Nonlinear chiral nematics

The course of versus x becomes nonlinear at elevated dopant concentrations mostly the absolute value of the slope deceases but some exceptions are known [23]. For a few cases a maximum twist has been found, especially when a lamellar phase is adjacent to the chiral nematic one. Then pretransitions obviously occur close to the lamellar state, as has been shown already in the basic paper by Radley and Saupe [9], [24]. So far, lyotropic chiral nematics seem to behave quite similar to their thermotropic counterparts. 

Blinov, L. M., Barberi, R., Kozlovsky, M. V., Lazarev, V. V., and de Santo, M. P. Optical anisotropy and four possible orientations of a nematic liquid crystal on the same film of a photochromic chiral smectic polymer. / Nonlinear Opt. Phys. Mat. 9, 1 (2000). 

If the mesogens are chiral, a twisted nematic, suprarmolecular, cholesteric (twisted) phase can form [51, 52]. The achiral nonlinear mesogens can also form chiral supramolecular arrangements in tilted smectic phases. 

The pitch of the helix depends on concentration c of a dopant for small c Po ac and a is called helical twisting power of the dopant [15]. However, with increasing c the dependence becomes nonlinear and the heUx handedness can even change sign (the case of cholesteryl chloride dopant in p-butoxybenzyli-dene-p -butylaniline, BBBA, see Fig. 4.24). The same chiral, locally nematic phase with a short pitch in the range of 0.1-1 pm is traditionally called cholesteric phase because, at first, it has been found in cholesteryl esters. Such short-pitch phases manifest some properties of layered (smectic) phases. 

The existence or nonexistence of mirror symmetry plays an important role in nature. The lack of mirror symmetry, called chirality, can be found in systems of all length scales, from elementary particles to macroscopic systems. Due to the collective behavior of the molecules in liquid crystals, molecular chirality has a particularly remarkable influence on the macroscopic physical properties of these systems. Probably, even the flrst observations of thermotropic liquid crystals by Planer (1861) and Reinitzer (1888) were due to the conspicuous selective reflection of the helical structure that occurs in chiral liquid crystals. Many physical properties of liquid crystals depend on chirality, e.g., certain linear and nonlinear optical properties, the occurrence of ferro-, ferri-, antiferro- and piezo-electric behavior, the electroclinic effect, and even the appearance of new phases. In addition, the majority of optical applications of liquid crystals is due to chiral structures, namely the ther-mochromic effect of cholesteric liquid crystals, the rotation of the plane of polarization in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals. 

The nematic phase of nonlinear mesogens may be biaxial - a translationally disordered fluid phase with two directors n and o specifying the orientational order (Fig. 5.3). Biaxial order in a nematic is predicted to occur [29] if the shape anisotropy of the idealized molecule (discoid) representing the nonlinear meso-gen is appropriately intermediate between the prolate shape of calamities and the oblate shape of discotics. Discoid-shaped mesogens lend themselves to a variety of stratified phases. Ferroelectric (Sapp) and antiferroelectric (Sapa) layer motifs in the normal smectic phases of discoid-shaped mesogens are readily envisioned (Fig. 5.4), but less obvious is the possibility of generating chiral supramolecular structures from such achiral discoid-shaped mesogens (Fig. 5.5) [30]. 

Presumed ferroelectric effects in liquid crystals were reported by Williams at RCA in Princeton, U. S. A., as early as 1963, and thus at the very beginning of the modern era of liquid crystal research [5]. By subjecting nematics to rather high dc fields, he provoked domain patterns that resembled those found in solid ferroelectrics. The ferroelectric interpretation seemed to be strengthened by subsequent observations of hysteresis loops by Kapustin and Vistin and by Williams and Heilmeier [7]. However, these patterns turned out to be related to electrohydrodynamic instabilities, which are well understood today (see, for instance, [8], Sec. 2.4.3 or [9], Sec. 2.4.2), and it is also well known that certain loops (similar to ferroelectric hysteresis) may be obtained from a nonlinear lossy material (see [10], Sec. 2.4.2). As we know today, nematics do not show ferroelectric or even polar properties. In order to find such properties we have to lower the symmetry until we come to the tilted smectics, and further lowering their symmetry by making them chiral. The prime example of such a liquid crystal phase is the smectic C. ... 

Besides normal alkyl chains, alkenyl chains (-C H2 CH CHCH3) are also important because they exhibit particularly beneficial elastic constants and low rotational viscosities desirable for use in supertwisted nematic (STN) displays. Branched alkyl chains Iowct transition temperatures and increase the viscosity. Thus, chiral liquid crystal compounds, which usually incorporate a branched chain alcohol, e.g., 2-methyl butanol or 2-octanol, are relatively viscous. Compounds with two long alkyl chains favor smectic C phase formation (3, K-S, 48°C S.-S 122°C S -N 128°C N-I 166°C), especially when the core system contains some kind of nonlinear stmcture (such as a lateral substituent and/or este group) which aids the formation of tilted phases. 

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