Liquid crystals long-range order

Liquid crystals (LCs) are organic liquids with long-range ordered structures. They have anisotropic optical and physical behaviors and are similar to crystal in electric field. They can be characterized by the long-range order of their molecular orientation. According to the shape and molecular direction, LCs can be sorted as four types nematic LC, smectic LC, cholesteric LC, and discotic LC, and their ideal models are shown in Fig. 23 [52,55]. 

It will be useful now to review some elementary facts regarding the structure of liquids at equilibrium. When a crystalline solid melts to form a liquid, the long range order of the crystal is destroyed. However, a residue of local order persists in the liquid state with a range of several molecular diameters. The local order characteristic of the liquid state is described in terms of a pair correlation function, g-i(R)> defined as the ratio of the average molecular density, p(R), at a distance R from an arbitrary molecule to the mean bulk density, p, of the liquid... 

Liquid crystals combine properties of both liquids (fluidity) and crystals (long range order in one, two, or three dimensions). Examples of liquid crystalline templates formed by amphiphiles are lyotropic mesophases, block copolymer mesophases, and polyelectrolyte-suxfactant complexes. Their morphological complexity enables the template synthesis of particles as well as of bulk materials with isotropic or anisotropic morphologies, depending on whether the polymerization is performed in a continuous or a discontinuous phase. As the templating of thermotropic liquid crystals is already described in other reviews [47] the focus here is the template synthesis of organic materials in lyotropic mesophases. 

Similarly, when an aerogel is impregnated with a nematic liquid crystal, the gel network randonuiess destroys the crystal long-range order and transforms the liquid crystal into a glassy state [179]. 

A crystalline solid is a solid in which the atoms, ions, or molecules lie in an orderly array (Fig. 5.16). A crystalline solid has long-range order. An amorphous solid is one in which the atoms, ions, or molecules lie in a random jumble, as in butter, rubber, and glass (Fig. 5.17). An amorphous solid has a structure like that of a frozen instant in the life of a liquid, with only short-range order. Crystalline solids typically have flat, well-defined planar surfaces called crystal faces, which lie at definite angles to one another. These faces are formed by orderly layers of atoms (Box 5.1). Amorphous solids do not have well-defined faces unless they have been molded or cut. 

In addition to the large number of silicate crystals, the Si04 tetrahedra are the basis of many glasses in which the structure derives from that of the liquid state. These structures have short-range but not long-range order. 

Similar to cholesteric liquid crystals, the nematics have an orientational long-range order with the deviation that the direetion of the preferred orientation does not rotate (Fig. 2a). If, however, a chiral mesogen is dissolved in a nematic liquid crystal, the latter will be transformed into a eholesterie liquid crystal. 

Liquid crystal polymers (LCP) are polymers that exhibit liquid crystal characteristics either in solution (lyotropic liquid crystal) or in the melt (thermotropic liquid crystal) [Ballauf, 1989 Finkelmann, 1987 Morgan et al., 1987]. We need to define the liquid crystal state before proceeding. Crystalline solids have three-dimensional, long-range ordering of molecules. The molecules are said to be ordered or oriented with respect to their centers of mass and their molecular axes. The physical properties (e.g., refractive index, electrical conductivity, coefficient of thermal expansion) of a wide variety of crystalline substances vary in different directions. Such substances are referred to as anisotropic substances. Substances that have the same properties in all directions are referred to as isotropic substances. For example, liquids that possess no long-range molecular order in any dimension are described as isotropic. 

Our understanding of lyotropic liquid crystals follows in a similar manner. The action of solvent on a crystalline substance disrupts the lattice structure and most compounds pass into solution. However, some compounds yield liquid crystal solutions that possess long-range ordering intermediate between solutions and crystal. The lyotropic liquid crystal can pass into the solution state by the addition of more solvent and/or heating to a higher temperature. Thermotropic and lyotropic liquid crystals, both turbid in appearance, become clear when they pass itno the liquid and solution states, respectively. 

Liquid Crystalline Polymers. One class of polymers that requires some special attention from a structural standpoint is liquid crystalline polymers, or LCPs. Liquid crystalline polymers are nonisotropic materials that are composed of long molecules parallel to each other in large clusters and that have properties intermediate between those of crystalline solids and liquids. Because they are neither completely liquids nor solids, LCPs are called mesophase (intermediate phase) materials. These mesophase materials have liquid-like properties, so that they can flow but under certain conditions, they also have long-range order and crystal structures. Because they are liquid-like, LCPs have a translational degree of freedom that most solid crystals we have described so far do not have. That is, crystals have three-dimensional order, whereas LCPs have only one- or two-dimensional order. Nevertheless, they are called crystals, and we shall treat them as such in this section. 

Melting point describing the temperature at which the solid to liquid transition takes place is one of the main characteristics of chemical substances. When heat is supplied to a crystalline species its temperature usually rises until it starts to melt. This temperature corresponding to the melting point is maintained until all the substance is liquified. During this process the long-range order of the crystalline solid is destroyed. Simultaneously anisotropy of the crystal, that is, a dependence of its optical and some other properties on the direction of, for... 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

Nematic phase this is the simplest structure. It is the most disordered mesophase and therefore very fluid. It is called N. In the nematic phase, the molecules are ordered mainly in one dimension with their long axes parallel, and they are free to move parallel to this axis (there is no long-range order). Nematic liquid crystal mixtures, containing various amounts of different liquid crystal compounds, are used in electro-optic display systems such as flat-panel displays. 

In the simplest emulsions just described, the linal separation is into two liquid phases upon deslahilizalinn. The majority of emulsions tire of this kind, but in some cases the emulsion is divided into more Ilian two phases. One ubvious reason lor such a behavior is the presence of it material thal does not dissolve in the oil or the water. One such case is Ihe presence of solid particles, which is common in emulsions lor food, pharmaceuticals, and cosmetics. Another less trivial reason is that the surfactant associates w ith the water and/or Ihe oil to form a colloidal structure that spontaneously separates from the two liquid phases. This colloidal structure may be an isotropic liquid or may he a. semisnlid phase, a liquid crystal, with long-range order. 

Fusion, as an order-disorder transition, is the concept that fusion of a crystalline solid is essentially a change from the almost perfectly ordered solid state to a disordered liquid slate. The vacant spaces in the crystal lattice correspond lo the other component in the binary alloys, which undergo order-disorder transition in the pure form. Evidence from x-ray diffraction measurements indicates that short-range order is retained during fusion but long-range order is lost. 

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