Limit-ordered models

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. 

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 already shown in Figure 2.29a, in the ideal limit-ordered model of form I of sPP, right- and left-handed twofold helical chains alternate along the a and b axes of the orthorhombic unit cell.59 In the electron diffraction patterns of single crystals grown at low temperatures, reported by Lovinger et al.,145 the... 

Figure 2.37 Limit-ordered models of packing of twofold helical chains of sPP in (a) form I (space group Ibca) and (b) form II (space group C222i).

Figure 2.47 Models of packing in limit-ordered forms (a) II and (c) IV of sPP and (b) model of conformationally disordered modification, presenting kink bands, intermediate between limit-ordered models of form II and form IV. In defective region of model (b), delimited by dashed lines, chains are packed as in form IV, whereas in ordered regions chains are packed as in the form II.

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. 

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...

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-... 

Fig. 17.3. Limit ordered models of packing proposed for a (A) and 7 (C) forms of iPP and model of the 0/7 disordered modifications intermediate between a and 7 forms (B). The dashed horizontal lines delimit bilayers of chains. Subscripts a and 7 identify unit cell parameters referred to the monoclinic [33] and orthorhombic [34] unit cells of a and 7 forms, respectively. In the disordered model (B) consecutive bilayers of chains are stacked along ba (oy) with the chain axes either parallel or nearly perpendicular, making a-like or 7-like arrangements of bilayers [32,36 ...

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"). 

In the limit ordered model proposed for the a form of iPP (Fig. 2.25c) up and down chains follow each other according to a well-defined pattern [101,102]. The limit disordered model (Fig. 2.25d) corresponds to a statistical substitution of up and down isomorphic helices in each site of the lattice [29]. The real crystalline modifications of the a form of iPP are intermediate between the limit ordered and limit disordered models of Figure 2.25, the degree of disorder in the positioning of up and down chains being dependent on the thermal and mechanical history of the sample [150]. 

Figure 2.28 Limit-ordered models of the a [29] (a) and y [108,109] (c) forms of iPP and disordered succession of bilayers of chains [18,19,156-163] (b).The dashed horizontal lines delimit bilayers of chains in the 3/1 helical conformation. R and L indicate right-handed and left-handed helices, respectively. Reproduced from Reference [159] with permission from...

Figure 2.29 Limit-ordered models of packing of forms II [31] (a) and IV [67] (c) of sPP and model of a conformationally disordered modification, presenting kink-bands (b), intermediate between forms II and IV. A kink-band in the form II of sPP, with (T2G2)n helices, is characterized by a defective region with (T2G2T6G2)n conformational sequence, as in form IV [154, 155]. Reprinted from Reference [143] with permission from American Chemical Society, Copyright 2006.

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