Biaxial Nematic Liquid Crystals

A survey of recent studies of biaxial liquid crystals, in the context of the reported biaxial nematic phase in low molecular mass bent-core mesogens, with emphasize on the use of NMR spectroscopy is available. A discussion of orientational order parameters particularly in smectic-C and biaxial nematic phases and their determination by various techniques including NMR has been presented. The relation between molecular dynamics and biaxiality of nematic polymers and elastomers has been studied by H NMR spectroscopy. "" It was observed that the side-on attachment of the mesogens hinder the rotation of the molecules around their long axes and that in nematic polymers and elastomers phase biaxiality... 

For each in a uniaxial phase there are two normal modes corresponding to a splay-bend distortion n q) and a twist-bend distortion ri2(q) biaxial liquid crystal phases have five normal modes for each value of q. The free energy density can be written in terms of the normal coordinates for torsional displacement in a uniaxial nematic as ... 

Luckhurst G R 1985 Molecular field theories of nematics systems composed of uniaxial, biaxial or flexible molecules Nuclear Magnetic Resonance of Liquid Crystals ed J W Emsiey (Dordrecht Reidel)... 

The aggregates created by amphiphiles are usually spherical (as in the case of micelles), but may also be disc-like (bicelles), rodlike, or biaxial (all three micelle axes are distinct) (Zana, 2008). These anisotropic self-assembled nanostructures can then order themselves in much the same way as liquid crystals do, forming large-scale versions of all the thermotropic phases (such as a nematic phase of rod-shaped micelles). 

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 fluctuation relations for the viscosities have also been generalised to biaxial nematic liquid crystals. They have been evaluated numerically for a biaxial version of the Gay-Beme fluid consisting of a linear string of oblate Gay-Beme ellipsoids, the axes of which point in the same direction. The flow... 

S. Sarman, Molecular Dynamics of Biaxial Nematic Liquid Crystals, J. Chem. Phys. 104 (1996) 342. 

However, in 1986, Chandrasekhar [70] published a derivative (Figure 35) which he claimed to show a biaxial nematic phase. This report was interesting because the biaxial nematic phase (Nb), demonstrated in lyotropic systems [71], had been long sought after in thermotropic materials. Further, the molecules were described as bridging the gap between rod- and disc-like materials (a reference perhaps better reserved for polycatenar liquid crystals—vide infra)... 

Ordered polymer films made from poly benzthiazole (PBZT) and poly benzoxazole (PBO) can be used as substrates for multilayer printed circuit boards and advanced interconnects to fill the current need for high speed, high density packaging. Foster-Miller, Inc. has made thin substrates (0.002 in.) using biaxially oriented liquid crystal polymer films processed from nematic solutions. PBZT films were processed and laminated to make a substrate with dielectric constant of 2.8 at 1 MHz, and a controllable CTE of 3 to 7 ppm/°C. The films were evaluated for use in multilayer boards (MLBs) which require thin interconnect substrates with uniform controllable coefficient of thermal expansion (CTE), excellent dielectric properties, low moisture absorption, high temperature capability, and simple reliable processing methods. We found that ordered polymer films surpass the limitations of fiber reinforced resins and meet the requirements of future chip-to-chip interconnection. 

The mono-substituted PEIs melt from a saniditic layered structure into a normal nematic phase whereas the disubstituted presumably yield a biaxially oriented nematic melt. The disubstituted PEIs isotropise from the melt around 200 °C lower than the monosubstituted of equal chain length. As the second substituent should increase chain stiffness rather than reduce it, Kricheldorf suggests that interactions between temporarily coplanar aromatic n systems, particularly donor-acceptor interactions, can make an efficient contribution to the stabilisation of nematic phases. If this hypothesis is correct then a greater variety of non-linear monomers may be regarded as building blocks for liquid crystal polymers. 

This experimental difficulty was overcome by simulating the behaviour of a model system and a biaxial nematic phase was indeed obtained [122], One way by which the problem of phase separation could be solved experimentally was suggested by Fletcher and Luckhurst and involved covalently linking a rod-like and disc-like unit via a flexible spacer yielding a non-symmetric discotic-calamitic liquid crystal dimer [123] ... 

A recent observation has been that not all porphyrin LC phases are discotic. Thus 5,15-meso-substituted porphyrins have been prepared which show a variety of smectic phases that are not discotic. The porphyrin macrocycle could be acting to impose biaxial symmetry within the meso-phase, which makes the new porphyrins of great interest as new nematic liquid-crystal materials. 

The applicability of homotopic theory becomes much less obvious for liquid crystal phases with more complicated order parameters such as biaxial nematics and cholesterics, which are both locally defined by three directors forming a tripod. This gives rise to a description of the line singularities in terms of the quaternion group, Q. This is particularly interesting because the quaternion group Q is non-Abelian, a property that... 

Y. Wang, H. Yoon, H.K. Bisoyi, S. Kumar, Q. Li, Hybrid rod-like and bent-core liquid crystal dimers exhibiting biaxial smectic-A and nematic phases. J. Mater. Chem. 22, 20363-20367 (2012)... 

A preparation of new liquid crystal polymers with bilaterally linked mesogens in main-chain was reported [57]. Such materials exhibit biaxial fluctuation in the nematic phase. This is interesting because most commonly encountered polymeric liquid crystals have mesogens linked at their ends to the polymer backbone by flexible spacers. On the other hand, liquid crystal polymers with mesogens linked bilaterally by flexible spacers are not common and only a few examples were reported [58]. One such material can be illustrated as follows ... 

Fig. 13.19 Intermolecular interactions responsible for formation of different liquid crystal phases attractive anisotropic van der Waals and repulsive steric interactions for nematics (a), van der Waals (bifilic) and steric for SmA (b), steric quadrupolar interaction for SmC (c) and SmC A (d) owed to molecular biaxiality. The density is increasing in a sequence orthogonal (b), synclinic (c) and anticlinic (d) phases. An interlayer steric correlations in SmC (e) are shown by displacements of grey molecules . Note that the displacement of gray molecules may influence the next to nearest layer via a kind of relay race mechanism...

R328 V. Domenici, A Brief Overview of NMR Experiments Used to Study the Phase Biaxiality in Nematic Liquid Crystals , Mol. Cryst. Liq. Cryst., [online computer file], 2012, 558, 37. 

Yoon, H. Kang, S. Lehmann, M. Park, J. O. Srinivasaraode, M. Kumar, S. Homogeneous and homeotropic alignment of bent-core uniaxial and biaxial nematic liquid crystals. Soft Matter 2011, 7, 8770. 

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