Symmetry nematic phase

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

NMR is not the best method to identify thennotropic phases, because the spectmm is not directly related to the symmetry of the mesophase, and transitions between different smectic phases or between a smectic phase and the nematic phase do not usually lead to significant changes in the NMR spectmm [ ]. However, the nematic-isotropic transition is usually obvious from the discontinuous decrease in orientational order. NMR can, however,... 

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

Here, ry is the separation between the molecules resolved along the helix axis and is the angle between an appropriate molecular axis in the two chiral molecules. For this system the C axis closest to the symmetry axes of the constituent Gay-Berne molecules is used. In the chiral nematic phase G2(r ) is periodic with a periodicity equal to half the pitch of the helix. For this system, like that with a point chiral centre, the pitch of the helix is approximately twice the dimensions of the simulation box. This clearly shows the influence of the periodic boundary conditions on the structure of the phase formed [74]. As we would expect simulations using the atropisomer with the opposite helicity simply reverses the sense of the helix. 

When the mesogenic compounds are chiral (or when chiral molecules are added as dopants) chiral mesophases can be produced, characterized by helical ordering of the constituent molecules in the mesophase. The chiral nematic phase is also called cholesteric, taken from its first observation in a cholesteryl derivative more than one century ago. These chiral structures have reduced symmetry, which can lead to a variety of interesting physical properties such as thermocromism, ferroelectricity, and so on. 

Anisotropic fluids, of which nematic liquid crystals are the most representative and simplest example, are characterized by an anisotropic dielectric permittivity. The nematic phase has D,yuh symmetry, and in a laboratory frame with the Z axis parallel to the C , symmetry axis (the director) the permittivity tensor has the form ... 

Sheldrick and Yesinowski40) have recently applied nematic phase nmr data to elucidate the H positions in H3Ru3(CO)9(CCH3), using the heavy atom positions derived from X-ray data. It is in principle an accurate method which does not require large crystals the only difficulties are that many hydrides react with nematic liquid crystals, and that some molecular symmetry is desirable41). 

Nematic phases are characterised by a uniaxial symmetry of the molecular orientation distribution function f(6), describing the probability density of finding a rod with its orientation between 6 and 6 + d0 around a preferred direction, called the director n (see Fig. 15.49). An important characteristic of the nematic phase is the order parameter (P2), also called the Hermans orientation function (see also the discussion of oriented fibres in Sect. 13.6) ... 

Such order can be described in terms of the preferential alignment of the director, a unit vector that describes the orientation of molecules in a nematic phase. Because the molecules are still subject to random fluctuations, only an average orientation can be described, usually by an ordering matrix S, which can be expressed in terms of any Cartesian coordinate system fixed in the molecule. S is symmetric and traceless and hence has five independent elements, but a suitable choice of the molecular axes may reduce the number. In principle, it is always possible to diagonalize S, and in such a principal axis coordinate system there are only two nonzero elements (as there would be, for example, in a quadrupole coupling tensor). In the absence of symmetry in the molecule, there is no way of specifying the orientation of the principal axes of S, but considerable simplification is obtained for symmetric molecules. If a molecule has a threefold or higher axis of symmetry, its selection as one of the axes of the Cartesian coordinate system leaves only one independent order parameter, with the now familiar form ... 

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]. 

The number of transitions in an NMR spectrum increases dramatically as the number of interacting nuclei in the spin system increases. The number of transitions appearing in a 1-quantum spectrum of a spin system (without any simplifying symmetry) partially oriented in a nematic phase is expressed by Eq. (2), with some examples shown in Table 1. 

This relation is simplified by molecular symmetry. The splitting of the Zeeman term above is determined by the indirect couplings/// and the direct couplings //, which are not averaged to zero in the nematic phase. The average Hamiltonian for a symmetric-top molecule is given in Eq. (6)... 

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