Uniaxial biaxial nematic transitions

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]. 

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... 

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... 

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... 

Figure 13.13 Phase transition temperatures from isotropic phase to various structures as a function of chirahty. (a) isotropic-uniaxial nematic transition, (b) isotropic-uniaxial cholesteric transition, (c) isotropic-biaxial cholesteric transition, (d) isotropic-cubic transition.

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. 

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]).

The majority of the existing molecular theories of nematic liquid crystals are based on simple uniaxial molecular models like sphe-rocylinders. At the same time typical mes-ogenic molecules are obviously biaxial. (For example, the biaxiality of the phenyl ring is determined by its breadth-to-thick-ness ratio which is of the order of two.) If this biaxiality is important, even a very good statistical theory may result in a poor agreement with experiment when the biaxiality is ignored. Several authors have suggested that even a small deviation from uniaxial symmetry can account for important features of the N-I transition [29, 42, 47, 48], In the uniaxial nematic phase composed of biaxial molecules the orientational distri-... 

Finally, the transition lines from uniaxial nematic to biaxial are determined Eq. (8) with the constraint a2 = d -. At lowest order in b, the slope of the two lines at their meeting point a = Z7 = 0 is given by . 

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... 

The values of the scaled transition temperature, l TNi/e2oo, together with the transitional values of the ord parameters ni, ni and ni are listed in TABLE 1 for several values of the biaxiality parameter, X. As the molecular biaxiality increases so the major order parameter at the transition decreases indeed when X is 0.3 ni has decreased to about half that for a uniaxial molecule. In contrast although as expected the biaxial ordo- parameter ni increases with X the value is extremely small. It would seem, therefore, that the molecular biaxiality has the greatest effect on Ni and that ni is essentially negligible. The influence of X on the second rank order parameter is mimicked by its fourth rank counterpart ni indeed when X is 0.3 this order parameter is four times smaller than that for uniaxial molecules. For X of 0.4 all of the transitional order parameters are extremely small, hinting at the approach of a second ord transition. This occurs when X is 1 / >/6 but now the transition from the isotropic phase is directly to a biaxial and not a uniaxial nematic phase, as we shall see. 

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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