  Polymer fibers consist of macromolecules oriented along the fiber axis.
Better alignment of chains leads to an increased strength of the fiber. It is
believed that the key factor preventing formation of a perfectly oriented fiber
is entanglement of polymers. We performed large-scale computer simulations of
uniaxial stretching of semicrystalline ultrahigh molecular weight polyethylene.
We discovered that there is an optimal number of entanglements per
macromolecule necessary to maximize chain orientation in a fiber. Polymers that
were entangled too strongly formed less oriented fibers. On the other hand,
when polymers had too few entanglements per chain, they disentangled during
stretching, and the strong fiber was not formed. We constructed a microscopic
analytical theory describing both the fiber formation and disentanglement
processes. Our work presents a novel view on the role of entanglements during
fiber production and predicts the existence of a single universal optimal
number of entanglements per chain maximizing the fiber quality: approximately
$10^2$ entanglements.
