Molecular director axis

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

On a molecular level the director is not rigorously defined, but the molecular director is typically considered to be the average long axis of the molecules, oriented along the macroscopic director with some order parameter less than one. This type of anisotropic order is often called long-range orientational order and, combined with the nonresonant optical properties of the molecules, provides the combination of crystal-like optical properties with liquidlike flow behavior characteristic of liquid crystals. 

Note 2 In uniaxial nematics, formed by compounds consisting of either rod-like or disclike molecules, the mean direction of the effective molecular symmetry axis coincides with the director. 

Table 3.14 Transition temperatures (°C), elastic constants fk/y, k22 kjj, 10 N), dielectric anisotropy ( e), dielectric constant measured perpendicular to the molecular long axis (e ), birefringence ( n), refractive index measured perpendicular to the director (noJ, rotational viscosity (y. Poise) and bulk viscosity (r, Poise) for tr ns-l-(4-cyanophe-nyl)-4-pentylcyclohexane (41), iTSins-l-(4-cyanophenyl)-4-[(E)-pent-l-enyl]cyclohexane (74) andtra.ns-l-(4-cyanophenyl)-4-[(E)-pent-3-enyI]cyclohexane (78) extrapolated to 100% at 22°...

Figure 5.6 Schematic representation of the smectic A phase (SmA) formed by calamitc, rod-like molecules. The director is parallel to the molecular long axis and normal to the plane of the layers.

Because the liquid crystals are up and down symmetrical, obviously (cos 6) (6 is the angle the molecular long axis makes with respect to the director) is not an appropriate candidate for the order parameter. What if (cos2 0) is adopted If so, for perfect alignment, the order parameter S = 1 but for the disordered distribution S = 1/3. For the sake of convenience, it is hoped that for the random distribution, i.e., the isotropic phase, S = 0, and for the perfect orientation, S = 1. Therefore, the statistical average of the second Legendre polynomial P2 is chosen as the order parameter... 

More direct studies of motion in this group of molecules by various types of NMR were often limited to the liquid crystalline state A largely motionally averaged spectrum for rotation about the molecular director and conformational disorder including in many cases rotation of the phenylenes about their para-axis is observed... 

Fig. 26. Scattering intensity as a function of / for a fixed moment transfer Qs. P is the pitch axis of the helix and n is the molecular director. The blocks of smectic layers have an infinite extent in the direction transverse to the pitch axis...

Table 1. Relaxation model parameteis obtained by a Levenberg-Marquardt fit optimization of equation (S) of the experimental Ti(v,A) data for 5CB and 8CB, shown in Fig. 2. Both data sets are rather similar, which on one hand demonstrates that the fitting is reproducible, and on the other shows the minor importance of the chain length variations on the Tj dispersion. The model constants denoted by ( ) could not be determined reliably and were estimated theoretically.Da, Dkj are the rotational diffusion constants parallel and perpendicular to the long molecule axis, and 0, 0the translational diffusion constants parallel and perpendicular to the nematic director is the mean translational jump width perpendicular to the molecular long axis and d the molecular diameter.

These authors have used the technique of lamellar decoration [76] which enables detailed assessment of cheu-acteristic mesophase defects and texture on a much finer scale than previously possible with conventional electron-microscopy preparations. The defects and texture existing in the polymer melt state are first retained by thermal quenching of the polymer fluid to room temperature. The glassy LCP film is then annealed above its glass transition, but below the melting point. Crystalline lamellae grow perpendicular to the local chain axis and effectively decorate the molecular director... 

The cholesteric phase is similar to that of the nematic phase on a local scale. As in the nematic phase, the molecules can be described by a director. However, the director in the cholesteric phase is twisted about an axis normal to the molecular orientation, following a helical path (Figure 1.3). The distance over which the molecular director rotates by 2tt along the helix axis is defined as the length of the cholesteric helix pitch, P. The twist is right-handed or left-handed depending on the molecular conformation. Iridescent colors are characteristic of cholesteric phases [1,2]. 

Consider the nematic phase. It has cylindrical symmetry and the orientational order parameter < 2> = V2(3cos i9 — l) with angle 9 between a molecular long axis and the symmetry axis (the director n). The tasks of the molecular theory is to use the symmetry arguments and properties of molecules and (a) to find the temperature dependence of (T), (b) to calculate thermodynamic and other properties in terms of , (c) to discuss the phase transition from finite to zero (N-Iso transition), and (d) to discuss the role of the higher order parameters , etc. 

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... 

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