Chiral coupling, ferroelectrics

Other more exotic types of calamitic liquid crystal molecules include those having chiral components. This molecular modification leads to the formation of chiral nematic phases in which the director adopts a natural helical twist which may range from sub-micron to macroscopic length scales. Chirality coupled with smectic ordering may also lead to the formation of ferroelectric phases [20]. 

In the most simple chiral polar tilted smectics, ferroelectric liquid crystals, the flexoelectric phenomenon influences the structure of the SmC phase only quantitatively. It affects the elastic and chiral couplings and consequently slightly changes the transition temperature to the tilted phase and the pitch of the helicoidal modulation. 

The new chiral terms are of first order and therefore describe spontaneous deformations. The Dj term means that there is a tendency for the c-vector to bend in the plane of the layer, which means that a coupled ferroelectric polarization (see next chapter) will have a tendency for a spontaneous splay. The D3 term is a spontaneous twist, describing the helical order of the SmC ground state. In the ground state, there is a pure twist in c. This means that c-Vxc = -q, and consequently,/c Vxc = 0. This reduces (4.60) near the equilibrium to ... 

The tilting of molecules in the B2 phase is clearly confirmed from the observation that the spherulites emerging from the isotropic phase show an electric field dependence of the position of the optical extinction lines (Fig. 9.26). Because of the tilting of banana molecules to the layer, chirality is spontaneously generated in addition to the polarity this fact sounds shocking but is so simple to be understood [132, 133]. If the molecule is rotated around their polar axis (the orientation of the bent in the molecules), which is akin to tilting the molecules in the layer, the rotation operation cannot be achieved by a simple translation (see Fig. 9.27). That is, these two states are in a mirror relation with left-handed and right-handed chirality. This is called the layer chirality. When the chirality couples with the polarity of the molecules, one would consider various smectic liquid crystal structures. There are two homochiral phases in which either (—) or (-I-) chiral molecules stack in the layers and a racemic phase in which layers are alternately stacked with layers of (—) and (-I-) chiral molecules. Each of those phases can be either ferroelectric or antiferroelectric, so that in total six different phases are present... 

In the operation of ferroelectric liquid crystal devices, the applied electric field couples directly to the spontaneous polarisation Ps and response times depend on the magnitude E Ps. Depending on the electronic structure (magnitude and direction of the dipole moment as well as position and polarity of the chiral species) and ordering of the molecules P can vary over several orders of magnitude (3 to 1.2 x 10 ), giving response times in the range 1-100 ps. 

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

The sign of the spontaneous polarization in ferroelectric smectics depends on both the sense of chirality and direction of the electrical dipole with respect to a molecular skeleton. The magnitude of the polarization is a function of the coupling between a chiral center and the transverse electrical dipole. The larger the dipole moment, and the closer its location to a chiral center, the higher polarization is observed [75]. 

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... 

The chirality in liquid crystal elastomers can be at the origin of additional physical properties such as ferroelectricity, pyroelectricity, circular dichro-ism, and nonlinear optics coupled to the polymer network. Applying external mechanical fields to the elastomers consequently causes electro-... 

The thermally excited cone motion, sometimes called the spin mode (this is very similar to the spin wave motion in ferromag-nets), or the Goldstone mode, is characteristic of the nonchiral SmC phase as well as the chiral SmC phase, but is of special interest in the latter because in the chiral case it couples to an external electric field and can therefore be excited in a controlled way. This Goldstone mode is of course the one that is used for the switching mechanism in surface-stabilized ferroelectric liquid crystal devices. The tilt mode, often, especially in the SmA phase, called the soft mode (although hard to excite in comparison with the cone mode, it may soften at a transition), is very different in character, and it is convenient to separate the two motions as essentially independent of each other. Again, this mode is present in the nonchiral SmA phase but cannot be detected there by dielectric methods, because a coupling to an electric field requires the phase to be chiral. In the SmA phase this mode appears as the electroclinic effect. 

Archer P, Dierking I (2005) Quantitative experimental determination of the Landau-potmtial of chiral enantiomer doped ferroelectric liquid crystals. EurPhys J E 18(4) 373-381 Archer P, Dierking I (2008) Elastic coupling in polymer stabilized ferroelectric liquid crystals. J Phys D Appl Phys 41(15) 155422... 

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