Phases nematic phase

Figure 27. Snapshots of typical instantaneous configurations (left panel) and inherent structures (right panel) for the model calamitic system GB(3, 5, 2, 1) at various mesophases. From top to bottom isotropic phase, nematic phase, and smectic phase. (Reproduced from Ref. 131.)...

DLCs generally exhibit two types of phases nematic phase and columnar phase (Fig. 7.1). Discotic nematic phases are rarely observed while columnar phases are commonly found. In the nematic phase, the molecules possess only orientational ordering however in the columnar phase, the disc-like molecules spontaneously self-assemble into infinite one dimensional (ID) stacks, which in turn self-organize to various two dimensional (2D) liquid crystalline lattices. The hexagonal columnar phase is the most commonly encountered phase in DLCs. Some discotic compounds are also known to exhibit lamellar and cubic phases. 

Of all liquid crystalline phases, the nematic phase is the phase with the highest symmetry, i.e. Dooh, and the least order. As shown in Fig. 3.3a, b, the mesogens solely possess orientational order. Positional order of the mass centers does not occur in this phase. Nematic phases are usually built up by either rod-like or disc-like mesogens. For thermotropic liquid crystals these mesogens are therefore calamitic or discotic molecules, respectively. In both cases the phase is simply denoted with the abbreviation N. For lyotropics, the notation typically distinguishes between nematic phases Nc, which are formed by rod-like micelles, and nematic phases Np, which are composed of disc-like micelles. 

Three different models have been proposed for the explanation of these shear-induced phenomena. The first assumes that such phenomena are due to the formation of a nematic phase under the influence of shear. According to this theory, the systems are in the isotropic micellar phase, but close to the boundary of the nematic phase, and the application of shear leads to the transition into this phase. Nematic phases can... 

Dielectric Studies at Elevated Pressures A. Isotropic Phase Nematic Phase... 

X-ray diffraction is one of the primary methods to determine the structure of a liquid crystal phase. Nematic phases are characterized by diffuse arcs at small angles which result from local smectic-type order ( cybotactic clusters . Section 5.7.1). Smectic phases are characterized by Bra spots which result from the layer periodicity (Fig. 5.14). In oriented smectic A phases, the Bragg reflections are normal to the layers and their position is reciprocally related to the smectic layer period. If q is the wavenumber defining the peak position, then from Bragg s law (Eq. 1.26) d = Injq. The molecules and layers in a smectic C phase can adopt different mutual orientations depending on how the phase is accessed. If it is obtained by cooling from an SmA phase, the layer orientation is retained and the molecules tilt. Because the layer orientation... 

Eppenga R and Frenkel D 1984 Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets Mol. Phys. 52 1303-34... 

Figure C2.2.2. Isotropic, nematic and chiral nematic phases. Here n denotes tire director. In tire chiral nematic phase, tire director undergoes a helical rotation, as schematically indicated by its reorientation around a cone.

Altliough in figure C2.2.2 they are sketched witli rodlike molecules, botli nematic and chiral nematic phases can also be fonned by discotic molecules. 

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. 

Disclinations in tire nematic phase produce tire characteristic Schlieren texture, observed under tire microscope using crossed polars for samples between glass plates when tire director takes nonunifonn orientations parallel to tire plates. In thicker films of nematics, textures of dark flexible filaments are observed, whetlier in polarized light or not. This texture, in fact, gave rise to tire tenn nematic (from tire Greek for tliread ) [40]. The director fields... 

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,... 

This can be inserted in equation (02.2.3) to give tlie orientational distribution function, and tlius into equation (02.2.6) to deteniiine the orientational order parameters. These are deteniiined self-consistently by variation of tlie interaction strength iin equation (c2.2.7). As pointed out by de Gemies and Frost [20] it is possible to obtain tlie Maier-Saupe potential from a simple variational, maximum entropy metliod based on tlie lowest-order anisotropic distribution function consistent witli a nematic phase. 

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... 

The nematic to smectic A phase transition has attracted a great deal of theoretical and experimental interest because it is tire simplest example of a phase transition characterized by tire development of translational order [88]. Experiments indicate tliat tire transition can be first order or, more usually, continuous, depending on tire range of stability of tire nematic phase. In addition, tire critical behaviour tliat results from a continuous transition is fascinating and allows a test of predictions of tire renonnalization group tlieory in an accessible experimental system. In fact, this transition is analogous to tire transition from a nonnal conductor to a superconductor [89], but is more readily studied in tire liquid crystal system. 

Wlren a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These fluctuations were called cybotactic clusters in tire early literature. Regardless of tire physical picture of such fluctuations. 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model [201. It is applied in the case of a second-order phase transition by combining a Landau expansion for the free energy in tenns of an order parameter for smectic layering with the elastic energy of the nematic phase [20]. It is first convenient to introduce an order parameter for the smectic stmcture, which allows both for the layer periodicity (at the first hannonic level, cf equation (C2.2A)) and the fluctuations of layer position ur [20] ... 

Using this order parameter, the free energy in the nematic phase close to a transition to the smectic phase can be shown to be given by [20, 88, 89, 91]... 

C and I account for gradients of the smectic order parameter the fifth tenn also allows for director fluctuations, n. The tenn is the elastic free-energy density of the nematic phase, given by equation (02.2.9). In the smectic... 

Monte Carlo computer simulations of spheres sectioned into a disc [104, 105] show tliat steric interactions alone can produce a nematic phase of discotic molecules. Columnar phases are also observed [104, 105]. 

Hamley I W, Garnett S, Luckhurst G R, Roskilly S J, Pedersen J S, Richardson R M and Seddon J M 1996 Orientational ordering in the nematic phase of a thermotropic liquid crystal A small angle neutron scattering study J. Chem. Phys. 104 10 046-54... 

Otlier possibilities for observing phase transitions are offered by suspensions of non-spherical particles. Such systems can display liquid crystalline phases, in addition to tire isotropic liquid and crystalline phases (see also section C2.2). First, we consider rod-like particles (see [114, 115], and references tlierein). As shown by Onsager [116, 117], sufficiently elongated particles will display a nematic phase, in which tire particles have a tendency to align parallel to... 

Flard spherocylinders (cylinders witli hemispherical end caps) were studied using computer simulations [118]. In addition to a nematic phase, such particles also display a smectic-A phase, in which tire particles are arranged in liquid-like layers. To observe tliis transition, ratlier monodisperse particles are needed. The smectic-A phase was indeed observed in suspensions of TMV particles [17]. 

The cholesteric phase maybe considered a modification of the nematic phase since its molecular stmcture is similar. The cholesteric phase is characterized by a continuous change in the direction of the long axes of the molecules in adjacent layers within the sample. This leads to a twist about an axis perpendicular to the long axes of the molecules. If the pitch of the heHcal stmcture is the same as a wavelength of visible light, selective reflection of monochromatic light can be observed in the form of iridescent colors. 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

Chira.lNema.tlc, If the molecules of a Hquid crystal are opticaHy active (chiral), then the nematic phase is not formed. Instead of the director being locaHy constant as is the case for nematics, the director rotates in heHcal fashion throughout the sample. This chiral nematic phase is shown in Figure 7, where it can be seen that within any plane perpendicular to the heHcal axis the order is nematic-like. In other words, as in a nematic there is only orientational order in chiral nematic Hquid crystals, and no positional order. Keep in mind, however, that there are no planes of any sort in a chiral nematic Hquid crystal, since the director rotates continuously about the heHcal axis. The pitch of the helix formed by the director, ie, the distance it takes for the... 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

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. 

---