Long-range ordered structure

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]. 

The defining property of a structural glass transition is an increase of the structural relaxation time by more than 14 orders in magnitude without the development of any long-range ordered structure.1 Both the static structure and the relaxation behavior of the static structure can be accessed by scattering experiments and they can be calculated from simulations. The collective structure factor of a polymer melt, where one sums over all scattering centers M in the system... 

Photonic band gap crystals can be dehned as long-range ordered structures whose relative permittivity varies as a spatially periodic function. These three-dimensional periodic structnres have a feature size comparable to or shorter than the wavelength of visible light. 

Persistent hydrate crystallites (long-range ordered structure), which were shown from neutron scattering to remain in solution for several hours after increasing the temperature above the hydrate dissociation temperature (Buchanan et al 2005). 

Other explanations for the drop in conductivity were related to the distribution of dopanu, which may be no longer random. For certain compositions and choice of dopants, long-range ordered structures, or structures containing ordered microdomains can be obtained. These have been reported to affect negatively conductivity ... 

In order to better understand ensemble-size requirements for reactions on Pt alloys and the role of Sn as a site-blocking agent, it is important to study other Pt-M surfaces that are isostructural with Pt-Sn surface alloys. However, this has turned out to be a difficult task. Different metals (M=Ge, Zn, Cu, Ag, Fe, and Ti) form different surface alloy structures. For example, on Pt(lll), Zn and Cu alloy but do not form long-range ordered structures, and Ge only forms a dilute, two-domain... 

X-ray diffraction does not allow us to identify which starch fraction contributes to the formation of crystalline structures since both amylose and amylopectin crystallize as B-type upon aging. On the other hand, the detection of birefringence means that long-range ordered structures are formed which are not... 

SEM studies shown in Fig. la revealed that the Pt/sepiolite ICP sample possessed a long range ordered structure at macroscopic level, with ink bottle pores of about 12 pm left by removal of the AC, accessed through an interconnected network with pore entrances of about 2 pm. When the support was a mixture sepiolite-alumina or sepiolite-titania, the bundles of sepiolite fibres act as a matrix in which the particles of alumina or titania are distributed as shown in Fig lb for Pt/sep.Ti02 ICP. 

Compared to crystalline materials, the production and handling of amorphous substances are subject to serious complexities. Whereas the formation of crystalline materials can be described in terms of the phase rule, and solid-solid transformations (polymorphism) are well characterised in terms of pressure and temperature, this is not the case for glassy preparations that, in terms of phase behaviour, are classified as unstable . Their apparent stability derives from their very slow relaxations towards equilibrium states. Furthermore, where crystal structures are described by atomic or ionic coordinates in space, that which is not possible for amorphous materials, by definition, lack long-range order. Structurally, therefore, positions and orientations of molecules in a glass can only be described in terms of atomic or molecular distribution functions, which change over time the rates of such changes are defined by time correlation functions (relaxation times). 

Rigorous application of MFT can be made to general cases with defined sublattices (long-range ordered structures) (Fuentes, Aburto Valenzuela, 1987). Net magnetisation is given by the resultant of contributions from all the sublattices ... 

The film becomes more passive during air exposure due to change in the structure of the film from an amorphous phase to long-range ordered structure [27]. The mechanism is controlled by reductive dissolution of iron into Fe in the solution... 

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