Limit disordered model structures

Fig. 2 (A) Chain conformation of isotactic polypropylene in the crystalline state. Symbols R and L identify right- and left-handed helices, respectively, in 3/1 conformations. Subscripts up and dw ( dw standing for down ) identify chains with opposite orientation of C - C bonds connecting tertiary carbon atoms to the methyl groups along the z-axis (B) Limit-ordered model structure (a2 modification, space group P2 /c) [113] (C) Limit-disordered model structure (otl modification, space group Cl/c) [114]. In the a2 modification up and down chains follow each other according to a well-defined pattern. The al modification presents a complete disorder correspon ng to a statistical substitution of up and down isomorphic helices...

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. 

Figure 2.29 (a) Limit-ordered model (space group Ibca or P2i/a) and (b) limit-disordered model (space group Bmcm) for crystal structure of form I of sPP172 (R = right-handed helix, L = left-handed helix). 

As an example, the structure of the a form of isotactic polypropylene may be described with reference to a limit-ordered model (defined a2-form) [113] and a limit-disordered model (defined ai-form) [114], shown in Fig. 2B and C, respectively. 

Discussing the electronic properties of fluids, we cannot ignore the basic fact that these materials are structurally disordered. When the electron-ion interaction is weak, as in the NFE limit, structural disorder is not too important. But Anderson (1958) showed that in the presence of a sufficiently strong disordered ionic potential, electrons inevitably become localized. The localized wave functions decay exponentially with distance from specific atomic sites and, at T = 0, an electron will not diffuse to another part of the material, even given an arbitrarily long time. In his original paper, Anderson considered a specific disordered model structure—a crystalline alloy having a random distribution of potential well depths. He showed that there exists a critical ratio of the width of the potential distribution V to the band width W of the ordered system. If V/W 1, the electronic states are localized. 

The polymorphism of SPS is further complicated by the presence of structural disorder in both a and p forms, so that the trans-planar forms are described in terms of disordered modifications intermediate between limit disordered models (a and PO and limit ordered models (a" and P"). 

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. 

The severe computational burden associated with assembling and carrying out adsorption calculations on disordered model microstructures for porous solids, such as those discussed in Sections ILA and II.B, has until recently limited the development of pore volume characterization methods in this direction. While the reahsm of these models is highly appealing, their application to experimental isotherm or scattering data for interpretation of adsorbent pore structure remains cumbersome due to the structural complexity of the models and the computational resources that must be brought to bear in their utilization. Consequently, approximate pore structure models, based upon simple pore shapes such as shts or cylinders, have been retained in popular use for pore volume characterization. 

Three limit-ordered models, shown in Fig. 15, were considered as possible ideal arrangements of EP chains in the mesomorphic bundles. In Fig. 15A and Fig. 15B,B the chains are arranged as in the orthorhombic [194] and monoclinic [196] polymorphs of PE, respectively. In Fig. 15C,C the chains are arranged as in triclinic form of long chains paraffins [197]. These models were chosen as reference, ideal structures, where different kinds of disorder were introduced, in order to better understand their influence on the cal-... 

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. 

It is important to note that, for important sub-cases of case /), which will be discussed in more detail in Sect. 2.4, there is a low extent of disorder entropy effects, if any, are small and changes of the lattice dimensions are absent or small. These particular disordered forms are not considered as mesomorphic. In such cases, the limiting models which are fully ordered or fully disordered may be designated respectively as ordered or disordered crystalline modifications, if their consideration is useful for the structural description of a polymeric material. Note... 

Several steps were needed to determine the structure of the core particle to higher resolution (Fig. Id). The X-ray phases of the low-resolution models were insufficient to extend the structure to higher resolution, since the resolution of the early models of the NCP was severely limited by disorder in the crystals. The disorder was presumed to derive from both the random sequences of the DNA and from heterogeneity of the histone proteins caused by variability in post-translational modification of the native proteins. One strategy for developing an atomic position model of the NCP was to develop a high-resolution structure of the histone core. This structure could then be used with molecular replacement techniques to determine the histone core within the NCP and subsequently identify the DNA in difference Fourier electron density maps. 

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