Role of Crystal Thickness on the Critical Tie Molecule Fraction in Semicrystalline Polymers

In semicrystalline polymers, polymer chains which connect two adjacent crystallites (known as tie molecules, or TMs) provide toughness, with the fraction of chains forming TMs (P) expected to increase with molecular weight. However, the factors controlling the minimum TM fraction required to impart ductility (P_BDT) remain elusive. In the present work, random copolymers of norbornene and hexylnorbornene (hPNrH) were synthesized, hydrogenated, and characterized to relate solid-state structure to P_BDT. Both domain spacing and crystallinity were varied by adjusting the hexylnorbornene mole fraction across four series of copolymers (0, 1, 3, and 5 mol %), with each series spanning a range of molecular weights that include the brittle–ductile transition (BDT). A strong inverse relationship between P_BDTand crystal thickness (L_c) was observed, indicating that ductility depends on both P and morphology. Compared to polyethylene (PE), hPNrH was found to require three times fewer TMs for ductility at a given L_c, principally due to the lower yield stress of hPNrH compared to PE. To rationalize the dependence of P_BDTon L_c, partial TM loss beyond the yield point is proposed, where polymers with thinner initial L_close a larger fraction of TMs. This idea is supported by measurements of the postyield strain hardening modulus ⟨G_p⟩, where polymers with comparable initial P show a progressive reduction in ⟨G_p⟩ as the initial L_cdecreases.