So in the real world, all polypropylene crystals have defects. Since the molecules are not long enough to span the entire fiber length, there are end defects where one chain ends and another chains starts. The existence of a distribution of molecular weights also contributes to chain end defects. Our inability to create full orientation of the chains introduces numerous defects, namely chain-folded crystals, where the molecule is folded back-and-forth many times in a crystal. Since this fold length is less than the length of the fully extended polymer, it is possible that one part of the polymer chain can extend into another crystal entirely. And then there are packing defects from numerous sources. Since the viscosity of the polymer is so high, that can limit its ability to get into the lattice in the time needed. Or packing defects can arise from branch points. As well as from losses in stereoregularity.
So while the perfect crystal initially described would a 100% crystalline material, polypropylene in the real world is lucky to reach more than about 60% crystallinity without special processing. The balance of the material are parts of chains that are caught out, unable to line up and crystallize with other chain fragments in their immediate vicinity.
All of this is prelude to
[*] A C-C bond is about 1.54 Å long, and there is about a 110 degree angle between one bond and the next. With that geometry, each C-C bond has a spans about 1.26 Å of length. A 12.6 cm long fiber would be made up of 107 monomers for a MW of 420,000,000 g/mole - about 500 times larger than what we can currently make. And this is just for a short span of fiber. Imagine a 50 meter rope!
Assuming I did the math correctly, there is still one flaw with geometry presented here, one that is present in polypropylene but not in polyethylene. Anyone care to comment on the little "spin" I should impose here?
Gauche interactions with the methyl sidechains of PP? You've already hinted at stereoregularity.
The α-crystals of PP (the most common morph) are a 3-sub-1 helix. I wasn't going to go into the extra geometrical calculations, as the point was already made. The helix "spin" only increases the number of monomers needed to span a given distance.
You could always add the requirement for 100% regioregularity, too.
You're right. I thought I had mentioned it, but it must have been only in my head.
Yes, regioregularity (head-to-head orientation) is of the utmost importance.
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