Chemistry Department, Brandeis University, Waltham, Massachusetts, USA
For a detailed analysis of the crystallization process, a realistic view of the chain trajectories in the lamellar semicrystalline morphology is of interest. We have come to the conclusion that the textbook models of melt-crystallized semicrystalline polymers unintentionally but inevitably contain layers with a higher density than in the crystallites. Such density anomalies can be avoided by chain ends at the crystal surface and/or chain tilt in the crystallites. NMR shows that most CH3 end groups of polyethylenes (PEs) are indeed in all-trans chains near the crystal surface. As a consequence, many chain folds cannot be tight, also in agreement with NMR data. Chain tilt in the crystallites, which decreases the density of chains emerging from the crystal, is another indispensable structural adjustment and is indeed observed ubiquitously in PE. It results in differential broadening of (hk0) Bragg peaks of PE, which had been mistakenly attributed to mosaicity. Published scattering patterns exhibit clear evidence of macroscopically aligned lamellar stacks with pronounced chain tilt in various oriented PE samples. Literature data furthermore show examples of increasing chain tilt angles of up to 60o at high molecular weights, where the density reduction by chain ends is minor. Chain tilt and chain ends at the crystal surface are required to “make space” for short loops, in conjunction with noncrystalline chain segments emerging from the crystal roughly along the surface normal; these four effects together make a structure without density anomalies possible. The density problem is particularly pronounced in polymers with planar zig-zag conformations in the crystallites, such as PE. A revision of Flory’s analysis shows that for poly(ethylene oxide) and other polymers with helical crystalline conformations, larger bond tilt angles result in a higher projected density along the chain axis in the crystallites, which reduces the problem of amorphous excess density and thus the need for chain tilt in the crystallites.
 K. Fritzsching, K. Mao, K. Schmidt-Rohr, Macromolecules (2017) DOI: 10.1021/acs.macromol.6b02000. (link)