Splay elastic constant constants

Table 7. Measurements of the Fredericks transition in the magnetic field 71) (H = critical field, r = relaxation time, kn = splay elastic constant, yl = twist viscosity coefficient...

Hur S-T, Gim M-J, Yoo H-J, Choi S-W, Takezoe H (2011) Enhanced thermal stability of liquid crystalline blue phase I with decreasing bend and splay elastic constant ratio K33/K11. Soft Matter, in press (DOI 10.1039/clsm06046e)... 

Measurement of the critical field for this transition is therefore a convenient method for measuring the splay elastic constant K. ... 

The strain increases the energy of the solid as a stress is applied. The distortion of the director in liquid crystals causes an additional energy in a similar way. The energy is proportional to the square of the deformations and the correspondent coefficients are defined as the splay elastic constant, K, twisted elastic constant K22 and bend elastic constant Kx, i.e., the respective energies are the half of... 

If the semi-flexible liquid crystalline polymers are well stretched along the director and thus the order parameter is high, the underlying equations are valid and can demonstrate qualitatively the effect of chain flexibility on the splay elastic constant. 

Preedericksz transition in planar geometry is uniform in the plane of the layer and varies only in the z direction. However, in some exceptional cases, when the splay elastic constant Ki is much larger than the twist elastic constant K2 (e.g., in liquid crystal polymers), a spatially periodic out-of-plane director distortion becomes energetically favourable. The resulting splay-twist (ST) Freedericksz state is manifested in experiments in the form of a longitudinal stripe pattern running parallel to the initial director alignment no x. 

In earlier publications3,6 have presented the results of our measurements of the bend and splay elastic constants of PBLG liquid crystals using the Frederik s magneto-optical distortion procedure. The central experimental necessity of this technique is the measurement of the change in the phase retardation of polarized light... 

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. 

The cell parameters thickness (d), twist (3o)> capacitive threshold voltage (Vc) and the liquid crystal material parameters birefringence (n ), dielectric anisotropy (Ea)> pitch (P), bend to splay elastic constant ratio (K3/KX) and twist elastic constant (K2) were varied one at a time over a wide range of values. Transmission versus voltage curves were calculated at 0 and 40 incidence in the principal viewing plane and values for M0, My,... 

Table 2. Dependence of figures of merit on the ratio of bend to splay elastic constants K3/K1.

Consider the flexoelectric effect in the splay geometry as shown in Figure 4.5. The cell thickness A is 5 microns. The splay elastic constant Kn of the liquid crystal is 10 N. The flexoelectric coefficient is 2 x 10 V. Calculate the tilt angle 6 at the cell surface when the applied field is 1 V/pm. 

Thus by this geometry the splay elastic constant can be measured. 

Modulated structures in the Prederiks transition could also arise in the case where a splay elastic constant Kn is large compared to the twist... 

Here, Kn is a splay elastic constant of the LC. By using this equation, we can calculate the relationship between the groove frequency and the anchoring energy, which is shown in Fig. 2.24. 

The threshold magnetic field, Bth> for Freedericksz transitions has a similar form to Eq. (5.25), but involves the permeability of free space, 1 0, and the anisotropy of diamagnetic susceptibility. A/. Obtain the appropriate equation and check it by dimensional analysis. Use it to calculate the splay elastic constant for 5CB (Fig. 5.1), given that the threshold magnetic field for a pure planar-homeotropic deformation was measured to be 0.54 T in a cell of thickness 10 qm. Use values for 5CB as follows mass diamagnetic susceptibility Ax = 2.14 x 10 m kg and density p = 1.008 g cm . ... 

The theoretical picture for the N-SmA transition has been succinctly summarized by Lubensky. [28] He explains that there are several important differences between the normal-metal-superconducting and the N-S mA transitions where AT, the splay elastic constant, emerges as a dangerous irrelevant parameter [28]. 

Note that, apart from the expected dependence on the dielectric anisotropy Ae, the threshold voltage is independent of the cell thickness and depends only on the splay elastic constant k. This elastic constant... 

Pretransitional behavior of twist and splay elastic constants was also measured in CBOOA by Chu and McMillan [193]. The splay is not renormalized, whereas the twist elastic constant shows a mean-field like divergence. They also report slowing down of the twist mode near Tg, which is in apparent disagreement with both mean-field and helium-like models. A similar slowing down of the twist mode was observed by Delaye [118]. Pretransitional bend mode behavior is reported by Birecki and Litster... 

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