Nematic-phase director

The surface tension (xlv) influences the angle between the surface and the nematic-phase director. It plays an iirqrortantrole in the selection of coatings for the creation of homeotropic ahgnment (where the molecules are perpendicular to the cell surfaces) or planar ahgnment (where the molecules are parallel to the surfaces) of LCs. The Friedel-Creagh-Kmetz rule states that if... 

Figure C2.2.2. Isotropic, nematic and chiral nematic phases. Here n denotes tire director. In tire chiral nematic phase, tire director undergoes a helical rotation, as schematically indicated by its reorientation around a cone.

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. 

Disclinations in tire nematic phase produce tire characteristic Schlieren texture, observed under tire microscope using crossed polars for samples between glass plates when tire director takes nonunifonn orientations parallel to tire plates. In thicker films of nematics, textures of dark flexible filaments are observed, whetlier in polarized light or not. This texture, in fact, gave rise to tire tenn nematic (from tire Greek for tliread ) [40]. The director fields... 

C and I account for gradients of the smectic order parameter the fifth tenn also allows for director fluctuations, n. The tenn is the elastic free-energy density of the nematic phase, given by equation (02.2.9). In the smectic... 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

Chira.lNema.tlc, If the molecules of a Hquid crystal are opticaHy active (chiral), then the nematic phase is not formed. Instead of the director being locaHy constant as is the case for nematics, the director rotates in heHcal fashion throughout the sample. This chiral nematic phase is shown in Figure 7, where it can be seen that within any plane perpendicular to the heHcal axis the order is nematic-like. In other words, as in a nematic there is only orientational order in chiral nematic Hquid crystals, and no positional order. Keep in mind, however, that there are no planes of any sort in a chiral nematic Hquid crystal, since the director rotates continuously about the heHcal axis. The pitch of the helix formed by the director, ie, the distance it takes for the... 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

If the molecules are chiral or if a chiral dopant is added to a discotic Hquid crystal, a chiral nematic discotic phase can form. The director configuration ia this phase is just like the director configuration ia the chiral nematic phase formed by elongated molecules (12). Recendy, discotic blue phases have been observed. 

Fig. 28. Room temperature 2H NMR spectra of the smectic liquid crystalline polymer (m = 6), oriented in its nematic phase by the magnetic field (8.5 T) of the NMR spectrometer with director ii parallel (left) and perpendicular (right) to the magnetic field...

Other more exotic types of calamitic liquid crystal molecules include those having chiral components. This molecular modification leads to the formation of chiral nematic phases in which the director adopts a natural helical twist which may range from sub-micron to macroscopic length scales. Chirality coupled with smectic ordering may also lead to the formation of ferroelectric phases [20]. 

The alignment of the director at the nematic free surface of real systems is not found to exhibit universal behaviour. Depending on the mesogen, homeotro-pic, tilted and planar anchoring have been observed. Clearly, to study this interface in a simulation a potential which exhibits a nematic phase in co-... 

The simplest mesophase is the nematic phase. It is very fluid and involves highly disordered molecules having only short-range positional order, but with the molecules preferentially aligned on average in a particular direction (the director). If the constituent compound is racemic then it is possible to form a phase from the enantiomerically pure compound which is a chiral nematic phase. 

The liquid crystal phases of calamitic mesogens fall into two types - nematic (N) and smectic (Sm). The nematic phase is the most disordered of the liquid crystal phases and possesses only orientational order, so that the long axes of the molecules are correlated in one direction (known as the director, n) while being positioned randomly (Fig. 2A). There are several smectic phases and these differ from the nematic phase in possessing partial posi-... 

The above spectral densities can be modified for the occurence of chain flexibility, and for the director being oriented at dLD w.r.t. the external BQ field in the L frame. For CD bonds located in the flexible chain, the effect of DF is reduced due to an additional averaging of the time dependent factor (/f g) by conformational transitions in the chain. Consequently, the spectral densities given in Eqs. (60)-(62) are modified by replacing Soc%0(Pm,q) by the segmental order parameter YCD of the C-D bond at a particular carbon site on the chain.146,147 As observed experimentally,148,149 the spectral densities in a flexible chain show a SqD dependence when DF dominate the relaxation rates. The general expression of Jm(co 0LD) due to DF in uniaxial nematic phases is given by... 

Discotic LC are formed by disk-like molecules with aromatic cores and side chains that are either hydrophobic (i.e., thermotropic) or hydrophilic (i.e., lyotropic). The discotic nematic (No) phase behaves like a normal nematic phase formed by rod-like molecules, and the disk-like molecules are oriented with their short molecular axes parallel to the director but show no positional order. More ordered columnar phases are commonly formed by thermotropic discotics. The two-dimensional structure can pack the columns into a hexagonal or rectangular columnar phase, while within the columns, disks can be... 

Note 1 The three Miesowicz coefficients (//i, 772, and 773) describe the shear flow of a nematic phase with three different director orientations, (see Fig. 31) namely 771 for the director parallel to the shear-flow axis 772 for the director parallel to the velocity gradient and 773 for the director perpendicular to the shear flow and to the velocity gradient. 

Fig. 31. Scheme of director alignment in the shear flow of velocity u of a nematic phase and... 

---