Viscoelasticity of an Entangled Polymer Solution with Special Attention on a Characteristic Time for Nonlinear Behavior

Nonlinear viscoelasticity was studied for a polystyrene solution in tricresyl phosphate; molecular weight = 5480 kg mol -1; concentration = 49 kg m -3 . The longest Rouse relaxation time, τ R, was estimated by fitting the Rouse theory to dynamic modulus at high frequencies. The Doi−Edwards tube model theory presumes that 2τ R is the characteristic time for equilibration of chain contour length; (2τ R ) -1 is the rate for an extended chain to shrink back to equilibrium. The τ R value was much lower than that evaluated with more widely accepted methods. However, the shear stress (σ) and the first normal stress difference ( N 1 ) in the start-up of shear flow with low rate of shear (<(2τ R ) -1 /5) were consistent with the assumption that the contour length is always at equilibrium value. At high rate of shear (>8(2τ R ) -1 ), the maxima of σ and N 1 were located at t = 2τ R and 4τ R, respectively, in accord with the interpretation that 2τ R is the characteristic time for chain shrink. The strain-dependent relaxation modulus, G ( t, γ), was also studied. At high magnitudes of shear, γ = 4 or 5, the ratio G ( t, γ)/ G ( t, 0) decreased rapidly around t = 2τ R and leveled off at t = 20(2τ R ): the chain shrink process plays the main role in damping but a slower process may also be involved. At γ = 1 or less, G ( t, γ)/ G ( t, 0) decreased only at times much longer than 2τ R . The damping of relaxation modulus involves some secondary process with a characteristic time longer than that of the chain contraction process.