Lath-Like Molecules

As a consequence, the refraction index component perpendicular to the director n is larger in case b than in case c, and the component n is smaller. Therefore, the optical anisotropy An = n — n i in case b is smaller. To take the new situation into account, two local order parameters are introduced for the uniaxial nematic phase, one is the same as discussed above for the longitudinal molecular axes (5 = 5 ), and the other describes the local order of the shortest molecular axes that is local biaxiality (D)  

For the ideal nematic with sim = 0 and %- 1 there is no difference between cases b and c. The locally (microscopically) biaxial nematic phase should not be confused with macroscopically biaxial phases to be discussed in the next section. 

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Mesogen composed of rod-like or lath-like molecules. Note Examples are ... 

In the non-amphiphilic smectic A mesophase (Figure 2b), the parallel, fairly rigid, lath-like molecules are grouped with orientational disorder (at right angles to their long axes) and end-to-end so that the molecules lie statistically normal to the sheets, constituting an optically uniaxial... 

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... 

All atoms and molecules can be polarized by an electric field. The polarization (induced dipole of a unit volume) is P = aE where a is molecular polarizability. For spherically symmetric atoms or molecules (like C60 fullerenes) the polarizability is a scalar quantity (tensor of zero rank) and P E. In general case of lath-like molecules, QLij is a second rank tensor (9 components) and Py = a,yE/. By a proper choice of the reference frame the tensor can be diagonalized... 

Fig. 3.17 Local packing of lath-like molecules thathindeis rotation of individual molecules about their longest axes (a) and illustration of a large (b) or zero (c) projections of a short molecular...

Optically, a nematic phase can be uniaxial or biaxial. The latter is formed by elongated lath-like molecules. Conventional nematic liquid crystals formed by rod-like molecules constitute a uniaxial medium with nonpolar symmetry. The constituent molecules rotate (freely or hindered) around both their short and long axes. Nonoriented samples are analogous in some measure to polycrystalline powders they consist of individual (liquid) crystallites, each of which has as a definite feature, a directed optical axis, which... 

A Mesophases of Disc-like and Lath-like Molecules... 

Chiral lath-like molecules can form biaxial cholesterics with properties different from those for conventional cholesterics. Moreover, the cholesteric to cholesteric phase transition has been predicted [23]. 

The Maier-Saupe theory assmnes high symmetry for molecules forming liquid crystals. In reahty, this is usually not the case and the theory has been extended [3.18] to lath-like molecules. The order parameter tensor S is given by Eq. (3.8) for a biaxial molecule in a uniaxial phase. In the principal axis x y z) system of 5, only two order parameters, Szz and D = Sxx — Syy, are needed, which are related to the Wigner matrices according to Eq. (2.43) ... 

As already mentioned, mesogens embrace a diversity of structure. We shall not, however, be concerned here with mesophases of disc-, pyramid-and phasm-like molecules, but shall confine attention to thermotropic mesomorphism exhibited by LMM compounds with elongated and relatively rigid lath-like molecules. Mesophases formed on heating such compounds are classified into three types nematic, cholesteric, and smectic. There are more than ten recognized smectic modifications and these are denoted by Sa, Sb, Sc-.-Sl- A description of the structural features of these phases may be found in standard books and reviews " and it is my intention in this section to bring the information on this subject up to date and to present it in a more concise form. 

The molecular arrangement in the smectic A phase involves a parallel arrangement of the lath-like molecules, with their ends in line, to form layers in which the long axes of the molecules tend to be orthogonal to... 

The smectic C phase is the tilted analogue of the smectic A phase, i.e. the smectic layers have a liquid-like, unstructured arrangement of the lath-like molecules which are tilted with respect to the layer planes (Fig. 2.8(b)). As a consequence, the material is optically biaxial. When it occurs in the company of other phases, the smectic C phase always occurs lower in the temperature scale than either an Sa or N phase, but higher in the scale than a more ordered smectic phase. This means that by heating it is possible to obtain the phase sequence Sc -> Sa - N I. If the smectic C phase is followed by an A phase, the tilt angle decreases gradually and finally becomes zero at the C-A transition point. If the C phase is not followed by an A phase, the tilt angle is often temperature independent and usually about 30-40°. 

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