Goldstone ferroelectrics

Ferroelectric liquid crystals where a continuous symmetry group is broken at Tc and the doubly degenerate relaxational soft mode of the high-temperature phase splits below Tc into an amphtudon -type soft mode and a symmetry restoring Goldstone (i.e., phason ) mode [e.g., p-decyloxybenzylidene p -amino-2-methylbutylcinnamate (DOBAMBC)]. 

Nevertheless, several authors, in studying SmC polyacrylates [22] or SmC poly-siloxanes [ 14,41,67], have observed the two expected collective relaxations in ferroelectric liquid crystals, namely the Goldstone mode and the soft mode. These two relaxations occur at frequencies lower than 10 Hz. 

We can answer the last question if consider a constraction of the so-called surface stabilised ferroelectric liquid crystal cell or simply SSFLC ceU [9]. Such SSFLC cell is only few micrometers thin and, due to anchoring of the director at the surfaces, the intrinsic helical stmcture of the SmC is unwound by boundaries but a high value of the spontaneous polarisation is conserved. The cell is con-stracted in a way to realise two stable states of the smectic C liquid crystal using its interaction with the surfaces of electrodes, see Fig. 13.6a. First of all, in the SSFLC cell, the so-called bookshelf geometry is assumed the smectic layers are vertical (like books) with their normal h parallel the z-axis. Then the director is free to rotate along the conical surface about the h axis as shown in Fig. 13.6b (Goldstone mode). It is important that, to have a bistability, the director should be properly... 

The process of the director reorientation in polymer ferroelectrics, as in their low-molecular counterparts, involves changes in the tilt 0) and azimuthal (f) angles. These two modes are characterized by quite different rates. The 6 process corresponds to the soft-mode distortion, and the corresponding time To diverges at the C A phase transition point. The process means the motion of the director over the conical surface around the normal to the smectic layer (the Goldstone mode). In the helical structure the latter involves the twisting-untwisting mode, tq and differ considerably from each other, because backbones participate in those modes to a different extent. This can be seen in the dielectric spectra [172], and in the pyroelectric and electrooptical response. 

Like the usual dielectrics, the ferroelectric smectic-C phase possesses contributions to its dielectric permittivity which are based on the deformation of molecular electron shells and the orientation of permanent molecular dipoles. The dielectric properties at low frequencies, however, are dominated by additional contributions, the Goldstone mode and the soft mode [43], which result from the presence of the spontaneous polarization P and the coupling between P and 9. 

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. 

Levstik A, Carlsson T, Filipic C, Levstik I, Zeks B (1987) Goldstone and soft mode at the smectic-A-smectic-C phase transition studied by dielectric relaxation. Phys Rev A 35 3527-3534 Li J, Wang Z, Cai Y, Huang X (1998) Study of EO properties of polymer network stabilized of ferroelectric hquid crystal in smectic C phase. Ferroelectrics 213 91-98 Li J, Zhu X, Xuan L, Huang X (2002) V-shaped electro-optic characteristics in ELC gels. Ferroelectrics 277 85-105... 

Pal Majumder T, Mitra M, Roy SK (1994) Dielectric relaxation and rotational viscosity of a ferroelectric liquid crystal mixture. Phys Rev E 50(6) 4976-4800 Petit M, Daoudi A, Ismaili M, Buisine JM (2006) Electroclinic effect in a chiral smectic-A liquid crystal stabilized by an anisotropic polymer network. Phys Rev E 74 061707 Petit M, Hemine J, Daoudi A, Ismaili M, Buisine JM, Da Costa A (2009) Effect of the network density on dynamics of the soft mode and the Goldstone modes in short-pitch ferroelectric liquid crystals stabihzed by an anisotropic polymer network. Phys Rev E 79 031705 Pirs J, Blinc R, Marin B, Pirs S, Doane JW (1995) Polymer network volume stabilized ferroelectric liquid crystal displays. Mol Cryst Liq Cryst 264 155-163 Polyanin AD, Zaitsev VF (2003) Handbook of exact solutions for ordinary differential equations, 2nd edn. Chapman Hall, Boca Raton... 

Fig. 4.9. Ferroelectric Goldstone and soft modes in the chiral smectic phase, (a) Temperature dependence of the relaxation rate /c (b) the dielectric loss spectrum as a function of bias d.c. voltage. (From Ref. 42, with permission.)...

It has to be noted that Kremer et al conducted their studies on purposely unoriented samples. They did so because the presence of the optically active end groups in the side mesogen chains usually leads to chirality of the mesophase. As a result, polymers 31, 37, 39, 41 and 43 exhibit the cholesteric (chiral nematic) phase, and polymer 40, 41 and 43 the chiral smectic C phase.Since the smectic C shows ferroelectric-ity, in order to separate the molecular rotational modes from the ferroelectric Goldstone and soft modes (cf. Section 4.3), samples should be unoriented. On the other hand, measurements performed on the oriented sample of the chiral C phase of polymer 43 led Vallerien et al to the observation of ferroelectric modes. 

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