Phase biaxiality

The local order in a cholesteric may be expected to be very weakly biaxial. The director fluctuations in a plane containing the helical axis are necessarily different from those in an orthogonal plane and result in a phase biaxiality . Further, there will be a contribution due to the molecular biaxiality as well. It turns out that the phase biaxiality plays a significant role in determining the temperature dependence of the pitch. Goossens has developed a general model taking this into account. The theory now involves four order parameters the pitch depends on all four of them and is temperature dependent. However, a comparison of the theory with experiment is possible only if the order parameters can be measured. 

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. 

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... 

The chemical shifts allowed the local order parameters to be computed which indicated the uniaxial to biaxial nematic phase transition. The nematic phase of a deuterated fiuorenone nematogen has been studied by NMR and X-ray and evidence for biaxial order close to its glass transition temperature has been inferred. The possible symmetries of the biaxial nematic phase have been examined based on experimental results and it is concluded that a monoclinic symmetry rather than an orthorhombic symmetry that is more likely to be the cause for the observed phase biaxiality in thermotropic bent-core and calamitic-tetrapode nematic systems. Density functional theory has been employed in a detailed conformational study of a bent-core mesogen The chemical shielding... 

The Gay-Berne potential has successfully been used for many liquid crystal simulations, and (depending on the parameterisation used and the state points studied) can be used to simulate nematic, smectic-A and smectic-B phases. Variants of the GB potential have also been used to study the biaxial nematic phase (biaxial GB potential) [21] and the smectic C phase (GB with quadrupole) [22]. The GB model has been used also to provide predictions for key material properties, such as elastic constants [23] and rotational viscosities [24], which have an important role in determining how a nematic liquid crystal responds in a liquid crystal display (LCD). 

Over the last few years, significant evidence has been obtained that nematic [4] as well as Sa [9] elastomers can show phase biaxiality over abroad temperature range. A biaxial-nematic phase from 15 °C to about 70 °C was found by means of H-NMR spectroscopy on a directly deuterated side chain end-on elastomer prepared by the Kupfer-procedure [4]. 

As mentioned in Section 3.1, phase biaxiality may be described by a set of microscopic order parameters when the mesogen is a rigid uniaxial particle, where a and (5 refer to the space-fixed axes x y z). Biaxial nematics [3.31], some smectic phases, like smectic C, and certain discotic phases [3.32] exhibit phase biaxiality. The order parameters 5, , and 5, , are different in these phases. NMR may be used to detect phase biaxiality through measurement of a non-zero motionally induced asymmetry parameter in nuclear spin interactions such as dipole-dipole and electric quadrupole interactions. To see how exists in biaxial mesophases, the previous discussion on motional averaging of spin Hamiltonian is gen-... 

Most experimental NMR work on phase biaxiality has employed a deuteron probe, whose time-averaged quadrupole Hamiltonian is... 

Finally, phase biaxiality has been studied by dissolving deuterated solute molecules in discotic liquid crystals [3.32]. Since discotic liquid crystals have negative Ax, an aligned sample consisting of one type of deuteron will exhibit a planar powder pattern (Fig. 3.7) without the necessity of sample rotation as in the conventional rod-like liquid crystals. Two discotic phases, Drd and have been studied by spectral pattern simulation using nonzero [3.32]. 

If the Saupe ordering matrix is written in terms of the laboratory axis frame, but assuming now that the molecules are uniaxial, then phase biaxiality can be described in terms of the order parameter P, which is nonzero for tilted smectic phases and other intrinsically biaxial phases. For example the diagonal ordering matrix for the molecular long axis z can be written as ... 

The description of the elastic properties of columnar phases, biaxial smectics, chiral... 

Phase biaxiality in lyotropic system was detected by NMR a long time ago [55, 56]. For the ternary system, sodium dodecylsul-phate/decanol/water, the transitions from the uniaxial nematic N and N phases to... 

Experimental evidence for phase biaxiality in various thermotropic liquid crystalline systems... 

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. 

PHASE BIAXIALITY IN NEMATIC LIQUID-CRYSTALLINE POLYMERS... 

Temperature dependent measurements of 2V showed phase biaxiality for mixtures containing more than 50% polymer. As seen in Figure 5-8, higher degrees of biaxiality, i.e., greater values of IV, were found for those mixtures with higher polymer contents, while a temperature dependence for the individual mixtures was not observed within their respective nematic and smectic phases. 

Conoscopy is known to be prone to artifacts because of its sensitivity to the symmetry of the refractive index, which might be tampered due to surface effects and flow phenomena. By using deuterium NMR spectroscopy. Severing et al. [11] confirmed phase biaxiality in a polymeric liquid crystal similar to that studied earlier by Leube. To evaluate different parameters that bias the formation of a biaxial nematic phase and gain a more general picture of the phase biaxiality in nematic liquid crystalline polymers, the investigations were expanded to side-chain polymers of different chemical constitutions as well as to mixtures of polymers and low molar mass liquid crystals [12],... 

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