Ferroelectric torque

When we apply an electric field across an FLC cell there will always be a dielectric torque acting on the director, in addition to the ferroelectric torque. This is of course the same torque as is present in all liquid crystals and in particular in nematics, but its effect will be slightly different here than it is in a nematic. This is because in the smectic C phase the tilt angle 0 is a hard variable, as earlier pointed out. It is rigid in the sense that it is hardly affected at all by an electric field. This is certainly true for a nonchiral smectic C and also for the chiral C, except in the immediate vicinity of Tc a. where we may not neglect the electroclinic effect. Hence we will consider the tilt angle 6 uninfluenced by the electric field, and this then only controls the phase variable <(> of Fig. 60. 

Figure 66. If the xz plane is parallel to the electrodes and the electric field is applied in the positive y direction, the ferroelectric torque will turn the tilt plane (given by ip) in the negative f direction.

Another way of ameliorating the optical properties is to take advantage not only of the ferroelectric torque ( ) exerted on the molecules, but also of the dielectric torque i E ). This torque always tries to turn the... 

In Eq. (291) we derived an expression for the director equation of motion with dielectric and ferroelectric torques included. If the origin of the dielectric torque is in the dielectric biaxiality, the equation (with the elastic term skipped) will be the closely analogous one... 

Furthermore, in FLCEs the macroscopic electric dipole moment provides a handle to apply a strong torque onto the director (see Fig. 14a). The resulting switching occurs on the cone of the so-called c-director, the projection of the director on the smectic layer plane (see Fig. 14a). Soon after the discovery of the potential of chiral smectic-C phases, the search for LC polymers with these phases started [130-132]. However, as ferroelectric switching is the final proof for the assignment of the phase, the more closely studied ferroelectric LC polymers were limited to several LC polysiloxanes, which have a low Tg and a relatively high switching speed [25, 66, 133-136] (see Scheme 1). These polymers form the basis for most of the FLCEs discussed here. 

In the absence of walls the dynamic behavior may be described, as in nematics, by adding a viscous torque to the elastic and electric ones. For the field-off state, the distortion decays with the nematic time constant (see Eq. (34), where K should be substituted for 22)- The time of the response to an electric field can only be calculated for the simplest case when jU=0, Te=7 / e sin 2 E -EI), where E is defined by Eq. (69). Thus, the response of the smectic C phase is sin 2 times slower than that of the nematic phase. However, in experiments the same substance often responds faster in the smectic C phase than in the nematic one [159-161]. This may be due to the smaller value of Yi when the motion of the director is confined by the cone surface. The same phenomenon has been observed for the ferroelectric smectic C phase [162]. The domain-wall motion makes the dynamics of switching more complicated the field-induced wall velocity has been calculated by Schiller et al. [70]. 

The dynamics of the electroclinic effect are, in fact, the same as the dynamics of the ferroelectric soft mode. The switching time may be derived from the equation for the balance of the viscous, elastic, and electric torques ... 

Finally, the parameter expresses the balance between the ferroelectric and the dielectric torque. As it appears in the dielectric term of Eq. (295) in the combination siT dlx, which is 0.15/ f for 0=22°, x would have to be less than about 0.5 in order for us to have to keep this term. With the same P and E values as before, this requires a I Ael value as high as >2.5. We will therefore skip this term for the moment, but return to this question later. 

In addition to the characteristic time rand length we had earlier introduced the dimensionless parameter x describing the balance between ferroelectric and dielectric torques. Its character appears even more clearly than in Eq. (298) if we write it as... 

Figure 74. (a) Typical pulse switching characteristic for a material with parameters giving ferroelectric and dielectric torques of comparable size (b) Possible routes for engineering materials to minimize both and (from [144]). 

The switching memory effect is a reflection of the fact that the electric displacement, being the function of both the applied field and the material s properties, needs some finite time to adjust to the value of the electric field. The widely accepted model of the instantaneous relationship between the electric displacement and the electric field in the NLC is invalid when the characteristic times of the director dynamics are close to the relaxation times for molecular permanent dipoles. This time scale is typically in the submillisecond range which is of great interest for modem fast-switching devices. The electric displacement (as well as the dielectric torque density) becomes a function of the static dielectric properties of the NLC, the present and past electric field, and the present and past director. We discussed the recently proposed theory and experimental verification of the phenomenon [11]. The model in Ref [11] should be applicable to dynamic reorientation of other LC phases in the appropriate range of times/frequencies. In the case of ferroelectric LCs, the theory should be supplemented by the consideration of spontaneous electric polarization. A similar approach should be also... 

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