Polyethylene chains do become entangled.  (RDC 6/23/2011)

Entanglements /Reptation
Polyethylene

Polymers /Resins
Polyolefins

Recent Journal Articles

Heterogeneity in the Distribution of Entanglement Density during Polymerization in Disentangled Ultrahigh Molecular Weight Polyethylene
(4952–4960)
Macromolecules 44 #12 (2011)
Pandey, Champouret, and Rastogi, United Kingdom and the Netherlands, showed that heterogeneity in the distribution of entanglement along the chain during polymerization occurs.  Because of living nature of the catalytic system, with increasing polymerization time molecular weight increases whereas the number of entanglement per unit chain decreases. These findings suggest that most of the entanglement is established at the initial stages of polymerization.  (RDC 6/22/2011)