperature at which the dielectric constant is a maximum, which may be different from the Curie temperature for - ferroelectric materials that undergo a first-order polar-nonpolar transition at this particular temperature. 

Figure 18.2 Perovskite crystal structure, (a) The nonpolar paraelectric cubic phase (b) A polar ferroelectric phase due to tetragonal distortion. Data for PbTiOs stem from Ref [10].

The spontaneously polarized crystal is anisotropic and has lower symmetry than the nonpolarized one. Ferroelectric materials below the Curie temperature are also always piezoelectric, because the polarized sample has no center of symmetry. If the nonpolarized crystal has the center of symmetry, the piezoelectricity of the sample vanishes above the Curie temperamre. All ferroelectrics below the Curie temperature also always show pyroelectric behavior. 

FIGURE 7.24. Various guest-host ferroelectric displays [126]. (a) Nonpolarized DGHFE and (b) fluorescent DGHFE. 

There are two common ways to categorize dielectric materials polar or nonpolar and paraelectric or ferroelectric. Polar materials include those that are primarily molecular in nature, such as water, and nonpolar materials include both electronically and ionically polarized materials. Paraelectric materials are polarized only in the presence of an applied electric field and lose their polarization when the field is removed. Ferroelectric materials retain a degree of polarization after the field is removed. Materials used as ceramic substrates are usually nonpolar and paraelectric in nature. An exception is silicon carbide, which has a degree of molecular polarization. 

Although the nematic phase is nonpolar, there are very interesting and important polar effects in this phase, in a sense analogous to piezoelectric effects in solid crystals. This was recognized by Meyer [18] in 1969. These so-called flexoelectric effects are discussed in Sec. 2.4 of this Chapter. Meyer also recognized [61] in 1974 that all chiral tilted smectics would be truly polar and the first example of this kind, the helielectric smectic C, was presented [62] in 1975. Out of Meyer s discovery grew the whole research area of ferroelectric and antiferroelectric liquid crystals, which is today a major part of liquid crystal physics and chemistry. 

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