Disordered structure models

H). As shown, a disordered structural model was obtained for the guest. The model comprises two mirror-related guest molecules. The oxygen atom and the proximal methyl C-atom are practically overlapping the same atomic positions in both orientations. However, the sulphur atomic positions do not average in the X-ray data and show a nearly 50/50 occupancy. As indicated by the comparison of the respective bond distances and intra-associate contact distances of the DMSO molecule (Table 17), the effect of disorder is serious (e.g. the S=0 distances appear abnormally short in the 20 DMSO instance). This precludes the possibility of assessing interaction between the O atom of the carboxyl and a methyl of dimethyl sulfoxide. 

The arrangement of Zr and P atoms in Zr(P03)4 [96] corresponds to that of the U and P atoms in the disordered structure model of U(P03)4 [92], It appears that the positions of the oxygen atoms alone are responsible for the larger unit cell, and the slight deviation from apparent orthorhombic symmetry in the ordered monoclinic structure of Zr(P03)4. 

Several examples follow of recent efforts to describe explicitly porous adsorbent materials using disordered structure models. 

Once the correlation functions have been solved, adsorption isotherms can be obtained from the Fourier transform of the direct correlation function Cc(r) [55]. The ROZ integral equation approach is noteworthy in that it yields model adsorption isotherms for disordered porous materials that have irregular pore geometries without resort to molecular simulation. In contrast, most other disordered structural models of porous solids implement GCMC or other simulation techniques to compute the adsorption isothem. However, no method has yet been demonstrated for determining the pore structure of model disordered or templated structures from experimental isotherm measurements using integral equation theory. 

A detailed analysis of the X-ray powder diffraction pattern of two borosilicates was used to develop a model for their structures (31). The material called BOR-C is reported to have the MFI structure containing regular stackings of pentasil layers related by inversion centers. On the other hand, the BOR-D material was found to have the MEL structure. It was structurally disordered, consisting mainly of pentasil layers related by inversion centers as well as layers related by mirror planes. The disordered structure model for BOR-D also was proposed for the aluminosilicate ZSM-11 and the silicalite-2 analog (32). 

In [221] the X-ray diffraction patterns of PE fibers in the high-pressure hexagonal form have been modeled assuming complete translational disorder along z, rotational disorder of chains around their axes and conformational disorder. The Fourier transforms of disordered structural models were calculated as a function of intra- and inter-molecular parameters related to the presence of conformational disorder and the relative arrangement of close neighboring chains (short-range correlation disorder). The results of the calculations were compared to experimental X-ray diffraction data. 

In the second section a classification of the different kinds of polymorphism in polymers is made on the basis of idealized structural models and upon consideration of limiting models of the order-disorder phenomena which may occur at the molecular level. The determination of structural models and degree of order can be made appropriately through diffraction experiments. Polymorphism in polymers is, here, discussed only with reference to cases and models, for which long-range positional order is preserved at least in one dimension. 

Let us consider a structural limiting model, in which the polymer molecules, presenting a periodic conformation, are packed in a crystal lattice with a perfect three-dimensional order. Besides this limiting ordered model, it is possible to consider models of disordered structures having a substantially identical lattice geometry. 

Disordered structures belonging to the class (i) are interesting because, in some cases, they may be characterized by disorder which does not induce changes of the lattice dimensions and of the crystallinity, and a unit cell may still be defined. These particular disordered forms are generally not considered as mesomorphic modifications. A general concept is that in these cases the order-disorder phenomena can be described with reference to two ideal structures, limit-ordered and limit-disordered models, that is, ideal fully ordered or fully disordered models. 

Fig. 2. Classes of structural models of amyloid-like fibrils. The Refolding models propose that a native protein (circle) partially or completely unfolds to attain a new fold (rectangle) in the fibril (stack of rectangles). In contrast, the Gain-of-Interaction models propose that only part of the native protein changes and takes on a new structure in the fibril. The remainder of the protein (partial circle) retains its native structure. The Natively Disordered models begin with disordered proteins or protein fragments, and these become ordered in the fibril. PolyQ refers to polyglutamine.

From the point of view of the NMR spectrum, it appears that y-AUOj is a highly disordered structure, and one takes as a model for quantitative interpretation the MgO type structure, AljgO, with the aluminum atoms randomly occupying % of the octahedral sites. This is an extremely simple type of lattice for which the necessary lattice sums of 1/R (second order interaction) are known. 

However, in recent years this basis has been somewhat undermined due to a critical reappraisal of experimental data on the benzene structure which, surprisingly, showed that a rigorous experimental proof of the generally accepted D6h structure of benzene is actually nonexistent It turned out that the X-ray structural data for benzene are compatible not only with the crystallographically ordered Dbh structure but also with the disordered Dih model associated with superposition of Kekule-type benzene molecules rotated by 60° with respect to each other about the threefold axis, both static and dynamic types of disorder being conceivable [87AG(E)782]. It has been shown by very simple calculations that if the difference between the C—C and C=C bond lengths in the D3h form is... 

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