Polymer Conformations in Crystals

The conformation of a polymer in its crystal will generally be that with the lowest energy consistent with regular placement of structural units in the unit cell. Helical conformations occur frequendy in polymer crystals. Helices are characterized by a number fj where / is the munber of monomer units per j number of complete turns of the helix. Thus, polyethylene could be characterized as a 11 helix in its unit cell with an aW-trans conformation. The arrangement of the molecules in the polyethylene crystal structure is illustrated in Fig. 2.7. 

Isotactic polypropylene crystalhzes as a 3i helix because the bulky methyl substituents on every second carbon atom in the polymer backbone force the molecule from an aW-trans conformation into a trans/gauche/trans/gauche... sequence with angles of rotation of 0° trans) fol- 

In polymers having polar groups, intermolecular electrostatic attractions exert strong in u-ence on chain conformation in their crystals. In polyamides, hydrogen bonds form between the carbonyls and NH groups of neighboring chains (Fig. 2.8) and in uence the crystalhzation of the polymer in the form of sheets, with the macromolecules themselves packed in planar zigzag conformahons [see Fig. 2.8(b)]. 

Problem 2,2 Explain the fact that conversion of the amide groups -CONH- in nylon to methylol groups -C0N(CH20H)- by reaction with formaldehyde, followed by methylation to ether groups -C0N(CH20CH3)- results in the transformation of the ber to a rubbery product with low modulus and high elasticity. 

Replacing the -NH- hydrogen in polyamides by an ether group curtails the intermolecular hydrogen bonding. Hence at low degrees of substitution the modulus is reduced and a more elastic ber is obtained. As the substitution increases, the crystallinity is completely destroyed and rubbery property appears. 

The van der Waals radii of the chain substituents affect the intermolec-ular space requirements. Thus, since fluorine atoms are significantly larger than hydrogen atoms, an a -trans crystal conformation of polyethylene is too crowded for poly(tetrafluoroethylene), which therefore crystallizes instead in a very extended helical conformation that allows the larger F atoms to be accommodated. Below 19°C the molecules are in the form of a 13e helix and at higher temperatures they untwist slightly into a ISj helix. 

Problem 2.4 What is the repeat distance between pendant methyl groups that form a row (a) in the 3i helix of isotactic polypropylene and (b) in the 2i helix of syndiotactic polypropylene. Assume each carbon-carbon bond length is 1.54 Aand each bond angle is 109.5°. 

In polymers having polar groups, intermolecular electrostatic attractions exert strong influence on chain conformation in their crystals. In polyamides, hydrogen bonds form between the carbonyls and NH groups of neighboring chains (Fig. 

8) and influence the crystallization of the polymer in the form of sheets, with the macromolecules themselves packed in planar zigzag conformations [see Fig. 2.8(b)]. 

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Our discussion above on polymer conformations in single chains and in crystals has assumed regularity of macromolecular structure. However, irregularities such as inversions of monomer placements (head-to-head instead of head-to-tail), branches, and changes in configuration may occur. These irregularities, which are considered in a later section, may Inhibit crystallization and have a profound effect on polymer properties. 

Fig. 10.11 Illustration of the metastable polymer conformation in the crystalline regions. From left to right are the fringed-micelle model, the lamellar crystal with adjacent chain folding, the switchboard model and the variable-cluster model...

Rather than having a situation where a unit cell consists of one or more molecules, as in small molecule crystals, the situation is reversed a single molecule participates in many unit cells. This has significant ramifications for the correlations, both structural and dynamical, between unit cells. Second, the periodicity of the crystal lattice usually implies a periodicity for the conformation of the polymer chain itself. This condition places a severe restriction on the conformation space available to the chain in a crystalline solid. Polymer chains in crystals are more appropriately described as helices rather than coils. A helix conformation consists of a regular repetition of the torsion angles characteristic of a small subsection of the chain, the helix repeat unit [4,5]. Each helix has an axis and a handedness of rotation (the direction in which the chain backbone winds around the helix axis). The helix itself is characterized by the translational displacement parallel to the helix axis, d, and the angle of rotation about the helix axis, a, executed by a single helix repeat unit. The coordinates of Eq. (1) may be expressed in terms of these helical parameters as follows ... 

Conformation of Polymer Chains in Crystals and Conformational Polymorphism, 33... 

CONFORMATION OF POLYMER CHAINS IN CRYSTALS AND CONFORMATIONAL POLYMORPHISM (a)... 

As described in X-ray Crystal Analyses section, DBF oligomers have been shown to have a jc-stacked, single-handed helical conformation in crystal. A jc-stacked structure was indicated also for poly(PDBF) by remarkable hypochromicity in absorption and exclusive dimer emission in fluorescence spectra (Fig. 34). Therefore, it will be reasonably assumed that the CD absorptions observed in this work are based on a helical conformation of poly(PDBF) with excess single handedness. Because the polymers showing clear CD bands in film did not show chiroptical properties in solution, molecular aggregation may amplify and stabilize the single-handed helical conformation induced by the asymmetric polymerization possibly due to intermolecular cooperative effects in the solid state. Atomic force microscopic (AFM) analyses supported this assumption (Fig. 39). The samples were prepared by... 

Polymers can be crystalline, but may not be easy to crystallize. Computational studies can be used to predict whether a polymer is likely to crystallize readily. One reason polymers fail to crystallize is that there may be many conformers with similar energies and thus little thermodynamic driving force toward an ordered conformation. Calculations of possible conformations of a short oligomer can be used to determine the difference in energy between the most stable conformer and other low-energy conformers. 

In addition to existing as helices in crystals, there is evidence that certain vinyl polymers also show some degree of regular alternation between trans and gauche conformations in solution. In solution, the chain is free from the sort of environmental constraints that operate in a crystal, so the length of the helical sequence in a dissolved isotactic vinyl polymer may be relatively short. 

Equivalence Principle. The conformation of a polymer chain in the crystalline state is defined by a succession of equivalent structural units which occupy geometrically (not necessarily crystallographically) equivalent positions with respect to the chain axis. The chain axis is parallel to a crystallographic axis of the crystal. 

Principle of Minimum Internal Conformational Energy. The conformation of a polymer chain in a crystal approaches one of the minima of the internal conformational energy, which would be taken by an isolated chain subjected to the restrictions imposed by the equivalence principle. 

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