Crystals phases

A Shearographic Inspection System Using a Liquid Crystal Phase Modulator. 

We are all familiar with tire tliree states of matter gases, liquids and solids. In tire 19tli century the liquid crystal state was discovered [1 and 2] tliis can be considered as tire fourtli state of matter [3].The essential features and properties of liquid crystal phases and tlieir relation to molecular stmcture are discussed here. Liquid crystals are encountered in liquid crystal displays (LCDs) in digital watches and otlier electronic equipment. Such applications are also considered later in tliis section. Surfactants and lipids fonn various types of liquid crystal phase but this is discussed in section C2.3. This section focuses on low-molecular-weight liquid crystals, polymer liquid crystals being discussed in tire previous section. 

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. 

Molecules tliat are capable of fonning liquid crystal phases are called mesogens and have properties tliat are mesogenic. From the same root, tire tenn mesophase can be used instead of liquid crystal phase. A substance in a liquid crystal phase is tenned a liquid crystal. These conventions follow tliose in tire Handbook of Liquid Crystals, [4, 5 and 6] tire nomenclature of which [7] for various liquid crystal phases is adopted elsewhere in tliis section. 

Liquid crystal phases can be divided into two classes. Thermotropic liquid crystal phases are fonned by pure... 

Thennotropic liquid crystal phases are fonned by anisotropic molecules witli long-range orientational order and in many types of stmcture witli some degree of translational order. The main types of mesogen are Arose tlrat are rodlike or calamitic and Arose Arat are disclike or discotic. 

Figure C2.2.7. Schematic illustrating tire classification and nomenclature of discotic liquid crystal phases. For tire columnar phases, tire subscripts are usually used in combination witli each otlier. For example, denotes a rectangular lattice of columns in which tire molecules are stacked in a disordered manner (after [33])...

Liquid crystal phases possess characteristic textures when viewed in polarized light under a microscope. These textures, which can often be used to identify phases, result from defects in tire stmcture. Compendia of micrographs showing typical textures exist to facilitate phase identifications [37, 38]. These monographs also discuss tire origins of defect stmctures in some detail. 

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

X-ray diffraction is one of the primary methods to detennine the stmcture of a liquid crystal phase [22, 51]. 

This method is used to locate phase transitions via measurements of the endothennic enthalpy of phase transition. Details of the teclmique are provided elsewhere [25, 58]. Typically, the enthalpy change associated with transitions between liquid crystal phases or from a liquid crystal phase to the isotropic phase is much smaller than the melting enthalpy. Nevertheless, it is possible to locate such transitions with a commercial DSC, since typical enthalpies are... 

Thennotropic liquid crystal phases are fonned by rodlike or disclike molecules. However, in the following we consider orientational ordering of rodlike molecules for definiteness, although the same parameters can be used for discotics. In a liquid crystal phase, the anisotropic molecules tend to point along the same direction. This is known as the director, which is a unit vector denoted n. 

Typical shapes of the orientation distribution function are shown in figure C2.2.10. In a liquid crystal phase, the more highly oriented the phase, the moreyp tends to be sharjDly peaked near p=0. However, in the isotropic phase, a molecule has an equal probability of taking on any orientation and then/P is constant. 

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. 

Figure C2.2.10. Orientational distribution functions for (a) a highly oriented liquid crystal phase, (b) a less well...

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. 

Pershan P S 1988 Structure of Liquid Crystal Phases (Singapore World Soientifio)... 

Frenkel D 1992 Computer simulations of phase transitions in liquid crystals Phase Transitions in Liquid Crystals ed S Martellucci and A N Chester (New York Plenum)... 

In practice, colloidal systems do not always reach tlie predicted equilibrium state, which is observed here for tlie case of narrow attractions. On increasing tlie polymer concentration, a fluid-crystal phase separation may be induced, but at higher concentration crystallization is arrested and amorjihous gels have been found to fonn instead [101, 102]. Close to the phase boundary, transient gels were observed, in which phase separation proceeded after a lag time. 

Kitakami O et al 997 Size effect on the crystal phase of cobalt fine particles Phys. Rev. B 56 13 849 Cullity B D 1978 Elements of X-ray Diffraction (Reading, MA Addison-Wesley)... 

Fig. 22. Effects of polyphosphate level and N P20 weight ratio on solubility of ammoniated phosphoric acids at 0°C, where A represents 70% of total P20 as polyphosphate B, 45% and C, 0%, and the various crystallizing phases are (1), (NH H2PO (2), (NH 2HPO (3), (NH g HEgO -HgO) (4),...

Crystal phase is P-quartz ZrTiO unless otherwise noted. Corning. 

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