Thermotropic liquid crystals positional ordering

Lyotropic Liquid Crystals, Some molecules in a sulvcni form phases with orientational antl/or positional order. In these systems, the transition from one phase to another can occur due to a change of concentration, so they arc given the name lyotropic liquid cry stals Of course temperature can also cause phase transitions in these systems, so this aspect of thermotropic liquid crystals is shared hy lyotropics. The real distinctiveness of lyotropic-liquid crystals is the fact that at least two very different species of molecules nttisl be present for these structures to form... 

Liquid crystalline phases can show not only long-range orientational order as nematic phases do but also long-range positional order. When this positional order is one-dimensional, the mesophase is called lamellar or smectic when it is two-dimensional, it is called columnar. The latter case is often found with thermotropic liquid-crystal disk-like molecules. Such molecules stack in columns that assemble on a 2-D lattice of hexagonal, rectangular, or oblique symmetry. The molecules in a given column only show 1-D liquid-Hke order and the uncorrelated columns are free to slide past each other, which ensures the mesophase fluidity [73]. 

Lyotropic liquid crystals are principally systems that are made up of amphiphiles and suitable solvents or liquids. In essence an amphiphilic molecule has a dichotomous structure which has two halves that have vastly different physical properties, in particular their ability to mix with various liquids. For example, a dichotomous material may be made up of a fluorinated part and a hydrocarbon part. In a fluorinated solvent environment the fluorinated part of the material will mix with the solvent whereas the hydrocarbon part will be rejected. This leads to microphase separation of the two systems, i.e., the hydrocarbon parts of the amphiphile stick together and the fluorinated parts and the fluorinated liquid stick together. The reverse is the case when mixing with a hydrocarbon solvent. When such systems have no bend or splay curvature, i.e., they have zero curvature, lamellar sheets can be formed. In the case of hydrocarbon/fluorocarbon systems, a mesophase is formed where there are sheets of fluorocarbon species separated from other such sheets by sheets of hydrocarbon. This phase is called the La phase. In the La phase the molecules are orientationally ordered but positionally disordered, and as a consequence the amphiphiles are arranged perpendicular to the lamellae. The La phase of lyotropics is therefore equivalent to the smectic A phase of thermotropic liquid crystals. 

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. 

Structure of thermotropic liquid crystals is rather well understood. There are three main structural types nematic, cholesteric, and smectic. In nematic liquid crystals molecules are aligned approximately in the same direction, but positionally molecules are disordered. An axis of preferable molecular orientation is called a director. More precisely, the director is defined as a unit vector n(r) that is parallel to the molecular orientation at the point r. If we use the long axis of the molecules as a reference and denote it as k, the microscopic scalar order parameter 5 is defined [16,17] as follow ... 

The structures of liquid crystals are intermediate between the amorphous and crystalline states. They have some short-range orientational order. Some also have positional order. Thousands of organic compounds exhibit liquid crystal structures. Most have molecules that are very long and thin, but some have molecules that are flat and pancake shaped. Many compounds may exist in more than one liquid crystalline state. Transitions from one state to another may be thermotropic (caused by temperature change) or lyotropic (caused by change of solute concentration). 

Structural forces due to long-range positional order are quite easily observed in the smectic A liquid crystals. SFA measurements have been performed on lamellar lyotropic smectics [42,43] and in thermotropic smectics [44-46]. These works extend to a nanometer scale the early studies on elasticity, viscoelastic response and layers instability of smectic A, observed in macroscopic wedge-shaped piezoelectric cells [47,48]. 

Chen, W. (1996) in Liquid-Crystalline Polymer Systems (ed. A.I. Isayev, T. Kyu and S.Z.D. Cheng), American Chemical Society, Washington, chapter 15], and liquid crystals (that is, condensed phases in which molecules exhibit orientational order and varying degrees of positional order [2]). The distinctions among these three mesophase types will be maintained throughout this chapter liquid crystalline systems which are thermotropic (that is, induced by changes in the temperature or pressure of a sample) rather than lyotropic (that is, induced by addition of an isotropic liquid as solvent ) will be emphasized. 

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