Chiral nematics chirality

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.

Altliough in figure C2.2.2 they are sketched witli rodlike molecules, botli nematic and chiral nematic phases can also be fonned by discotic molecules. 

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. 

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... 

Fig. 7. The chiral nematic Hquid crystal stmcture. The director (arrow) traces out a heHcal path within the medium. Siace the rotation of the director is continuous, the figure does not mean to imply the existence of layers perpendicular to the heHcal axis.

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. 

The positional order of the molecules within the smectic layers disappears when the smectic B phase is heated to the smectic A phase. Likewise, the one-dimensional positional order of the smectic M phase is lost in the transition to the nematic phase. AH of the transitions given in this example are reversible upon heating and cooling they are therefore enantiotropic. When a given Hquid crystal phase can only be obtained by changing the temperature in one direction (ie, the mesophase occurs below the soHd to isotropic Hquid transition due to supercooling), then it is monotropic. An example of this is the smectic A phase of cholesteryl nonanoate [1182-66-7] (4), which occurs only if the chiral nematic phase is cooled (21). The transitions are aH reversible as long as crystals of the soHd phase do not form. 

The polyamides are soluble in high strength sulfuric acid or in mixtures of hexamethylphosphoramide, /V, /V- dim ethyl acetam i de and LiCl. In the latter, compHcated relationships exist between solvent composition and the temperature at which the Hquid crystal phase forms. The polyamide solutions show an abmpt decrease in viscosity which is characteristic of mesophase formation when a critical volume fraction of polymer ( ) is exceeded. The viscosity may decrease, however, in the Hquid crystal phase if the molecular ordering allows the rod-shaped entities to gHde past one another more easily despite the higher concentration. The Hquid crystal phase is optically anisotropic and the texture is nematic. The nematic texture can be transformed to a chiral nematic texture by adding chiral species as a dopant or incorporating a chiral unit in the main chain as a copolymer (30). 

Liquid Crystalline Structures. In certain ceUular organeUes, deoxyribonucleic acid (DNA) occurs in a concentrated form. Striking similarities between the optical properties derived from the underlying supramolecular organization of the concentrated DNA phases and those observed in chiral nematic textures have been described (36). Concentrated aqueous solutions of nucleic acids exhibit a chiral nematic texture in vitro (29,37). 

Liquid crystalline behavior occurs in the exocuticle of certain classes of beetles. The bright iridescent colors that are reflected from the surface of Scarabaeid beetles originates from a petrified chiral nematic stmctural arrangement of chitin crystaUites in the exocuticle (38). It is suggested that this chiral nematic texture forms spontaneously in a mobile, Hquid crystal phase that is present during the initial stages of the exocuticle growth cycle. 

The selective redection of chiral nematic Hquid crystals has also been used to develop sensors for pressure, radiation (especially infrared), wind shear over surfaces, stmctural fatigue, and foreign chemical vapor (48). Other types of Hquid crystals have been used to make sensors to measure both electric and magnetic fields. 

Many cellulose derivatives form Hquid crystalline phases, both in solution (lyotropic mesophases) and in the melt (thermotropic mesophases). The first report (96) showed that aqueous solutions of 30% hydroxypropylceUulose [9004-64-2] (HPC) form lyotropic mesophases that display iridescent colors characteristic of the chiral nematic (cholesteric) state. The field has grown rapidly and has been reviewed from different perspectives (97—101). 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

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 prime requirement for the formation of a thermotropic liquid crystal is an anisotropy in the molecular shape. It is to be expected, therefore, that disc-like molecules as well as rod-like molecules should exhibit liquid crystal behaviour. Indeed this possibility was appreciated many years ago by Vorlander [56] although it was not until relatively recently that the first examples of discotic liquid crystals were reported by Chandrasekhar et al. [57]. It is now recognised that discotic molecules can form a variety of columnar mesophases as well as nematic and chiral nematic phases [58]. 

The structures of phases such as the chiral nematic, the blue phases and the twist grain boundary phases are known to result from the presence of chiral interactions between the constituent molecules [3]. It should be possible, therefore, to explore the properties of such phases with computer simulations by introducing chirality into the pair potential and this can be achieved in two quite different ways. In one a point chiral interaction is added to the Gay-Berne potential in essentially the same manner as electrostatic interactions have been included (see Sect. 7). In the other, quite different approach a chiral molecule is created by linking together two or more Gay-Berne particles as in the formation of biaxial molecules (see Sect. 10). Here we shall consider the phases formed by chiral Gay-Berne systems produced using both strategies. 

Here, ry is the separation between the molecules resolved along the helix axis and is the angle between an appropriate molecular axis in the two chiral molecules. For this system the C axis closest to the symmetry axes of the constituent Gay-Berne molecules is used. In the chiral nematic phase G2(r ) is periodic with a periodicity equal to half the pitch of the helix. For this system, like that with a point chiral centre, the pitch of the helix is approximately twice the dimensions of the simulation box. This clearly shows the influence of the periodic boundary conditions on the structure of the phase formed [74]. As we would expect simulations using the atropisomer with the opposite helicity simply reverses the sense of the helix. 

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