Positional ordering, discotic liquid crystals

The simplest discotic liquid crystal phase is the nematic discotic phase, Nd, in which the normals of the molecular discs tend to align with respect to a preferred direction, i.e., the director, but the mass centers of molecules do not have any positional order. The discs in Figure 1.11 represent the disclike molecules, the molecules are packed in the way a pile of coins is packed randomly. The discotic nematic phase has its chiral counterpart, i.e., the... 

Figure 1.1(b) shows a typical discotic liquid crystal molecule [6]. It also has a rigid core and flexible tails. The branches are approximately on one plane. The space-filling model of the molecule is shown in Figure 1.1 (d). If there is no permanent dipole moment perpendicular to the plane of the molecule, it can be regarded as a disk in considering its physical behavior as shown in Figure 1.1(f) because of the fast rotation around the axis which is at the center of the molecule and perpendicular to the plane of the molecule. If there is a permanent dipole moment perpendicular to the plane of the molecule, it is better to visualize the molecule as a bowl, because the reflection symmetry is broken and all the permanent dipoles may point in the same direction and spontaneous polarization occurs. The flexible tails are also necessary, otherwise the molecules form a crystal phase where there is positional order. 

In the discotic phase, disclike molecules form liquid crystal phases in which the axis perpendicular to the planes of the molecules, orients along a specific direction. The nematic discotic phase has orientational order but no positional order. In the columnar discotic phase, the disclike molecules form columns and therefore exhibit orientational and positional order. In a chiral discotic liquid crystal, the director rotates in a helical path throughout the system. 

The structure of liquid crystals can broadly be classified as nematic, cholesteric and smectic, see Fig. 1. None of them have full three-dimensional (3-D) positional order, but some degree of orientational order. Most often the constituent molecules are elongated, as indicated in Fig. 1, but distinctly flat molecules make up the socalled discotic liquid crystals. The nematic phase has only orientational ordering of the molecules. The collection of molecules have one symmetry axis called the director n. The cholesteric phase has only orientational order, formed by the constituent chiral molecules. The director twists with a pitch comparable to the wavelength of light. 

The directors (long molecular axes) of the constituent molecules in nematic phases are parallel to one another on average. This is the only order present in nematic liquid crystals, which are the most fluid type of liquid-crystalline phase. Molecules that form cholesteric phases must be optically active or contain an optically active dopant. As the phase name implies, the constituent molecules are frequently steroids and most commonly are cholesteric esters or halides. A conceptual model of the cholesteric phase includes layers of molecules in nematic-like positions, each layer being twisted slightly with respect to the ones above and below it. When the phase consists only of optically active molecules, the angle of twist between layers is typically less than one degree. Several subclasses of discotic phases exist. In all, the molecular planes of the constituent molecules are parallel. However, the discs can pack in nematic-like arrangements (ND) or in columns that are internally ordered (D ) or disordered (Dd) and may be stacked vertically,... 

The term mesophase also includes ordered liquids (nematic, smectic, cholesteric and discotics), which present long-range orientational order like in a solid, but positional disorder like in a liquid [2]. In these materials, large-scale molecular motion is possible, which is a characteristic of the liquid state rather than of the solid state. The term liquid crystals is conventionally used to address them. This sub-class of mesophases will not be treated in this context. 

Liquid crystals are mesophases between crystaUine solid and isotropic liquid [1-3]. The constituents are elongated rod-Kke (calamitic) or disk-like (discotic) organic molecules as shown in Figure 1.1. The size of the molecules is typically a few nanometers (nm). The ratio between the length and the diameter of the rod-like molecules or the ratio between the diameter and the thickness of disk-like molecules is about 5 or larger. Because the molecules are non-spherical, besides positional order, they may possess orientational order. 

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. 

Different types of LC systems are found in elastomers. In nematic liquid crystals, the molecules have orientational but no positional order, their center of mass positions being randomly distributed. Most nematic elastomers are employed in uniaxial deformation. If the LC elements contain chiral groups, they are termed as cholesteric elastomers. Discotic nematic LC elastomers contain disk-shaped molecules that can be oriented in layers. Smectic LC elastomers form well-defined layers. 

---