Liquid crystals defined

The initial research on electro-optic phenomena in side-chain polymer liquid crystals concentrated on systems that exhibited nematic phases so that a ready comparison could be made with low molar mass mesogens. Such measurements have established that electro-optic devices are feasible and have allowed elastic constants to be deduced from applications of the continuum theory. This theory, originally derived for low molar mass nematic liquid crystals, defines a relationship for the free energy density F in terms of the elastic constants (/ ) and the director n such that ... 

We are all familiar with gases, liquids and crystals. However, in the nineteenth century a new state of matter was discovered called the liquid crystal state. It can be considered as the fourth state of matter (although plasmas are also candidates for this accolade). The essential features and properties of liquid crystal phases and their relation to molecular structure are discussed in this chapter. Specifically, the focus is on thermotropic liquid crystals (defined in the next section). These are exploited in liquid crystal displays (LCDs) in digital watches and other electronic equipment. Such applications are outlined later in this chapter. Surfactants and lipids form various types of liquid crystal phase but this was discussed separately in Chapter 4. Finally, this chapter focuses on low molecular weight liquid crystals, liquid crystalline polymers being touched upon in Section 2.10. 

The label liquid crystal seems to be a contradiction in tenns since a crystal cannot be liquid. However, tire tenn refers to a phase fonned between a crystal and a liquid, witli a degree of order intennediate between tire molecular disorder of a liquid and tire regular stmcture of a crystal. Wlrat we mean by order here needs to be defined carefully. The most important property of liquid crystal phases is tliat tire molecules have long-range orientational order. For tliis to be possible tire molecules must be anisotropic, whetlier tliis results from a rodlike or disclike shape. 

An orientational order parameter can be defined in tenns of an ensemble average of a suitable orthogonal polynomial. In liquid crystal phases with a mirror plane of symmetry nonnal to the director, orientational ordering is specified. 

If we compare with figure C2.2.I I, we can see that this defonnation involves bend and splay of the director field. This field-induced transition in director orientation is called a Freedericksz transition [9, 106, 1071. We can also define Freedericksz transitions when the director and field are both parallel to the surface, but mutually orthogonal or when the director is nonnal to the surface and the field is parallel to it. It turns out there is a threshold voltage for attaining orientation in the middle of the liquid crystal cell, i.e. a deviation of the angle of the director [9, 107]. For all tliree possible geometries, the threshold voltage takes the fonn [9, 107]... 

Liquid crystal displays depend upon the reorientation of the director , the defining alignment vector of a population of liquid crystalline molecules, by a localised applied electric field between two glass plates, which changes the way in which incident light is reflected directional rubbing of the glass surface imparts a... 

The anisotropy of the liquid crystal phases also means that the orientational distribution function for the intermolecular vector is of value in characterising the structure of the phase [22]. The distribution is clearly a function of both the angle, made by the intermolecular vector with the director and the separation, r, between the two molecules [23]. However, a simpler way in which to investigate the distribution of the intermolecular vector is via the distance dependent order parameters Pl+(J") defined as the averages of the even Legendre polynomials, PL(cosj r)- As with the molecular orientational order parameters those of low rank namely Pj(r) and P (r), prove to be the most useful for investigating the phase structure [22]. 

It is also possible that a membrane might have an even lower symmetry than a chiral smectic-C liquid crystal in particular, it might lose the twofold rotational symmetry. This would occur if the molecular tilt defines one orientation in the membrane plane and the direction of one-dimensional chains defines another orientation. In that case, the free energy would take a form similar to Eq. (5) but with additional elastic constants favoring curvature. The argument for tubule formation presented above would still apply, but it would become more mathematically complex because of the extra elastic constants. As an approximation, we can suppose that there is one principal direction of elastic anisotropy, with some slight perturbations about the ideal twofold symmetry. In that approximation, we can use the results presented above, with 4) representing the orientation of the principal elastic anisotropy. 

Liquid crystals are thermodynamic phases composed of a great many molecules. These molecules, termed mesogens, possess a free energy of formation, of course. LCs (their structure, properties, everything that gives them their unique identity), however, are not defined at the level of the constituent molecules any more than a molecule is defined at the level of its constituent atoms. LCs are supermolecules. How do they differ from supramolecular... 

On a molecular level the director is not rigorously defined, but the molecular director is typically considered to be the average long axis of the molecules, oriented along the macroscopic director with some order parameter less than one. This type of anisotropic order is often called long-range orientational order and, combined with the nonresonant optical properties of the molecules, provides the combination of crystal-like optical properties with liquidlike flow behavior characteristic of liquid crystals. 

The values of these autocorrelation functions at times t = 0 and t = 00 are related to the two order parameters orientational averages of the second- and fourth-rank Legendre polynomial P2(cos/ ) and P4 (cos p). respectively, relative to the orientation p of the probe axis with respect to the normal to the local bilayer surface or with respect to the liquid crystal direction. The order parameters are defined as... 

Another mechanism of chiral amplification that extends over an even larger scale has been reported by Huck et al. [119] The molecule 12-(9 H-thioxantbene-9 -yli-dene-12H-benzo[a]xanthene (Fig. 11.6), which has no chiral center, nevertheless exists, like the helicenes, in two chiral forms defined by their enantiomeric configurations. Consistent with the discussion in Section 11.2.3, a small net handedness (ca. 0.7 %) could be induced in racemic solutions of this molecule by use of ultraviolet CPL. However, introducing 20 wt% of this molecule, which contained a 1.5% chiral excess of one roto-enantiomer, into a nematic phase of liquid crystals produced macroscopic (100 pm) regions of a chiral cholesteric liquid crystal phase. The... 

We present here some very general exact results, which hold for arbitrary reorientation mechanisms of any molecule in an equilibrium isotropic fluid (but not a liquid crystal). A coordinate frame (R) is rigidly attached to the molecule of interest. Its orientation in the laboratory frame (L) is defined by the Euler rotation = (affy) that carries a coordinate frame from coincidence with the laboratory frame L to coincidence with the molecular frame R/ The conditional probability per unit Euler volume [( (0r at time t must depend only on the Euler rotation A = 1 (i.e., rotate first by < 0 then... 

One may consider a series of physical states ranging from the crystalline, where molecular aggregation and orientation are large, to the dilute gaseous state, where there are no significant orientational limits. States of intermediate order are represented by micelles, liquid crystals, monolayers, ion pairs, and dipole-dipole complexes. In the crystalline state, the differences between pure enantiomers, racemic modifications, and diastereomeric complexes are clearly defined both structurally and energetically (32,33). At the other extreme, stereospecific interactions between diastereomerically related solvents and solutes, ion pairs, and other partially oriented systems are much less clearly resolved. 

Note 2 A virtual transition temperature is not well defined it will, for example, depend on the nature of the liquid-crystal components used to construct the phase diagram. 

Fig. 29. Schematic representation of a bend deformation (a) changes in the components of the director, n defining the orientation change (b) bend deformation of an oriented layer of a nematic liquid crystal.

Coefficients that define the energy dissipation associated with a rotation of the director in an incompressible, nematic liquid crystal. 

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