Director axis

The ordered columnar arrangement of the hexapentyloxytriphenylene molecules provides good overlap of the -electrons of the triphenylene moieties along the director axis. This results in efficient hole transport in the mesophase. The hole photocurrent shows nondispersive transport with a high mobihtyup to 1 X 10 cm /Vs (24). 

It has been assumed that the director axis defining the orientational order of the mesophase has the same direction as the static magnetic field. 

For simplicity, in equation (3c) S oc is assumed to be mainly along the director axis n, and n is aligned parallel tol. For Btoc Bo, the total 7, is equal to 7,2, whereas in the opposite case B,oc Bq one has 7, = 7,o- Evidently, the finite local field contribution complicates the control of the angle adjustment without an exact knowledge of, oc, and because of equation (3c) the inclinations of 90° become impossible by external field switches. Furthermore, the spectral densities for 7,0 are not discussed in the literature to the same extent as for 7,2, nor does there exist a critical experimental examination of the validity of the basic expression equation (3a). Approximate predictions about with the Redfield formalism give, for the completely isolated, i.e., uncoupled proton spin-pair (/ = 1) and high spin-temperature approach ... 

The new FC technique made possible extensive measurements of the self-diffusion constans Dg and Dj of liquid crystals, parallel ( ) and perpendicular (-L) to the director axis, with v ues as low as 10 m s . The most challenging requirements exist for nematic mesophases because their low viscosity facilitates flow in the nonequilibrium state and so necessitates the fast FC procedure to establish the magic angle rotation of the director... 

In general k has nine components, but the presence of symmetry in the liquid crystal reduces this number. The distribution of molecules around any point is cylindrically symmetric, so that the choice of the x axis is arbitrary apart from the requirement that it should be normal to the director axis z. Therefore... 

Consider a nematic film of negative dielectric anisotropy (e < 0) aligned homeotropically between glass plates. If an electric field is applied along the director axis (z axis) a distortion will set in when the field exceeds the critical Freedericksz value given by... 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

Fig. 5 Schematic depiction of the optical field propagating as an o-wave in a planar nematic liquid crystal cell, ba is the orientational fluctuation of the director axis. 

More quantitatively, consider the equation governing the laser induced director axis reorientation Sn ... 

Solving for the director axis fluctuation in in the steady state, and equations (10) and (11) for an input e-wave (E ) gives a steady state... 

A linearly polarized cw Argon laser operating at the 5145A line is electronically chopped to yield pulses of variable millisecond duration, is focused onto the nematic liquid crystal sample with its electric field polarization vector Ep parallel to the director axis Ho, i.e., an e-wave. The transmitted beam is reflected, focused back onto the sample, where it intersects the incident beam at a crossing angle in air of 3. The polarization of the reflected beam is rotated so that it is orthogonal to the polarization direction of the incident beam, i.e., an o-wave. 

In the nematic phase, this ratio is larger than unity (R /R 1.3) (Warner and Terentjev, 1996), but after a nematic-isotropic phase transition, this ratio approaches unity as a result of the formation of a random coil of polymer chains, which makes the polymer material contract along the director axis of LCEs. In the smectic A phase, the ratio R /R is in general smaller than unity because the polymer chains are likely to exist between the smectic layers (Cotton and Hardouin, 1997). 

The situation is illustrated in Fig. 22 for the case of a -H-labeled methylene segment of a surfactant molecule residing in a micelle. The director axis, Z , corresponds to the micellar surface normal. The field gradient tensor is cylindrically symmetrical around the C- H bond axis, with the maximum component in the bond axis direction, Zm. 

In the first approximation, the parameter of the local orientational order of a cholesteric liquid crystal is the same uniaxial traceless tensor Qij = S njnj — 5,y/3) as in the nematic phase with the director axis always lying in the x,y-plane, e.g. along the x directirMi at a selected cross-section of the helix ... 

A change of the order parameter modulus S (r) can also create polarization, for example due to transformation of the ellipsoidal shape of Q tensor in space. In this case we deal with the so-called ordoelectric polarization [14]. Indeed, decreasing S value results in less extended (less prolate) ellipsoid form without reorientation of its principal axes. Such a transformation may be caused by a scatter of the rigid molecular quadrupoles with respect to the director axis the stronger the scatter, the lower is the quadmpole order S and the less prolate ellipsoid Q. This is illustrated by Fig. 10.12 in sketch (a) the order parameter is stronger at the surface and... 

Due to the linear profile of 9(z) it is very easy to calculate the phase retardation of the initially homeotropic cell for the normal light incidence, kHz. Without electric field, the longest axis of the dielectric ellipsoid coincides with the director axis z. Therefore, refraction index for any polarization is o = With increasing field E, due to deflection of the director within plane xz, the y- and -components of the refraction index will correspond to the ordinary and extraordinary rays, Uy = no = n , rix(z) = rig(z). Integration provides us with the average extraordinary index ... 

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