Liquid crystals short-range order

The field of soft condensed matter/complex systems spans a seemingly diverse spectrum, including isotropic liquids with short-range order at the one end, and liquid crystals with long-range order in their anisotropic phases, often called mesophases, at the other [2-4]. Anisotropy in molecular shape plays a crucial... 

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. 

Multilamellar bilayers in the fluid phase are also ordered in the sense that they are smectic liquid crystals. Of great interest is the range of molecular order this is long-range in the sense that the molecules are confined to two dimensions there is also some kind of short-range order in molecular orientations and conformations, but the range of this latter ordering is not known at present. 

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. 

Liquid crystals can be in the smectic, nematic, or isotropic states. In the smectic liquid crystalline state there is a long-range order in the direction of the long axis of the molecules. These molecules may be in single- or bilayer conformation, have molecular axis normal or tilted to the plane of the layer, and frozen or melted chains. In the nematic liquid crystalline state the molecules are aligned side by side but not in specific layers. The isotropic liquid crystalline state is more or less a liquid state, but where clusters with short-range order persist (Small, 1986, pp. 49-51). 

This can be accounted for qualitatively by employing a simple model which permits the prediction of H (and S and G) for the above phases. Schematically we can think of our respective solid, liquid and gas as shown in Figure 22.1. The structure of a liquid, unlike that of a solid, cannot be specified in terms of an array of identical cells in a so called crystal structure specified by atomic coordinates, it has only a limited degree of short-range order and radial distribution (probability) functions are employed in its description. In the case of an (ideal) gas the molecules are unconstrained by attractive forces between them and here the gas (as also does a liquid) assumes the shape of its containing envelope. The enthalpy term, II, is related to the degree of attraction between the molecules in the respective phases and this is indicated by the fact (as we shall see below) that enthalpy has to be expended (Frame 21, section 21.2) in order to convert one phase into another in the sequence solid —> liquid — gas. 

Liquids, Gases and Disordered Solids. Liquids, disordered solids, gases, and single crystals can diffract X rays. For liquids and disordered solids, where there is no long-range order, and the short-range order extends from 0 to maybe 1 or 2 nm, the diffraction consists of very broad maxima in the intensity function 7(s), where s is the scattering vector defined in Eq. (11.23.2). The one-dimensional Fourier transform of I(s) is the radial distribution function R(r) ... 

A14N NMR study of order fluctuations in the isotropic phase of liquid crystals has been reported. (209) The experimental data for the isotropic phases of -azoxyanisole and of diethylazoxy benzoate are accounted for in terms of short range order fluctuations of the nematic and of the smectic types respectively. 

Liquids are systems devoid of both long-range translational and orientational order whereas short-range order still remains at molecular scales resulting from the subtleties of forces acting on their constituent molecules. In turn, rotator-phase (plastic) crystals are liquid-like in the sense that molecules... 

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