The strain-hardening behaviour of linear and long-chain-branched polyolefin melts in extensional flows

By generalizing the Doi-Edwards model to the Molecular Stress Function theo ry of Wagner and Schaeffer, the extensional viscosities of polyolefin melts in uniaxial, equibiaxial and planar constant strain-rate experiments start ing from the isotropic state can be described quantitatively. While the str ain hardening of four linear polymer melts (two high-density polyethylenes, a polystyrene and a polypropylene) can be accounted for by a tube diameter that decreases affinely with the average stretch, the two long-chain-branc hed polymer melts considered (a low-density polyethylene and a long-chain b ranched polypropylene) show enhanced strain hardening in extensional flows due to the presence of long-chain branches. This can be quantified by a mol ecular stress function, the square of which is quadratic in the average str etch and which follows from the junction fluctuation theory of Flory. The u ltimate magnitude of the strain-hardening effect is governed by a maximum v alue of the molecular stress, which is specific to the polymer melt conside red and which is the only free non-linear parameter of the theory.