Shapes biaxial nematics

Disk-shaped molecules based on a metal atom possess discotic Hquid crystal phases. An example is octasubstituted metaHophthalocyanine. FiaaHy, metallomesogens which combine both rod-like and disk-like features iato a single molecule adopt the biaxial nematic phase. In addition to there being a preferred direction for orientation of the longest molecular axis as is tme for the nematic phase, perpendicular to this direction is another preferred direction for orientation of the shortest molecular axis (12). NonmetaHomesogens which combine both rod- and disk-like features iato a single molecule also adopt a biaxial nematic phase, but at least ia one case the amount of biaxiaHty is very small (15). 

Note 2 Short board-like shaped molecules usually form biaxial nematic mesophases. It is recommended that the use of the term disordered sanidic mesophases for such mesophases be discontinued (see Definition 3.3.1, Note 5). 

In the simplest liquid-crystalline phase, namely the uniaxial nematic, there is at rest a special direction designated by a unit vector n called the director (see Fig. 10-2). In the plane transverse to the director, the fluid is isotropic. The most common nematics are composed of oblong molecules that tend to point in a common direction, which defines the director orientation. Oblate, or disc-like, molecules can also form uniaxial nematics for these discotic nematics, the director is defined by the average orientation of the short axis of the molecule. Lath-like molecules or micelles (shaped like rectangular slabs), in which all three dimensions of the molecule are significantly different from each other, can form biaxial nematics (Praefcke et al. 1991 Chandrasekhar 1992 Fialtkowski 1997). A biaxial... 

Molecules which combine the features of the rod and the disc may be expected to form new types of mesophases. An example is the biaxial nematic phase reported in thermotropic systems (see 6.6). Malthete et a/. have prepared an interesting series of mesogens shaped like stick insects called phasmids (fig. 6.1.5(n)). Some of them form columnar mesophases the structure proposed for the hexagonal phase is shown schematically in fig. 6.1.5( >). 

The biaxial nematic (NJ phase was first identified by Yu and Saupe in a ternary amphiphilic system composed of potassium laurate, 1-decanol and D2O. In such systems the constituent units are molecular aggregates, called micelles, whose size and shape are sensitive to the temperature and concentration the phase was found to occur over a range of temperature/concentration. There are obvious advantages in having a single-component, low-molar-mass thermotropic phase. The sugges-... 

In certain cases, nematic (orientational but not positional) order may be observed in phases of (relatively small) micellar rods (canonic) or disks (discotic) [177], which are associated with lower temperature hexagonal and lamellar phases, respectively [178]. (See Fig. 17.) The nematic isotropic phases were thought to be built up of discrete aggregates of different shapes, but the presence of continuous aggregates has also been recently suggested in this case [178]. Some systems (e.g., potassium laurate-decanol-water) form biaxial nematic phases. In this case, the micelles are believed to be neither rods nor disks but rather to... 

Under just the right conditions, a mixture of a highly polar liquid, a slightly polar liquid, and an amphiphilic molecule form micelles that are not spherical. They can be rodlike, disc-like, or biaxial (all three axes of the micelles are different). These anisotropic micelles sometimes order in the solvent just as liquid crystal molecules order in thermotropic phases. There is a nematic phase of rod-shaped micelles, another nematic phase of disc-shaped micelles, and even a biaxial nematic phase, in which the molecular axes transverse to the long molecular axis partially order. Chiral versions of these phases with the same structure as the chiral nematic phase also form. 

Molecules of the lath-like shape can form the thermotropic biaxial nematic phase [23] shown in Fig. 1.9. The point group symmetry of this phase is i 2h the rotation of molecules around their longitudinal axes is considerably hindered. An example of the biaxial nematic is [bis-l-(p-n)-decylbiphenyl)-3-(p-ethoxyphenyl) propane-1,3-dionatocopper] [18]. 

FIGURE 1.9. Biaxial nematic phase composed of lath-shape molecules. 

There exists a more complicated situation for boardshaped molecules. The mesophase composed of board-shaped molecules is characterized by long-range ordering of both the longer and the shorter molecular axes. In this case, a biaxial nematic mesophase is realized (Table 2). 

Fig. 5.3. A Schematic diagram of the molecular arrangement in a biaxial nematic phase (Nb) comprised of discoid-shaped mesogens. The primary director is designated by the usual letter, n, and the secondary director, o, is orthogonal to n.

Thus we see that the effect of shape biaxiality can indeed be very strong. It seems that this can be the main reason why the molecular theories, based on rod-like molecular models, overestimate the first orderness of the nematic-isotropic transition. 

It is well known that a smectic C liquid crystal which has a monoclinic symmetry is optically biaxial [3]. A biaxial nematic (N ) phase in which the molecules are oriented along the three directions in space, i.e., they have three directors which are perpendicular to one another, is possible. Thus the shape of molecules exhibiting the Nb phase should be different from those exhibiting the uniaxial nematic phase. 

Figure 1. Phase diagram of the uniaxial and biaxial nematic phases as predicted by the microscopical theories (N(. calamitic nematic N, biaxial nematic and Nj discotic nematic). In the case of systems of hard rectangular plates, the parameter a is the shape anisotropy of the elementary units (i.e., the width to length ratio of the rectangles). In the case of mixtures of rodlike and disk-like particles, x is the relative concentration of the disk-like particles. The first order transition to the isotropic phase is marked as a dashed line. The second order N -Nb phase transitions are represented with solid lines (from [8, 13]).

If the liquid crystal molecules and the rodlike molecules are aligned vertically, there is a possibility that a novel biaxial nematic phase exists on the uniaxial nematic phases Ni and N2. So far, biaxial nematic phases have been attracting attention for molecules having a biaxial molecular shape (plate-shaped or discshaped molecules) [53, 54], but based on the above discussion, the novel biaxial phase can also be produced in the combinations of molecules with uniaxial symmetry. 

Preiser s prediction stimulated not only a synthetic effort in the design of molecules with the desired shape to form a biaxial nematic phase but also a search for an experimental method to unambiguously prove the existence of this phase biaxiality. 

An accepted experimental proof for the existence of a biaxial nematic phase in a thermotropic liquid crystal remained missing for a very long time. However, in recent years, biaxial nematic phases have been found in liquid crystalline polymers as well as in liquid crystals made of rod-disc mesogens, banana-shaped (bent-core) molecules, and organo-siloxane tetrapodes. Here, some characteristics of these systems and the corresponding experimental procedure for the investigation of phase biaxiality will be introduced. Further details for the individual systems can be found in the cited literature. 

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