Critical Tie Molecule Density for Ductility in Linear Polyethylene

Semicrystalline polymers of low Tg, such as polyethylene (PE), can be brittle or ductile depending on whether sufficient intercrystalline tie chains are present, which depends in turn on molecular weight (M) and crystallization conditions. In linear PEs of narrow M distribution, the strain at break increases steeply over a narrow range of M. However, converting M to a molecular size (melt Rg) and scaling by the solid-state intercrystalline distance (d) fails to collapse the breaking strains for the same PEs crystallized under different conditions (different d); the brittle-ductile transition occurs at smaller values of Rg/d (or equivalently, smaller values of the Huang-Brown tie molecule probability P) for PEs crystallized slowly vs. quenched. Combining these results with literature data for hydrogenated polybutadiene, a lower-crystallinity PE, reveals a strong correlation between the critical value of Rg/d (or P) and the polymer's crystallinity, a behavior strongly mirrored in the yield stress, which increases with crystallinity. The number (or density) of tie chains required for ductility thus decreases strongly with increased crystallinity, as those tie chains become more solidly anchored in less-deformable crystals of higher yield stress.