Packing of Macromolecules in Polymer Crystals

Besides the energy factors, defined by the closepacking principle, entropic factors guide the mode of packing of molecules. A molecule in a crystal tends to maintain part of its symmetry elements, provided that this does not cause a serious loss of density. As outlined by Kitajgorodskij, in a more symmetric position a molecule has a greater freedom of vibrations that is, the structure is more probable (entropy factor) because it occupies a wider potential well on the multidimensional energy surface [73]. 

Corradini has shown that almost all the known crystal structures of polymers are easily rationalizable in terms of these principles [1]. In particular, he suggested that the mode of packing of polymer chains first depends on the outside envelope of the chains [1]. Depending on the conformation, the form of a polymer chain may be approximated by a cylinder of radius r, corresponding to the outside envelope of the atoms of the main chain, bearing a periodic helical relief of radius R, 

When the ratio r/R is different from 1 the form of the chains may be approximated by a cylinder in which hollows and bulges are periodically repeated that is, the chains have an outside envelope similar to a screw [1] (Fig. 2.11a). If the ratio r/R is very small, close to 0.1-0.2, such as for chains in threefold helical conformation, a trigonal packing of enantiomorphous chains may arise. Each 3i right-handed chain is surrounded by three left-handed isoclined or anticlined chains, and vice versa (space group R3c or R3, respectively), such as in iPS (Fig. 2.12a) [40], form I of iPB (Fig. 2.12b) [45], poly (vinyl methyl ether) [83], isotactic l,2-poly(l,3-butadiene) [84], and isotactic poly(o-fluorostyrene) [8.  

Higher values of the ratio r/R, close to V2 -1 (similar to the situation stabilizing NaCl), are obtained in the cases of many vinyl polymers with chains in complex helical conformation s M N) with a fractional ratio MIN, ranging between 3 and 4, such as form I of isotactic poly(4-methyl-l-pentene) (7/2 helix) [38], form II of isotactic poly(l-butene) (11/3 helix) [46], isotactic poly(m-methylstyrene) (11/3 helix) [86], and syndiotactic poly(4-methyl-l-pentene) (12/7 helix) [72]. In these cases, a tetragonal packing of enantiomorphous chains. 

In the case of optically active poly(a-olefins) containing a chiral side group, the chirality of the monomeric units favors the formation of helices of one specific chirality (right- or left-handed) [38a, 39,92,93]. This is, for instance, the case of poly((S)-3-methyl-l-pentene) 

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PACKING OF MACROMOLECULES IN POLYMER CRYSTALS 3.1 General Principles... 

Within the class of polymer crystals having, ideally, long-range positional order for all the atoms, different crystalline forms (polymorphs) may arise as a result of having different almost isoenergetic macromolecular conformations (of the main chain, in most known cases) or as a result of different, almost isoenergetic modes of packing of macromolecules with identical conformations [1-3]. 

Chain Packing and Crystal Structures. The chain packing and the suhmolecular arrangement of repeat units and pendant side groups of macromolecules in crystalline domains of polymers can be visualized using contact mode SFM. The resolution is in most cases not true resolution, since the area of the contact area (1 — few nm ) exceeds the molecular scale and must be considered lattice resolution instead. The first example of molecularly resolved structures of a polymer dates back to 1988, when Marti and co-workers reported on an SFM study on a polydiacetylene film (128). Examples for resolved chain packing and polymer crystal structure determination at the surface of semicrystalline polymers include poly(tetrafiuoroethylene) (PTFE) (129,130), polyethylene (PE) (131-133), polypropylene (PP) (134,135), poly(ethylene oxide) (PEO) (136), aramids (137,138), and poly(oxy methylene) (POM) (139). 

The preparation of oriented polymers by the method of the directed polymerization is of interest since it is possible to avoid the complex process of disentangling the macromolecules already packed randomly in the bulk of the unoriented polymer. However, methods involving conversion of these needle-shaped crystals into actual fibres have not yet been developed. 

It is clear that the quenched material has lamellae that are both thinner in the chain direction and smaller in lateral extent. Both these parameters increase with slower rates of cooling. So, too, does density. The microstructure of PTFE prepared this way may be likened to a pack of rods (the helical polymer chains), which in turn comprise lamellar crystals. Consider a hexagonal poker chip as a macroscopic analogue of one lamella. The diameter of die poker chip is the lamellar breadth and its thin dimension is the lamellar thickness. The fully extended chain length of a 10-million-MW PTFE macromolecule would be ca. 26 pm while our thickest observed lamellae are ca. 0.5 pm thick. It therefore... 

Polyamides are an important example of polymers which do not contain pseu-doasymmetric atoms in their main chains. The chain conformation and crystal structure of such polymers is influenced by the hydrogen bonds between the carbonyls and NH groups of neighboring chains. Polyamides crystallize in the form of sheets, with the macromolecules themselves packed in planar zigzag conformations. 

Polymer, as solid, has imperfect supermolecular structure it has amorphous regions, regions without structures and ciystalline regions with well packed maeromolecules. Lamellar monociystals (lamellae) in which maeromolecules are placed perpendicular to wide surface of a plate are the main structure of polymer crystalline part. Usually length of macromolecule being crystallized greatly exceeds thickness of lamella and, to be placed into the crystal, macromolecule must repeatedly fold. 

The densities of amorphous and crystalline polymers can differ by up to 15% (Table 5-3). Polymers with unsubstituted monomeric units, such as poly(ethylene) and nylon 6,6, for example, show the greatest difference in density. These chains crystallize in an dAVtrans conformation with particularly close packing of molecular chains. In helix-forming macromolecules with large substituents, such as it-poly(styrene), for example, the packing is, by contrast, less efficient. 

Polymer crystals are extreme anisotropic. Along the molecule the bonds are covalent. In the two transverse directions the molecular packing is generated by much weaker secondary forces (van der Waals, dipole, and hydrogen bonds, depending on the chemical structure of the molecule). Ilie most important consequence of this for the mechanical properties is that the moduli of the crystal depend critically on direction. In the direction of the molecule the modulus of polyethylene is of the order of 200 GPa (Problem 2.19) this value is typical of macromolecules, whose moduli (along the molecule) fall roughly in a band 100 to 400 GPa. In both transverse directions, the modultis is 100 times lower. 

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