Transition biaxial nematics

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... 

Scientists have investigated uniaxial-biaxial phase transition for nematic liquid crystal polymers and have tried to describe it through the order parameters and also by considering the terms that account for the energy of elastic deformation and the... 

The complete phase diagram is obtained with the selection rule (tI (7 and reproduced in Fig. 1 [1]. Note that a direct transition I-Nb occurs at a single point a = b = 0 on the line (Eq. 10) [7]. The biaxial nematic region separates two uniaxial nematics N+ and N of opposite sign. N -Nb transitions are second order since the condition 2 = (7 can be approached continuously from the biaxial phase. 

While both side-on side-chain liquid crystal polymers [16] and low molecular weight liquid crystals [17] have been reported to have biaxial nematic phases, only in a lyotropic liquid crystal system [18], has the uniaxial-biaxial nematic transition been studied in detail from the point of view of critical phenomena. This transition is found to be second order. So far, it is the one liquid crystal system where earlier theoretical expectations [19] of fluctuation dominated phase transitions and later experimental results are most fully in agreement with respect to both static [20] and dynamic [21] aspects of critical phenomena. In particular, static critical phenomena predicts 3D-XY exponents which have been observed (with irrelevant corrections to scaling) by Saupe et al. [19]. Transport parameters were not expected [19] to show any singularities at the transition [19] as later verified by Roy et al. [21] because the dynamics of the biaxial order parameter is nonconserved (Model A) [19]. 

For negative dielectric anisotropy of the nematic phase, < 0, the external field may induce a biaxial nematic phase. With increasing field one may reach the tricritical point [18] where the first-order N-I transition becomes a second-order one. 

They calculated the coefficients of an expansion of the Kij(S, T) up to fourth order in the order parameter S and the degree of biaxiality T. In case of weak biaxiality Telastic moduli (/= /, m, n)) are predominant and the deformation state may be described satisfactorily with three bulk and one surface elastic constant, as in the uniaxial case. Recently, these three quasi-uni-axial bulk elastic constants of slightly biaxial nematic copolyesteramide have been determined by De Neve et al. [313] from an optical observation of the Freedericksz transition in different geometries. 

Based on the interaction employed in the Maier-Saupe theory of the nematic state, Preiser [4] was the first to predict the possible existence of an N, phase as an intermediate between two uniaxial nematic phases. Later, a number of other theoretical investigations were carried out [5-7] using various models to predict the possibility of obtaining an liquid crystal. In all these models, a system consisting of hard rectangular plates was considered. These approaches gave the same result, an Nb phase should be obtained between two uniaxial nematics of opposite sign, i.e., those made up of rod-like and plate-like molecules. They also predicted that a transition from a uniaxial nematic to a biaxial nematic would be second order. 

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]).

In advancing possible explanations of the observed appearance of birefringence in a homeotropically oriented sample, the probability of only partial perturbation of the homogeneous orientation of the film and slope of the optical axis due to a change in the ccmformational state of the main chain of the macromolecule at the linkages of the side groups at the transition point is indicated in [62]. Nevertheless, the formation of an unusual biaxial nematic phase is also possible in comb-sh )ed polymers, but additional expmmental evidence is required. 

Roetting O, Hinrichsen G (1994) Blends of thermotropic liquid crystalline and thermoplastic polymers a short review. Adv Polym Technol 13(l) 57-64 Roth D, Thomas L (1989) Why LCP film. In Abstracts of papers of the American Chemical Society, vol 198, p 3-CMEC. American Chemical Society, Washington, DC Rudko O (2002) Liquid crystalline polymers. Uniaxial-biaxial nematic phase transition Scott CE, Macosko CW (1995) Morphology development during the initial stages of polymer-polymer blcmding. Polymer 36(3) 461-470... 

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. 

---