Elastic constants splay

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. 

In the toroidal droplet, the liquid crystal director is aligned along concentric circles on planes perpendicular to a diameter, as shown in Figure 11.15(b). There is a line defect along the diameter of the droplet. There is a rotational symmetry around the defect line. The bend elastic deformation is the only one involved. Toroidal droplets exist when bend elastic constant is smaller than the splay elastic constant otherwise the droplets take the bipolar configuration. Toroidal droplets rarely exist because for most liquid crystals the bend elastic constant is usually larger than the splay elastic constant. Nevertheless, toroidal droplets have been... 

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... 

The A" and K22, terms, which vanish identically in the apolar nematic and cholesteric phases, are not considered here. As discussed above, the volume integrals of the free energy terms containing the splay-bend elastic constant and the saddle-splay elastic constant K24 can be transformed into integrals over the nematic surface... 

Here the equilibrium direction of the long molecular axies is along the z-axis and the wave-vector of the excitation is in the x-z plane, as shown in Fig. 1. 3 is the bend elastic constant, is the splay elastic constant and K2 is the twist elastic constant. The magnetic field H is applied in the z-direc-... 

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