Polymer crystallization lattice models

Menon, G., Pandit, R. Crystallization and vitrification of semiflexible living polymers A lattice model. Phys. Rev. E 1999, 59, 787. 

An X-ray beam, of a finite width, samples a small volume of the polymer structure. The diffraction pattern gives no information about the location of crystals within that volume, but it gives information about the range of crystal orientations in the volume this can be used with optical microscopy to build up a picture of the microstructure. The crystal lattice model, used to interpret diffraction patterns, contains many sets of parallel planes. Polymer crystals often have lower lattice symmetry than metals, so the relationship between the interplanar spacing d and the Miller indices hkl) of the plane are complex (Kelly and Groves, 1970). The Bragg condition... 

Figure 11 Projection down the c-axis of crystallized structures of medium size PaAA-n obtained by molecular mechanics caicuiations (a) the hypotheticaiiy hexagonai structure of Po AA-G note that the helix is tilted about 30° with respect to the c-axis (b) the crystal lattice model of PofAA-O including 16 chains note that overlapping of side chains is preferred along the direction normal to the layers (a-axis). (Taken from J.J. Navas, C. Aleman, F. Lopez-Carrasquero, and S. Muhoz-Guerra. Polymer 38 3477, 1997. With permission.)...

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. 

Such weaknesses of the present implementation include the lack of an explicit inclusion of intermolecular forces other than excluded volume, resulting in a qualitatively inaccurate description of the equation of state. Another weakness is that the model shows lattice artefacts when dealing with problems of polymer crystallization or liquid-cristalline order only rather flexible poly-... 

Abstract In this review, we consider a variety of aspects of polymer crystallization using a very simple lattice model. This model has three ingredients that give it the necessary flexibility to account for many features of polymer crystallization that have been observed experimentally. These ingredients are (1) a difference in attraction between neighboring (nonbonded) components, (2) attraction between parallel bonds, and (3) temperature-dependent flexibility due to the energy cost associated with kinks in the... 

A lattice model that takes such attractions between parallel bonds into account provides a reasonable prediction of polymer melting points [13] and of their interplay with liquid-liquid demixing in polymer solutions [14]. The same factors that favor freezing do affect to a greater or lesser extent the formation of mesophases hence, there is a close relation between polymer crystallization and the formation of mesophases, which are frequently observed before polymer crystallization (see other papers in this issue). 

If identification of lattice vibrations with those of a continuum is made as in Bom s theory then frequencies even lower than the Raman LA mode would be expected from the extreme anisotropy of the polymer crystal. This may in fact be the case, but to assign continuum properties to the rod used in the accordion mode model is not likely to be... 

Such differences in reactivities would be plausible if during chain growth in the solid phase, polymerization and crystallization were simultaneous. This means that a newly added monomer unit is incorporated into the crystal lattice at the same time that it is attached chemically to the polymer chain. This would imply that the cationic chain ends are directly on the crystal surface (simultaneous polymerization and crystallization as symbolized by Model A in Figure 2). 

Some important aspects of topochemical polymerizations can be understood by inspection of Eq. (1), All reactivity comes about by very specific rotations of the monomers and by 1,4-addition of adjacent units and an extended, fully conjugated polymer chain is formed. The unique feature of the topochemical polymerization of diacetylenes is the fact that in many cases the reaction can be carried out as a single phase process. This leads to macroscopic, defect-free polymer single crystals which cannot be obtained, in principle, by crystallization of ready-made polymers by conventional methods. Thus, polydiacetylenes are ideal models for the investigation of the behaviour of macromolecules in their perfect three dimensional crystal lattice. 

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