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
eme...