Mixtures biaxial nematics

An interesting similarity of what we discussed here appears if one deals with mixtures of rodlike and disklike micelles. These systems could behave very similarly to a truly biaxial nematic, but show interesting differences to them. Whereas for the usual orthorhombic biaxial nematics both directors are perpendicular to each other by construction, in mixtures there is no need to impose this restriction. Pleiner and Brand [70] investigated how mixtures are influenced by an external field (magnetic field or shear flow) and found that the angle between the two directors exhibits a flow aligning behavior similar to the one studied in [42,43],... 

The existence of the thermotropic biaxial nematic phase was theoretically predicted almost thirty years ago [119] but such a phase has yet to be unambiguously identified. Indeed, as we saw in the previous section, a biaxial nematic phase has been claimed for a class of discotic dimers [111], Theory predicts that mixtures of rod-like and disc-like molecules should exhibit the biaxial nematic phase [120] but experimentally such systems phase separate... 

Yu, L.J., Saupe, A. Observation of a biaxial nematic phase in potassium-laurate -1-decanol-water mixtures. Phys. Rev. Lett. 45, 1(X)0 (1980)... 

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. 

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]).

Fig. 10.17 Uniaxial planar nematic (Ni) and biaxial nematic (Nib) phase in mixtures of a rod and a liquid crystal, where both components favor perpendicular orientations to each other...

Fig. 10.18 Phase diagram of biaxial nematic phases in a rodAiquid crystal mixture...

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],... 

Rod- and disc-shaped mesogens are likewise capable of forming uniaxial nematic phases N . In the early 1970s, Alben [20] published a theoretical calculation based on a mean-field lattice model in which he predicted the appearance of a biaxial nematic phase Ng for mixtures containing certain ratios between discs and rods. The phase diagram corresponding to his prediction is schematically shown in Figure 5-16. 

To avoid phase separation between the two moieties, a vast effort was devoted towards the synthesis of chemically linked disc-rod molecules [25-27], Beyond that, mixtures of prolate and oblate mesogens have stimulated theorists to perform intensive computer simulations. Simulations and molecular field theories predict the biaxial nematic phase to occur around the minimum of the transition temperature T from the nematic to the isotropic phase [22]. Furthermore, a strong decrease of the transition enthalpy is expected upon approaching the tricritical point. 

Mixtures of discs and rods have been predicted to form a biaxial nematic phase [20]. Avoiding the problem of phase separation between the two moieties, chemically linked disc-rod molecules have been studied. Optical textures, miscibility studies, and DSC experiments all resulted in the conclusion that, for a mixture with a certain ratio between the combined mesogen and the pure disc mesogen, a biaxial nematic phase had indeed been found [28]. However, this conclusion will have to be confirmed using additional experimental techniques, as, for example, deuterium NMR spectroscopy. 

Intermicellar forces are generally of a repulsive nature (i.e., charged amphiphiles) and a reduction of such repulsion accompanies the transformation from spherical to cylindrical micelles. Further increase of concentration results in the formation of linear assemblies and liquid crystalline lyotropic mesophases (cf. Section ni.B). Not only nematic (Nc and Nd from rodlike or disklike shapes, respectively), hexagonal, and smectic phases, but also biaxial (mixtures of Nc and Nd) and complex cubic phases (bicontinuous networks or plastic crystals)... 

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. 

For molecules of this shape, the isotropic phase is found to undergo a transition directly into the biaxial phase on compression. A biaxial phase has also been observed in simulations of mixtures of rods and platelets, in which the different species are modelled ellipsoids with aspect ratios of x = 20 and X = 1/20, respectively [19]. However, here the range of the biaxial phase is severely limited by demixing into two coexisting uniaxial nematics, one rich in rods, the other rich in discs. 

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