Smectic Goldston mode

Fig. 5.10.6. The dielectric constant for measuring field parallel to the layers as a function of temperature in the smectic C phase of [S]-4 -(2-chloro-4-methyl-pentanoyloxy)phenyl

Fig. 5.10.8. The temperature variation of the Goldstone mode and soft mode viscosity coefficients, and y, in the smectic C phase of DOBAMBC. (After...

The Goldstone mode in an achiral SmC tries to restore the symmetry of the smectic A phase Cooh —> Dooh by free rotation of the director along the conical surface with the smectic layer normal as a rotation axis. Thus, like chiral molecules convert a nematic into a cholesteric, they convert an achiral SmC into chiral SmC without any phase transition. In addition, mixing left (L)- and right (R)-handed additives results in a partial or complete compensation of the helical pitch both in cholesterics and chiral smectic C. For example, the L- and R- isomers of the same molecule taken in the equal amounts would give us a racemic mixture, that is achiral SmC without helicity and polarity. 

The last criterion (4) is bistability. In the non-helical structure the direction of the polar axis is fixed in the sense that the three vectors, the polar axis Pj, the director n and the smectic normal h form either right or left vector triple. This depends on molecular handedness and cannot be changed. In this sense there is no bistability. On the other hand, the Goldstone mode allows the thresholdless rotation of Pj together with n about h through any angle by an infinitesimally low electric field. So, a number of possible states is infinite. 

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 theory of the dielectric properties of chiral smectic liquid crystals is far from complete, particularly with respect to a molecular statistical approach. Simple Landau theory [31 ] gives expressions for the contributions of soft modes (jj g) and Goldstone modes (Xo) to the low frequency permittivity as ... 

As explained earlier, both the Goldstone and soft modes contribute to the perpendicular permittivity component in the smectic C phase, although away from the Goldstone mode dominates in twisted structures. 

Using dielectric relaxation spectroscopy, it is possible to determine the values of the rotational viscosity tensor corresponding to the three Euler angles in the chiral smectic C and A phases. These viscosity coefficients (Ye, Yq>, 7i) active in the tilt fluctuations (the soft mode), the phase fluctuations (the Goldstone mode), and the molecular re-... 

In the standard description of the dielectric properties of the chiral tilted smectics worked out by Carlssonet al. [152], four independent modes are predicted. In the smectic C the collective excitations are the soft mode and the Goldstone mode. In the SmA phase the only collective relaxation is the soft mode. Two high frequency modes are connected to noncollective fluctuations of the polarization predicted by the theory. These two modes become a single noncollective mode in the smectic A phase. There is no consensus [153] as yet as to whether these polarization modes really exist. Investigations of the temperature dependence of the relaxation frequency for the rotation around the long axis show that it is a single Cole-Cole relaxation on both sides of the phase transition between smectic A and smectic C [154]. The distribution parameter a of the Cole-Cole function is temperature-dependent and increases linearly (a=a-pT+bj) with temperature. The proportionality constant uj increases abruptly at the smectic A to SmC transition. This fact points to the complexity of the relaxations in the smectic C phase. 

Figure 78 shows a plot of the soft mode and Goldstone mode rotational viscosities measured on either side of the phase transition between the smectic A and SmC. It can be seen that, except in the vicinity of the phase transition, the viscosity seems to connect fairly well between the two phases. The activation energies of these two processes are, however, different. This result may be compared to results obtained by Pozhidayev et al. [148], referred to in Fig. 67. They performed measurements of y beginning in the chiral nematic phase of a liquid crystal mixture with corresponding measurements in the SmC phase, and have shown the viscosity values on an Arrhenius plot for the N and SmC phases. Despite missing data of y in the smectic A phase they extrapolate the N values of y down to the smectic C phase and get a reasonably smooth fit. Their measurements also show that y is larger than y, and this is universally the case.

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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... 

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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