Frederiks transition threshold field

The oscillations of I (U) are well seen in the experimental plot. Fig. 11.21. The measurements were made at 27°C on 55 nm thick cell filled with a mixture having ta = 22. From the I (U) curve, the field dependence of the phase retardation 8(17) and the Frederiks transition threshold Uc were obtained. In mm, from Ec = UJd and Fq. (11.56) the splay elastic constant Ku was found. The bend modulus "33 was calculated from the derivative dbldU. The same material parameters may be found for the whole temperature range of the nematic phase. 

When the applied field is much higher than the threshold of the Frederiks transition the field coherence length becomes comparable with the surface extrapolation length itself H,E b. This condition corresponds to the second threshold of the complete reorientation of a liquid crystal including surface layers, curve 3 in Fig. 3.11(a). Thus, the second threshold field allows 6 (and W ) to be calculated. 

FIGURE 6.16. Bistable switching in long-pitch cholesterics with a tilt of the director o- (a) Tilted states with n/2 turns in zero field, = 55 . (b) Free energies g as functions of thickness to pitch ratio d/Po at zero field, dlPoY = 0.89 is the operating point, (c) g(d/PoY in an electric field versus reduced volteige U/Ufi Uf is the Frederiks transition threshold, Ae > 0. 

Three kinds of Frederiks transitions can be used to measure the three elastic constants of nematic polymers. The magnetic threshold fields Hci are functions of Ku(i = 1,2,3) respectively,... 

In Chapter 11 we have found that, for the Frederiks transition in nematics, the threshold field coherence length is determined by the cell thickness, = din, see Eq.(11.53). Now we shall briefly discuss another type of instability with a threshold determined by the geometrical average of the two parameters mentioned [17],... 

From Eq. (13.29) is seen that, at (p = 0, there is no electric torque exerted on the director. Thus, there should be a threshold for the distortion as in the case of the Frederiks transition in nematics. We can find the threshold field Ec, considering a small distortion (p 0. The equation... 

Here, the first term describes the nematic-like elastic energy in raie crmstant approximation (K in 9). This term allows a discussion of distortions below the AF-F threshold (a kind of the Frederiks transition as in nematics in a sample of a finite size). In fact, the most important specific properties of the antiferroelectric are taken into account by the interaction potential W between molecules in neighbour layers the second term in the equation corresponds to interaction of only the nearest layers (/) and (/ + 1). Let count layers from the top of our sketch (a) then for odd layers i, i + 2, etc. the director azimuth is 0, and for even layers / + 1, / + 3, etc. the director azimuth is n. The third term describes interactimi of the external field with the layer polarization Pq of the layer / as in the case of ferroelectric cells. Although for substances with high Pq the dielectric anisotropy can be neglected, the quadratic-in-field effects are implicitly accounted for by the highest order terms proportiOTial to P. ... 

Carrying out the experiment under the microscope, we observe that nothing happens for very small values of H. The visual field remains dark when viewed with crossed polarisers. Then at a threshold value Hq, the field of view is suddenly lit up. The sample has been deformed. This is the Frederiks transition., named after the Russian physicist who first observed the phenomenon in the 1930s. The experiment is easy to carry out in the laboratory, with quite rudimentary equipment. For a nematic slab of thickness 25 gm. He is about 0.2 Tesla and Eq about 400 V/cm. 

Fig. 9.7. Electrical Frederiks transition for a twisted nematic, (a) Anchoring of molecules on the substrate creates a constant twist throughout the sample, (b) Electric field E is applied parallel to the twist axis. From a threshold value Ec, molecules stand up, and for E Ec they lie parallel to E throughout most of the sample...

Elastic moduli could be measured from the electro- (and magneto)-optical characteristics of the Frederiks transition, such as the threshold voltage C/p oi the threshold magnetic field ifp, according to the relationships... 

Dynamics of fiuctuations, arising below the threshold of the Frederiks transition, were studied in [42]. The fiuctuations are modulated and amplified just above the critical (threshold) strength of the field. 

It is shown in [26] that the (a) and (c) deformations in Fig. 4.30 do not have a threshold, i.e., they can occur with any small qxternal voltage, and the stabilizing dielectric torque (because of Ae < 0) partially depresses the flexoelectric deformation. For (b) and (d) the deformation has a threshold and, with the conditions Wsi Ws2, the threshold depends on the polarity of the field. When the flexoelectric and dielectric torques are simultaneously destabilizing, the flexoelectric effect reduces the threshold of the Frederiks transition. In the opposite case, the dielectric torque raises the threshold of the flexoelectric effect. 

The field-induced reorientation of nematic polymers caused by the coupling of the electric field with their dielectric anisotropy was studied in a variety of papers [229, 231-238]. Unfortunately, only in a few papers (e.g., [237]) is a certain preliminary orientation of a polymer specified and we can speak of the true Frederiks transition with a well-defined threshold voltage. Nevertheless, the general opinion is that the Prank elastic moduli of both comb-like [232-235, 238] and linear-chain [236, 237] nematic polymers are of the same order of magnitude as of their low-molecular mass counterparts. 

The moduli were calculated from the threshold of the Frederiks transition ((4.9) induced by a magnetic (Ax > 0) and electric (Ae < 0)) field in homeotropically oriented liquid crystal layers. The same order of magnitude (10 -10 dyn), which is typical of conventional nematics, has been found for elastic moduli Kn and for other nematic polymers [233, 234]. Unwinding of the helical structure of chiral nematic polymers allowed the elastic constant K22 to be calculated K22 10" dyn for an arylic comb-like copolymer with cholesterol and cyanobiphenyl side-chair mesogens [229]). 

When the field is oriented along the director, a Frederiks transition is possible when 2 > 3- The director should rotate around the z-axls not changing its angle ft, so that in its final position, i.e., in the strong field limit, its projection onto the smectic planes, coincides with the y-axis. The corresponding threshold field (Eo)3 is proportional to ( 2 A field... 

Figure 10. Three typical geometries for observing the Frederiks transition the splay (a), bend (b), and twist (c) distortions induced by a magnetic field H. (Top) Initially, the director n is along the L axis, but when the field exceeds a certain threshold (bottom) distortion occurs.

Texture transitions are particularly pronounced when an electric field is applied to materials having a large dielectric anisotropy. A planar texture undergoes transition to a quasihomeotropic optically transparent texture via intermediate structural defects [150,151]. The threshold voltage observed experimentally for a transition from a planar to a homeotropic texture depends on the layer thickness according to f/oc (for the Frederiks transition the threshold voltage is independent of thickness). A model that accounts for the experimental data (at least partly) has been developed by Parodi [152] who assumed the formation of transition layers between the surface and the bulk of a sample. A discrepancy between the calculated and observed periods of the texture instability may be due to a nonuniform... 

The most extensive theoretical and experimental studies of this problem have been done by Bocharov [76], who used an apparatus in which a SAW was excited at the substrate (1) (Fig. 7 a). The nematics was sandwiched between the glass plate (2) and the substrate (1) bearing transparent electrodes, to which an ac voltage (/ 50Hz) was applied. The dependence of the layer optical transmission m on the amplitude of the SAW with and without an applied electric field is shown in Fig. 9 b. The threshold value of the Frederiks transition was 4.65 V. It is evident that in the vicinity of this transition the sensitivity of the nematics to the action of the SAW increases by more than an order of magnitude. According to Vuzhva s theory, near the threshold of the Frederiks transition (E— Eq)... 

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