Tilt Angle and Spontaneous Polarization

Relation Between Tilt Magnitude and Polarization Magnitude Bilinear and Biquadratic Coupling Between Tilt Angle and Spontaneous Polarization... 

Table 2. Comparison of the transition temperatures, tilt angle and spontaneous polarization measured at 25 °C for (S)-4-(2-methylbutyl)-2-hydroxyresorcylidene 4-octylaniline, (5)-4-(4-methylhexyl)-2-hydroxyresorcyli-dene 4-octylaniline and ( S)-4-(6-methyloctyl)-2-hydroxyresorcylidene 4-octylaniline [39,40].

Table 5. Comparison of the transition temperatures, tilt angle and spontaneous polarization measured at ...

Table 14. Transition temperatures, response time (10 Vpp/pm square wave, time to maximum current), tilt angle and spontaneous polarization measured at 25°C in a 2 pm cell with polyimide alignment containing mixtures of 2 mol% of the (25, 4R)-trans- (a-[4 -pentyl-l,r-biphenyl-4-yl]-y-pentyl)lactone or (2R, 4R)-cis- (a-[4 -pen-tyl-1, l -biphenyl-4-yl]-y-pentyl)lactone and a host mixture (Cr-SmC <25 °C SmC-SmA 51 C SmA-N 63 °C N-I 69 °C) [85].

Figure 8.6. Temperature-dependence of tilt angle 0, spontaneous polarization P, and ratio PJO in the ferroelectric smectic-C phase of the compound DOBAMBC (from [37]).

Table 6. Exponents of the power law equations fitting the tilt angle and the spontaneous polarization of polysiloxanes XII and XIII, as well as their piezoelectric (O and biquadratic (i2) coefficients.

Since the discovery, by Meyer et al. [1] in 1975, of ferroelectric liquid crystals (FLGs) they remain the object of intensive investigations. In 1978 Pikin and Indenbom suggested a model for the thermodynamic description of the FLC physical properties, including the macroscopic response to the external fields [2]. Later on, this model was corrected by Zeks et al. [3] in order to obtain more precisely such delicate features of an FLC as the temperature dependence of the tilt angle, the helical pitch and spontaneous polarization, anomalies of dielectric permittivities, etc. 

The ferroelectric liquid-crystal compounds which have been studied in chiral-racemic systems possess large values of the spontaneous polarization Ps, i.e., these compounds show a strong bilinear coupling between tilt angle and polarization. The behavior in chiral-racemic systems of these compounds can be well described assuming a simple proportionality of the bilinear P-9 coupling constant C and the enantiomeric excess Xee- This applies also for the electroclinic effect in the smectic- phase which has been studied in [74], [77]. Figure 8.12 shows the electroclinic tilt susceptibility /51 as a function of Xee at constant temperature difference to the transition to the smectic-C phase. The observed proportionality between xe ee is vvell in... 

Table 17. Comparison of the tilt angle, helical twisting power (HTP) and spontaneous polarization (extrapolated to 100%) measured at 71SmC -15°C of a mixture of 7 wt% of the dioxanes in a host mixture [96],...

Both polymers form the smectic C phase in a certain temp ture range. When the polymers are cooled from a melt, at the time of the transition from smectic A to smectic C, the mesogenic side groups are tilted with respect to the normal of the smectic layer (angle P), and spontaneous polarization appears in the sample when a small electric field is applied (Fig. 6.15). 

This behavior of yg in case of PSFLCs may be due to four specific reasons First, during the onset of the polymerization process, the viscosity of the FLC-monomer dispersion is reduced as monomers are now used up to form the polymer network second, the phase-separated polymer network acts as the source of elastic interactions with the LC molecules, which can also be held responsible for an effective viscosity observed in Fig. 6.2 third, the polymer network influences the tilt angle and the spontaneous polarization, which creates cascading effect on yg finally, the free volumes present in between the polymer chains restrain the director mobility, which further reduces yg. Therefore, it seems combination of effects resulting from a complex picture of interaction mechanism in case of PSFLCs produces the effective viscosity of the medium. 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

Shibaev et al. (1984) first synthesized a ferroelectric side chain polymeric liquid crystal. In the following years a lot of liquid crystalline polymers of such kind were synthesized. In early research studies techniques used to understand polymers and whether they showed the liquid crystal phase were limited so that the conclusion was ambiguous. It was only in 1988 when Uchida et al. (1988) measured the spontaneous polarization and the tilt angle that people became convinced that this side chain polymer in the literature (Shibaev et al., 1984) is indeed a ferroelectric liquid crystal. 

Similarly to the molecular engineering of calamitic molecules to produce ferroelectric smectic C phases [129], disk-like molecules with chiral peripheral chains tilted with respect to the columnar axis were predicted to lead to ferroelectric columnar mesophases [130]. Indeed, as it is the case with all flat disk-shaped mesogenic molecules, the tilt is mainly associated with the flat rigid aromatic cores of the molecules, the side-chains being in a disordered state around the columnar core. Thus, the nearest part of the chains from the cores makes an angle with the plane of the tilted aromatic part of the molecules. If the chiral centre and the dipole moment are located close to the core, then each column possesses a non-zero time averaged dipole moment, and therefore a spontaneous polarization. For reasons of symmetry, this polarization must be, on average, perpendicular to both the columnar axis and to the tilt direction in other words, the polarization is parallel to the axis about which the disk-shaped molecules rotate when they tilt as shown in Fig. 29. 

The absolute values of the spontaneous polarization Ps and the tilt angle 0 as a function of temperature are well fitted to the following power law equations... 

The main features of the antiferroelectric switching in FLCPs are a third state, which shows an apparent tilt angle of zero, a less marked threshold between the three states when compared to the low molecular weight antiferroelectric liquid crystals, a hardly observed hysteresis, and an anomalous behavior of the spontaneous polarization with temperature (Fig. 24), which is not encoun-... 

As we have seen, locally the smectic C layers are polar, belonging to pyroelectric class C2. Macroscopically SmC either forms a helical structore or does not. So, we can discuss a structure without helicity. In a sense, the formation of a helix is equivalent to formation of ferroelectric domains which would reduce overall macroscopic polarisation. Thus we can consider the (1) (very important) and (2) (additional) requirements fulfilled. As to the phase transition (3), we know that in the smectic A phase, even chiral, there is no polar axis, therefore that phase can be considered as a paraelectric phase. The two-component order parameter of the A -C transition is the same as the parameter of the A-C transition in an achiral substance, namely 9exp (i(p), where we recognise the tilt 9 and azimuth (p angles. The spontaneous... 

In the SmC phase the tilt is 9 = 9s - - 89 where 9s and 89 are spontaneous and the field induced tilt. In the absence of the field, 9s is constant and minimisation of Eq. (13.10) with respect to P relates the spontaneous polarization to the tilt angle ... 

Fig. 13.12 Clark-Lagerwall effect in thin SSFLC cell. Application of the electric field E between the ITO electrodes causes up-down switching of spontaneous polarization accompanied by conical motion of the director n. The projection of the n-vector on plane xy is C-director forming an angle

Figure 5.1.21 shows the coordinate systems of the director in the chevron layer structure, where n is the director, c is the c-director, and p is the spontaneous polarization vector. It is assumed that the tilt angle 9 and the layer tilt angle S are constant, and the azimuthal angle depends only on the cell thickness, direction Y. The director is expressed as... 

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