Ordering in Nematic Liquid Crystals

Hillert, Phase Equilibria, Phase Diagrams and Phase Transformations, Cambridge Univ. Press, New York (1998). 

Structural formulae for typical liquid crystal molecules widi dieir shorthand names given in parentheses. The lateral thickness perpendicular to the long axis is -4.5A in each case. 

This is equivalent to saying that the order formed in the nematic phase is not governed by electric dipole interactions but rather by the molecular shape and the van der Waals forces between molecules. Note that, although entropy is also related to the order of a system, the symbol S used here does not refer to entropy. 

The variation of 5(7) near the N-I phase transition will be measured in this experiment and will be compared with the behavior predicted by Landau theory, which is a variant of the mean-field theory first introduced for magnetic order-disorder systems. In this theory, local variations in the environment of each molecule are ignored and interactions with neighbors are represented by an average. This type of theory for order-disorder phase transitions is a very useful approximate treatment that retains the essential features of the transition behavior. Its simplicity arises from the suppression of many complex details that make the statistical mechanical solution of 3-D order-disorder problems impossible to solve exactly. 

For the magnetic system in zero external field, the Landau expression for the free energy can be written as an expansion in p about the G value for = 0  

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We consider first the Maier-Saupe tlieory and its variants. In its original foniiulation, tills tlieory assumed tliat orientational order in nematic liquid crystals arises from long-range dispersion forces which are weakly anisotropic [60, 61 and 62]. However, it has been pointed out [63] tliat tlie fonii of tlie Maier-Saupe potential is equivalent to one in... 

A. Ferrarini and G. J. Moro, Molecular order in nematic liquid crystals from shape-dependent repulsive and attractive interactions, J. Chem. Phys., 114 (2001) 596-608. 

X-ray diffraction is also useful in investigating the order in nematic liquid crystals. The size of the molecule itself implies that there should be a slight variation in the density, with the spatial period being roughly a molecular length along the director and roughly a molecular width perpendicular to the director. The motion of the molecules ensures that these periodicities are very small, but they should produce a diffuse maximum in the... 

Solid substrates also induce the smectic order in nematic liquid crystals. This has been shown by direct measurements of an attraction force acting between two mica substrates separated by a nematic layer [17]. The force oscillates with a decreasing gap. Fig. 3.4, the period being equal to the molecular length. It means that smectic layers are pushed out of the gap one after the other (insert to Fig. 3.4). The total thickness of the smecticlike surface layer is about 100 A. The other direct confirmation of the surface-induced smectic order is X-ray measurement [18] which revealed both smectic A and smectic C ordering in surface nematic layers being in contact with an evaporated SiO layer. 

J. G., De Lange, G. A. Molecular solutes in nematic liquid crystals orientational order and electric field gradients. Chem. Phys. Lett. 1983, 99, 271-274. 

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,... 

D. Forster, Hydrodynamics and Correlation Functions in Ordered Systems Nematic Liquid Crystals, Ann. Phys. 505 (1974) 85. 

As mentioned earlier, the proton NMR spectra of small molecules oriented in nematic liquid crystals become rapidly complex with the increase of number of interacting nuclei. In order to obtain information on orientation and structure, it is therefore essential to develop strategies to interpret such spectra with the help of special techniques. Techniques such as Automatic Analysis and the use of Multiple Quantum Spectroscopy have been employed for these purposes during the period under report. A method based on the Automatic Analysis of Multiple Quantum proton spectra of flexible molecules dissolved in liquid crystalline phases has been suggested for extracting starting parameters for the... 

In nematic liquid crystals, the molecular axes are ligned up in the same direction without any 2 dimensional ordering. Cholesteric and smectic liquid crystals are composed of layers of molecules with long molecular axes parallel and perpendicular to the planes, respectively. 

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