A model relating the elastic properties of high‐density polyethylene melts to the molecular weight distribution

An earlier model relating the variation of the steady‐shear melt viscosity of high‐density polyethylene to the molecular weight distribution is applied toward predicting the steady‐shear elastic compliance, the first normal stress difference, and relaxation spectrum as a function of shear rate from the molecular weight distribution. The model envisions the cutting off of longer relaxation times as the shear rate is raised such that at any shear rate ${\rm \dot \gamma }$ the molecular weights and their corresponding maximum relaxation times τ m are partitioned into two classes; the relaxation times are partitioned into operative and inoperative states, depending on whether they are less than or greater than τ c , the maximum relaxation time allowed at ${\rm \dot \gamma }$ . Equations relating molecular weight and relaxation time to the steady‐shear elastic compliance and viscosity are assumed valid at nonzero shear rates, except for the partitioning effect of shear rate. The shear rate dependence of the first normal stress difference and the steady‐shear viscosity for polyethylene melts is successfully predicted over the range covered by the cone‐and‐plate viscometer. The assumed proportionality constant between τ c and 1/ ${\rm \dot \gamma }$ was determined to be 1.7. Using this relation, the maximum relaxation time at 190°C for a polyethylene molecule of molecular weight M is given by τ m = 1.4 × 10 −19 ( M ) 3.33 . Reasonable agreement has been obtained between the experimentally determined relaxation spectrum of a polyethylene melt and that predicted from the molecular weight distribution. The agreement is best at the longest relaxation times.