Paracrystallinity model

A second important event was the development by Hosemann (1950) of a theory by which the X-ray patterns are explained in a completely different way, namely, in terms of statistical disorder. In this concept, the paracrystallinity model (Fig. 2.11), the so-called amorphous regions appear to be the same as small defect sites. A randomised amorphous phase is not required to explain polymer behaviour. Several phenomena, such as creep, recrystallisation and fracture, are better explained by motions of dislocations (as in solid state physics) than by the traditional fringed micelle model. 

In the present concept of the structure of crystalline polymers there is only room for the fringed micelle model when polymers of low crystallinity are concerned. For polymers of intermediate degrees of crystallinity, a structure involving "paracrystals" and discrete amorphous regions seems probable. For highly crystalline polymers there is no experimental evidence whatsoever of the existence of discrete amorphous regions. Here the fringed micelle model has to be rejected, whereas the paracrystallinity model is acceptable. 

FIG. 2.11 Diagrammatic representation of the paracrystallinity model (after Hosemann, 1962). 

Furthermore, the structure factor can be expressed within a paracrystalline model by Eq. (6) [42]. 

Figure 1.7. The Hosemann paracrystalline model, including the concept of chain folding.

It is worth considering that in [97] an explanation of the origin of the diffraction maxima along the meridian at 0.40 and 0.80 A is provided, consistent with the paracrystalline model proposed by Lyndenmeyer and Hosemann [48] for PAN. The halo at f 0.80 is not necessarily the second-order diffraction of the maximum at f 0.40 A since it is apparent from calculations of Fig. 12 that these two meridional maxima may originate from different contributions. The maximum at 0.40 A arises from the average periodicity of lateral - CN groups alone (Fig. 12C), whereas the maximum at C = 0.8oA- arises from the contribution of only the backbone carbon atoms (Fig. 12D). 

If the monomeric units have different lengths, as it is the case for another copolyester under study CPE-2, aperiodic reflections in the meridian and several Bragg spots on the equator and in quadrants are observed in X-ray patterns of oriented fibers. That means that the crystalline phase of the material may be described by one of two models proposed by Windle (1) or Blackwell (2) for such unusual structures, namely, the model of non-periodic layer crystals and paracrystalline model, respectively. 

Figure 34 Average values of the crystal (circles) and amorphous layer (squares) thickness, (fj and (i,), as a function of dwelling time at 205 C (left) and temperature (right). Filled and empty squares correspond to the paracrystalline model fits with a low (A/=3) and high N=20) number of crystals per stack, respectively. With permission from Ivanov, D. A. ...

Figure 33 Processed SAXS curves (s (/(s) - B)) corresponding to isothermal melt crystallization of PTT at 205 °C (left) and subsequent heating (right). The fits with the generalized paracrystalline model (solid lines) are offset vertically for clarity. With permission from Ivanov, D. A. Bar, G. Dosifere, M. Koch, M. H. J. Wacromo/eco/es 2008, 41,9224. ...

R. Hosemann Paracrystalline model with disorder within the lamellae (see Figure 6.38) (1, m, n)... 

Figure 6.37 The paracrystalline model of Hosemann (134). Amorphous structures are illustrated in terms of defects. A radius of gyration approaching amorphous materials might be expected.

It is of interest to compare the results of this modem research with Hosemann s paracrystalline model, first published in 1962. As illustrated in Figure 6.37 (134), this model emphasizes lattice imperfections and disorder, as... 

In the Hosemann model, which is based on a paracrystalline model, each crystalline region consists of N alternating stacks of crystalline and amorphous layers. The scattered intensity I(s) calculated from this model as a function of s is given by... 

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