Clearing biaxial nematics

The bent core molecules do not only exhibit spontaneous resolution in smectic phases. One achiral derivative resolves in a nematic phase in this fluid state [ 145], while a substituted oxadiazole which forms a biaxial nematic phase also segregates [ 146]. The bent core clearly has a special stereochemical influence as a result of the effects it induces beyond the molecule, at least for liquid crystals. 

The shape of these mesogens is clearly biaxial. However, the stability of a biaxial nematic phase strongly depends on the inter-arm angle 6. A theoretical model based purely on repulsive molecular interactions [30] as well as another model including attractive and repulsive anisotropic interactions [31] both predict the Landau point, i.e., the point where a direct transition from the isotropic state to the biaxial nematic state occurs, to be achieved when the inter-arm angle adopts the tetrahedral value of 109.47°. On the other hand, the stability of the biaxial nematic phase is limited by the crystallization of the system. Therefore, the range of angles for which a biaxial nematic phase can be expected is extremely small, on the order of 2° from the tetrahedral value. 

As observed earlier, the assumption that the molecule is cylindrically symmetric is clearly not valid for real systems, and consequently the use of a single order parameter is not adequate. Most molecules are lath-shaped and have a biaxial character. Therefore two order parameters are required to describe the uniaxial nematic phase composed of biaxial molecules. If are the principal axes of the molecule (C defining the molecular long axis), it is necessary to introduce an additional order parameter... 

Figure 3. Plot of the transition temperatures (y-ax-is) versus the number of methylene units (j -axis) in the alkyl bridge of the twin ethers (compound 9). C crystal Nu t, discotic nematic biaxial I isotropic x melting points clearing points (from [18]).

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