Discotic Nematics

Very few data exist for the viscosities or Frank constants of discotic nematics—that is, nematics composed of disc-Uke particles or molecules (Chandrasekhar 1992). One can estimate values of the Leslie viscosities from the Kuzuu-Doi equations (10-20) by setting the aspect ratio p equal to the ratio of the thickness to the diameter of the particles thus /j — 0 for highly anisotropic disks. This implies that R(p) —1, and Eq. (10-20b) implies that the viscosity o 2 is large and positive for discoidal nematics, while it is negative for ordinary nematics composed of prolate molecules or particles. If, as expected, is much smaller in magnitude than 0 2. the director (which is orthogonal to the disks) will tend 

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McMillan s model [71] for transitions to and from tlie SmA phase (section C2.2.3.2) has been extended to columnar liquid crystal phases fonned by discotic molecules [36, 103]. An order parameter tliat couples translational order to orientational order is again added into a modified Maier-Saupe tlieory, tliat provides tlie orientational order parameter. The coupling order parameter allows for tlie two-dimensional symmetry of tlie columnar phase. This tlieory is able to account for stable isotropic, discotic nematic and hexagonal columnar phases. 

Disc-like particles can also undergo an Onsager transition—here tire particles fonn a discotic nematic, where tire short particle axes tend to be oriented parallel to each other. In practice, clay suspensions tend to display sol-gel transitions, witliout a clear tendency towards nematic ordering (for instance, [22]). Using sterically stabilized platelets, an isotropic-nematic transition could be observed [119]. 

A relatively new class of high-performance carbon fibers is melt-spun from mesophase pitch, a discotic nematic liquid crystalline material. This variety of carbon fibers is unique in that it can develop extended graphitic crystallinity during carbonization, in contrast to current carbon fibers produced from PAN. 

The rigid nature of the mesophase pitch molecules creates a strong relationship between flow and orientation. In this regard, mesophase pitch may be considered to be a discotic nematic liquid crystal. The flow behavior of liquid crystals of the nematic type has been described by a continuum theory proposed by Leslie [36] and Ericksen [37]. 

Discotic LC are formed by disk-like molecules with aromatic cores and side chains that are either hydrophobic (i.e., thermotropic) or hydrophilic (i.e., lyotropic). The discotic nematic (No) phase behaves like a normal nematic phase formed by rod-like molecules, and the disk-like molecules are oriented with their short molecular axes parallel to the director but show no positional order. More ordered columnar phases are commonly formed by thermotropic discotics. The two-dimensional structure can pack the columns into a hexagonal or rectangular columnar phase, while within the columns, disks can be... 

Note 3 In some cases the discotic nematic mesophase is formed by compounds that do not have molecules of discotic shape (for example, phasmidic compounds, salt-like materials and oligosaccharides). 

Note 4 Chiral discotic nematic mesophases, N, also exist. 

Fig. 13. Illustrating the organization of molecules in a discotic nematic mesophase.

Note 5 If the mesogenic side-groups are rod-like (calamitic) in nature, the resulting polymer may, depending upon its detailed structure, exhibit any of the common types of calamitic mesophases nematic, chiral nematic or smectic. Side-on fixed SGPLC, however, are predominantly nematic or chiral nematic in character. Similarly, disc-shaped side-groups tend to promote discotic nematic or columnar mesophases while amphiphilic side-chains tend to promote amphiphilic or lyotropic mesophases. 

Frenkel [412] also examined the behaviour of systems consisting of hard spheres in which the top and bottom have been cut off to form disclike structures. Here it is possible to demonstrate the existence of both discotic nematic and hexagonal columnar discotic phases. 

Discotic liquid crystals The molecules possess a disc shape in many cases they are polysubstituted benzene or triphenyl derivatives with lateral extended aliphatic chains. These molecules arrange, e.g., in large columns a discotic nematic phase is known too. 

Akopova reported liquid crystalline phthalocyanines 116ac (Scheme 63) with eight peripheral crown ethers devoid of alkyl chains [132]. Nonetheless, discotic nematic phases could be observed as derived from miscibility experiments with the discotic nematogen hexa(cyclohexanebenzoyloxy)triphenylene and optical textures. In the case of metal-free 116a, a phase width of 43 K was found. Complexation with Zn(II) (116b) decreased the phase range to 35 K and with... 

Fig. 4 Hekates with shape-persistent oligothiophene and oxadiazole arms. Only the endcapped molecules with extended arms revealed LC phases. Colob columnar oblique phase, ND discotic nematic phase. All transition temperatures are given in °C...

G. Ayton and G. N. Patey, Phys. Ref. Lett., 76, 239 (1996). Ferroelectric Order in Model Discotic Nematic Liquid Crystals. 

In contrast to calamitic mesogens, discotic liquid crystals are built from disk-like molecules that can arrange into different structures, such as the discotic nematic mesophase, the discotic columnar mesophase, or the discotic hexagonal meso-phase. 

Onsager s potential also applies to oblate particles or disks of high aspect ratio, if the parameter Uq ts redefined as 47rvdisk-shaped particles or molecules can therefore also undergo a transition to a nematic phase, called a discotic nematic. 

In the simplest liquid-crystalline phase, namely the uniaxial nematic, there is at rest a special direction designated by a unit vector n called the director (see Fig. 10-2). In the plane transverse to the director, the fluid is isotropic. The most common nematics are composed of oblong molecules that tend to point in a common direction, which defines the director orientation. Oblate, or disc-like, molecules can also form uniaxial nematics for these discotic nematics, the director is defined by the average orientation of the short axis of the molecule. Lath-like molecules or micelles (shaped like rectangular slabs), in which all three dimensions of the molecule are significantly different from each other, can form biaxial nematics (Praefcke et al. 1991 Chandrasekhar 1992 Fialtkowski 1997). A biaxial... 

Figure 2.19 Orderings in LC mesophases. (a) nematic (b) smectic (c) cholesteric (d) discotic-nematic (e) discotic-columnar.

Molecules of a disc-like shape form either nematic or columnar phases. Structurally the most simple mesophase is the discotic nematic phase (Nd). Just as in the case of the nematic phase formed by calamitic molecules, the molecules possess orientational order, but no positional order (Figure 2.8). The columnar nematic phase (Nc) consists of short columns of a few molecules that act like the rod-like molecules in the nematic calamitic phase (Figure 2.9). There is no organisation of the columns in a two-dimensional lattice. 

Figure 2.8 Schematic representation of a discotic nematic phase (No)...

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... 

The apparent disagreement between simulation results and experimental observations on the the existence of power law relaxation near the isotropic-columnar (I-C) phase boundary needs further attention. This appears to be associated with the existence of nematic-like fluctuations in the experimental system. This can be checked, on the experimental side, by studying the relaxation near the I-C phase boundary located away from the discotic-nematic phase. For simulation, a careful analysis should be done by changing the temperature and density along the phase coexistence line and studying the existence or lack of nematic-like orientational fluctuations. 

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