Polymer disentanglement in steady-shear flow

A procedure is presented for investigating entanglement loss in polymer liquids during steady-shear flow. The method combines steady shearing with small-amplitude step strain measurements to determine the elastic modulus Ge of an entangled polymer network under steady-state flow conditions. In this study, superimposed step/steady-shear measurements are used to investigate entanglement loss in narrow molecular weight distribution polystyrene/diethyl phthalate solutions with variable entanglement density (9 < N/Ne < 58). For all materials studied, Ge decreases with increasing shear rate γ̇ over a wide range of rates. At high shear rates, an approximate scaling relation Ge(γ̇)∼γ̇−1/2 can be defined for all but the most weakly entangled polymer solution; for this material, a related scaling form Ge(γ̇)∼γ̇−1 correctly describes the experimental results. We also find that the ratio of limiting shear modulus Ge(0) to modulus at finite rate Ge(γ̇) is related to a molecular stretching functional 〈|E⋅u|〉 by Ge(0)/Ge(γ̇)≈〈|E⋅u|〉p, where p takes on values of 1 and 1/2, depending on whether contour length stretching is taken to be affine p=1, or nonaffine p=1/2. For the lowest molecular weight polymer investigated, the affine stretch result Ge(0)/Ge(γ̇)≈〈|E⋅u|〉 fairly describes the experimental results over the entire range of shear rate investigated. Other materials manifest a transition from an initially affine to a square-root nonaffine response Ge(0)/Ge(γ)≈〈|E⋅u|〉1/2, as the rate is increased. Implications of these results on polymer contour length dynamics are discussed.