Polarity, nematics

This interpretation was confirmed to some extent by experimental results, since it had been found that nematic mixtures composed of apolar nematic compounds and polar nematic compounds (nitriles) consist of a number of unassociated polar and non-polar monomers as well as associated polar dimers. This not only gives rise to a high value for the observed dielectric anisotropy of the mixture due to the non-associated polar compounds, but also... 

The worm chain in a possible polar nematic phase was discussed as well (Wang Lam, 1992). The dipolar interaction was taken into account in addition to the quadrupolar interaction. It results in the complexity of the phase diagram. 

The isotropic phase formed by achiral molecules has continuous point group symmetry Kh (spherical). According to the group representations [5], upon cooling, the symmetry Kh lowers, at first, retaining its overall translation symmetry T(3) but reduces the orientational symmetry down to either conical or cylindrical. The cone has a polar symmetry Coov and the cylinder has a quadrupolar one Dooh- The absence of polarity of the nematic phase has been established experimentally. At least, polar nematic phases have not been found yet. In other words, there is a head-to-tail symmetry taken into account by introduction of the director n(r), a unit axial vector coinciding with the preferred direction of molecular axes dependent on coordinate (r is radius-vector). 

As we shall see further on, the terms linear in dnjdx, allow us to discuss not only conventional nematics with Dooh symmetry but also some biased nematic phases. For example, we can discuss the phases with a spontaneous twist (cholesterics with broken mirror symmetry) or a spontaneous splay (uniaxial polar nematics with broken head-to-tail symmetry, n -n). For a standard nematic only quadratic terms will remain. 

However, when molecules have mirror symmetry (achiral molecules), the inversion center appears and g ist becomes invariant with respect to the following frame transformation x = —x, y = —y, z = —z. As a result, modulus Kg vanishes and we have a tensor corresponding to a polar nematic ... 

Fig. 8.7 Packing of conical pear-shape) molecules in the conventional nematic phase (a) and in a hypothetical polar nematic phase (b)...

Between the polarized nematic and soHd phases a density region seems to exist where dipolar hard and soft spheres form ferroelectric columns with square ordering in the plane perpendicular to the coliunns [102,134], The stabihty and density range of this phase needs further investigation. Such a columnar phase has also been identifled in a system of extended dipoles where the coliunns order on a hexagonal lattice [ 146]. 

K22 are zero, and in the nonpolar nonchiral uniaxial nematic Ki, K2, K 2 and K23 are zero and five elastic moduli remain in Eq. (1). In enantiomorphic phases (cholesterics), the nonzero K2 term leads to a spontaneous equilibrium twist =- 2/ 22-There, the unbiased director field forms a helix of pitch length p=lKlq. The sign of K2 gives the handedness of the helix. In the case of a hypothetical polar nematic phase (which has not yet been found experimentally), a nonzero term would lead to spon-... 

In order to sharpen the observance for inconsistencies in a theory, it is sometimes instructive to present one which does not work. For instance, let us see if we can describe the transition to a polar nematic phase by a Landau expansion. It might also be thought of as describing the transition isotropic-polar smectic A or nematic-polar smectic A. (In either interpretation it will suffer from serious deficiencies.) We write the free energy as... 

Ferroelectricity in liquid crystals was first considered by Max Bom in 1916, who proposed a model to explain the isotropic-nematic transition by dipole-dipole interactions. He showed that polar rod-shape molecules of dipoles larger than about 5 Debye would align parallel to each other. The concept turned out to be false, since apolar nematic liquid crystals exist, too. In fact there is no evidence for polar nematic phases yet. 

Interacting living amoeboid cells themselves form nematic liquid crystals phases. It was observed that (1) a cluster of a polar nematic liquid crystal is formed by cells, which emit molecules for attracting other cells, and... 

Homogeneous swollen and partially swollen elastomers were prepared by immersing each dry elastomer in a solution composed of a nematic solvent and of cyclohexane. A small amount of toluene was subsequently added to the solutirai to progressively and non-destructively swell the sample. After waiting for a few hours, cyclohexane and toluene were evaporated. Most of the experiments were performed with the 4-n-pentyl-4 -cyanobiphenyl (5CB) as nematic solvent. Some additional experiments were performed with p-methoxybenzylidene p-butylanUine (MBBA), a non-polar nematic solvent. The weight concentration X of the solvent, for example 5CB, in the swollen sample is given by... 

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