Electroclinic coefficient

In addition to the sensitivity to ring structure, slight alterations of the hydrocarbon chain may lead to dramatic differences in electro-optic performance in chiral compounds [43]. For example, in some electroclinic Sm-A materials it has been reported that if the chain is shortened or if a double bond is localised at the end of the hydrocarbon chain, the tilt angle, electroclinic coefficient, and switching time are significantly suppressed [43]. 

We see, that the phase transitimi temperature increases, because the dipole-dipole interactions (f -term) stabilise the smectic C phase. Note that the held induced tilt angle (or electroclinic coefficient Cc) diverges at a temperature T. This means, that at even inhnitesimally low held would create a finite tilt. This is the soft mode of the director motion any small force (not necessary electric) would cause the tilt of the director, because, at the transition, the medium becomes soft with respect to the tilt. The corresponding dielectric susceptibility shows the Curie-Weiss law ... 

In conclusion, we can state that the field behavior of polymer ferroelectric liquid crystals is very similar to that of the low molecular mass compounds. It can be interpreted in the framework of the theory discussed above (Sections 7.1, 7.2) with the high viscosity coefficients 7, (and others) taken into account. The other physical parameters (spontaneous polarization, the electroclinic coefficient, and elastic moduli) are of the same order of magnitude as for their low molecular counterparts. 

The induced tilt angle depends linearly on the applied field, but the electroclinic coefficient col/Ei modulated between 0 (for x = Jr/2 n E) and a... 

The electroclinic effect is a new form of dielectric response in a liquid crystal. If we increase the electric field E, the induced polarization P will increase according to the first curve of Fig. 5. With a small field, P is proportional to E, and then P saturates. As the coupling between tilt and polarization is also linear at small values of tilt, we get a linear relationship between 6 and E. With 9 = e E, the proportionality factor e is called the electroclinic coefficient. It has an intrinsic chiral quality. (We have used an... 

This non-linear behavior with saturation is well known experimentally. It means that the electroclinic coefficient becomes field-dependent and falls off rather strongly ( E ) at high fields. It also means the same for the electroclinically induced polarization which acquires relatively high values at low applied fields but then shows saturation. It explains the shape of the measured P T) curves near as illustrated in Fig. 18 (dashed line). 

The dynamics of the electroclinic effect is, in fact, the dynamics of the elastic soft mode. From Eqs. (13.18) and (13.19) follows that the switching time of the effect is defined only by viscosity and the term a(T — T ) and is independent of any characteristic size of the cell or material. It means that the relaxation of the order parameter amplitude is not of the hydrodynamic type controlled by term Kq (K is elastic coefficient). For the same reason Xg is independent of the electric field in agreement with the experimental data, shown in Fig. 13.9b. At present, the electroclinic effect is the fastest one among the other electro-optical effects in liquid crystals. 

Fig. 16. Electrostriction of a ferroelectric LC-elastomer (43). Big diagram Thickness variation Ah as a function of the applied ac voltage (/ac- Interferometric data were obtained at the fundamental frequency of the electric field (piezoelectricity, first harmonic -t) and at twice the frequency (electrostriction, second harmonic o). Sample temperature 60°C. Inset Electrostrictive coefficient a (-I-) versus temperature. At the temperature where the non-cross-linked polymer would have its phase transition Sc -Sa (about 62.5 0, the tilt angle of 0° is unstable. That is why the electroclinic effect is most effective at this temperature. An electric field of only 1.5 MV/m is sufficient to induce lateral strains of more than 4%.

Fume H, Takahashi T, Kobayashi S, Yokoyama H (2002) Models of molecular alignment stmcture in polymer-stabilized ferroelectric liquid crystals. Jpn J Appl Phys 40(l) 7230-7233 Giepehnann F, Zugenmaier P (1995) Mean-field coefficients and the electroclinic effect of a ferroelectric hquid crystal. Phys Rev E 52(2) 1762-1772 Giepehnann F, Hermann A, ZugeranaiCT P (1997) Experimental determination of Landau-expansion coefficients in ferroelectric liquid crystals. Ferroelectrics 200 237-256 Guymon CA, Hoggan EN, Walba DM, Qark NA, Bowman CN (1995) Phase behaviour and electro-optic characteristics of a polymer stabilized ferroelectric liquid crystal. Liq Cryst 19 719-727... 

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