The biaxial nematic phase

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). 

NMR experiments carried out on one of these co-dendrimers have proved that the symmetry of the nematic phase is imiaxial, in contrast to the biaxial nematic phase observed for some side-on-polymers [219]. 

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)... 

The existence of the biaxial SmA phase (SmAj,), also known as the McMillan phase, has been demonstrated in some charge-transfer complexes (CT complexes) formed with the metallomesogens 126 and TNF by textural observations and X-ray investigations. (Like the biaxial nematic phase mentioned earlier, the SmAt phase has additional long-range order in a direction perpendicular to the principal director, n (Figure 7)). Two novel... 

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... 

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( >). 

Fig. 6.6.1. Two examples of molecules which exhibit the biaxial nematic phase (a) (bis-l-(p-n-decylbiphenyl)-3-(p-ethoxyphenyl) propane-1,3-dionatocopper (II))(8i.82) (hereafter referred to as complex A) (b) I,12- >w(pentakis((4-pentyl-phenyl)ethy nyl)pheny loxy)dodecane. ...

Fig. 6.6.3. Raw microdensitometer scans of the X-ray intensity plotted against diffracting angle (20) for magnetically aligned nematic samples (a) the uniaxial nematic phase of 80CB at 77 °C (b) the biaxial nematic phase of complex A at 168.5 C, (i) meridional scan (parallel to H), (ii) equatorial scan (perpendicular to H). M represents the diffraction peaks from the mylar film which covered the windows of the sample holder and heater assembly. ...

Fig. 6.6.4. Schematic diagram of the molecular order in (a) the uniaxial nematic phase and (b) the biaxial nematic phase.

Figure 11. The three possible half integer disclination lines in the biaxial nematic phase of Vectra B 950 . (a) Rotation around the X axis, (b) rotation about the Y axis and (c) rotation around the Z axis [53], It is worth noting that the Ey line is perpendicular to the main director Y.

Now the biaxial nematic phase has two order parameters Q and and, in general, three different phases can be distinguished, namely, isotropic (Q = Qi = 0), uniaxial nematic Q, Q i = 0) and biaxial nematic (01,02) phases. Note that biaxial molecules may form both biaxial and uniaxial phases the latter appear due, for instance, to free rotation of biaxial molecules around their long molecular axes. As to the uniaxial molecules, they may also form either uniaxial (as a rule) or biaxial phases the latter may be formed by biaxial dimers or other building blocks formed by uniaxial molecules. 

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... 

Omnes, L. Timimi, B. A. Gelbiich, T. Hursthouse, M. B. Luckhurst, G. R. Bruce, D. W. Specific molecular interactions in Pd(II) complexes identify a new approach to the biaxial nematic phase. Chem. Commun. 2001, 2248-2249. 

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). 

Figueirinhas JL, Cruz C, Filip D, Feio G, Ribeiro AC, Frere Y, Meyer T, Mehl GH (2005) Deuterium NMR investigation of the biaxial nematic phase in an organosiloxane tetrapode. Phys Rev Lett 94 107802... 

Longa Lech, Grzybowski Piotr, Romano SUvano, and Virga Epifanio. Minimal coupling model of the biaxial nematic phase. Phys. Rev. E. 71 no. 5 (2005) 051714. 

The biaxial nematic phase presented by an organosiloxane tetrapode has been characterized by registering NMR spectra while the sample is continuously rotating around an axis perpendicular to the magnetic field. The presence of slow movements of the tetrapode mesogenic units could also be detected through the analysis of the NMR spectra. 

In the biaxial nematic phase it is possible to define two orthogonal directors n and m. In this case the magnetic susceptibility tensor can be rewritten as... 

Now the traceless part of the magnetic susceptibility is a sum of two terms proportional to two tensor order parameters of the biaxial nematic phase and Bap-... 

To conclude, it now seems accepted that the NAC point has a universal topology. The biaxial nematic phase has not been found experimentally, and there is still a need for theoretical analysis of fluctuations in the vicinity of the NAC point. 

Figure 8. Interference patterns of the biaxial nematic phase of compound 9 (/j=12) at 137°C. (a) The trace of the optic axial plane lies parallel to the polarizer or analyzer (extinction position) (b) and (c) represent the trace of the optic axial plane enclosing an angle of +45° or -45° with the polarizer position (from [24]).

Phase diagram of the potassium laurate (KL)-l-decanol-D20 system, with the Landau point. Nc and Nl are uniaxial nematic phases with cylindrical and lamellar micelle structures, and Nj, denotes the biaxial nematic phase. (Figure reproduced from Reference [8] with permission... 

Figure 10.17 shows schematically the biaxial nematic phase Njb and the uniaxial nematic phase Ni [55]. The orientatiOTi of the rodlike molecules in a plane perpendicular to the direction of the major director (n) is random in the uniaxial N1 phase. However, with increasing cmicentration of the rodlike molecules, the rodlike molecides may orient by mutual attraction and the excluded volume effect in a second direction with the minor director (m) as shown in the figure on the right. Thus, the novel biaxial nematic phase Nib may be possible. In the same fashion, in the N2 phase, it may be possible to have a biaxial nematic N2b phase, where the additional ordering of liquid crystals appears in the minor director (in) perpendicular to the major director (h) of rodlike molecules. 

The biaxial order parameter A represents the minor director and defines the degree of orientation along an axis that is perpendicular to the z-axis. In the isotropic phase = A = 0, in the uniaxial nematic phase 0, A = 0, and in the biaxial nematic phase 0, A y 0. 

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. 

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. 

The fact that the angle 6 of 140° between the two mesogenic arms in the mesogens investigated above is far outside the range for which a biaxial nematic phase has been predicted, indicates the important role of the large transverse electrical dipole for the stabilization of the biaxial nematic phase. 

In a recent publication, these findings have been nicely confirmed by deuterium NMR investigations of a spin probe dissolved in the organo-siloxane tetrapodes [40], where the same sample-flip technique was applied as in [4, 11], In their study, the authors point out that the mode of stabilization of the biaxial nematic phase in tetrapodes and liquid-crystalline side-chain polymers, i.e., the lateral fixation of the mesogenic group, may in fact be similar. 

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