Director tilt angle

Equation (39) shows that nematic degrees of freedom couple to simple shear, but not the smectic degrees of freedom the modulus of the nematic order parameter has a non-vanishing spatially homogeneous correction (see (39)), whereas the smectic order parameter stays unchanged. The reason for this difference lies in the fact that J3 and /3 include h and p, respectively, which coupled differently to the flow field (see (22) and (23)). Equation (38) gives a well defined relation between the shear rate y and the director tilt angle 9o, which we will use to eliminate y from our further calculations. To lowest order 0O depends linearly on y ... 

Fig. 13.13 Geometry for discussion of the anchoring energies for the c-diiector. a and P are the angtes the director n forms with the easy axis z coinciding with the normal to smectic layers 9 is the director tilt angle and AC is the c-director forming angle (p with y-axis...

Fig. 6. Computed director tilt angle at midplane (O ) and at surface (0 j), and transmittance for 90° twisted cholesteric cell with surface energy function Ug. Surface tilt at zero field Is 86°. (Listed kg and risO...

If there is a pretilt, i.e., the director tilt angle at the walls is nonzero, the changes near Vq are gradual. We then define as the intersection of the extrapolated linear portion of the capacitance/voltage curve with the horizontal C=C(V 0) curve (see Fig. 1). We assume the surface coupling to be strong, so that the tilt angle at the surface is constant. 

Fig. 5.28 Optically measured director tilt angle 6opt of different C50/formamide mixtures in dependence of the temperature T - Tc relative to the lamellar L to lyotropie SmC analog phase transition (adapted from [17]. Cop5oight 2015 Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission) (See Footnote 6)...

The switching time of the director tilt angle in the electroclinic effect is independent of the electric field, and is defined only by the rotational viscosity je and the elastic modulus A. The corresponding switching times are derived from the Landau-Khalatnikov equation for the balance of the viscous and elastic torques... 

The transmitted light intensity was calculated by the Berreman 4x4 matrix method [22]. The director tensor is determined by the director tilt angle 7 and the director twist angle (f), which are expressed as... 

As mentioned in the last section, the L and K trancation parameters must in general be increased as the motion slows. If the calculation involves an ordering potential with nonzero director tilt angles (including MOMD spectra), the M trancation parameter must also be increased. Separate maxima are specified for even and odd L values. The reason for this is that the number of odd L values required depends on the symmetry of the system in general, no odd L values are needed at aU in the case of axial symmetry, and higher odd values are required as systems deviate further from axial symmetry. 

Pig. 5.1.21 Coordinate systems used for simulations. Y and Z represent the cell thickness direction and the smectic layer normal, respectively, and z is the perpendicular line of the cone, (a) Chevron layer system, (b) Cone system, (c) Director tilt angle 7 and director twist angle . (d) Definition of the smface... 

Note the presence of fan-shaped domains, with crosses either parallel or obliquely with respect to the polarizers. The oblique crosses indicate tilt of the optical axis with respect to the layer normal by the director tilt angle, 0. This is explained in Figure 6.15. Also note that the synclinic SmA and SmCg textures have higher birefringence than the anticlinic SmC texture. This can be followed on Figure 6.14, where the green areas (4-pm thick cells)... 

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