Abstract
On the basis of sufficiently realistic chain models and simulations, it is concluded that the commonly used models of the lamellar structure of melt-crystallized semicrystalline polymers unintentionally but inevitably contain layers with a higher density than in the crystallites (density anomalies). The density excess would be particularly pronounced in polymers with planar zigzag conformations in the crystallites, such as polyethylene (PE). To avoid density anomalies, the structural models must be modified, with chain ends at the crystal surface and/or chain tilt in the crystallites. NMR and X-ray evidence for these structural features in PE is presented. Termination of chains at the crystal surface keeps dangling chain ends out of the crowded interfacial layer, reducing the density at the interface by about 17% for M n = 15 kg/mol, a common value in commercial high-density polyethylenes. NMR of PEs shows that most CH3 end groups are indeed in all-trans chains in a nearly solid-like environment. When the ends of polydisperse polymers are trapped at the crystal surface, many chain folds cannot be tight, in agreement with NMR showing fast trans–gauche isomerization even for solution crystals of PE. We propose that for polydisperse PE, interfacial chain ends are required for the formation of regular stacks of flat melt-crystallized lamellae without extreme chain tilt or density anomalies. Chain tilt in the crystallites, which decreases the area density of chains emerging from the crystal surface, is another indispensable structural adjustment in PE that reduces excess noncrystalline density; it has occasionally been reported but was usually considered as incidental. For instance, in X-ray analyses of PEs, chain tilt was ignored, and differential broadening of the (hk0) Bragg peaks was mistakenly attributed to mosaicity, in extreme cases resulting in the assumption of overly thick, rod-shaped rather than lamellar crystallites. For various oriented PE samples, including blown films and annealed fibers, published scattering patterns exhibit clear evidence of macroscopically aligned lamellar stacks with pronounced chain tilt. Literature data for PE also show examples of the increasing importance of chain tilt at high molecular weights, where the density reduction by chain ends is minor and evidence of extreme chain tilts of up to 60° has been shown. Alternatively, when chain-end concentrations are very low, the assumption of wide regularly stacked lamellae may have to be given up in favor of ribbon-shaped crystallites. The interplay of the density effects of chain ends and chain tilt can explain many molecular-weight-dependent structural features in polyethylene. On the basis of the combined effects of chain ends at the crystal surface, chain tilt in the crystallites, and adjacent reentry of ∼1/3 of chains, we can construct a lamellar model of PE without density anomalies. 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 enable a structure without density anomalies. In solution crystals, the absence of tie molecules and long loops, which produce a more extensive density increase than short loops, reduces the crowding problem and allows for lamellar crystals (with strongly tilted chains) even without chain ends, e.g., at ultrahigh molecular weights. In poly(ethylene oxide) and other polymers with helical conformations in the crystallites, the higher density along the chain axis associated with greater bond tilt angles in the crystal reduces the problem of amorphous excess density relative to Flory’s prediction and thus the need for chain tilt in the crystallites.